# Colloquium Winter Term 2023/2024

Das CeNoS Kolloquium beginnt um 16.30 s.t. in R 222, Angewandte Physik, Corrensstr. 2.

10.10.2023 17.10.2023 24.10.2023 31.10.2023 07.11.2023 14.11.2023 21.11.2023 28.11.2023 05.12.2023 12.12.2023 19.12.2023 09.01.2024 16.01.2024 23.01.2024 30.01.2024

# Colloquium Summer Term 2023

The CeNoS Colloquium starts at 4.30 p.m. in room 222, Angewandte Physik, Corrensstr. 2.

18.04.2023 **An Ensemble Mean Approach to the Hydrodynamic Madelung Equations of Quantum Mechanics****Prof. Eyal Heifetz**

^{Faculty of Exact Sciences, Department of Geophysics / Tel Aviv University}The Madelung equations transform the real and the imaginary parts of the Schrodinger equation into continuity and momentum equations of a compressible barotropic-like fluid. The density of the fluid is the probability density function to find the quantum particle in space, whereas the flow velocity is proportional to the gradient of the phase of the quantum wave function. In a first look it seems odd that the Schrodinger equation, describing the dynamic of a single quantum particle, is translated into the equations of a continuum fluid. Here we suggest that the Madelung equations can be regarded as well as describing the ensemble mean realizations of a repeated experiment with a single particle undergoing stochastic motion. Toward this end we first derive the general ensemble mean equations, which indeed take an hydrodynamic-like form, and then compare them with the Madelung equations. The comparison suggests that the stochastic process is represented by a turbulent Favre-Reynolds-like stress tensor, where the RMS velocity, comprising the tensor, appears to result from a diffusion-like process. We will discuss the plausible physical interpretations of this representation.

Im Anschluss findet ab 17.45 Uhr die

**Mitgliederversammlung**satt.02.05.2023 **Demand-driven Design of Bicycle Infrastructure Networks****Dr. Malte Schröder**

^{Institute for Theoretical Physics, TU Dresden}Sustainable urban transportation critically relies on a sufficiently developed infrastructure. However, designing efficient infrastructure networks constitutes a highly complex problem that requires balancing multiple, often opposing, constraints. Bike path networks in particular need to enable both safe and direct travel for all cyclists with an often strongly limited budget and strong competition for limited road space. Here, we present a framework to create a sequence of efficient bike path networks by reversing the network formation process and iteratively removing bike paths from an initially complete bike path network. During this process, we continually update cyclists’ route choices, explicitly taking into account the cyclists’ demand and their safety and convenience preferences. In this way, we ensure that the networks are always adapted to the current cycling demand. The framework may thus enable the theoretical study of structural properties of efficient bike path networks across cities and quantify the inherent impact of the demand distributions and street networks on a cities bikeability.

09.05.2023 **InterKI-Sonderkolloquium**(veranstaltet gemeinsam mit dem Zentrum für Wissenschaftstheorie)

**"Künstliche Intelligenz" — Die Quintessenz naturwissenschaftlicher Borniertheit? Durchbrüche und Grenzen akuteller KI Entwicklungen****Prof. Dr. Benjamin Risse**

^{Institut für Geoinformatik, WWU Münster}Joseph Weizenbaum, einer der Pioniere moderner KI Forschung, bezeichnete künstliche Intelligenz als die Quintessenz naturwissenschaftlicher Borniertheit. In meinem Vortrag möchte ich die technischen Grundlagen und Durchbrüche der aktuellen KI Forschung vorstellen, und ansprechen, inwieweit Weizenbaums Kritik heute noch gültig oder überholt ist. Insbesondere ist es mein Ziel, eine allgemeinverständliche Beschreibung moderner KI Algorithmen, sowie den damit verbundenen Möglichkeiten und Grenzen zu präsentieren, um einen Beitrag zur aufgeklärten Diskussion zu leisten.

Die Veranstaltung findet im

**Hybridformat**statt.(geänderter!) Ort: Hörsaal S 8, Schloss

Zeit: 16.30 Uhr s.t.

Zoom: https://wwu.zoom.us/j/66086865952?pwd=VXJuZ1NPNHNJRTErbmFMWkVqekVtUT09

Meeting-ID: 660 8686 5952

Passcode: 213129

11.05.2023 **Informationsveranstaltung InterKIWWU****Dr. Oliver Kamps**

^{Center for Nonlinear Science (CeNoS), WWU Münster}Die Veranstaltung richtet sich an alle interessierten Studierenden, Lehrenden und Wissenschaftler*innnen der WWU. Zunächst stellt der Projektkoordinator Dr. Oliver Kamps InterKI und das zugehörige Lehrprogramm im Rahmen eines Vortrags vor und beantwortet Fragen zum Projekt. Im Anschluss haben Sie die Möglichkeit, mit weiteren Projektbeteiligten ins Gespräch zu kommen.

Ort: S 10 (Schlossplatz 2)

Zeit: 14 -16 Uhr s.t.

16.05.2023 **Incub.AI Convention by REACH and InterKI WWU**Tauche ein in die faszinierende Welt der künstlichen Intelligenz auf der incub.AI convention! Gemeinsam mit dem REACH und dem Projekt interKI präsentieren wir dir Einblicke in die praktische Anwendung von KI in Unternehmen. Lass dich von erfahrenen EntwicklerInnen inspirieren und tausche dich mit KI-Experten und Expertinnen aus forschungsstarken regionalen Unternehmen und REACH Start-ups aus. In verschiedenen Workshops werden Unternehmen und Start-ups ihre Anwendungen in den Bereichen Education, Sustainability und Industrie 4.0 vorstellen und die Rolle von Data Scientists in ihrem Unternehmen erläutern. Ein besonderes Highlight ist der Workshop "AI for Beginners", der sich speziell an Studierende ohne Vorkenntnisse im Bereich Machine Learning richtet. Zielgruppe der Veranstaltung sind Studierende und Doktoranden der gesamten WWU, Gründungsinteressierte und WissenschaftlerInnen mit dem Interesse an Ausgründungen aus der Forschung. Nutze die Gelegenheit, dich mit anderen TeilnehmerInnen interdisziplinär auszutauschen und neue Impulse für deine eigene Karriere oder Gründungsidee zu gewinnen. Sei dabei und erlebe die Zukunft der Technologie hautnah auf der incub.AI convention!

**Keynote: tba**Zeit:

geänderter Ort: REACH Euregio Start-up Center

**Anmeldung erforderlich!**Weitere Informationen:06.06.2023 **A Control Theory of (mal)adaptive Mind and Behavior****Prof. Dr. Hamidreza Jamalabadi**

^{Klinik für Psychiatrie und Psychotherapie / Psychatrische Kontrollsysteme, Philips Universität Marburg}The field of psychology, in its broader sense, fundamentally diverges from most quantitative fields, such as physics and engineering, due to the lack of a principled mathematical framework that can derive the governing equations underlying the human mind and behavior. This deficiency has substantial ramifications, including our inadequate ability to comprehend and reverse the course of psychiatric disorders. In this presentation, I investigate the possibility of utilizing empirical longitudinal data and data-driven dynamical system identification methodologies to deduce these governing equations. I demonstrate how these models allow for precise prediction of psychiatric disorder symptoms, daily mood fluctuations, and further the trajectories of thoughts. Additionally, I discuss the potential of these models to inform control strategies, currently dominated by linear models, to achieve optimal performance. Finally, I conclude by addressing the experimental and mathematical limitations.

13.06.2023 **How to See the Invisible - Linking Growth Models and Image Data to Estimating the Extent of Glioblastoma Tumors****Prof. Dr. Christian Engwer**

^{Institut für Angewandte Mathematik, WWU}Glioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in the form of advection-diffusion-reaction equations. The patient-wise parametrization of these models, and their validation via experimental data has been found to be difficult, as time sequence measurements are mostly missing. Also the clinical interest lies in the actual (invisible) tumor extent for a particular MRI/DTI scan and not in a predictive estimate.

Based on an instationary model with patient specific model parameters, derived from MRI/DTI scans, we present a stationalized approach to estimate the extent of glioblastoma (GBM) invasion at the time measurement.

The underlying dynamics can be derived from an instationary GBM model, falling into the wide class of advection-diffusion-reaction equations. The stationalization is introduced via an analytic solution of the Fisher-KPP equation, the simplest model in the considered model class. We investigate the applicability in 1D and 2D, in the presence of inhomogeneous diffusion coefficients and on a real 3D DTI-dataset.

# Colloquium Winter Term 2022/2023

The CeNoS Colloquium starts at 4.30 p.m. as zoom session. If you are interested in the zoom link, please send an email to okamp@uni-muenster.de

18.10.2022 Online Colloquium / ZOOM Session

**Collocation-Based EEG/MEG Inverse Problem Solution Based on Helmholtz Reciprocity Principle: The Same MNE?****Sergey N Makarov**

^{Worcester Polytechnic Institute (Worcester MA) and Martinos Faculty at Massachusetts General Hospital (Charlestown MA)}Helmholtz reciprocity principle makes it possible to expand an unknown cortical dipole density into global bases - cortical fields of sequentially excited electrodes (EEG) or coils (MEG). Some results will be given and a connection to the minimum norm estimation (MNE) formulation will be discussed.

15.11.2022 Online Colloquium / ZOOM Session

**Critical Transitions in the Earth System****Niklas Boers**

^{Professur für Earth System Modelling, TUM School of Engineering and Design, Technische Universität München}

In response to anthropogenic release of greenhouse gases, the Earth is warming at unprecedented rates. It has been suggested that several components of the Earth’s climate system may respond with abrupt transitions between alternative stable states in response to gradual changes in forcing. Based on the theory of stochastically forced dynamical systems and their bifurcations, a methodology is presented to measure changes in the stability of a given equilibrium state from observational time series. The method is applied to observation-based data to investigate if and how the stability of the Greenland Ice Sheets, the Atlantic Meridional Overturning Circulation, the Amazon rainforest, and the South American monsoon, has changed in the course of the last century.29.11.2022 Online Colloquium / ZOOM Session

**The German Climate Computing Center - In-situ Data Processing of Large Climate Model Data****Nil****s-Arne Dreier**

^{Deutsches Klimarechenzentrum, Hamburg}The German Climate Computing Center (DKRZ) provides the central research infrastructure for the German climate and earth system research community. Besides operating the supercomputer, DKRZ also provides support for users and contributes to the development of climate models. Based on a brief introduction to the climate model ICON, I will present my work at DKRZ as a research software engineer, which concerns the in-situ visualization and analysis of large climate model data. With higher resolutions the amount of data that is produced by the simulation increases. This makes traditional data processing workflows unusable, as they include the storage on a hard drive. We are following two strategies, the first approach develops an interconnection to paraview via the catalyst interface. This enables us to produce high-quality 3d visualizations of the high-resolution data. In the second approach, we develop a python interface for domain scientists, enabling them to execute their analyses and visualization in an in-situ fashion.

20.12.2022 **Interfaces and Dynamical Transitions in Strongly Interacting Many-body Systems****Aljaz Godec**

^{Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Göttingen}Our understanding of collective phenomena, especially in inhomogeneous systems, is mostly based on mean-field ideas that neglect correlations, whose importance in turn grows with the strength of interactions. This raises doubts whether mean-field ideas sensibly describe the physical behavior of strongly interacting systems. In the talk I will describe our recent efforts to account for and understand pair-correlation effects in classical many-body systems in and out of equilibrium. I will illuminate unexpected effects of correlations in the kinetics [1] and interfacial phenomena [2], and show that they give rise to global speed limits during non-equilibrium relaxation [3].

[1] K. Blom & AG, Phys. Rev. X 11, 031067 (2021)

[2] K. Blom, N. Ziethen, D. Zwicker, & AG, arXiv:2204.02962 (2022).

[3] K. Blom & AG, arXiv:2209.14287 (2022)

24.01.2023 **Nuclei Coordinate Cell Division in Space and Time****Lendert Gelens, PhD**

^{Laboratory of Dynamics in Biological Systems, KU Leuven}Upon fertilization, the early Xenopus laevis frog egg quickly divides about ten times to go from a single cell with a diameter of a millimeter to several thousands of cells of somatic cell size. Using cytoplasmic extracts made from frog eggs, many cellular processes have been reconstituted and studied in vitro. Homogenized extracts can also spontaneously self-organize into various cellular spatial structures when mixing isolated components back together.

Here, we will discuss our recent experimental and modeling efforts to understand how biochemical oscillations and waves form in the frog cytoplasm, and how they help organize the cell division cycle. We study an artificial cell system consisting of droplets of frog egg extracts of varying sizes, which allows characterizing the spatiotemporal dynamics of cell cycle oscillations, periodic nuclear assembly and destruction, and cytoskeletal organization. We complement our experimental analysis by developing computational models incorporating nuclear dynamics, illustrating the role of the nucleus in setting the cell cycle oscillation period. Nuclei are shown to function as pacemakers, regions which oscillate faster than its surroundings. As a result, nuclei send out biochemical waves that can synchronize the whole medium and ensure that cell division is properly coordinated in the large frog egg.

31.01.2023 **Quasi-Stationarities Relative to the Collective Market Motion in Financial Markets****Anton Heckens**

^{Universität Duisburg-Essen, Fakultät für Physik}

Financial markets are non-stationary and their dynamics is dominated by strong collective effects. When studying correlation matrices in subsequent epochs, quasi-stationary patterns,

referred to as market states, are detected by applying clustering methods. They emerge, disappear or reemerge, but they are dominated by the collective motion of all stocks. By removing the dominating market motion in a proper way, we uncover different market states

which are stable over a long period of time.

We discuss their precursor properties in the US stock markets and collective effects relative to the dominating collective market behavior.

# Colloquium Summer Term 2022

The CeNoS Colloquium starts at 16.30 s.t as zoom session. If you are interested in the zoom link, please send an email to okamp@uni-muenster.de

10.05.2022 **Online Colloquium / ZOOM Session****Data-Driven Analysis of Complex Systems for a Sustainable Future****Dr. Benjamin Schäfer**

^{Karlsruher Institut für Technologie (KIT) / Institut für Automation und angewandte Informatik (IAI)}The transition to a sustainable energy system raises numerous complex challenges, as power generation becomes more uncertain, while simultaneously more operational data becomes available. Still, a coherent approach to fully utilize such data is missing. Within this talk, I will sketch our efforts in developing a data-driven framework, combining data analysis, machine learning and modelling approaches to study complex (energy) systems. I will emphasize the need for open data but also for transparency in physical and machine (learning) models. In particular, I will show how we may extract scaling laws, obtain forecasts, and identify drivers in different power grids from a purely data-driven perspective.

17.05.2022 **Online Colloquium / ZOOM Session****Modelling and controlling turbulent vortex dynamics in cardiac systems and active fluids****Prof. Dr. Markus Bär**

^{Physikalisch-Technische Bundesanstalt (PTB), Berlin }Many relevant experimental systems and applications exhibit irregular dynamics such as spatiotemporal chaos or turbulence. In this talk, I will present two examples of such behavior where control of such states by transforming their dynamics into homogeneous or periodic steady states or regular periodic patterns is desirable. The specific applications are (i) defibrillation of cardiac tissue by periodic pacing and (ii) turbulence in active suspensions. For the cardiac system, we used simulations as well as data analysis not only to identify suitable conditions e. g. pacing strength and periods [1, 2], but also to determine the mechanism of defibrillation in this specific modus. For active turbulence, a simple phenomenological deterministic continuum model was used for quantitative modelling of experimental control in bacterial suspensions. Detailed investigations showed how the turbulent collective dynamics could be transformed into more regular, periodic spatiotemporal patterns of different symmetries using a periodic array of obstacles. This is in line with recent experimental findings using confinement by an arrays of pillars [3]. A recent study addresses the competition between the controlling effect of confinement and a nonlinear advection term behind the emergence of turbulence in active fluids demonstrating that the breakdown of control occurs through an Ising-like phase transition in a coarse-grained description of the model [4].

References

[1] P. Buran, M. Bär, S. Alonso and T. Niedermayer. Chaos 27, 113110 (2017).

[2] P. Buran, T Niedermayer, and M Bär. Preprint on https://www.biorxiv.org (2021).

[3] H. Reinken, D. Nishiguchi, S. Heidenreich, A. Sokolov, M. Bär, S. H. L. Klapp, and I. Aranson. Comm. Phys. 3, 76 (2020).

[4] H. Reinken, S. Heidenreich, M. Bär, S. Klapp. Phys. Rev. Lett. 128, 048004 (2022).

31.05.2022 **Online Colloquium / ZOOM Session****Machine Learning for Nanophotonics and Nanophotonics for Machine Learning****Prof. Dr. Carsten Schuck**

^{Physikalisches Institut (WWU) / Center for NanoTechnology (CeNTech) / Center for Soft Nanoscience (SoN)}Machine Learning techniques offer novel approaches to a wide range of complex problems that may defy human intuition. One area where this is particularly relevant is the field of nanophotonic design. Nanostructured Photonic Integrated Circuits (PICs) are replacing their electrical equivalents in high bandwidth telecommunication as well as sensing applications and play a key role in modern quantum technology. However, designing nanophotonic circuit components today relies primarily on combining intuitive concepts, such as interference and coupled mode theory, with brute force parameter optimization. In view of the vastness of possible device configurations, such conventional design approaches only consider an infinitesimal part of the solution space. We here show how to go beyond this paradigm by employing an inverse design technique that relies on reinforcement learning for finding non-intuitive configurations of nanophotonic devices that exceed conventional designs in both performance and compactness.

Nanophotonics, on the other hand, also provides means for novel hardware implementations of neural networks. Optical artificial neural networks (OANNs) allow for extremely energy-efficient signal processing at the speed of light, therewith overcoming the performance limitations of corresponding implementations on electronic hardware, such as CPUs or GPUs, that are subject to the von Neumann bottleneck. Here we show a path towards realizing the linear and nonlinear building blocks of OANNs on a nanophotonic platform that could be scaled to large system size, thus realizing a photonic neural network processing unit. In particular, we leverage a variety of molecular compounds developed in the context of the collaborative research center on “Intelligent Matter” (CRC 1459) to realize nonlinear activation functions and develop interfaces between nanophotonic OANN components and photoresponsive molecular systems. We further study the performance of such nanophotonic neural networks that are trained in the presence of noise, naturally occurring in ensembles of molecular compounds but absent in digital electronic implementations.

14.06.2022 **Online Colloquium / ZOOM Session****What is the Use of Nonlinear Dynamics in Practice? - Use Cases from Critical Infrastructures and Life Sciences****Dr. Arndt Telschow**

^{Cuculus GmbH, Erfurt }Nonlinear dynamics and nonlinear effects are ubiquitous in complex systems, including ecosystems, technical and social systems. In the lecture, I will use selected examples from critical infrastructure and the life sciences to show the great benefits that nonlinear approaches can have in practice. The use cases are partly based on my work at the Westfälische Wilhelms-Universität Münster and partly on my current work at the software company Cuculus (www.cuculus.com). Use cases discussed include: (1) Forecasting. I present the ZONOS 24insight software module for forecasting electricity consumption and generation (see https://24insight.zonos.de for a live demo). (2) Fraud Detection. I present the results of a white paper describing a new approach to identifying electricity theft. (3) Anticipate critical transitions. I present a new method for quantifying resilience in complex systems and show how it can be used to predict tipping points. By analyzing empirical data, the method is used to anticipate (i) power grid collapse, (ii) global climate change (end of last greenhouse earth), bacterial population collapse, physiological changes and intracellular switching.

21.06.2022 **Online Colloquium / ZOOM Session****Design and Theory of Self-Avoiding Active Matter****Dr. Mazi Jalaal**

^{University of Amsterdam }Active matters present systems made of micro-scale agents that consume energy from the environment. In many types of such systems, the active agent leaves a trace behind, creating memory in space and time. In this talk, I will first give a brief overview of different classes of active matter with such a feature and then present a frugal and tuneable experimental framework in which one could synthetically design active particles with a self-avoiding memory. I will then present a theoretical framework based on mathematical billiards and show how active matter with memory can result in complex, chaotic patterns in a simple deterministic dynamical system.

25.08.2022 **Additional date / Two talks****1. Talk: On-off Intermittency due to Parametric Lévy Noise****Dr. Adrian van Kan**

^{University of California, Berkeley | UCB · Department of Physics }Instabilities arise in many physical systems at some parameter threshold. Typically the system is embedded in an uncontrolled noisy environment. The fluctuating properties of the environment affect the control parameters of the instability, which leads to multiplicative noise. The result of multiplicative noise close to an instability threshold is on-off intermittency, which is characterised by an aperiodic switching between a large-amplitude “on” state and a small-amplitude “off” state.

I present a new type of intermittency, Lévy on-off intermittency, which arises from multiplicative α-stable white noise close to an instability threshold [1]. We study this problem in the linear and nonlinear regimes, both theoretically and numerically, for the case of a pitchfork bifurcation with fluctuating growth rate. In a recently introduced point-vortex model of 3-D perturbations in 2-D flows [2], the perturbation amplitude obeyed such an equation. We compute the stationary distribution analytically and numerically from the associated fractional Fokker-Planck equation in the Stratonovich interpretation.

We characterize the system in the parameter space (α, β) of the noise, with stability parameter α ∈ (0, 2) and skewness parameter β ∈ [−1, 1]. Five regimes are identified in this parameter space, in addition to the well-studied Gaussian case α = 2. Three regimes are located at 1 < α < 2, where the noise has finite mean but infinite variance. They are differentiated by β and all display a critical transition at the deterministic instability threshold, with on-off intermittency close to onset. Critical exponents are computed from the stationary distribution. Each regime is characterised by a specific form of the density and specific critical exponents, which differ starkly from the Gaussian case. A finite or infinite number of moments may converge, depending on parameters. Two more regimes are found at 0 < α ≤ 1. There, the mean of the noise diverges, and no transition occurs. In one case the origin is always unstable, independently of the distance μ from the deterministic threshold. In the other case, the origin is conversely always stable, independently of μ. In summary, we demonstrate that an instability subject to non-equilibrium, power-law-distributed fluctuations can display substantially different properties than for Gaussian thermal fluctuations, in terms of statistics and critical behavior.[1] van Kan, A., Alexakis, A. and Brachet, M.E., 2021. Lévy on-off intermittency. Physical Review E, 103(5), p.052115.

[2] van Kan, A., Alexakis, A. and Brachet, M.E., 2021. Intermittency of three-dimensional perturbations in a point-vortex model. Physical Review E, 103(5), p.053102.**2. Talk: Pressure-driven Wrinkling of Soft Inner-lined Tubes****Dr. Ben Foster**

^{University of California, Berkeley | UCB · Department of Physics }A simple equation modelling an inextensible elastic lining of an inner-lined tube subject to an imposed pressure difference is derived from a consideration of the idealised elastic properties of the lining and the pressure and soft-substrate forces. Two cases are considered in detail, one with prominent wrinkling and a second one in which wrinkling is absent and only buckling remains. Bifurcation diagrams are computed via numerical continuation for both cases. Wrinkling, buckling, folding, and mixed-mode solutions are found and organised according to system-response measures including tension, in-plane compression, maximum curvature and energy. Approximate wrinkle solutions are constructed using weakly nonlinear theory, in excellent agreement with numerics. Our approach explains how the wavelength of the wrinkles is selected as a function of the parameters in compressed wrinkling systems and shows how localised folds and mixed-mode states form in secondary bifurcations from wrinkled states. Our model aims to capture the wrinkling response of arterial endothelium to blood pressure changes but applies much more broadly.

# Colloquium Winter Term 2021/2022

The CeNoS Kolloquium starts at 16.30 s.t as zoom session. If you are interested in the zoom link, please send an email to okamp@uni-muenster.de

14.12.2021 **Smart grid communication and cyber security: a computer-science perspective****Prof. Anna Remke**

^{Institut für Informatik, WWU }Within smart grids the safe and dependable distribution of electric power highly depends on the security of Supervisory Control and Data Acquisition (SCADA) systems and their underlying communication protocols. Existing network-based intrusion detection systems for Industrial Control Systems (ICS) are usually centrally applied at the SCADA server and do not take the underlying physical process into account. A recent line of work proposes an additional layer of security via a process-aware approach applied locally at the field stations. We broaden the scope of process-aware monitoring by considering the interaction between neighboring field stations, which facilitates upcoming trends of decentralized energy management (DEM). Local security monitoring is lifted to monitoring neighborhoods of field stations, therefore achieving a broader grid coverage w.r.t. security.

11.01.2022 **The role of non-conservative interactions in nonequilibrium complex systems****Dr. Sarah Loos**

^{International Center for Theoretical Physics, Trieste, Italy }The complex world surrounding us, including all living matter and various artificial complex systems, is mostly far from thermal equilibrium. A major goal of modern statistical physics and thermodynamics is to unravel the fundamental principles and in particular the collective phenomena of such nonequilibrium systems, like the swarming of fish, flocking of birds, or pedestrian crowd dynamics. A key novel concept to describe and classify nonequilibrium systems is the stochastic entropy production, which explicitly quantifies the breaking of time-reversal symmetry. However, so far, little attention has been paid to the implications of non-conservative interactions, such as time-delayed (i.e., retarded) or nonreciprocal interactions, which cannot be represented by Hamiltonians contrasting all interactions traditionally considered in statistical physics. Time-delayed and nonreciprocal interactions indeed emerge commonly in biological, chemical and feedback systems, and are widespread in engineering and machine learning. In this talk, I will use simple time- and space-continuous models to discuss technical challenges and unexpected physical phenomena induced by nonreciprocity [1,2] and time delay [3,4].

[1] Loos and Klapp, NJP 22, 123051 (2020)

[2] Loos, Hermann, and Klapp, Entropy 23, 696 (2021)

[3] Loos and Klapp, Sci. Rep. 9, 2491 (2019)

[4] Holubec, Geiss, Loos, Kroy, and Cichos, Phys. Rev. Lett. in press (2021)01.02.2022 **Complexity meets energy: A slightly biased, high-variance survey on modeling power grid dynamics****Dr. Katrin Schmietendorf**

^{Center for Nonlinear Science, WWU}In the course of the energy transition the ‚traditional‘ power grid with large conventional plants injecting constant feed-in adjustable to the current demand is progressively being transformed into a decentralized grid with small and medium generating units, many of which are volatile and display feed-in variations on time scales ranging from annual to sub-seconds. This development poses novel challenges with respect to stable and reliable grid operation, frequency quality, storage facilities, control schemes and grid design. Against this backdrop, power system analysis has evolved from a primarily engineering topic to an interdisciplinary research area involving, inter alia, statistics, meteorology, computer science, turbulence research, network and complex systems theory.

About a decade ago, Filatrella et al. uncovered that the most basic generator model standardly used in electrical engineering corresponds to a modification of the Kuramoto model, a paradigmatic model for self-organized synchronization. Building on this relationship, a new branch of research, also referred to as Kuramoto-like power grid modeling, evolved within the nonlinear dynamics community. In Kuramoto-like power grid modeling power systems are analyzed as networks of coupled oscillators. Various application-oriented issues have been addressed so far, e. g. power outages due to severe perturbations and transmission-line overloads, cascading failures, the impact of fluctuating feed-in on power quality and grid stability, storage and new control strategies.

The purpose of my talk is to give a survey across the major branches of Kuramoto-like power grid modeling, summarize the main results obtained so far and attempt an outlook to future focuses of research, both thematically and methodologically. Despite its summary character, the talk will put emphasis on findings me and collaborators obtained during my doctoral research which concern the impact of short-term wind power fluctuations on grid stability and power quality. The overview and outlook is also intended to serve as basis for identifying potential synergy effects and points of contact for follow-up research projects at the WWU.

# Colloquium Summer Term 2021

13.04.2021 **Social insects as models for complex systems?****Prof. Jürgen Gadau**

^{Institute for Evolution and Biodiversity , WWU}Social complexity is a central theme in complex system theory, biological sciences, and social sciences, and yet features that underlie it, and the evolutionary processes that shaped them, are not well understood. It is unclear what composition of features is needed for the emergence of a high-level social organization, and what are their relative weights. The broad diversity of social structures in insects (such as bees, ants, termites) presents a unique opportunity to study the features that underlie social complexity, and their evolutionary trajectories.

20.04.2021 **Artificial Intelligence: Theory or Tool? A Brief Discussion Drawn From Interdisciplinary Machine Learning Research Examples.****Jun. Prof. Benjamin Risse**

^{Institut für Informatik, WWU}Artificial Intelligence (AI) is arguably the most discussed technology of our times: On the one hand, AI algorithms have led to a variety of substantial breakthroughs which have inspired the use of AI for many qualitatively different research questions. On the other hand, no other research paradigm has a comparable history in falling behind its theoretical considerations causing recurring 'AI winters'. In order to provide a balanced discussion I will present several successful deep learning applications which will naturally lead to intrinsic challenges and limitations of state-of-the-art AI algorithms. These limitations are particularly apparent in interdisciplinary projects in which AI is predominantly used as a tool to 'solve' a particular problem from the respective field. An in-depth investigating of the mathematical foundation of these algorithms is therefore pivotal to bridge the gap between theory and practice in order to save AI from its self-induced hypes. Therefore, the overall goal of my talk is to present some hopefully inspiring AI examples while advocating for truly interdisciplinary research projects beyond the borders of traditional academic disciplines.

27.04.2021 **Mathematical and statistical models for causal inference in public health decision-making**

**Prof. Dr. med. André Karch**

^{Institute of Epidemiology and Social Medicine, WWU}The current SARS-CoV-2 pandemic reveals the importance of evidence-based decision-making in public health. The underlying research questions are often complex, need to be assessed in real-time and need to rely on routinely collected data. Dependent on the research question, dynamic mathematical models, statistical models and modern epidemiological concepts need to be applied to come into a position where causal inference is possible. In this talk I will present examples from our work from the fields of infectious diseases modelling, microbiome research and the evaluation of cancer screening programs to discuss challenges of and solutions for evidence-based decision-making in public health.

04.05.2021 **Self-assembly in soft matter with multiple length scales**

**Alberto Scacchi**

^{Department of Chemistry and Materials Science, Aalto University, Finnland}Spontaneous self-assembly in molecular systems is a fundamental route to both biological and engineered soft matter. Simple micellization, emulsion formation, and polymer mixing are well understood. However, the principles behind emergence of structures with competing length scales in soft matter systems remain unknown. Examples include droplet-inside-droplet assembly in many biomacromolecular systems undergoing liquid-liquid phase separation, analogous multiple emulsion formation in oil-surfactant-water formulations, and polymer core-shell particles with internal structure.

We developed a microscopic theoretical model based on effective interactions between the constituents of a soft matter system to explain self-organization both at single and multiple length scales.

The findings provide guidelines to understanding the length scales rising spontaneously in biological self-assembly, but also open new venues to the development and engineering of biomolecular and polymeric functional materials and pharmaceutical formulations.

11.05.2021 **Computational molecular design of bioactive compounds**

**PD. Dr. Oliver Koch**

^{Institute of Pharmaceutical and Medicinal Chemistry, WWU}My research interest lies in the development and application of computational methods in rational drug design with focus on structure-based design, ‘big data’ driven decisions and molecular machine learning in order to develop bioactive molecules and to understand selectivity and promiscuity of protein-ligand interactions. This work is generally aimed at applying and improving the success of computational methods in delivering novel and safe small molecule therapeutics

18.05.2021 **Dynamic behavior of growth processes: Phase separation, self-similarity, and oscillations**

**Prof. Dr. André Schlichting**

^{Arbeitsgruppe Dynamik komplexer Systeme, Mathematik, WWU}The talk reviews some growth processes describing the evolution of clusters consisting of atomic parts called monomers. The growth and shrinkage can only occur by adding and removing single monomers, which is specified through a rate kernel depending solely on the involvedclusters' size.

First, I discuss the exchange-driven growth model, which was recently obtained as the mean-field limit of stochastic particle systems (zero-range process). This model's longtime behavior can be described entirely under a detailed balance condition on the kernel. Here, the total mass density, determined by the initial data, acts as an order parameter, in which the system shows a phase separation.

Next, we consider the model for a family of product kernels, which do not satisfy a detailed balance condition. After a suitable rescaling to self-similar variables, the equation becomes a discrete Laplace with a power-law as diffusion coefficient, which in particular degenerates at

the origin. We will see that the solution converges to a stretched exponential self-similar profile.Lastly, we consider the now-classic Becker-Döring system to which an injection of monomers and a depletion of large clusters is added. These equations have been extensively used to model chemical-physical systems, especially bubbleator dynamics. By formal asymptotics, the model is approximated by a transport equation with a conservation law entering the boundary condition. For the limit model, a Hopf bifurcation is shown, indicating temporal oscillations in the model.

01.06.2021 **Stretched Brownian Motion**

**Prof. Dr. Martin Huesmann**

^{Institut für Mathematische Stochastik, WWU}Given two marginal measures μ and ν we discuss in this talk how to find a natural martingale interpolation between μ and ν mimicking Brownian motion as closely as possible. Our approach relies on martingale versions of the Benamou-Brenier formula from optimal transport. A key step is the development of a dual theory which connects the optimal diffusion coefficients to solutions of the porous medium equation. In the end of the talk, we discuss how this interpolant can be viewed as a natural projection of Brownian motion onto the set of all martingales with initial law μ and terminal law ν wrt a metric that takes the information flow into account, the so called causal Wasserstein metric.

15.06.2021 **Internal restructuring and reorganization in systems of soft and active matter**

**Prof. Dr. Andreas Menzel**

^{Institut für Physik, Otto-von-Guericke-University Magdeburg}The interplay between internal structure and internal or external driving can lead to pronounced nonlinear behavior in systems of soft or active matter. We concentrate on two examples of this kind. First, we address the internal restructuring in magnetic gels or elastomers. These soft materials consist of magnetizable colloidal particles enclosed by an elastic polymer matrix. Driven by an external magnetic field and the induced magnetic interactions, the particles reposition against the elastic restoring forces of the surrounding medium. They can even reversibly collapse towards each other [1]. The process supports pronounced hysteresis [1], features interesting dynamics already in the overdamped regime and in simple one-dimensional settings [2], and affects the overall system behavior [3].

Second, we investigate the collective dynamic behavior of self-propelled particles that migrate on a substrate and are assembled in regular, crystal-like arrangements [4]. Specifically, we focus on chiral active agents that feature a persistent bending in their trajectories, implying circular motion in the unperturbed case [5]. The circular motion of the individuals conflicts with the collective motion of the whole structure. With increasing chirality, collective motion thus breaks down. However, it can be restored by introducing phase boundaries into the system, leading, for example, to self-shearing or self-rotating crystallites.

Future studies should, for instance, analyze in more detail the transitional regimes and the consequences for the overall dynamics in these situations.[1] M. Puljiz, S. Huang, K. A. Kalina, J. Nowak, S. Odenbach, M. Kästner, G. K. Auernhammer, A. M. Menzel, Soft Matter 14, 6809 (2018).

[2] S. Goh, A. M. Menzel, H. Löwen, Phys. Chem. Chem. Phys. 20, 15037 (2018).

[3] G. Pessot, M. Schümann, T. Gundermann, S. Odenbach, H. Löwen, A. M. Menzel, J. Phys.: Condens. Matter 30, 125101 (2018).

[4] A. M. Menzel, T. Ohta, H. Löwen, Phys. Rev. E 89, 022301 (2014).

[5] Z.-F. Huang, A. M. Menzel, H. Löwen, Phys. Rev. Lett. 125, 218002 (2020).06.07.2021 **Gibbs measures with space-time singularities**

**Prof. Dr. Chiranjib Mukherjee**

^{Institut für Mathematische Stochastik, WWU}Consider a finite volume Gibbs measure which descends from any translation-invariant interaction of Brownian paths in space and time. The class of interactions we are interested in include singularities in space and time (corresponding to the case of Fröhlich Polaron well-known in quantum mechanics) as well as a general class of Kac interactions arising in statistical mechanics. We show the existence of a unique Gibbs measure in the infinite volume (thermodynamic) limit and identify it explicitly. Next, in the strong coupling (resp. in the vanishing Kac) limit we show that the infinite volume limit coincides with the increments of the corresponding mean-field models. These results, which include various joint works with S.R.S. Varadhan (New York), confirm a series of conjectures of Spohn from 1980s.

13.07.2021 **Stochastic dynamics in evolutionary ecology and gene regulation**

**Dr. Peter Czuppon**

^{Institute for Evolution and Biodiversity, WWU}The seminar gives a brief and non-exhaustive overview about non-linear dynamics in biological applications. I will focus on stochastic processes that describe dynamics of genetic variants (alleles) in a population of individuals of the same species. As an example, I will study evolutionary dynamics of (gametophytic) self-incompatibility (SI) alleles in a plant population. Self-incompatibility refers to the inability of self-reproduction, i.e., in order to produce plant offspring, the parental plant needs to be fertilized by a pollen with a different SI-allele. I study the (quasi-)stationary distribution of allele frequencies in a plant population of a fixed size and relate our findings to experimental data. As a second example of a non-linear stochastic process in biology, I will talk about auto-regulation in gene expression. Genes can self-regulate their expression, either by enhancing or reducing the transcription of a gene. These different regulation mechanisms lead to different gene expression profiles. A negative feedback (gene inhibition) reduces the variance of the number of produced proteins, while a positive feedback (genetic upregulation) strongly increases the variance. To quantify this effect precisely, we use an approximation based on the central limit theorem for Markov processes under a separation of time-scales.

**Colloquium Winter Term 2020/2021**12.01.2021 **Monitoring Subcellular Energy Physiology using Fluorescent Protein Biosensors**

**Prof. Markus Schwarzländer**

^{Institut für Biologie und Biotechnologie der Pflanzen, WWU}The energy conversion that occurs in cells requires tight surveillance and dynamic adjustment to meet demands, maintain efficiency and avoid dysfunction. This is particularly relevant in plant cells which are directly exposed to frequent and often dramatic changes in their immediate environment, including light-dark transitions or changes in oxygen availability. Yet, our understanding of the dynamics of energy physiology and their regulation at the sub-cellular or even sub-compartmental level is limited. We have been using quantitative confocal microscopy and fluorimetry to assess transitions in respiratory physiology in vivo using a growing set of genetically-encoded fluorescent protein sensors. I would like to introduce both fundamental considerations as well as the recent progress that we have made in the dissection of cellular energy physiology highlighting ATP dynamics, redox regulation and calcium transport. I will discuss our efforts towards multiparametric monitoring, as an approach towards an integrated picture of subcellular stress physiology, while appraising technical and biological limitations.

19.01.2021 **The human dynamic system - Myonardo - a computational model of the human musculoskeletal system**

**Prof. Heiko Wagner**

^{Institut für Sportwissenschaften, WWU}In my lecture I will give a brief insight into the high complexity and non-linearity of the human musculoskeletal system. For the mathematical-physical description of human movement, we have developed a computer model that describes all important joints, segments and muscles in humans. With this computer model, the stress and strain within a person's body can now be analyzed. I will first introduce the Myonardo and then show a few examples of use, e.g. from the field of sports, ergonomics, and crash tests.

02.02.2021 **PhD Kolloquium**

Machine Learning in der Medizin

**Lukas Fisch**

^{Medical Machine Learning Lab, WWU}Age predicted from stochastic models using neuroimaging data of the brain has proven to be a useful biomarker to quantify the progress of neurological diseases and aging. However, most of these stochastic models rely on the neuroimaging data to be highly preprocessed, yielding a significant computational overhead and resulting in the predicted brain-age to be sensitive to preprocessing parameters. The few brain-age models which use so-called raw T1 neuroimaging data, rely on the voxels to be registered to a standard atlas which is still computationally expensive. In this work a 3D convolutional neural network (CNN) using the ResNet architecture is trained on raw non-registered T1 MRI neuroimaging data from N=10,691 samples from the German National Cohort and applied to N=4,004 samples from three independent studies. Additionally, seven models which are common in brain-age research are trained and validated on the same samples using preprocessed neuroimaging data. The 3D CNN predicts age with a median average deviation of as low as 2.59 years, outperforming all common brain-age models despite using raw non-registered brain scans.

09.02.2021 **!!!! Postponed to 13.04.2021 !!!!****Social insects as models for complex systems?**

**Prof. Jürgen Gadau**

^{Institute for Evolution and Biodiversity , WWU}Social complexity is a central theme in complex system theory, biological sciences, and social sciences, and yet features that underlie it, and the evolutionary processes that shaped them, are not well understood. It is unclear what composition of features is needed for the emergence of a high-level social organization, and what are their relative weights. The broad diversity of social structures in insects (such as bees, ants, termites) presents a unique opportunity to study the features that underlie social complexity, and their evolutionary trajectories.

**Colloquium Winter Term 2018/2019**23.10.2018 **Mitgliederversammlung**06.11.2018 **Neuronale Netze und Machine Learning - Einsatzgebiete in Industrie und Wirtschaft**

**Uwe Westerhoff**

^{saracus consulting GmbH, Münster}Das Themenfeld Machine Learning, Neuronale Netze und Künstliche Intelligenz hat insbesondere in den letzten kanpp zehn Jahren eine enorme Aufmerksamkeitssteigerung erfahren und dies sowohl im wissenschaftlichen Bereich als auch auf Seiten der Industrie. Inzwischen gibt es kaum eine Branche, welche nicht zumindest von sich behauptet, Verfahren der KI einzusetzen. Im Rahmen dieses Vortrags werden wir einen Blick hinter die Kulissen werfen. Der erste Teil liefert einen Überblick über verschiedene Neuronale Netze und weitere Algorithmen. Außerdem werden wir uns zumindest kurz anschauen, wie Neuronale Netze letztlich auf Ebene der einzelnen Rechenoperationen arbeiten und trotz vergleichsweise einfacher Einzeloperationen ihre beeindruckende Leistungsfährigkeit erreichen.

Im zweiten Teil stellen wir einige Anwendungsfälle aus Industrie und Wirtschaft vor und beschreiben die jeweils eingesetzten Verfahren.Einladender: O. Kamps

27.11.2018 **Bayesian Statistical Modeling for the Natural and Social Sciences**

**Paul Buerkner**

^{Fachbereich Psychologie, WWU}In recent years, Bayesian Statistics has gained a lot of popularity in the Natural and Social Sciences. Not only does it offer a consistent framework for probabilistic models, but it also provides researchers with an enormous modeling flexibility. It is this flexibility that allows creating statistical models tailored to the requirements of data, not the other way around. In this talk, I will present some general principles that guide the development, estimation, and interpretation of Bayesian statistical models. Among other things, I will talk about the choice of appropriate response distributions, the modeling of non-linear relationships as well as approaches to model comparisons in the Bayesian framework.

Einladender: O. Kamps

11.12.2018 **Fluctuation response and large signal stability in power grids**

**Dr. Frank Hellmann**

^{Potsdam Institute for Climate Impact Research, Potsdam}In the complex network study of power grids, their dynamics are typically modeled as a Kuramoto model with inertia. In order to simplify the analysis it is often the case that losses are neglected, leading to symmetric effective network Laplacian in the stability and fluctuation analysis. I will present new results and analysis that show that losses, which appear as a phase shift parameters as in the Kuramoto-Sakaguchi type inertial oscillator models, dramatically alter the nonlinear and frequency characteristics of these systems.

Einladender: O. Kamps

04.12.2018 **Solvent mediated interactions between nanostructures in suspension and the influence of solvophobicity**

**Andy Archer**

^{Loughborough}

When pairs of objects immersed in a liquid medium encounter one another there is, of course, a direct interaction between then, but there is also a solvent mediated interaction, which depends on the size difference between the objects and the solvent molecules and many other factors. This interaction can be attractive, repulsive or even both, at different separations and distances between the objects. If the forces between the objects are strongly attractive, then this leads to aggregation of the particles, so controlling carefully these forces are important in maintaining the particles in solution. When the surface of the objects are solvophobic, or have solvophobic patches, then this can lead to strong attractive forces. For example, hydrophobic forces such as these are important in determining protein folding in water and other molecular ordering in living systems. I will give an overview of some of the physics of solvent mediated interactions and show how such potentials can be calculated using classical density functional theory (DFT), focussing in particular on the influence of solvophobicity.Einladender: Prof. U. Thiele

18.12.2018 **Machine Learning in Psychiatry - Promises, Problems, and Perspectives**

**PD. Dr. Tim Hahn**

^{Klinik für Psychiatrie und Psychotherapie, WWU}While our knowledge regarding the biological bases of psychiatric disorders has expanded massively in the last two decades, none of these findings have yet been translated into concrete clinical applications. One reason for this is that commonly conducted statistical analyses – while allowing for inference on the group level – do not enable predictions on the level of the individual. Another reason is the multifaceted nature of mental disorders which necessitates the integration of multiple sources of information when aiming to comprehensively represent relevant patient characteristics. Against this background, methods from the field of machine learning and multivariate pattern recognition have recently gained increasing attention, especially in the area of neuroimaging. The presentation gives an overview of the most recent developments in the emerging field of Predictive Analytics in Mental Health Research, providing concrete examples based on functional and structural Magnetic Resonance Imaging assessments, proteomic data as well as large-scale psychometric measures. Specifically, we will detail best practive project planning and common pitfalls when constructing models 1) predicting therapeutic response, 2) supporting differential diagnoses and 3) optimizing risk detection in the context of prevention and patient management. Finally, we will suggest specific guidelines for Deep Learning and Big Data approaches in multi-center research with the goal of providing the clinician with easy-to-use predictive algorithms and databases enabling early diagnosis and, ultimately, more efficient and successful treatment.

Einladender: Dr. O. Kamps

15.01.2019 **Formation and Spatial Localization of Phase Field Quasicrystals****Priya Subramanian**

^{Leeds}The dynamics of many physical systems often evolve to asymptotic states that exhibit spatial and temporal variations in their properties such as density, temperature, etc. Regular patterns such as graph paper and honeycombs look the same when moved by a basic unit and/or rotated by certain special angles. They possess both translational and rotational symmetries giving rise to discrete spatial Fourier transforms. In contrast, an aperiodic crystal displays long range order but no periodicity. Such quasicrystals lack the lattice symmetries of regular crystals, yet have discrete Fourier spectra. We look to understand the minimal mechanism which promotes the formation of such quasicrystalline structures arising in diverse soft matter systems such as dendritic-, star-, and block co-polymers using a phase field crystal model. Direct numerical simulations combined with weakly nonlinear analysis highlight the parameter values where the quasicrystals are the global minimum energy state and help determine the phase diagram. By locating parameter values where multiple patterned states possess the same free energy (Maxwell points), we obtain states where a patch of one type of pattern (for example, a quasicrystal) is present in the background of another (for example, the homogeneous liquid state) in the form of spatially localized dodecagonal (in 2D) and icosahedral (in 3D) quasicrystals. In two dimensions, we compute several families of spatially localized quasicrystals with dodecagonal structure and investigate their properties as a function of the system parameters. The presence of such metastable localized quasicrystals is significant as they affect the dynamics of the soft matter crystallization process.

Einladender: Prof. U. Thiele

22.01.2019 **Intermittent behavior across scales in biology****Fernando Peruani**

^{Université de Nice Sophia Antipolis}Intermittent behavior is observed in biological systems at all scales, from bacterial systems to sheep herds. First, I will discuss how Escherichia coli explores surfaces by alternating stop and moving phases. Specifically, I will show that a stochastic three behavioral state model is consistent with the empirical data. The model reveals that the stop frequency of bacteria is tuned at the optimal value that maximizes the diffusion coefficient. These results provide a new perspective on how evolution may have reshaped bacterial motility apparatus. Intermittent motion is also observed in sheep, where again a stochastic three behavioral state model provides a quantitative understanding of the empirical data. However, in sheep, individual transition rates depend on the behavioral state of other individuals and collective behaviors emerge. Specifically, I will show that small sheep herds display highly synchronized intermittent collective motion, with the herd behaving as a self-excitable system.

Einladender: Prof. U. Thiele

29.01.2019 **Computational Social Science****Jun.-Prof. Dr. Annie Waldherr**

^{Institut für Kommunikationswissenschaft, WWU Münster}Computational social science (CSS) is a growing interdisciplinary approach to study social processes using big data, advanced data analytics, and computer simulation. Besides just scaling traditional research approaches to massive data sets, some strands of CSS - such as network science and social simulation - also stress the interconnectedness and nonlinearity of social processes, embracing ideas from complexity science. After giving a broad overview on the main areas of current CSS, I will present an example of studying the public sphere as a complex system with agent-based modeling. In terms of complexity theory, the public sphere can be conceptualized as an arena where heterogeneous, autonomous and adaptive agents interact and self-organize. Multiple feedback mechanisms lead to the emergence of non-linear macro patterns such as news waves or opinion spirals. I show how the public sphere can be modeled as an agent-based system, and how the social simulation approach helps to develop theories of the public sphere, specifically by offering proof of concepts of existing theories, finding underlying mechanisms able to generate observed empirical patterns, and exploring possible futures.

Einladender: Dr. O. Kamps

# Colloquium Summer Term 2018

17.04.2018 **A quantiative theory for transport equations**

Prof. Dr. Christian Seis

^{Institut für Analysis und Numerik}In this talk, I will review a new quantitative theory for transport equations with rough coefficients and discuss some of its main applications. More precisely, we consider examples in the context of fluid mixing and of numerical and stochastic approximations and investigate properties of solutions to the 2D Euler equations.

18.04.2018

24.04.2018

**A short course on Markov properties for physicists: Theory, numerical simulations and applications to biophysics**Prof. Dr. Manuel Morillo Buzón

^{Universidad de Sevilla}

The description of Markov Processes (MP) and their relevance to the physical

sciences will be discussed. The random propagator and its density function will be

the key ingredients to characterize several interesting types of MP:

a) continuous MP and the Langevin description of Brownian motion

b) jump continuous MP

c) discrete jump MP and birth-death MP with applications to (bio)chemical kinetics.

Issues like stability, stationary states and mean passage times between multistable

systems will be addressed. The nonlinearity of realistic processes precludes their

full analytical treatment. We will then discuss how the different types of problems

can be numerically simulated.18.04.2018 (Mi.) 14 – 16 Uhr SR 304, Wilhelm-Klemm-Straße 9

20.04.2018 (Fr.) 14 – 16 Uhr HS 404, Wilhelm-Klemm-Straße 9

23.04.2018 (Mo.) 16 – 18 Uhr HS 404, Wilhelm-Klemm-Straße 9

24.04.2018 (Di.) 16:30 – 18 Uhr HS 404, Wilhelm-Klemm-Straße 908.05.2018 **Predictive Modelling of Time Series in Neuroscience: The State Space Approach**

Dr. Andreas Galka

^{Christian-Albrechts-University of Kiel, Institute for Medical Psychology and Medical Sociology}Laith Hamid M.Sc.

^{Christian-Albrechts-University of Kiel, Institute for Medical Psychology and Medical Sociology}The last two decades have witnessed a major advancement of predictive modelling of time series data in Neuroscience. A key concept within this field is given by the methodology of Linear State Space (LSS) Modelling. In this talk we will review the basic concepts of LSS Modelling and discuss several practical applications, such as signal separation, noise reduction, artifact suppression, time series fusion and source analysis. While time series may have very different data dimensions and temporal sampling rates, LSS modelling provides a unifying framework for capturing the dynamics of the underlying neural processes. The parametric structure of LSS models enables the definition of "dynamical templates" which have been successfully applied to various filtering tasks. Additionally, in source analysis the generalization of the system model in LSS models enables region-specific modeling of dynamic processes in the brain. The generalization of the measurement equation allows for multimodal fusion. Compared to inverse solutions that ignore the temporal aspect in the data, dynamical inverse solutions based on LSS modelling may perform better in case of oscillatory activity, deep brain sources, presence of measurement noise and recordings with a small number of sensors.

15.05.2018 *Joint work with Botond Cseke, Ramon Grima and Guido Sanguinetti.***Using ideas form statistics for analysing (spatio-temporal) stochastic processes**Dr. David Schnörr

^{Theoretical Systems Biology group, Imperial College London}Many systems in nature consist of stochastically interacting agents or particles. Stochastic processes have been widely used to model such systems, yet they are notoriously difficult to analyse. In this talk I will show how ideas from statistics can be used to tackle some challenging problems in the field of stochastic processes.

In the first part, I will consider the problem of inference from experimental data for stochastic reaction-diffusion processes. I will show that multi-time distributions of such processes can be approximated by spatio-temporal Cox processes, a well-studied class of models from computational statistics. The resulting approximation allows us to naturally define an approximate likelihood, which can be efficiently optimised with respect to the kinetic parameters of the model.

In the second part, we consider more general path properties of a certain class of stochastic processes. Specifically, we consider the problem of computing first-passage times for Markov jump processes, which are used to describe systems where the spatial locations of particles can be ignored. I will show that this important class of generally intractable problems can be exactly recast in terms of a Bayesian inference problem by introducing auxiliary observations. This leads us to derive an efficient approximation scheme to compute first-passage time distributions by solving a small, closed set of ordinary differential equations.29.05.2018 **Pattern selection through directional quenching**Prof. Dr. Arnd Scheel

^{University of Minnesota, School of Mathematics}Interfaces or boundaries affect the formation of crystalline phases in sometimes quite dramatic ways. We are interested in examples where such interfaces arise through directional quenching and separate a striped phase from a uniform, non-crystalline state. Examples range from the alignment of convection roles in Benard convection to the robust patterning through presomites in limb formation, or the formation of helicoidal precipitates in recurrent precipitation. It turns out that growing the crystalline region leads to the selection of crystallographic parameters near the interface. We describe results for model problems such as Allen-Cahn, Cahn-Hilliard, and Swift-Hohenberg equations that quantify crystalline strain for small and large speeds and predict alignment parallel, perpendicular, or at oblique angles to the growth interface.

12.06.2018 **Rethinking Nonlinear Dynamics - Self-organized Protein Pattern Formation**Dr. Jacob Halatek

^{Faculty of Physics, Statistical and Biological Physics, Ludwig-Maximilians-Universität Munich}Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. More generally, these systems serve as model systems for self-organization, one of the core principles of life. We present a rigorous theoretical framework able to generalize and unify pattern formation for quantitative mass-conserving reaction-diffusion models in complex system geometries. Within this framework, separation of diffusive mass redistribution on the level of conserved species provides a general mathematical procedure to decompose complex reaction-diffusion systems into effectively distinct functional units. Our approach reveals the general underlying bifurcation scenarios and the influence of system geometry on pattern formation. We apply this general framework to a range of specific intracellular pattern forming protein networks, and show how it facilitates the identification of general self-organisation principles.

19.06.2018 **Transport und Aufbewahrung bestrahlter Brennelemente in CASTOR®-Behältern**

Dr. Frank Jüttemann

^{GNS Gesellschaft für Nuklear-Service mbH}Die Präsentation vermittelt einen Überblick zur trockenen Zwischenlagerung bestrahlter Brennelemente in CASTOR® V Behältern. Für den Transport und die Zwischenlagerung solcher Brennelemente entwickelte GNS bereits vor mehr als 30 Jahren einen damals neuartigen Behältertyp, den CASTOR®. Die CASTOR®-Familie mit ihren unterschiedlichen, kontinuierlich weiterentwickelten Baureihen ist heute ein international bekanntes Markenzeichen und Synonym für nukleare Sicherheit, Zuverlässigkeit und Innovation. Die Präsentation gibt Einblicke zu den Aspekten bestrahlte Brennelemente, Regelwerksanforderungen, Behälterentwicklung, Behälterherstellung und zur Situation der trockenen Zwischenlagerung bestrahlter Brennelemente in Deutschland.

26.06.2018 **Creation and collapse of an (almost) axisymmetric air cavity in water**Prof. Dr. Devaraj van der Meer

^{Physics of Fluids, University of Twente}In this talk, we discuss an experiment in which we create (almost) axisymmetric air cavities by driving a metal disc through an initially quiescent water surface and observe their subsequent gravity-induced collapse. We will shed light onto the observed phenomena using an approach that combines (i) experiments, (ii) numerical simulations based on a boundary integral method, and (iii) a simplified model of the collapse of a slender cavity in terms of a modified Rayleigh equation. First, we find that the neck of the cavity closes in a singular manner and is described by a power-law with exponent 1/2 plus logarithmic corrections that depend on the aspect ratio of the cavity. Secondly, we observe that the liquid jet that is formed at the singularity is preceded by an air jet that becomes supersonic when the cavity neck diameter equals roughly a millimeter. And finally, we break axisymmetry using disks with a slight azimuthal harmonic disturbance of the rim and find that the cavity walls oscillate linearly during collapse, with nearly constant amplitude and increasing frequency. This behavior can be understood from a linear amplitude equation that fully explains even the most complex shape that was observed.

10.07.2018 **Bubbles with Great Potential! Molecular Control of Foam Properties**Prof. Dr. Björn Braunschweig

^{Institute of Physical Chemistry, Westfälische Wilhelms-Universität Münster}Foams are ubiquitous in our daily lives and in industrial applications. The vast number of possibilities to use foam in processes and products originate from their unique physico-chemical properties. Classically, surfactants, polyelectrolytes and proteins are used as molecular building blocks to stabilize aqueous foam. In order to formulate foam with specific properties, its structure must be controlled at the molecular level of the ubiquitous gas-fluid interfaces [1-3].

Molecular-level characterizations of fluid interfaces are essential and help to reveal structure-property relations inside foam. Here, the molecular composition, molecular order and interactions such as electrostatics dominate, and thus must be addressed with molecular level probes that can provide access to both interfacial solvent and solute molecules. For that reason, we perform experiments on different hierarchical elements and at several length scales. The interfacial molecular structure and interactions are studied by using nonlinear optical spectroscopy, tensiometry and surface dilatational rheology, while measurements of disjoining pressure isotherms and foam analysis provide information on single foam films (air/liquid/air) and macroscopic foams (stability and structure). In this presentation, building blocks like macromolecules and surfactants are discussed and are shown to give rise to classical (consistent with DLVO theory) and non-classical foam stabilization mechanisms which are controlled by their self-organisation at the interface. The latter can be tailored by the choice of the electrolyte’s pH, ionic strength and composition.

While the properties of most foams cannot be changed after their formation a new class of photo-switchable surfactants (arylazopyrazoles) and their 2D assemblies at the air-water interface offer the opportunity to render fluid interfaces as well as macroscopic foam responsive to light irradiation. This opens exciting new possibilities for foams such as self-healing capabilities or the possibility to adapt foam properties by photo-switching of the surfactants.**Acknowledgements**

Funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No 638278) is gratefully acknowledged.**References**

[1] M. Schnurbus, L. Stricker, B.J. Ravoo and B. Braunschweig, Langmuir, 2018, under revision.

[2] S. Streubel, F. Schulze-Zachau, E. Weißenborn and B. Braunschweig, J. Phys. Chem. C, 2017, 121, 27992

[3] F. Schulze-Zachau and B. Braunschweig, Langmuir, 2017, 33, 3499

# List of Previous Talks

**Winter Term 2017/2018****Stability with respect to shocks**Prof. Dr. Ulrike Feudel

^{Universität Oldenburg}

Natural or technical systems possess often several possible stable states of operation. Linear stability theory is the appropriate tool to study the stability properties of such states with respect to small perturbations. However, in nature perturbations are not necessarily small but are finite in size. We discuss two different methods how to investigate the stability with respect to large perturbations such as single shocks. Both methods aim to determine the distance to the boundary of the basin of attraction or the edge of chaos, respectively. The first method determines the minimal destabilizing perturbation for large dynamical systems such as networks. Besides the size of this perturbations the method allows also to obtain the direction of this perturbation. We illustrate this method using pollinator networks in ecology and energy networks and identify relations between the topology of a network and its stability properties. The second method measures return times to a stable state at the edge of chaos. This is demonstrated for the transition from laminar to turbulent motion in a shear flow.**Data Science als Berufsfeld für Physiker und Mathematiker**

Dr. Anton Daitche

^{New Yorker}

In den letzten Jahren hat der Beruf Data Science enorm an Bedeutung gewonnen, mit einer stark steigenden Nachfrage. Aus meiner Sicht kann Data Science ein sehr interessantes Betätigungsfeld für Physiker und Mathematiker sein. Ich werde erläutern vorstellen, was Data Science und ins besondere Machine Learning ist, ein paar aktuelle Entwicklungen in dem Feld beleuchten und konkrete Anwendungsfälle vorstellen. Im Anschluss gebe ich ein paar Tips für Studenten und Doktoranden, die in dieses Feld einsteigen wollen.**A Phase Field Model for Thin Elastic Structures with Topological Constraint**Prof. Patrick Dondl

^{Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg}With applications in the area of biological membranes in mind, we consider the problem of minimizing Willmore’s energy among the class of closed, connected surfaces with given surface area that are confined to a fixed container. Based on a phase field model for Willmore’s energy originally introduced by de Giorgi, we develop a technique to incorporate the connectedness constraint into a diffuse interface model of elastic membranes. Our approach uses a geodesic distance function associated to the phase field to discern different connected components of the support of the limiting mass measure. We obtain both a suitable compactness property for finite energy sequences as well as a Gamma-convergence result. Furthermore, we present computational evidence for the effectiveness of our technique. The main argument in our proof is based on a new, natural notion of convergence to describe phase fields in three dimensions.

**Nonlinear dynamics and time delays in engineering applications**Dr. Andreas Otto

^{Institut für Physik, TU Chemnitz}

Time delay effects appear in many dynamical systems. Often the delay effect is a result of a transport phenomena and feedback and the systems are nonlinear. In this talk we discuss general aspects of such systems, which can be often found in engineering. The relevant applications ranging from manufacturing processes, such as rolling and metal cutting over gasoline engines to traffic flow dynamics. After an introduction to the field of time delay systems, we will first focus on systems with state-dependent delays. We show that in many situations equivalent representations with constant delays exist, which are much easier to analyze. In a second part systems with multiple and distributed delays are studied and we discuss our recent results on systems with dissipative delays. Dissipative delays are a specific class of time-varying delays and may lead to a hitherto unknown type of chaotic behavior in nonlinear delay systems.**Adaptive mesh-refinement for nonconforming finite element methods**

Prof. Dr. Mira Schedensack

^{Angewandte Mathematik, WWU}

Non-conforming finite element methods lead to robust discretizations for almost incompressible materials in solid mechanics or to pointwise divergence-free ansatz functions in fluid mechanics. If the exact solution is not smooth enough (e.g., if the underlying

domain is not convex), finite element methods show suboptimal convergence rates. Adaptive mesh-refinement algorithms driven by error estimators automatically refine the mesh at the singularity. This talk introduces nonconforming finite element methods and adaptive mesh-refinement and shows optimal convergence rates of the algorithm for some problems.**Thin film modelling of surfactant-driven biofilm spreading**Sarah Trinschek (AG Thiele)

The spreading of bacterial colonies at solid air interfaces hinges on physical processes connected to the properties of the involved interfaces. The production of surfactant molecules by the bacteria is one strategy that allows the bacterial colony to efficiently expand over a substrate. These surfactant molecules affect the surface tension which results in an increased wettability as well as in

outward-pointing Marangoni fluxes that promote spreading. These fluxes may cause an instability of the circular colony shape and the subsequent formation of fingers. In this work, we study the front instability of bacterial colonies at solid-air interfaces induced by surfactant production in the framework of a passive hydrodynamic thin film model which is extended by bioactive terms. We show that the interplay between wettability and Marangoni fluxes determines the spreading dynamics and decides whether the colony can expand over the substrate. We observe four different types of spreading behaviour, namely, arrested and continuous spreading of circular colonies, slightly modulated front lines and the formation of pronounced fingers.

**Collective Cell Migration in Embryogenesis Follows the Laws of Wetting**Bernhard Wallermeyer (AG Betz)

Collective cell migration is a fundamental process during embryogenesis and its initial occurrence, called epiboly, is an excellent in vivo model to study the physical processes involved in collective cell movements that are key to understand organ formation, cancer invasion and wound healing. In zebrafish, epiboly starts with a cluster of cells at one pole of the spherical embryo. These cells are actively spreading in a continuous movement towards its other pole until they fully cover the yolk. Inspired by the physics of wetting we determine the contact angle between the cells and the yolk during epiboly. Similar to the case of a liquid drop on a surface one observes three interfaces that carry mechanical tension. Assuming that interfacial force balance holds during the quasi-static spreading process, we employ the physics of wetting to predict the temporal change of the contact angle. While the experimental

values vary dramatically, the model allows us to rescale all measured contact angle dynamics onto a single master curve explaining the collective cell movement. Thus, we describe the fundamental and complex developmental mechanism at the onset of embryogenesis by only three main parameters: the offset tension strength 𝛼, the tension ratio 𝛿 and the rate of tension variation 𝜆.**Branched Covering Surfaces**Prof. Dr. Konrad Polthier

^{Freie Universität Berlin, AG Mathematical Geometry Processing}Multivalued functions and differential forms naturally lead to the concept of branched covering surfaces and more generally of branched covering manifolds in the spirit of Hermann Weyl's book "Die Idee der Riemannschen Fläche" from 1913. This talk will illustrate and discretize basic concepts of branched (simplicial) covering surfaces starting from complex analysis and surface theory up to their recent appearance in geometry processing algorithms and artistic mathematical designs.

Applications will touch differential based surface modeling, image and geometry retargeting, global surface and volume remeshing, and novel weaved geometry representations with recent industrial applications.**Interfacial turbulence and regularization in falling films**Dmitri Tseluiko

^{School of Mathematics, Loughborough University, UK}

We consider a liquid film flowing down an inclined wall that may be subjected to an additional external effects, such as an electric field. We analyse the Stokes-flow regime, using both a non-local long-wave model and the full system of governing equations. For an obtuse inclination angle and strong surface tension, the evolution of the interface is chaotic in space and time. However, a sufficiently strong electric field has a regularising effect, and the time-dependent solution evolves into an array of continuously interacting pulses, each of which resembles a single-hump solitary pulse. For an acute inclination angle and a sufficiently small supercritical value of the electric field, solitary-pulse solutions do not exist, and the time-dependent solution is instead a modulated array of short-wavelength waves. When the electric field is increased, the evolution of the interface first becomes chaotic, but then is regularised so that an array of pulses is generated. A coherent-structure theory for such pulses is developed and corroborated by numerical simulations.**Turbulence and pattern formation in a model for active fluids**Dr. Michael Wilczek

^{MPISD Göttingen}We consider a liquid film flowing down an inclined wall that may be subjected to an additional external effects, such as an electric field. We analyse the Stokes-flow regime, using both a non-local long-wave model and the full system of governing equations. For an obtuse inclination angle and strong surface tension, the evolution of the interface is chaotic in space and time. However, a sufficiently strong electric field has a regularising effect, and the time-dependent solution evolves into an array of continuously interacting pulses, each of which resembles a single-hump solitary pulse. For an acute inclination angle and a sufficiently small supercritical value of the electric field, solitary-pulse solutions do not exist, and the time-dependent solution is instead a modulated array of short-wavelength waves. When the electric field is increased, the evolution of the interface first becomes chaotic, but then is regularised so that an array of pulses is generated. A coherent-structure theory for such pulses is developed and corroborated by numerical simulations.

**Curve fitting on Riemannian manifolds**Prof. Pierre-Antoine Absil

^{Universitté Catholique de Louvain}In this talk I will discuss curve fitting problems on manifolds. Manifolds of interest include the rotation group SO(3) (generation of rigid body motions from sample points), the set of 3x3 symmetric positive-definite matrices (interpolation of diffusion tensors) and the shape manifold (morphing). Ideally, we would like to find the curve that minimizes an energy function E defined as a weighted sum of (i) a sum-of-squares term penalizing the lack of fitting to the data points and (ii) a regularity term defined as the mean squared acceleration of the curve. The Euler-Lagrange necessary conditions for this problem are known to take the form of a fourth-order ordinary differential equation involving the curvature tensor of the manifold, which is in general hard to solve. Instead, we simplify the problem by restricting the set of admissible curves and by resorting to suboptimal Riemannian generalizations of Euclidean techniques.

**Branched flows in weakly scattering random media: from electronic transport to tsunami propagation**Dr. Ragnar Fleischmann

^{Max-Planck-Institut für Dynamik und Selbstorganisation, Göttingen}Wave propagation in random media — this might sound abstract but is in fact very tangible and almost omnipresent in science and everyday life. Examples are wind driven ocean waves, but also light, sound, electrons, tsunamis and even earth quakes are waves that in a natural environment typically propagate through a complex medium. Due to its complexity, the medium is often best described as random with inherent correlations. Examples include the turbulent atmosphere, complex patterns of ocean currents or semiconductor crystals sprinkled with impurities. In recent years it has become clear that even very small fluctuations in a random medium, if they are correlated, lead to focussing of the waves in pronounced branch-like spatial structures and to heavy-tailed intensity distributions. These branches are closely connected with the occurrences of random caustics, i.e. singularities in the corresponding ray fields.

I will give an overview over the phenomenon of branching and the statistical characteristics of branched flows, discussing examples from ballistic electron transport in semiconductors to the random focusing of tsunamis waves.# Summer Term 2017

**How to tie a (linear optical) field into a knot**

Prof. Mark Dennis

^{School of Physics, University of Bristol}

It is a challenging question to write down a function from real 3-dimensional space to the complex numbers such that the preimage if zero (say) is a given knot or link. If, in addition, the function appears as a solution of some physically interesting partial differential equation, or minimizes some physically motivated functional, then the knotted field might be realisable in nature. I will discuss our approach and (partial) solution this problem applied to such knotted fields in coherent optical fields (i.e. laser beams), but with applications to other systems such as knotted vorticity lines in fluids. If there is time, I will also describe how random fields (which model modes of chaotic wave systems) naturally contain a tangle of many knotted nodal lines.

**Nach dem Physikstudium in die KI-Industrie oder: Wie man die schlauen Maschinen endlich zum Arbeiten bringt**Dr. Michael Köpf

^{Cognotekt GmbH, Köln}Die Ergebnisse jahrzehntelanger Grundlagenforschung im Bereich der Künstlichen Intelligenz schlagen sich aktuell in immer mehr Produkten und Anwendungen nieder. Mittlerweile ist KI in den Unternehmen angekommen und verändert durch die Automatisierung einfacher geistiger Tätigkeiten unsere Art zu arbeiten fundamental. Neben großen Playern wie Google, Amazon oder Baidu tragen auch mehr und mehr kleine bis mittelständische Firmen zu diesem Wandel bei. Physikerinnen und Physiker sind aufgrund der ihnen im Studium vermittelten Fähigkeiten besonders geeignet, diesen Umbruch mitzugestalten. Um ein Gefühl für dieses sehr moderne Berufsfeld zu vermitteln, werde ich anhand konkreter Beispiele aus der Versicherungsbranche die mit der Kommerzialisierung künstlicher Intelligenz verbundenen Herausforderungen vorstellen.

**Nonlinear dynamics of beating cilia and flagella: Swimming, steering, and synchronization**Dr. Benjamin M. Friedrich

^{TU Dresden, Center for Advancing Electronics Dresden (cfaed), Biological Algorithms Group}Cilia and flagella represent a best-seller of nature: their regular bending waves propel cellular swimmers such as sperm cells and green alga in a liquid. Collections of these slender cell appendages can synchronize their beat to pump fluids inside human airways and brain ventricles effectively.

In this talk, I will address the physics of flagellar swimming and how mechanical and chemical signals control these biological oscillators.

In the first part, I will a present a theory of sperm chemotaxis, i.e. the directed navigation of flagellated sperm cells in response to signaling molecules released by the egg. We show how swimming along helical paths results in an effective navigation strategy that can cope with molecular shot noise of cellular concentration measurements. Thereby, spatial information about a concentration gradient becomes encoded in the phase of an oscillatory temporal signal perceived by the swimming cell along its helical path. This theory has recently been confirmed by experiments that track swimming sperm cells in three space dimension in artificial concentration fields of signaling molecules [1].

In the second part, I will discuss flagellar synchronization as an emergent phenomenon in collections of several flagella, which arises from mutual a hydro-mechanical coupling. We present a theory of the beating flagellum as a noisy limit-cycle oscillator, which is fully calibrated by experimental data. In particular, we show using theory and experiment how external mechanical forces change speed and shape of the flagellar beat, or even stall the beat reversibly [2]. This flagellar load-response is key prerequisite for flagellar synchronization.

We present a link between the efficiency of the flagellum to convert chemical energy into mechanical work and its ability to synchronize. Finally, we characterize the beating flagellum as a noisy oscillator, whose non-equilibrium fluctuations induce stochastic phase-slips in pairs of phase-locked flagella [3].[1] J.F. Jikeli et al.: Sperm navigation along helical paths in 3D chemoattractant landscapes, Nature Communications 6, 2015

[2] G.S. Klindt, C. Ruloff, C. Wagner, B.M. Friedrich, Load-response of the flagellar beat, Phys. Rev. Lett. 117, 2016

[3] R. Ma, G.S. Klindt, I.-H. Riedel-Kruse, F. Jülicher, B.M. Friedrich: Active phase and amplitude fluctuations of flagellar beating, Phys. Rev. Lett. 113, 2014**Timing stability of quantum dot based semiconductor lasers**Dr. Stefan Breuer

^{Technische Universität Darmstadt, Angewandte Halbleiteroptik und Photonik}Passively mode-locked semiconductor lasers based on nano-scale quantum dots offer access to sub-picosecond short optical pulses thanks to their broad spectral bandwidth and ultra-fast gain dynamics. Their small footprint, multi-Gigahertz repetition rates, direct modulation capability as well as their monolithic layout makes them promising candidates for optical clock distribution, high bit-rate optical time division multiplexing and compact microwave/millimeter-wave signal generation. Their intrinsic pulse train timing stability and fixed pulse repetition rate however can be limiting factors towards their widespread implementation into time-critical applications. Experimental concepts to improve the timing stability and to enable repetition rate agility are therefore demanded. This talk will start by reviewing timing stability fundamentals of semiconductor lasers. Then, a selection of experimental concepts to improve the timing stability will be described in detail. Next, by means of a reconfigurable laser layout, higher harmonics of the fundamental repetition rate can be generated leading to a substantially improved timing stability. Finally, experimental results will be discussed and explained in the framework of a time-domain description that is able to reproduce the timing stability improvement and repetition rate agility.

**On-chip generation of complex optical quantum states and their coherent control**Dr. Michael Kues

^{Institut national de la recherche scientifique, Varennes (Québec), Canada / Centre Energie Matériaux Télécommunications}Entangled optical quantum states are essential towards solving questions in fundamental physics, and are at the heart of applications in quantum information science [1]. For advancing the research and development of quantum technologies, practical access to the generation and manipulation of complex photon states is required. Recently, integrated (on-chip) photonics has become a leading platform for the compact, cost-efficient, and stable generation and processing of optical quantum states [2]. However, on-chip sources are currently limited to basic two-dimensional (qubit) two-photon states.

Within this presentation, I will show that integrated frequency combs (on-chip light sources with a broad spectrum of evenly-spaced frequency modes) based on high-Q nonlinear microring resonators can provide solutions towards scalable complex quantum state sources. Particularly, by using spontaneous four-wave mixing within the microring resonators, we demonstrate the generation of bi- and multi-photon entangled qubit states over a broad frequency comb spanning the telecommunications band, and control these states coherently to perform quantum interference measurements and tomographic reconstruction of their density matrix [3-5]. Moreover, we demonstrate the on-chip generation of entangled high-dimensional (quDit) states, where the photons are created in a coherent superposition of multiple pure frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions. Furthermore, using off-the-shelf telecommunications components, we introduce a platform for the coherent manipulation and control of frequency-entangled quDit states.

Our results suggest that microcavity-based entangled photon states and their coherent control using accessible telecommunications infrastructure can open up new venues for reaching the processing capabilities required for meaningful quantum information science.References

[1] Knill, E., Laflamme, R. & Milburn, G. J. “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).

[2] Tanzilli, S. et al. “On the genesis and evolution of integrated quantum optics,” Laser Photonics Rev. 6, 115–143 (2012).

[3] C. Reimer, M. Kues, et al., “Integrated frequency comb source of heralded single photons,” Opt. Express. 22, 1023 (2014).

[4] C. Reimer, M. Kues, et al., “Cross-polarized photon-pair generation and bi-chromatically pumped optical parametric oscillation on a chip,” Nat. Commun. 6, 8236 (2015).

[5] C. Reimer, M. Kues, et al., “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176 (2016).**Structure formation in confinement: photonic balls and active granular rotors**Prof. Dr. Michael Engel

^{Friedrich-Alexander Universität Erlangen-Nürnberg, Institute for Multiscale Simulation}Natural and biological systems achieve emergent behavior with elementary building blocks. Research in my group focuses on modeling structure formation processes in soft and hard condensed matter. In this talk, I discuss two joint computational-experimental works that have in common that they concern structure formation of particles in confinement. (1) A binary mixture of 3D-printed macroscopic rotors with opposite sense of rotation is excited on an electromagnetic shaker in circular confinement. Phase-separation reminiscent of spinodal decomposition is observed. Evolution of the domain size is compared to two-dimensional Langevin dynamics simulations. (2) Droplet-based microfluidics creates homogeneous emulsion droplets as sources for defined spherical confinement. We observe a discrete series of multiply twinned colloidal clusters with icosahedral symmetry. To understand and explain the formation of the clusters, we test a geometric model and extract extremal principles.

**Network robustness and the impact of transmission line failures**Prof. Dr. Dirk Witthaut

^{Forschungszentrum Jülich GmbH, Institut für Energie- und Klimaforschung, Systemforschung und Technologische Entwicklung (IEK-STE)}The robust operation of physical distribution and supply networks is fundamental for economy, industry, and our daily life. For instance, a reliable supply of electric power fundamentally underlies the function of most of our technical infrastructure. In periods of high loads, the breakdown of a single element of the power grid can cause a global cascade of failures implying large-scale outages with potentially catastrophic consequences.

In this talk I will review the theory of transmission line outages and the robustness of networks. Once a line in the network fails, the flow must be rerouted over alternative pathways. To assess the robustness of a network we must understand where flows are rerouted and quantify how much capacity is available for this task. I will discuss the mathematical formulation of the problem, present some recent results, and demonstrate some illuminating connections to other fields of theoretical physics and applied math.**Spontaneous and Coherent Raman microscopy for biomedical applications**Dr. Cees Otto

^{University of Twente, Faculty of Science and Technology, Medical Cell BioPhysics (MCBP)}Raman microscopy is well known as a powerful method for the study of molecular changes and processes. In biomedical applications the chemical information is usually extremely complex.

The laser-based implementation of vibrational spectroscopy that underlies modern spontaneous and Coherent Raman microscopy however enables a broad range of applications also in the biomedical field. In this presentation an introduction to various forms of Raman microscopy will be presented with applications on cells and tissues.**Theory, structure and experimental justification of the metal/electrolyte interface**Dr. Manuel Landstorfer

^{Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin}Various types of modeling approaches are used to investigate the structure of the metal/electrolyte interface and its behaviour due to adsorption, intercalation and other surface effects [1]. While atomistic resolved models address reaction mechanisms, continuum models are the foundation for a comparison to voltage- or current-controlled experiments.

In this talk I will provide insight to our model framework which explicitly accounts for solvation and adsorption effects. We will show that this model is the very basis for a qualitative and quantitative understanding of the capacitive behaviour of a variety of electrolytes. We will further show that our approach is also the very basis for a model based understanding of cyclic voltammetry and thus a key tool for analytical electrochemistry.

Most common continuum models essentially relay on simplified Poisson–Boltzmann equations to model the electrochemical double layer. However, it is long known [2] that this equation is not able to predict the capacitive behaviour of electrochemical interfaces. We showed that this is due to the negligence of the incompressibility [3] and solvation effects [4] of electrolytic solutions. Our new model essentially leads to a coupled Poisson–momentum equation system and is able to predict the non-linear behaviour of the double layer capacity over the whole potential range. Additionally, our surface mixture theory [5] accounts for adsorption on the metal surface and for partial solvation, thus leading to an overall precise model which is able to predict the unsymmetric capacity curve of strongly adsorbing ions (i.e. NaF or NaClO4[5]). Based on this, we are able to predict the thermodynamic structure of the space charge layer at the metal/electrolyte interface, which is in full agreement to experimental data.References

[1] M. Landstorfer and T. Jacob, Chem. Soc. Rev., 2013, 42, pp 3234–3252.

[2] J. Bockris, A. Reddy and M. Gamboa-Aldeco, Modern Electrochemistry 2A: Fundamentals of Electrodics, Springer, 2001, vol. 2.

[3] W. Dreyer, C. Guhlke and R. Müller, Phys. Chem. Chem. Phys., 2013, 15 , pp 7075–7086.

[4] W. Dreyer, C. Guhlke and M. Landstorfer, Electrochemistry Communications, 2014, 43 , pp 75 – 78.

[5] W. Dreyer, C. Guhlke and M. Landstorfer, Electrochimica Acta, 2016, 201, 187 – 219.

[6] G. Valette, J. of Electroanal. Chemistry and Interfacial Electrochemistry, 1981, 122 , pp 285 – 297.

[7] G. Valette, Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 1982, 138, pp 37 – 54.**Static and Dynamic Functional Brain Connectivity at Sensor and Source level: Evidences from EEG-MEG Group Analysis**Dr. Stavros Dimitriadis

^{Aristotle University of Thessaloniki}The human brain can be modelled as a complex networked structure with brain regions as individual nodes and their anatomical/functional links as edges. Functional brain networks are constructed by first extracting weighted connectivity matrices, and then thresholding them to minimize the noise level. Different methods have been used to estimate the dependency values between the nodes The adaptation of both bivariate (mutual information) and multivariate (Granger causality) connectivity estimators to quantify the synchronization between multichannel recordings yields a fully connected, weighted, (a)symmetric functional connectivity graph (FCG), representing the associations among all brain areas. The aforementioned procedure leads to an extremely dense network of tens up to a few hundreds of weights. Therefore, this FCG must be filtered out so that the “true” connectivity pattern can emerge. For that reason, statistical filtering based on surrogates analysis and also topological filtering based on the maximization of information flow in the network under the constraint of the wiring cost (Dimitriadis et al., 2017) should be adopted to get a subject and condition specific functional connectivity pattern.

The whole methodology relies on data-driven techniques without using a priori information for the subjects e.g. labels. Subject-specific approaches increase the reproducibility of the dataset avoiding optimizing it independently for each study. Complementary, one can add more subjects to the original cohort without re-optimizing the parameters, an approach that can lead to controversy findings to the original study.

I will demonstrate how different connectivity estimators in both static and dynamic functional connectivity with the incorporation of arbitrary statistical and topological filtering schemes can give contradictory results. The selection of appropriate surrogates and data-driven topological filtering scheme will give more reproducible and stable results. The whole analysis will focus on electro/magneto-encephalography (EEG/MEG) at resting-state in normal populations and in mild cognitive impairments (MCI) subjects. First evidences of similarities of connectivity patterns between sensor and source-level will be also demonstrated.References:

[1] Dimitriadis SI et al., . Topological Filtering of Dynamic Functional Brain Networks Unfolds Informative Chronnectomics: A Novel Data-Driven Thresholding Scheme Based on Orthogonal Minimal Spanning Trees (OMSTs). Front. Neuroinform., 26 April 2017 | https://doi.org/10.3389/fninf.2017.00028

**Winter Term 2016/2017**

**Variational Mean Field Games**Prof. Dr. Filippo Santambrogio, Laboratoire de Mathématiques d'Orsay, Université Paris-Sud

I will give a brief introduction to the the emerging topic of Mean Field Games, introduced by J-M Lasry and P-L Lions some years ago as a model for the Nash equilibrium of a population of agents each selecting his own evolution, taking into account the density of the other agents that he meets, in the form of a congestion charge. This gives rise to a coupled system of PDEs, a continuity equation where the density moves according to the gradient of a value function, and a Hamilton-Jacobi equation solved by the value function, where the density also appears.

I will mainly deal with the case where this equilibrium problem may be seen as optimality conditions of a convex variational problem, and give the main results in this framework. I will also present some recent regularity results which allow to give a precise mathematical meaning to the equilibrium condition. At the end of the talk I will present an interesting variant, where the congestion cost is replaced by a capacity constraint. In this case an extra unknown appears, which plays both the role of a pressure in the fluid mechanics point of view, and of a price in the economical interpretation.**Nonlinear dynamics of bacterial and active colloidal suspensions**

Prof. Dr. Hartmut Löwen, Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf

This talk addresses the nonlinear dynamical aspects of active matter for both biological and

artificial colloidal microswimmers.

[1]. A number of collective phenomena in active matter will be proposed. In detail, we shall discuss active turbulence in bacterial systems [2] and its ability to steer the transport of shuttles [3]. Then we turn to kinetic phase separation in artificial swimmers [4]. The late time kinetics of phase separation can be mapped on the Cahn-Hilliard model [5]. Moreover we put forward the concept of negative interfacial tension [6] in nonequilibrium phase-separated swimmer systems and that of the swim pressure at system boundaries [7].

References:

[1] For a recent review, see: C. Bechinger, R. di Leonardo, H. Lowen, C. Reichhardt, G. Volpe, G. Volpe,

Active Brownian motion in complex and crowded environments, arXiv: 1602.00081

[2] H. H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R. E. Goldstein, H. Lowen, J. M. Yeomans, PNAS 109, 14308 (2012).

[3] A. Kaiser, A. Peshkow, A. Sokolov, B. ten Hagen, H. Lowen, I. S. Aranson, Physical Review Letters 112, 158101 (2014).

[4] I. Buttinoni, J. Bialke, F. Kummel, H. Lowen, C. Bechinger, T. Speck, Physical Review Letters 110, 238301 (2013).

[5] T. Speck, J. Bialke, A. M. Menzel, H. Lowen, Physical Review Letters 112, 218304 (2014).

[6] J. Bialk'e, J. T. Siebert, H. Lowen, T. Speck,Physical Review Letters 115, 098301 (2015).

[7] F. Smallenburg, H. Lowen, Physical Review E 92, 032304 (2015).**Physical modeling of cellular motility**

PD Dr. Falko Ziebert, Physikalisches Institut Fakultät für Mathematik und Physik, Albert-Ludwigs-Universität Freiburg

Substrate-based crawling motility of eukaryotic cells is essential for many biological functions, both in developing and mature organisms. Motility dysfunctions are involved in several life-threatening pathologies such as cancer and metastasis. Motile cells are also a natural realization of active, self-propelled ‘particles’, a popular research topic in nonequilibrium physics. Finally, from the materials perspective, assemblies of motile cells and evolving tissues constitute a class of adaptive self-healing materials that respond to the topography, elasticity, and surface chemistry of the environment and react to external stimuli.

Although a comprehensive understanding of substrate-based cell motility remains elusive, progress has been achieved recently in its modeling on the whole cell level. I will survey our recent advances in computational approaches to cell movement on structured substrates (with modulated adhesion or stiffness), as well as on collective cell migration.

Ziebert, F. & Aranson, I. S. Effects of adhesion dynamics and substrate compliance on the shape and motility of crawling cells. PLoS ONE 8, e64511 (2013).

Löber, J., Ziebert, F. & Aranson, I. S. Modeling crawling cell movement on soft engineered substrates. Soft Matt. 10, 1365–1373 (2014).

Löber, J., Ziebert, F. & Aranson, I. S. Collisions of deformable cells lead to collective migration. Sci. Rep. 5, 9172 (2015).

Ziebert, F., Löber, J. & Aranson, I. S. Macroscopic model of substrate-based cell motility. in Physical Models of Cell motility, Ed. I. S. Aranson, Springer (Switzerland) 1–67 (2016).**The Fibonacci family of dynamical universality classes**

Prof. Dr. Gunter M. Schütz, Theoretical Soft Matter and Biophysics, Forschungszentrum Jülich GmbH

We use the theory of nonlinear fluctuating hydrodynamics to study stochastic transport far from thermal equilibrium in terms of the dynamical structure function which is universal at low frequencies and for large times and which encodes whether transport is diffusive or anomalous. For generic quasi one-dimensional systems we predict [1] that transport of mass, energy and other locally conserved quantities is governed by mode-dependent dynamical universality classes with dynamical exponents z which are Kepler ratios of neighboring Fibonacci numbers, starting with z = 2 (corresponding to a diffusive mode) or z = 3/2 (Kardar-Parisi-Zhang (KPZ) mode). If neither a diffusive nor a KPZ mode are present, all modes have as dynamical exponent the golden mean z=(1+\sqrt 5)/2. The universal scaling functions of the higher Fibonacci modes are Lévy distributions. The theoretical predictions are confirmed by Monte-Carlo simulations of a three-lane asymmetric simple exclusion process.[1] V. Popkov, A. Schadschneider, J. Schmidt, and G. M. Schütz, PNAS Early Edition (2015), www.pnas.org/cgi/doi/10.1073/pnas.1512261112

**Asymptotic homogenization for fluid and drug transport in vascularized tumors: theory and applications**

Dr. Raimondo Penta, Departamento de Mecanica de los Medios Continuos y T. Estructuras,

E.T.S. de caminos, canales y puertos, Universidad Politecnica de Madrid

A vascularized tumor is characterized by a sharp length scale separation between the intercapillary distance (microscale) and the average tumor size (macroscale). Application of the asymptotic homogenization technique leads to the macroscale double Darcy, double advection-diffusion-reaction type model for fluid and drug transport in the tumor, vessels, and across the capillaries’ walls. We recover microscopic information solving cell problems representative of the microvessels’ geometries. We present the theory [1], and applications concerning the role of the vessels’ geometry on blood convection [2] and diffusion/consumption of anticancer drugs [3].

[1] R. Penta, D. Ambrosi, and A. Quarteroni. Multiscale homogenization for fluid and drug transport in vascularized malignant tissues. Mathematical Models and Methods in Applied Sciences, 25(1):79–108, 2015.

[2] R. Penta and D. Ambrosi. The role of the microvascular tortuosity in tumor transport phenomena. Journal of theoretical biology, 364:80–97, 2015.

[3] P.Mascheroni and R.Penta. The role of the angiogenic network structure on diffusion and consumption of anti-cancer drugs, Int. J. Numer. Meth. Biomed. Engng, submitted (2016).**Bending, Buckling and Bifurcations**Prof. Dr. Andrew Hazel, School of Mathematics,The University of Manchester

Quantifying and controlling the buckling and bending of solid materials has applications from molecular scales (DNA) to large-scale natural and artificial structures. In general, buckling can be interpreted as a consequence of bifurcation phenomena in nonlinear systems. In this talk, I shall present results from our recent investigation of a new buckling mode that can arise after introducing internal structure, a line of holes, into a simple column [Soft Matter (2016), 12, pp 7112--7118]. This simple geometric modification introduces a smaller lengthscale into the system and has a profound effect on the solution structure, which becomes increasing complex as the number of holes increases.

Doktorandenkolloquium

**Controlling caustics: Weaving catastrophic structures in Airy-, Pearcey-, and swallowtail beams**Alessandro Zannotti, AG Denz, Institut für Angewandte Physik

Catastrophe science is a branch of bifurcation theory in the study of dynamical systems; it is also a special case of more general singularity physics. Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behaviour arising from small changes in circumstances, analysing how the qualitative nature of solutions depends on control parameters. In optics, these dramatic changes manifest as geometrically stable caustics, which, as natural phenomena, are associated with the arcs close to rainbows, or may occur as high-intensity networks on the floor of shallow waters. Similar to their formation behind refractive index lenses with imperfections, the formation of corresponding structures has been observed for numerous kinds of lenses with importance in optics, astrophysics and surface analytics.

The most prominent representative of catastrophe that manifests as wave package is the fold catastrophe that has been realized as paraxial Airy beam, and shows a form-invariant and accelerated propagation. Here, we present higher-order catastrophes as paraxial light, discuss the mapping of corresponding cusp and swallowtail catastrophes to these beams and demonstrate their unique propagation effects. Their often auto-focusing propagation of curved trajectories is well suited to optically induce photonic structures, waveguides to nonlinear photosensitive materials.**Delay-induced Dynamics in a Swift-Hohenberg Model with Spatial Inhomogeneities**Felix Tabbert, AG Thiele, Institut für Theoretische Physik

We study pattern formation in a Swift-Hohenberg model that, aside from many other applications, describes the evolution of the electric field envelope in the transverse plane of a bistable optical cavity pumped by an external injection beam.

Typical solutions of the Swift-Hohenberg equation are homogeneous, periodic and localized states. Here, we focus on the destabilization of stable localized solutions by time-delayed feedback, which can be implemented by using an external cavity in optical applications. We show that by varying the delay time and the delay strength, one can induce a variety of different dynamics including the drift or the annihilation of the localized solutions as well as travelling wave solutions.

A special focus lies on the introduction of spatial inhomogeneities into the system, e.g., by introducing a spatially inhomogeneous injection beam, which changes the delay-induced dynamics drastically. We report on pinned localized solutions, oscillating solutions and depinning due to timedelayed feedback. The competition of a pinning inhomogeneity and a destabilizing time-delayed feedback is studied both analytically and numerically.**Rational design of stimuli-responsive nanoreactors**Prof. Dr. Joe Dzubiella, HU Berlin und Helmholtz Zentrum Berlin

The catalysis by metal nanoparticles is one of the fastest growing fields in nanoscience. However, the optimal control of catalytic activity and selectivity in nanoparticle catalysis remains a grand scientific challenge. Here, we describe our ongoing efforts how to theoretically derive design rules for the optimization of nanoparticle catalysis (in the fluid phase) by means of thermosensitive yolk-shell and core-shell carrier systems [1-3]. In the latter, nanoparticles are stabilized in solution by an encapsulating, thermosensitive hydrogel shell. The latter contains and shelters the reaction. The physicochemical properties, in particular the permeability, of this polymeric 'nanogate' react to stimuli in the environment and thus permit the reactant transport and with that the catalytic reaction to be switched and tuned, e.g., by the temperature [1-3], salt concentration, or solvent composition. Hence, the novel hybrid character of these emerging 'nanoreactors' opens up unprecedented ways for the control of nanocatalysis due to new designable degrees of freedom, if theoretical understanding and rational design principles are available.

References[1] S. Wu, J. Dzubiella, J. Kaiser, M. Drechsler, X. Guo, M. Ballauff, Y. Lu, Angewandte Chemie 51, 2229 (2012).

[2] P. Herves, M. Perez-Lorenzo, L. M. Liz-Marzan, J. Dzubiella. Y. Lu, and M. Ballauff, Chem. Soc. Rev. 41, 5577 (2012).

[3] S. Angioletti-Uberti, Y. Lu, M. Ballauff, and J. Dzubiella, J. Phys. Chem. C 119, 15723 (2015).

**Temporal Localized Structures and Light Bullets in Passively mode-locked Lasers**

Dr. Julien Javaloyes, Departament de Fisica, Edifici Mateu Orfila, Universitat de les Illes Baleares

Localized structures (LS) are nonlinear states of dissipative extended systems characterized by a correlation range much shorter than the size of the system, thus allowing for individual addressing. They appear ubiquitously in nature and they are very appealing in optical systems for applications to information processing, especially in semiconductor lasers which are fast, scalable and cheap devices. We investigate the relationship between passive mode-locking and the formation of temporal localized structures in the output intensity of a laser coupled to a saturable absorber, in the framework of time delayed dynamical systems. We present experimental and theoretical evidences [1] regarding how the mode-locked pulses transform into lasing localized structures, allowing for individual addressing and arbitrary low repetition rates. Our analysis reveals that this occurs when i) the cavity round-trip is much larger than the slowest medium timescale, namely the gain recovery time and ii) the mode-locked solution coexists with the stable off solution. These conditions enable the coexistence of a large quantity of stable solutions, each of them being characterized by a different number of pulses per round-trip and with different arrangements. A modulation of the bias current allows controlling the number and the location of the pulses traveling within the cavity [2, 3]. These results formed the basis for a very recent prediction [4] as we theoretically demonstrated the existence of three dimensional dissipative localized structures in the output of a broad area passively mode-locked laser coupled to a saturable absorber in self-imaging conditions. These phase invariant light bullets are individually addressable and can be envisioned for three dimensional optical information storage. An effective theory provides for an intuitive picture and allows to relate their formation to static auto-solitons.

[1] M. Marconi, J. Javaloyes, S. Balle, and M. Giudici. How lasing localized structures evolve out of passive mode locking. Phys. Rev. Lett., 112:223901, Jun 2014.

[2] M. Marconi, J. Javaloyes, P. Camelin, D.C. Gonzalez, S. Balle, and M. Giudici. Control and generation of localized pulses in passively mode-locked semiconductor lasers. Selected Topics in Quantum Electronics, IEEE Journal of, 21(6):1-10, Nov 2015.

[3] J. Javaloyes, P. Camelin, M. Marconi, and M. Giudici. Dynamics of localized structures in systems with broken parity symmetry. Phys. Rev. Lett., 116:133901, Mar 2016.

[4] J. Javaloyes. Cavity light bullets in passively mode-locked semiconductor lasers. Phys. Rev. Lett., 116:043901, Jan 2016.**Inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation**

Dr. Bertram Düring, Department of Mathematics, University of Sussex

In recent years different kinetic models to describe opinion formation have been proposed. Such models successfully use mathematical tools from statistical mechanics to describe the behaviour of a large number of interacting individuals in a society. This leads to generalizations of the classical Boltzmann equation for gas dynamics. Most approaches in the literature assume a homogeneous society. To model additional sociologic effects in real societies, e.g. the influence opinion leaders, one needs to consider inhomogeneous models.

In this talk we discuss such kinetic models for opinion formation, where the opinion formation process depends on an additional independent variable, e.g. a leadership or a spatial variable. More specifically, we consider:

(i) opinion dynamics under the effect of opinion leadership, where each individual is characterised not only by its opinion, but also by another independent variable which quantifies leadership qualities;

(ii) opinion dynamics modelling political segregation in `The Big Sort', a phenomenon that US citizens increasingly prefer to live in neighbourhoods with politically like-minded individuals. Based on microscopic opinion consensus dynamics such models lead to inhomogeneous Boltzmann-type equations for the opinion distribution. We derive macroscopic Fokker-Planck-type equations in a quasi-invariant opinion limit and present results of numerical experiments.**Summer Term 2016**

**Integrated frequency combs meet quantum optics**Dr. Michael Kues, Institut national de la recherche scientifique, Centre Energie Matériaux Télécommunications, Varennes (Québec), Canada

Einladender: Prof. Dr. C. Fallnich

The generation of optical quantum states on an integrated platform will enable low-cost and accessible advances for quantum technologies such as secure communications and quantum computation [1-4]. We demonstrate that integrated quantum frequency combs (based on high-Q microring resonators made from a CMOS-compatible, high refractive-index doped-glass platform – Hydex [5]) can enable the generation of pure heralded single photons, cross-polarized photon pairs, as well as bi- and multi-photon entangled qubit states over a broad frequency comb covering the S, C, L telecommunications band, with photon frequencies corresponding to standard telecommunication channels spaced by 200 GHz.

Exploiting a self-locked, intra-cavity excitation configuration, a highly stable integrated source of multiplexed heralded single photons is demonstrated, operating continuously for several weeks with less than 5% fluctuation. The measured photon bandwidth of 110 MHz is compatible with quantum memories, and high photon purity was confirmed though single photon auto-correlation measurements [6]. In turn, by simultaneously exciting two orthogonal polarization mode resonances, we introduce a new type of spontaneous four-wave mixing (FWM) to the toolbox of integrated photonics. In particular, we demonstrate the first realization of type-II spontaneous FWM (in analogy of type-II spontaneous parametric down-conversion in second-order media), which allows the direct generation of orthogonally-polarized photon pairs on a chip [7].

By using double-pulse excitation, we demonstrate the generation of time-bin entangled photon pairs [8] over the entire frequency comb spectrum. We measure qubit entanglement with visibilities above 90% and perform a tomographic density matrix reconstruction with a fidelity of 96%, enabling the implementation of quantum information processing protocols. Finally, the excitation field and the generated photons are intrinsically bandwidth-matched due to the resonant characteristics of the ring cavity, enabling the multiplication of Bell states and the generation of a four-photon time-bin entangled state. We confirm the generation of this four-photon entangled state through four-photon quantum interference with a measured visibility of 89% without background correction [9]. Integrated quantum frequency combs are thus a scalable and versatile platform for quantum information processing.References

[1] D. Bonneau, J. W. Silverstone, M. G. Thompson, in Silicon Photonics III, L. Pavesi, D. J. Lockwood, Eds. (Springer, ed. 3rd, 2016), pp. 41–82.

[2] H.J. Kimble,“The quantum internet,” Nature 453, 1023 (2008)

[3] M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71, 1539 (1999)

[4] P. Walther et al., “Experimental one-way quantum computing,” Nature. 434, 169 (2005)

[5] D. J. Moss et al., “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7, 597 (2013).

[6] C. Reimer et al., “Integrated frequency comb source of heralded single photons,” Opt. Express. 22, 1023 (2014)

[7] C. Reimer et al., “Cross-polarized photon-pair generation and bi-chromatically pumped optical parametric oscillation on a chip,” Nat. Commun. 6, 8236 (2015).

[8] J. Brendel et al., “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 86, 1392–1393 (2001).

[9] C. Reimer et al., “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351(6278), 1176-1180 (2016).

**Bulk and beyond: Scale bridging perspective on phase separation near surfaces and interfaces**

Prof. Dr. R. Spatschek, Forschungszentrum Jülich, Abteilung Thermochemie von Energiewerkstoffen

Einladender: Prof. Dr. A. Heuer

Phase separation is one of the key features of materials science with severe implications for various systems. Conventional thermodynamic concepts apply to bulk systems and deliver descriptions, which are of highest importance for many applied multicomponent systems. However, the aspect of elastic distortions, which arise due to lattice mismatches, are still not captured e.g. in thermodynamic databases. The situation becomes even more complex in the presence of surfaces and interfaces. We look at at this issue on various scales from a theoretical and computational perspective. As a result, we obtain a description which allows to include long-ranged elastic effects in a terminology accessible to atomistic and ab initio simulations. In particular find a drastic reduction of the solubility limit near free surfaces due to elastic coherency effects. This mechanism favours nucleation at free surfaces even in the absence of external stresses. We discuss the implications of this effect for hydrogen containing systems, where it may favor material failure due to hydrogen embrittlement, and compare the predictions to experimental observations.**Risiko ! -- Modellierung von Risiken im Finanzbereich als Jobchance**

Dr. C. Romeike, Dr. Felix Huerkamp, Dr. C. Honisch, d-fine GmbH

Einladender: Dr. O. Kamps**Quantenzustandsrekonstruktion und Nachweis von nichtklassischen Eigenschaften von Lichtfeldern**Prof. Dr. Boris Hage, Universität Rostock

Einladender: Prof. Dr. C. Fallnich

Die Quanteneigenschaften (im Gegensatz zu den klassischen) von Lichtfeldern stellen die Grundlage für die modernen Forschungsfelder der optischen Quantenkommunikation, -kryptographie und -informationsverarbeitung dar. Die Rekonstruktion von optischen Quantenzuständen, etwa anhand der Wignerfunktion durch Quantenzustandstomographie, ist eine etablierte Methode. Wir berichten über unsere Anstrengungen den vermutlich wegen des Kerr-Effekts verschränkten Quantenzustand eines Solitonenmoleküls nach der Propagation durch eine optische Glasfaser zu rekonstruieren. Grundsätzlich ist die Rekonstruktion einer innerhalb der Messgenauigkeit eindeutigen Darstellung diese Quantenzustands möglich, jedoch sind anhand dessen im allgemeinen nur wenige Charakteristika ablesbar, etwa ob der Zustand auch eine rein klassische Darstellung hat und somit im einleitenden Sinne unbrauchbar ist. Daher beschäftigen uns mit der experimentellen Umsetzung von Nichtklassizitätskriterien, die in jüngster Zeit auf theoretischer Seite entwickelt wurden. Als Referenzobjekte mit wohl bekannten Eigenschaften verwenden wir hier gequetschte Zustände, die wir mithilfe der Dreiwellenmischung in entarteten optisch-parametrischen Verstärkern herstellen.

**Phase-field models for the growth and evolution of complex structures**

Prof. Dr. Mathis Plapp, Laboratoire PMC - Ecole Polytechnique

Einladender: Prof.Dr. U. Thiele

Complex ramified structures are generated naturally by growth and self-organization in a large number of processes. The ramification usually arises from morphological instabilities that are due to a coupling of interface motion to transport processes in the bulk. A complete understanding of structure formation therefore requires to follow the complex interface dynamics and the resulting nonlinear pattern selection processes.

In recent years, the phase-field method has emerged as a method of choice for the numerical modelling of such free-boundary problems. It is based on phenomenological equations of out-of-equilibrium thermodynamics that are combined with free-energy functionals of Ginzburg-Landau type; interfaces are represented implicitly by profiles of suitable order parameters. Using relatively simple codes, structure evolution can be simulated qualitatively, and for some cases even quantitatively. I will first give an introduction to the principles of this method, taking as an example the growth of crystal dendrites during solidification, and then discuss other applications to structure formation in hard and soft matter systems.**Spatiotemporal patterns with pde2path**

Prof. Dr. H. Uecker, Institut für Mathematik, Carl von Ossietzky Universität Oldenburg

Einladender: Prof. Dr. U. ThieleThe Matlab continuation and bifurcation package pde2path [1] has originally been developed for elliptic PDE over 2D spatial domains, but has recently been extended to also treat Hopf bifurcations. In this talk we review the basic ideas of pde2path, and give some examples of Hopf and other bifurcations for PDEs over 1,2 and 3 space dimensions.

[1] www.staff.uni-oldenburg.de/hannes.uecker/pde2path/index.html

**Learning from fluctuations: The mechanics of active and passive cellular assemblies**Prof. Dr. Timo Betz , Institut für Zellbiologie, WWU Münster

Einladender: Dr. O. Kamps

From a physics perspective living cells are impressive systems. They operate extremely reliably under nonlinear and non-equilibrium conditions, all embedded in a highly fluctuating background that is agitated by thermal Brownian motion. To understand the physical principles used by cells to perform their function, we use optical tweezers as well as high sensitive motion detectors to study both the mechanical properties of cells and the passive (thermal) and active (ATP dependent) fluctuations of cellular systems. This leads to new insights into the non-equilibrium physics used by living cells to maintain their organization even in a highly noisy environment. Combining the experimental data with non-equilibrium

Langevin models we are able to extract molecular parameters such as forces and timescales from mesoscopic observables.

**Reward-based Learning and Decision Making**Prof. Dr. Klaus Obermayer, TU Berlin - Institute of Software Engineering and Theoretical Computer Science - Neural Information Processing

Einladender: PD Dr. C. Wolters

Reinforcement learning provides a framework for making agents learn policies by feedback (reward) about whether their actions or action sequences were successful or not. Reinforcement learning also provides a framework for understanding, how humans learn and decide given reward information only. Standard reinforcement learning assumes that good decisions / actions / policies are the ones which maximize expected reward as a proxy of success. Humans and animals, on the other hand, often do not behave this way, and there is ample evidence for multiple reward-based learning systems as well as for multiple factors influencing learning and decision making.In my talk I will first address the interaction between stimulus-response and response-outcome learning in two tasks, where subjects are presented with both visual stimuli and rewards.

One task involves implicit (shifts of covert visual attention) the other task explicit (button presses) decisions and actions.

Using a model-based analysis I will show, how "bottom-up" stimulus and "top-down" reward information interact, and I will discuss the signatures of these interactions in neural signals measured with EEG and fMRI.Second I will address the interaction between risk and reward. I will present a new mathematical framework for including risk into reinforcement learning on Markov decision processes, and I will

derive a risk-sensitive variant of the (model free) Q-learning scheme. The new framework is then applied to quantify the risk-sensitivity of human subjects playing a stock-market investment game. We find that the risk-sensitive variant provides a significantly better fit to the behavioral data and leads to an interpretation of the subject’s responses that is consistent with prospect theory. The analysis of simultaneously measured fMRI signals shows a significant correlation of the risk-sensitive

valuation with neural activity in the striatum, cingulate cortex, and insula that is not present if standard Q-values are used.**CeNoS Doktorandenkolloquium****Theoretical analysis of structure formation on pre-patterned surfaces**

O. Buller, AG HeuerThe Rayleigh-Plateau-like instability of ridges formed by molecules on pre-patterned substrates is studied by means of kinetic Monte Carlo (KMC) simulations and a thin film continuum model.

We show systematically the qualitative agreement of the occurring instability in both models.

In particular, we demonstrate that in the KMC model the transversal instability of ridges occurs on well defined scales which are significantly larger than the intrinsic scales of thermodynamical fluctuations. In the thin film model, the transversal instability for a single ridge and two weakly interacting ridges is investigated through a transversal linear stability analysis. We show the dispersion relations for transversal modulations and investigate their dependency on the system parameters.

In regimes accessible to direct simulations, similar results are obtained for the KMC model.

**Sliding Drops - Dynamics of Large Ensembles**

M. Wilczek, AG ThieleWe analyze the dynamics of a thin liquid film on a substrate using the thin film equation for partially wetting liquids. When including a lateral driving force due to, e.g., an inclined substrate and gravity, structures described by the equation, like drops and ridges, begin to move.

In addition, also stability properties of the structures can change. In particular, large drops may undergo a pearling instability, where they emit small satellite droplets until their volume is small enough to be stable.

We conduct direct numerical simulations on a large spatial domain in order to examine the interaction of many sliding drops. As the sliding velocity of the drops depends on their volume, larger drops overtake smaller drops and merge with them, possibly leading to an overall volume which is large enough for the pearling instability to occur. Studying a large ensemble, we find that this merging and pearling behaviour can lead to a stationary distribution of drop sizes, whose shape depends on the inclination angle of the substrate and the overall volume of liquid in the system.

We explain the long-term evolution of the drop size distribution using stability properties of single drops obtained when studying families of droplet solutions with continuation techniques.

Einladender: O. Kamps**Winter Term 2015/2016**

**Multi-physics of nonlinear metamaterials**Dr. Mikhail Lapine, University of Technology, Sydney

Einladender: Dr. J. Imbrock

The extravagant field of metamaterials has been bubbling with bright ideas and promising designs for more than a decade of its dramatic progress. I will present a brief conceptual overview of the origins and development of nonlinear metamaterials, addressing the basics of theoretical approaches, key ideas on implementation, and certain interesting phenomena. Particular emphasis will be given to the most recent development, including the use of new degrees of freedom in metamaterial design, and the arising multi-physics of their response. Most recent examples include various aspects of electromagneto—mechanical nonlinearities, artificial electrostriction, nonlinear 'traffic lights' and phase matching with hyperbolic metamaterials.**Unfitted finite element methods using bulk meshes for surface partial differential equations**Dr. Thomas Ranner, University of Leeds

Einladender: Prof. Dr. C. Engwer

I introduce a family of novel finite element methods for partial differential equations on surfaces. The key idea is that the finite element space is based on continuous piecewise linear finite element functions on a bulk triangulation which is independent of the surface. I will present robust numerical analysis for a simple model elliptic problem and provide computational examples to show the flexibility and efficiency of the methods to the evolving and coupled bulk-surface cases.**Unbalanced Optimal Transport: Dynamic and Static Perspective**

Dr. Bernhard Schmitzer, CEREMADE, Université Paris-Dauphine

Einladender: Prof. Dr. B. WirthToday Optimal transport is a popular modelling tool in image analysis and other fields of applied mathematics. Its original formulation dates back to Monge. There is a `static' linear programming formulation due to Kantorovich and more recently a `time-dynamic' perspective has been introduced by Benamou & Brenier. While the former is usually the foundation for efficient algorithms the latter is a popular basis for constructing more general models that also allow for creation and annihilation of mass.

We introduce a class of generalizations of the original dynamic problem and prove equivalence with a corresponding generalized class of static problems. This could allow for combining the advantages of efficient algorithms with more general models. A particular candidate in this framework will be discussed: the interpolation between the Fisher-Rao and the Optimal Transport metric, which we believe to be well-suited for the modelling of natural growth processes.

Based on joint work with Lenaic Chizat, Gabriel Peyré and François-Xavier Vialard

Blockvorlesung:

**Dealing with noise in the physical sciences**

Prof. Manuel Morillo, Universität SevillaIn most of the problems of interest involving complex systems (physico-chemical, biological, financial, sociological, etc.) the fluctuations of the quantities characterizing those systems are essential. Thus, a probabilistic description of their dynamics is needed.

In this course, we will discuss first how noise arises even in a simple Hamiltonian system when one concentrates on a subset of relevant variables, rather than on the full phase space. Dealing with noise requires the use of probabilistic ideas. We will introduce the concept of stochastic process in general and Markov processes in particular. We present three descriptions of Markov processes: the Master equation, the Langevin equation and the Fokker-Planck equation. After discussing the theoretical ideas behind those descriptions we apply them to some simple cases amenable to analytical solutions. Unfortunately, most of the interesting realistic problems can not be tackled with pure analytical tools. Numerical simulation methods become essential to deal with realistic problems. We discuss some of the numerical simulation procedures.**Vortragsreihe: Ehemalige im Beruf**

Wie konnte das passieren? Physik und UnfallrekonstruktionDr. Ingo Holtkötter, Schimmelpfennig + Becke GbR, Ingenieurbüro für Unfallrekonstruktion, Münster

Einladender: Dr. O. Kamps

Unfälle im Straßenverkehr sind an der Tagesordnung, obwohl es für die meisten Beteiligten ein einzigartiges Erlebnis in ihrem Leben ist. Eine objektive Beurteilung des Unfallgeschehens aus der Erinnerung heraus ist nur schwer möglich, da der kurze Zeitraum von oftmals zwei bis drei Sekunden, in denen sich ein Unfall entwickelt, mit ungewöhnlichen Eindrücken überladen ist.Für den Unfallanalytiker hingegen stellt dieser kurze Zeitraum den Kern seiner Arbeit dar. Im Fachgebiet der Unfallrekonstruktion geht es darum, den Unfallhergang in seinen wesentlichen Details zu rekonstruieren und für den Nichttechniker in nachvollziehbarer Weise darzustellen.

Hierzu werden sowohl die Spurendokumentation an der Unfallstelle und die technische Untersuchung der Unfallfahrzeuge als auch Crashversuche und Computersimulationen erangezogen, um objektive und gerichtsfeste Gutachten zu erstellen, die die Basis für Regulierungsentscheidungen und Gerichtsurteile bilden.

Der Vortrag bietet eine Übersicht über die Methoden der Unfallrekonstruktion, stellt das Berufsbild des Unfallanalytikers als Schnittstelle zwischen Polizei, Versicherungen, Beteiligten und Gerichten vor und zeigt auf, wie trotz Computersimulationen auch heute noch in Münster täglich Crashversuche durchgeführt werden, unfallanalytische Gutachten auf eine solide Basis zu stellen. Dabei werden nicht nur Straßenverkehrsunfälle, sondern auch Spiel-/Sport- und Arbeitsunfälle behandelt, die häufig sehr spezielle Untersuchungen und Versuche erfordern.

Dr. rer. nat. Ingo Holtkötter ist öffentlich bestellter und vereidigter Sachverständiger für Straßenverkehrsunfälle sowie Sachverständiger für Unfälle mit mechanisch-technischem Gerät im Ingenieurbüro Schimmelpfennig und Becke (Münster). Nach dem Physikstudium und der Promotion am physikalischen Institut in Münster ist er dem Themengebiet Kollisionsmechanik treu geblieben. Nur, dass nichtmehr spinpolarisierte Elektronen auf Moleküle geschossen und mit Quantenmechanik beschrieben werden, sondern Fahrzeuge gecrasht werden und klassische Mechanik zum Einsatz kommt …

**Optimal Control Theory and Dengue Fever**

Prof. Olga Vasilieva

Einladender: Prof. Dr. A. Telschow

Dengue is a viral disease principally transmitted by Aedes aegypti mosquitoes. There is no vaccine to protect against dengue; therefore, dengue morbidity can only be reduced by appropriate vector control measures, such as:- suppression of the mosquito population,

- reduction of the disease transmissibility.This presentation will be focused on implementation of these external control actions using the frameworks of mathematical modeling and control theory approach. In the first part, I will resent and endemo-epidemic model derived from registered dengue case in Cali, Colombia and then propose a set of optimal strategies for dengue prevention and control. In the second part, I will present an alternative and unconventional vector control technique based on the use of biological control agent (Wolbachia) and formulate a decision-making model for Wolbachia ransinfection in wild Aedes aegypti populations.

**Neuro-Inspired Information Processing Using Nonlinear Systems with Delayed Feedback**

Ingo Fischer, IFISC Palma de Mallorca, Spain

Einladende: Prof.Dr. C. Denz

The increasing demands on information processing require novel computational concepts. This challenge induced reawakened interest also in the role of optics and other alternative hardware in supercomputing. Particularly novel neuro-inspired concepts are being considered and developed. We present a simple architecture based on a nonlinear system with delayed feedback and demonstrate that it can tackle computationally hard tasks efficiently. Via time-multiplexing, we emulate a complex nonlinear network using only a single or few nonlinear nodes. Our approach employs the learning-based method of Reservoir Computing. Among the successfully addressed tasks are spoken digit recognition, nonlinear prediction [1] and matrix multiplication problems [2].

Based on our minimal design approach [3,4], we demonstrate a semiconductor laser based implementation achieving unprecedented information processing rates, injecting the information all-optically at rates up to several GSamples/s, and high energy-efficiency. We will discuss the requirements and conditions that allow nonlinear systems with delayed feedback to process information efficiently and future perspectives of our approach.References:

[1] Brunner, D., Soriano, M. C., Mirasso, C. R., & Fischer, I. , Parallel photonic information processing at gigabyte per second data rates using transient states. Nature Communications, 4, 1364 (2013).

[2] Brunner, D., Soriano, M. C., & Fischer, I. , High-Speed Optical Vector and Matrix Operations Using a Semiconductor Laser. IEEE Photonics Technology Letters, 25(17), 1680–1683 (2013).

[3] Appeltant, L., Soriano, M. C., Van der Sande, G., Danckaert, J., Massar, S., Dambre, J., … Fischer, I. , Information processing using a single dynamical node as complex system. Nature Communications, 2, 468 (2011).

[4] Soriano, M.C., Brunner, D., Escalona-Moran, M., Mirasso, C.R. and Fischer, I., Minimal approach to neuro-inspired information processing. Front. Comput. Neurosci. 9:68. doi: 10.3389/fncom.2015.00068 (2015).

**Artificial microswimmers**

Dr. Raphael Wittkowski

Einladender: Prof.Dr. U. Thiele

Many microorganisms including different species of archaea, bacteria and protozoa are motile and can swim autonomously through a surrounding liquid. Inspired by these natural microswimmers, several realizations of artificial microswimmers have been developed during the last decade. This talk is an introduction to this topic and will discuss the self-propulsion mechanisms of different types of artificial microswimmers. The talk will also address their properties, their relevance for different scientific fields and possible future applications.**Modelling and simulation of free boundary problems as gradient systems**

Dr. Dirk Peschka, WIAS Berlin

Einladender: Prof. Dr. U. Thiele

This talk addresses modelling of thin-film flows for viscous liquids. I will introduce a gradient structure for a corresponding free boundary problem and develop an algorithm to solve it. The proper treatment of the underlying contact line problem will be highlighted as the main mathematical challenge. Finally I will compare numerical solutions with experiments and discuss limitations and perspectives.**Data assimilation for a stochastic urban crime model and equation-free continuation**Dr. David Lloyd, University of Surrey, Department of Mathematics

Einladender: Prof.Dr. U. Thiele

In this talk we introduce several of the novel mathematical challenges one has to face when trying to analyse, model, incorporate and forecast crime data. In order to elucidate the issues involved, we concentrate on burglary crime and the LA model that has links with the PREDPOL model used by the LA Police Department. Using a combination of stochastic modelling, dynamical systems analysis, stochastic bifurcation analysis/equation-free techniques and novel filtering methods, we show how one can in principle carry out data assimilation for this set-up. In doing, so we start to raise more fundamental sociological and societal issues that requires a Steering Complex Adaptive Systems Methodology. This is work done with Naratip Santitissadeekorn (Surrey) and Martin B. Short (Georgia Tech.)**Growth and Patterns**

Prof. Dr. Arnd Scheel, University of Minnesota, School of Mathematics

Einladende: Prof. A. Stevens

It's been long known that growth can act as a selection mechanism for spatio-temporal, self-oprganized patterns, determining for instance crystallographic types of patterns, "strain" in periodic structures, and distribution of defects in patterns. After showing several motivating examples from biology and engineering, I'll give a subjective and selective overview of work that strives to describe these effects qualitatively and quantitatively, in a universal, model-independent fashion.**Speeding up "slow" liquid crystals**Dr. Andrey Iljin, Institute of Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine

Einladende: Prof. Denz

Liquid crystals (LC) acquired their popularity due to large birefringence and easy response to applied electric or light field. The LC director reorientation results in substantial changes of the effective refractive index of the LC medium providing efficient control of the optical performance of the LC cell, with one of its lonely drawbacks being a rather slow relaxation.

Apart from quite comprehensive and ingenious tricks aimed to bring the response times of orientational processes down, an alternative approach has been gaining particular attention recently. Influencing the order parameter of LC one can realise switching with the characteristic times being several orders of magnitude shorter than that of the LC director reorientation with good prospects in nonlinear photonics.**Nonlinear dynamics of systems with time-varying delay and its relevance for modern machining processes**

Prof. Günter Radons, TU Chemnitz

Einladender: Dr. O. Kamps

Delay differential equations provide well-known models for many processes in nature and technology. While models with constant delay are a reasonable and much investigated starting point for many applications, it is also clear that in reality delays fluctuate naturally and often can be influenced to vary systematically. Despite its high, practical relevance, the consequences of such time-varying delays is still poorly understood. I first introduce into the general topic of delay systems and subsequently elaborate the relevant developments in machining applications, such as turning and milling. Finally I report on our own recent results, which reach from applications in machining to fundamental aspects of systems with time-varying delay.**Coupled Bulk-surface reaction-diffusion systems and pattern formation**

Prof. Dr. Matthias Röger, Technische Universität Dortmund, Fakultät für Mathematik

Einladender: Prof. Dr. B. Wirth

In living cells many spatially coupled reaction and diffusion processes contribute to the function of a cell. Activation or deactivation processes are partly localized at the outer membrane whereas diffusion and transport through the cytosol are important to process and amplify signals. We introduce different mathematical models that express the coupling of bulk (cytosol) and surface (membrane) processes and in particular discuss mechanism for symmetry breaking and spatial patterning.**Summer Term 2015**

**Vortragsreihe: Ehemalige im Beruf****Simulierte Motoren mit Hilfe Neuronaler Netze: Echzeitfähige Motormodelle am HiL-Prüfständen**Michael Grevenstette, Bertrandt AG Ehningen

Einladender: O. Kamps

Die Elektrifizierung des Automobils hat in den vergangenen Jahrzehnten deutlich zugenommen. 60 und mehr elektronische Steuergeräte (Electronic Control Units - ECUs) für die einzelnen Komponenten (Motor, Getriebe, ABS, ESP, usw.) sind in modernen Autos keine Seltenheit. Die funktionale Entwicklung und Absicherung dieser Steuergeräte geschieht nicht mehr nur im realen Fahrzeug, sondern immer öfter auch an HiL (Hardware-in-the-Loop)-Simulatoren. Auf diesen läuft dann ein möglichst genaues Simulations-Modell des Gesamtfahrzeugs bzw. der zu testenden Komponente, welches die Steuersignale der ECU auswertet und dann dem Steuergerät in Echtzeit die entsprechenden Sensorsignale zur Verfügung stellt, analog zur realen Komponente.Am Beispiel eines Motor-HiLs möchte ich einmal die Grundzüge einer Motor-Simulation mit Hilfe eines echtzeitfähigen, neuronalen Prozessmodells vorstellen und des Weiteren aufzeigen, welche Möglichkeiten diese Simulation bietet und wo die Grenzen zur genauen physikalischen Abbildung liegen.

**Nonlinear dynamics of Vertical-Cavity Surface-Emitting Lasers: deterministic chaos and random number generation**Prof. Dr. Krassimir Panajotov, B-Phot Brussels Photonics Team

Einladende: S. Gurevich

We discuss recently discovered deterministic chaos in Vertical-Cavity Surface-Emitting Lasers (VCSELs). Our quantum dot (QD)-VCSEL emits linearly polarized light at threshold and undergoes a pitchfork bifurcation when increasing injection current that creates two symmetrical elliptically polarized solutions. Then, a sequence of bifurcations brings it to two single-scroll chaotic attractors. Finally, the two chaotic attractors merge into a double-scroll "butterfly" chaotic attractor. Experimentally, this "butterfly" attractor is observed as a mode hopping between two elliptically polarized modes. The dwell time exponentially decreases with injection current which is opposite to noise-induced polarization mode hopping in quantum well VCSELs. We report on bistability between two limit cycles, which originate from a bifurcation on the two elliptically polarized states. Asymmetry in the system, namely a misalignment between the VCSEL phase anisotropy and dichroizm explains well all experimental features. Finally, we demonstrate the physical generation of random bits at high bit rates (> 100 Gb/s) using the optical chaos from the solitary QD VCSEL.**Dynamics of localized structures in cavity nonlinear optics subject to injection and delayed feedback**Dr. Mustapha Tlidi, Université Libre de Bruxelles

Einladende: S. GurevichLocalized structures in dissipative media have been observed in various field of nonlinear science such as fluid dynamics, optics, laser physics, chemistry, and plant ecology. Localized structures consist of isolated or randomly distributed spots surrounded by regions in the uniform state They may consist of peaks or dips embedded in the homogeneous background. They are often called spatial solitons, dissipative solitons, localized patterns, cavity solitons, or auto-solitons depending on the physical contexts in which their were observed.

We investigate a control of the motion of localized structures of light by means of delay feedback in the transverse section of a broad area nonlinear optical systems. The delayed feedback is found to induce a spontaneous motion of a solitary localized structure that is stationary and stable in the absence of feedback. In the absence of the delay feedback we present an experimental evidence of stationary localized structures in a 80 μm aperture vertical cavity surface emitting laser. The spontaneous formation of localized structures takes place above the lasing threshold and under optical injection. Then, we consider the effect of the time delayed optical feedback and investigate analytically the role of the phase of the feedback and the carrier lifetime on the motion of the localized structures. We show that these two parameters affect strongly the space time dynamics of two- dimensional localized structures.**Mathematical modeling of tumor-driven angiogenesis. An hybrid approach: deterministic mean fields driving a stochastic system**Prof. Dr. Vincenzo Capasso, University of Milano

Einladender: M. BurgerIn the mathematical modeling of tumor-driven angiogenesis, the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the family of interacting underlying fields is a major source of complexity from both the analytical and computational point of view.

Our main goal is thus to address the mathematical problem of reduction of the complexity of such systems by taking advantage of its intrinsic multiscale structure; the (stochastic) dynamics of cells will be described at their natural scale (the microscale), while the (deterministic) dynamics of the underlying fields will be described at a larger scale (the macroscale).**Nanowires in fibers: a novel base for nonlinear optics and nanophotonics**Prof. Dr. Markus A. Schmidt, Leibniz Institute of Photonic Technology, Fiber Sensors Research Group, Jena and Max Planck Institute for the Science of Light, Erlangen

Einladende: C. DenzHybrid optical fibers are microstructured optical fibers which include axially invariant nanostructures in the form of nanowires. Such nanowires can modify the properties of the fibers in a unprecedented way leading to novel devices with applications in various fields of science and technology. In this talk I will report on our latest results in fiber-based plasmonics (e.g., plasmonic hybridization in arrays of gold nanowires or the development of monolithic near field nanoprobes) and in nonlinear optics using hybrid chalcogenide-silica waveguides (e.g., coherent mid-IR supercontinuum generation).

**Application of delay differential equations to the analysis of nonlinear dynamics in mode-locked lasers**A.G. Vladimirov, Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin

Einladende: S. GurevichAn approach to the modeling of nonlinear dynamics in multimode semiconductor lasers using delay differential equations (DDEs) is discussed. We consider DDE models of different multimode laser devices: passively mode-locked semiconductor lasers generating short optical pulses with high repetition rates, frequency swept lasers used in optical coherence tomography, and multi-stripe laser arrays with off-axis optical coherent feedback. We present the results of numerical simulations of different dynamical states in these lasers and discuss asymptotic approaches to the stability analysis of stationary and periodic operation regimes. In particular, using a DDE model of a multimode ring laser we provide a theoretical interpretation of the dynamical behavior observed experimentally in long- and short-cavity frequency swept lasers operating in the Fourier domain and sliding frequency mode-locked regimes, respectively.

**Data-driven model reduction in the Loewner framework**Athanasios Antoulas, Rice Univ. & Jacobs Univ. Bremen

Einladender: M. OhlbergerInterpolatory model reduction methods have matured quickly in the last decade and have been adopted by an ever-growing number of researchers. They have emerged as one of the leading choices for truly large scale problems. These methods have their roots in numerical analysis and linear algebra and are related to rational interpolation and Pade approximation. In the case of linear dynamical systems, the main idea behind these methods is to generate a reduced-model whose transfer function interpolates that of the original system at select interpolation points. Recently, major advances showed how to apply interpolation methods to nonlinear systems. The resulting approach turns out to global,

in other words no small inputs are required.In this talk we will give an overview of recent advances in model reduction of linear and nonlinear dynamical systems by means of interpolatory methods and in particular the Loewner framework. Several examples illustrating the theory will also be presented.

A few references

A.C. Antoulas, S. Lefteriu, and C.A. Ionita,

A tutorial introduction to the Loewner Framework for Model Reduction

In 'Model Reduction and Approximation for Complex Systems', Edited by P. Benner, A. Cohen, M. Ohlberger, and K. Willcox, Birkhauser, ISNM Series (2015).S. Gugercin, C.A. Beattie and A.C. Antoulas,

Data-driven and interpolatory model reduction

Book in preparation, SIAM (2015).**Nematic elastomers: a biomimetic material**Len Pismen, Israel Institute of Technology, Haifa

Einladender: U. ThieleNematic elastomers, made of cross-linked polymeric chains with embedded mesogenic structures, combine orientational properties of liquid crystals with solid elasticity. Their specific feature is a strong coupling between the director orientation, that can be affected by chemical reactions and light, and mechanical deformations. This property enables their usage in actuators and self-propelling devices. The feedback interactions between nematic order, elastic stress, and composition lead to a variety of patterns in nemato-elastic films and their spontaneous bending into three-dimensional forms, which are strongly affected by topological defects of nematic order.

**Active phase field crystals on substrates and at interfaces**Dr. Andreas Menzel, Institut für Theoretische Physik II - Soft Matter , Heinrich-Heine-Universität Düsseldorf

Einladender: U. ThieleThe phase field crystal model was developed to effectively describe diffusive processes in periodic structures on the length scale of the individual constituents. It can be viewed as an approximation of dynamic density functional theory. We developed an active phase field crystal model to characterize the behavior of periodic active structures composed of self-propelled or self-driven particles. Interestingly, even in the absence of an explicit mechanism that would organize the self-propulsion directions of the individual particles, the periodic structures are found to start to move collectively along a global direction. Apart from that, our recent investigations on ensembles of self-propelled microswimmers within the framework of dynamic density functional theory will be addressed.

**Mid-IR-driven Electron Recollision: Molecular Diffraction Imaging and Attosecond soft-X-rays**Prof. Dr. Jens Biegert, ICFO - The Institute of Photonics Sciences, Mediterranean Technology Park, Barcelona

Einladender: H. ZachariasElectron recollision in an intense laser field is at the centre of attoscience research and gives rise to a variety of phenomena, ranging from electron diffraction to coherent soft X-ray emission. We have, over the years, developed intense sources of waveform controlled mid-IR light, i.e. few-cycle duration and carrier to envelope phase stable pulses, to exploit ponderomotive scaling, quantum diffusion and quasi-static photo emission. I will briefly highlight the laser technology that enables this new direction of strong field research and our recent achievements in sub-Angstrom resolution imaging of an entire polyatomic molecule, the generation of isolated attosecond pulses at the carbon K-shell edge (284 eV) and application to soft X-ray absorption spectroscopy in condensed matter.

**Interfacial phenomena in thin liquid films: mathematical modeling and scientific computation**Prof. Dr. Te-Sheng Lin, Department of Applied Mathematics,National Chiao Tung University

Hsinchu, Taiwan

Einladender: U. ThieleThe mechanics of thin liquid films can be modeled by a fourth-order nonlinear partial differential equation, the so-called thin film equation, which describes the evolution of the film thickness. In the first part of the talk we will discuss two approaches in the model derivation: one is the long-wave model derived through asymptotic expansion of the full governing equations and the other one is the gradient dynamics formulation based on an underlying free energy functional. As an example we discuss the model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We show that the two derivations should agree with each other.

In the second part of the talk we will discuss several computational methods in investigating the models. One is the alternating-direction-implicit type finite difference solver to look for the time dependent solution for a given intial condition. The other one is to take advantages of the numerical continuation method to look for the stable or unstable steady state solutions and the time-periodic solutions. As a result one is able to construct the full bifurcation diagram of the solutions. We show the behavior of partially wetting liquids on a rotating cylinder as an example.**Winter Term 2014/2015**

**Colloid crystallisation in a phase field crystal model - localised states and front motion**Prof. Dr. U. Thiele, Institut für Theoretische Physik

Im Rahmen des Kolloquiums der Materialphysik in Raum MP 619 in der IG 1We discuss the modelling of aspects of colloidal crystallisation with two types of continuum models, namely, dynamical density functional theory (DDFT) and its local approximation, the phase field crystal (PFC) model [aka conserved Swift-Hohenberg (cSH) equation].

After introducing the field and the overall modelling approach, we first consider the structure of localised solutions of the PFC model that provides the simplest microscopic continuum description of the thermodynamic transition from a fluid state to a crystalline state and is frequently used to model colloidal crystallisation [1]. In particular, we analyse steady states and their bifurcations thereby focussing on the variety of spatially localized structures, that is found in addition to periodic structures [2]. The location of these structures in the temperature versus concentration plane is determined using a combination of numerical continuation in one dimension and direct numerical simulation in two and three dimensions. Localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases, and may lie outside of the binodal for these states. The relation of the existence of localised states and an amorphous solid phase is discussed.

Second, we analyse crystallisation fronts as described by the PFC model [3] and as well a full DDFT for soft particles [4]. We show that in the case of the PFC equation in 1d front speeds may be obtained via a marginal stability criterion [3]. The full 2d picture within the DDFT is more involved as there one needs to distinguish between linearly driven pulled fronts and nonlinearly driven pushed fronts as shown for the DDFT [4]. The relation of quench depth, front speed, created disorder and subsequent aging is discussed.

In the final part an outlook is given towards similar studies for binary colloidal mixtures that show stronger aging effects [4,5].

[1] H. Emmerich, H. Lowen, R. Wittkowski, T. Gruhn, G. Toth, G. Tegze, and L. Granasy, Adv. Phys. 61, 665 (2012).

[2] U. Thiele, A. J. Archer, M. J. Robbins, H. Gomez, and E. Knobloch, Phys. Rev. E. 87, 042915 (2013).

[3] A. J. Archer, M. J. Robbins, U. Thiele, and E. Knobloch, Phys. Rev. E 86, 031603 (2012).

[4] A.J. Archer, M.C. Walters, U. Thiele, and E. Knobloch, Phys. Rev. E , at press (2014).

[5] M. J. Robbins, A. J. Archer, U. Thiele, and E. Knobloch, Phys. Rev. E 85, 061408 (2012).**Instabilities and singularities in problems involving phase change**Dr. Pierre Colinet, University Libre de Bruxelles

Einladender: U. ThielePhase change phenomena such as evaporation or solidification can lead to several types of instabilities, and may even trigger (or prevent) the formation of apparent singularities. In this talk, three topics will be considered: i) the surface-tension-driven instability of a thin liquid film evaporating into ambient atmosphere, for which the resulting polygonal pattern dynamics is examined both experimentally and theoretically; ii) the relaxation of viscous and thermal contact line singularities by evaporation/condensation processes, and the origin of evaporation-induced contact angles; iii) the formation of a cusp-like singularity at the final stage of the freezing of a water drop on a cold substrate, for which experiments and theory allow highlighting a universal behavior as far as the selection of the final cusp (cone) angle is concerned.

**Coarse-grained simulation of nanoparticle-protein interactions**

Dr. Hender Lopez . School of Physics, University College Dublin

Einladender: U. ThieleGemeinsames Kolloquium mit dem CMTC

When nanoparticles (NP) enter a living organism, they are first exposed to biological fluids, which leads to formation of a protein layer (protein corona) around the NP. It has been proposed that the composition and dynamics of the NP-protein corona determines its biological reactivity and toxicity [1]. Understanding the molecular mechanisms that lead to formation of the NP-protein corona is of capital importance and will certainly help to design NPs with specific functions for nanomedicine and to predict the toxicity of engineered nanoscale materials.In the first part of the seminar we will review our recent work on a general Coarse-Grained (CG) model developed to calculate the adsorption energies of proteins onto hydrophobic NPs of arbitrary size. In this presentation, we give a detailed description of our model and numerical results on adsorption of six most abundant human blood plasma proteins on NPs of different radii and charge. Our results allow us to quantify the influence of NP surface curvature and charge on the adsorption energies. Our results for the adsorption energies and preferred globule orientations agree with previous full atomistic simulations [2]. We also present qualitative predictions for the composition of the NP-protein corona that agreed with experimental results [3].

In the second part of the talk we will present a CG model to describe the kinetics of adsorption of blood plasma proteins onto NPs. In contrast to previous works [4], our model includes the effect of hydrodynamics interactions on the formation of the NP-protein corona.

[1] Monopoli et al., Nature Nanotechnology 7 779 (2012)

[2] Brancolini et al., ACS Nano 6 9863 (2012). Ding et al., Nanoscale, 5 9162 (2013). Khan et al., J. Phys. Chem. Lett. 4 3747 (2013).

[3] De Paoli et al., ACS Nano 4 365 (2010).

[4] Vilaseca et al., Soft Matter 9 6978 (2013).**Data-driven inference of epileptic brain networks**Prof. Dr. Klaus Lehnertz, Neurophysics Group, Dept. of Epileptology, Medical Center University of Bonn

Einladender: O. KampsComplex networks are powerful representations of spatially extended systems and can advance our understanding of their dynamics. A large number of analysis techniques is now available that aim at inferring the underlying network from multivariate recordings of system observables. Despite great successes in various scientific fields, there still exist a number of problems, both conceptual and methodological, for which there are currently no satisfactory solutions. At the example of large-scale epileptic brain networks, I will present how the network approach can advance our understanding of the complex disease epilepsy and will discuss current shortcomings as well as possible research directions that may help to find better solutions.

**From Markov State models to transition based equilibrium estimators: a systematic approach to analyse molecular dynamics simulations**Dr. Antonia Mey, Freie Universität Berlin, Computational Molecular Biology Group

Einladender: A. HeuerExtracting quantitative equilibrium and dynamic estimates from molecular simulations, in particular with the interest of comparing these to experimental observables, is the aim of most simulators. However, this is often not a trivial task due to the complexity of the system and the timescales at which interesting processes occur. Markov state models (MSM) are a tool that allow to address these goals, by giving not only quantitative results for the equilibrium population of a molecular system, but can also be used to determine the dominant (slowest) processes (e.g. internal rearrangement of side chains of a protein) occurring in the system of interest. MSMs can even resolve timescales that are much longer than the individual trajectories used for the analysis, therefore trying to close the timescale gap which often plagues molecular simulations.

First, I will give a non-expert introduction to Markov state models and show how these can be readily constructed. As an illustrative example, I will show recent work of using MSMs to compare the influence of the choice of empirical molecular forcefield on the underlying dynamics of a few model peptides and highlight their differences.

Secondly, I will show how ideas from MSMs can be used to vastly improve stationary population estimates from multi-ensemble simulations (such as umbrella sampling or parallel tempering) by introducing a novel class of equilibrium estimators; the transition based analysis method (TRAM) estimators. TRAM estimators are asymptotically correct and reduce to estimation methods such as the weighted histogram analysis method (WHAM) and the multistate Bennet acceptance ratio method (MBAR) as special cases.

I will demonstrate how TRAM can outperform the state-of-the-art MBAR estimator by up to an order of magnitude, with respect to the total data used for analysis, on a selection of example systems of varying complexity.References:

1. Speed of forcefields, J. Chem. Phys., under review

2. arXiv:1407.0138v1 Accepted for publication Phys. Rev. X**An Interfacial growth model for actin filament networks with a mechano-chemical coupling**Dr. Karin John, UJF Grenoble

Einladender: U. Thiele (zusammen mit dem TRR61 Münster-Beijing)Many processes in eukaryotic cells, including cell motility, rely on the growth of branched actin filament networks from surfaces. Despite its central role, the mechano-chemical coupling mechanisms which guide the growth process in the presence of mechanical pre-stresses are poorly understood, and a general continuum description combining growth and mechanics is lacking.

We develop a theory based on discrete homogenization techniques, that bridges the gap between mesoscale and continuum limit and propose a general framework, that provides the evolution law of actin networks growing under stress. This formulation opens an area for the systematic study of actin dynamics in arbitrary geometries. Our framework predicts a morphological instability of actin growth on a rigid sphere, leading to a spontaneous polarization of the network with a mode selection corresponding to a comet, as reported experimentally. We show that the mechanics of the contact between the network and the surface plays a crucial role, in that it determines directly the existence of the instability. We extract scaling laws relating growth dynamics and network properties offering basic perspectives for new experiments on growing actin networks.

**Optimal Control of Static Elastoplasticity with Hardening**Prof. Dr. Christian Meyer, Technische Universität Dortmund

Einladender: B. WirthWe consider an optimal control problem governed by a variational inequality (VI) of the first kind, which arises from a time discretization of a quasi-static model of elastoplastic deformation processes. The model is restricted to small strains and includes hardening of the material in form of linear kinematic hardening with the von Mises yield condition. After a short discussion of the VI and its reformulation in terms of a complementarity system, we focus on the derivation of necessary and sufficient optimality conditions. A severe issue in this context is the lack of regularity of the solution mapping associated with the VI, which is in general not Gateaux-differentiable. We present two different ways to circumvent this issue, a regularization approach and another technique which employs the directional derivative of the solution operator. While the latter one also allows to derive second-order sufficient optimality conditions, the regularization approach leads to an efficient optimization algorithm which allows to solve the problem numerically. The talk ends with the presentation of some numerical results.

**Localised structures in nonlocal neural field models**Daniele Avitabile, School of Mathematical Sciences, University of Nottingham

Einladender: U. ThieleI will discuss the formation of stationary localised solutions in 1D and 2D integral neural field models. First, a 1D inhomogeneous synaptic kernel with Heaviside firing rate will be considered. In this case, interface methods allow for the explicit construction of a bifurcation equation for localised steady states, so that analytical expressions for snakes and ladders can be derived. Similarly, eigenvalue computations can be carried out analytically to determine the stability of the solution profiles. I will then discuss a 2D model with homogeneous synaptic kernel that does not admit an equivalent PDE formulation. In this (and other neural field models featuring a convolution structure) it is advantageous to combine FFT and Newton-Krylov solvers to perform numerical bifurcation analysis directly on the integral model. I will present numerical results that show how the choice of synaptic kernel affects the bifurcation structure.

**Sparse optimization of PDEs with application to light source placement in FDOT**Prof. Dr. Christian Clason, Fakultät für Mathematik Universität Duisburg-Essen

Einladender: B. WirthThe problem of optimal placement of point sources such as optodes can be formulated as a distributed optimal control problem with sparsity constraints. Although well-posedness of this non-differentiable optimization problem requires a measure space setting, a conforming discretization of the space of Radon measures allows deriving primal-dual optimality conditions that conserve the relevant structural properties of the measure space problem and are amenable to solution by semismooth Newton methods.

**Nonlinear stochastic differential equations: models, analysis and approximations**Prof. Dr. Arnulf Jentzen, ETH Zürich

Einladender: S. DereichThis talk reviews recent developments in the regularity analysis and the numerical approximation of nonlinear stochastic differential equations (SDEs) and their associated deterministic second-order linear Kolmogorov partial differential equations (PDEs). Nonlinear SDEs appear, for example, in fundamental models from financial engineering, neurobiology and quantum field theory. In particular, we outline in this talk how nonlinear SEEs are day after day used in the financial engineering industry to estimate prices of financial derivatives. The nonlinearities in the SDEs from applications often fail to be globally Lipschitz continuous. A key topic of this talk is therefore the regularity analysis and the numerical approximation of SDEs with non-globally Lipschitz continuous nonlinearities.

**Summer Term 2014**

**Liquid drops on soft solids**

Jacco H Snoeijer, Fac. of Science and Technology, University of Twente

(Einladender: Prof. Dr. U. Thiele)The wetting of a liquid on a solid usually assumes the substrate to be perfectly rigid. However, this is no longer appropriate when the substrate is very soft: capillary forces can induce substantial elastic deformations, as has been demonstrated e.g. for drops on elastomers. In this talk we discuss the fundamentals of elasto-capillary interactions. Theory, simulations and experiments reveal the surprising nature of capillary forces, which turn out to be different from anything proposed in the literature. We also discuss how the law for the contact angle (Young's law) is modified for soft substrates.

**Reduced basis methods for problems involving parametrized PDEs**

Dr. Laura Iapichino, Fachbereich Mathematik und Statistik, Universität Konstanz

(Einladender: Prof. Dr. M. Ohlberger)Often a physical model is represented by a set of partial differential equation where a set of parameters characterizes the system of interest and describes physical quantities (like source terms, boundary conditions, material properties) and/or geometrical configuration, so that the system solution is parameter dependent. The reduced order methods are innovative techniques to solve parametric partial differential equations that, compared with the classical numerical methods, require a lower computational time by maintaining a suitable level of the solution accuracy.

The presented model reduction paradigms are particularly suitable for solving problems that require considerable number of input-output evaluations in realtime for many different values of the parameters, not feasible with the classical numerical techniques.

In particular, the proposed strategies combine reduced basis (RB) method with both domain decomposition and optimal control theories. The combination of these frameworks becomes a very effective tool for real applications since we have the possibility to deal with complex geometrical configurations obtained as composition of simpler geometry deformable through suitable parametric transfinite maps and with optimal control problems related to systems modeled by parametric PDEs.

Some numerical results show the effectiveness of the proposed approaches by ensuring a certain level of solution accuracy and a very low computational time.

**Probabilistic solution methods for position target problems**

Prof. Dr. Stefan Ankirchner, Universität Jena

(Einladender: Prof. Dr. S. Dereich)We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a cost functional depending on the position and speed. The talk presents a probabilistic solution method based on a maximum principle and on backward stochastic differential equations possessing a singularity at the terminal time T. We illustrate our results in a financial application, where we derive optimal trading strategies for closing financial asset positions in markets with stochastic price impact.

The talk is based on joint work with Monique Jeanblanc and Thomas Kruse.

**Dynamical density functional theory: solidification of soft matter and why disordered solids or states with quasicrystaline order can form**Andrew Archer, Department of Mathematical Sciences, Loughborough University

(Einladender: Prof. Dr. U. Thiele)Over the last few years, a number of dynamical density functional theories (DDFT) have been developed for describing the dynamics of the one-body density of both colloidal and atomic fluids. The DDFT is capable of describing the dynamics of the fluid down to the scale of the individual particles. DDFT is particularly successful for colloidal fluids, for which one may assume that the particles have stochastic equations of motion and from the resulting Fokker-Plank equation one is able to derive the DDFT. I will give an overview of the DDFT and show applications to the description of solidification fronts in supercooled (colloidal) suspensions. As the solidification front advances into the unstable liquid phase, we find that the density profile behind the advancing front develops density modulations and the wavelength of these modulations is a dynamically chosen quantity. For shallow quenches, the selected wavelength is that of the crystalline phase and so well-ordered crystalline states are formed. However, when the system is deeply quenched, we find that this wavelength can be quite different from that of the crystal, so the solidification front naturally generates disorder in the system. Significant rearrangement and ageing must subsequently occur for the system to form the regular well-ordered crystal that corresponds to the free energy minimum. We illustrate these findings with simulation results from DDFT and also a more simplified so called "phase-field crystal" model. Results for a system with quasicrystaline ordering are formed from such a quench will also be presented, explaining a new mechanism for how and why such structures can form.

**From wildly branched drying patterns to bifurcations of driven flows**

Uwe Thiele, Institut für Theoretische Physik, Universität MünsterA phenomenon well known in our daily life is the coffee stain effect, where a drying drop of coffee leaves behind a well defined ring and not a uniformly distributed stain. Similar effects occur for many liquid mixtures and suspensions over a range of different length scales, where they may result in a rich variety of beautiful patterns ranging from regular and irregular lines to networks and wildly branched structures.

First, examples of such structures are shown that are created by several interacting physical phenomena: the tendency of liquids to cover or uncover a solid substrate (wettability), evaporation of volatile components, and the possible decomposition of a complex liquid into its components. Then, several types of mathematical models are introduced that describe thin layers of liquids on a surface either in a discrete or continuous way. In particular, these are a kinetic Monte Carlo model, dynamical density functional theory and thin film hydrodynamics.

The final part shows that such models can not only describe the dynamics of relaxational processes (systems approaching equilibrium) but as well driven systems that are permanently out of equilibrium as, for example, the deposition of a simple or complex liquid onto a moving plate. We show that this may result in complex behaviour manifested in a very rich bifurcation structure. The general concepts behind the models are explained, their successes are illustrated with selected results, and their limitations are discussed.

**How can time-delays induce patterns?**

Serhiy Yanchuk, Institute of Mathematics ,Humboldt University of Berlin

(Einladende: Dr. S. Gurevich)Dynamical systems with time delays are common in many fields, such as optics, vehicle systems, neural networks, information processing, etc. A finite propagation velocity of the information or processing times introduce in such systems a new relevant scale, which may change the dynamics drastically. In my presentation, I would like to show how such time delays lead to spatio-temporal patterns. Firstly, I present a system with multiple hierarchically long time delays, whose dynamics "encodes" such spatio-temporal patterns as spiral defects of defect turbulence. Finally, I show a two-dimensional lattice of delay-coupled oscillators, which is capable to produce practically arbitrary periodically oscillating pattern.

**Collective motion in heterogeneous media and in confined geometries: theory and experiments.**

F. Peruani

(Einladender: Prof. Dr. U. Thiele)The rapidly expanding study of active particles has focused so far almost exclusively, theoretically as well as experimentally, on the statistical description of particle motion in idealized, homogeneous spaces. However, the great majority of natural active particle systems take place, in the wild, in heterogeneous media: from active transport inside the cell, which occurs in a space that is filled by organelles and vesicles, to bacterial motion, which takes place in highly heterogeneous environments such as the soil or complex tissues such as in the gastrointestinal tract. I will show that the presence of spatial heterogeneities brings new physics unseen in homogeneous systems at the level of the transport properties and collective dynamics of such systems. I will show first that a random distribution of “obstacles” can lead to spontaneous trapping of active particles. Such “obstacles” represent undesirable areas that the active particles avoid and may correspond to a source of a repellent chemical, a light gradient, or whatever threat sensed by the moving particles. Inside traps, active particles exhibit a vortex-like motion and remain arbitrary long times. Particle motion then becomes genuinely sub-diffusive. We also find that the presence of such obstacles has a dramatic effect on the collective dynamics of usual self-propelled particle systems in two dimension. In particular, we observe: i) the existence of an optimal (angular) noise amplitude that maximizes collective motion, and ii) quasi-long range order and the existence of two critical points (cf. with the so-called Vicsek model in homogeneous spaces where order is long-range and there is a unique critical point).

Equally true and important is the fact that most active natural systems and experiments are subject to boundary conditions. How a confined geometry affects the collective properties of such active systems remains largely unexplored. I will show that often observed effect of accumulation of particles close to walls as well as the boundary-following phenomenon can both be collective effects controlled by the alignment strength. I will provide evidence that indicates that though a density-instability occurs at all system sizes, ordering vanishes in the thermodynamical limit.

This collection of results opens a new perspective for the design and control of active particle systems. Moreover, I will show that these observations are consistent with recent experiments performed with Quincke rollers in D. Bartolo’s Lab.

References:

O. Chepizhko, E. Altmann, F. Peruani, PRL 110, 238101 (2013)

O. Chepizhko, F. Peruani, PRL 111, 160604 (2013)**Multi-scale analysis of nonlocal Fokker-Planck equations**

Prof. Dr. Michael Herrmann, Angewandte Mathematik, Universität Münster

(Einladender: Prof. Dr. M. Ohlberger)The hysteretic behaviour of certain many-particle systems (e.g., Lithium-ion batteries) can be modeled by nonlocal

Fokker-Planck equations which involve two small parameters and are driven by a dynamical constraint. In this talk we study two

small-parameter limits by asymptotic analysis and derive reduced models for the effective dynamics of the macroscopic quantities. In the fast react regime, the limit dynamics turns out to be rate-independent and phase transitions can be described by a variant of Kramers formula. In the slow reaction regime, however, the small-parameter evolution is more involved and governed by a subtle interplay of the kinetic and the parabolic terms.(joint work with Barbara Niethammer and Juan J.L. Velazquez)

**Mathematical modelling of cell motility and antibody optimisation in germinal centres**

Prof. Dr. Michael Meyer-Hermann, Helmholtz Centre for Infection Research, Braunschweig

(Einladende: Dr. O. Kamps, Prof. Dr. A. Telschow)The generation of high-affinity antibodies in germinal centres (GC) happens in the course of an in-body evolutionary process which involves high-speed division, high-frequency somatic hypermutation and affinity-dependent selection of B cells. 40 years of GC research revealed many mechanisms and factors controlling division, mutation and selection. In the last decade, intravital multi-photon imaging of secondary lymphoid tissues during affinity maturation offered the opportunity to actually see the cells in action and to validate previously developed theories like competitive collection of antigen from follicular dendritic cells or the B cell recycling hypothesis. In addition, quantitative information were added to GC research allowing for an improved level of mathematical modelling.

With the help of agent-based modelling it is shown that tanszone B cell migration data support a high fraction of recycling of selected B cells. Furthermore, the models show that affinity maturation is optimised if T cell help in GCs is affinity-dependent and limiting. Mathematical predictions of the impact of limiting T cell help were confirmed by experimental data. Finally, the agent-based models are used to reproduce recent data of asymmetric distribution of collected antigen onto the daughters of dividing B cells. The model reveals that if the presence or absence of antigen in the daughters is used as fate decision criterion for the final differentiation of B cells to plasma and memory cells, this leads not only to an improved information processing in the GC but also leads to a 10-fold increased number of generated GC output cells provided T cell help is limiting. This prediction is not yet confirmed by experiments but supported by some experimental observations.

**Modeling and simulation of Lithium intercalation and conversion batteries**

Prof. Dr. Arnulf Latz , Deutsches Zentrum für Luft- und Raumfahrt e.V. Ulm

(Einladender: Prof. Dr. A. Heuer)The electrodes of the majority of modern Li Ion batteries have very complex porous microstructures. Even if all chemical equirements for constructing a working battery as e.g. mutual chemical compatibility of electrolytes and materials, used for the electrodes, separator and the binder are fulfilled, it is not guaranteed that the final battery can reach its theoretical capacity or the required power density under operation condition. These properties are strongly influenced by the interplay of the morphological properties of the porous electrodes and the transport and reaction mechanisms of the chemical active ions. Even the extent and the type of degradation mechanisms are likely to be influenced by the morphology of the electrodes. For being able to better understand, evaluate and optimize these dependencies, proper electrochemical and physical reaction and transport models as well as efficient numerical algorithms are needed to study the resulting coupled nonlinear partial differential equations in the complex microstructure of Li ion intercalation and conversion batteries.

After giving a short general introduction on Li based intercalation and conversion batteries, a validated fully thermodynamically consistent model for transport and chemical reactions in the microstructure of the battery is presented. Simulation examples are used to demonstrate the importance of the microstructure on the distribution of ions, currents and heat sources in the microstructure of Li ion intercalation batteries. The necessary conditions for the onset of Lithium plating at low temperatures and high current densities are discussed. In the second part the challenges of developing theories for the next generation Li based conversion batteries like Li air and Li – Sulfur batteries are outlined. Results of an elementary kinetic modeling approach developed at the DLR and the HIU in a simple 1D effective porous media setting are shown for the example of Lithium sulfur batteries.

**Winter Term 2013/2014**

**On the Role of the Microenvironment in Optimal Protocols for Mathematical Models for Cancer Treatments**

Prof. Dr. Heinz Schättler, Washington University, St. Louis, USA

(Einladender: Prof. Dr. H. Maurer)**Phase transitions and hysteresis due to nonlocal and nonlinear material behavior of lithium-ion batteries**Prof. Dr. Wolfgang Dreyer, Weierstraß-Institut, Berlin

(Einladender: Prof. Dr. A. Heuer)**Fitness landscapes and the predictability of evolution**

Prof. Dr. Joachim Krug, Institut für Theoretische Physik, Universität Köln

(Einladender: Prof. Dr. S. Dereich)**Turbulent transport - size matters**

Dr. Holger Homann, Laboratoire Lagrange Observatoire de la Côte d’Azur, Nice

(Einladender: Dr. O. Kamps)**Fast methods to analyze crystal images**

Prof. Dr. Benedikt Wirth, Institut fuer Numerische und Angewandte Mathematik , Biomedical Modelling and Computing

(Einladender: Dr. O. Kamps)**Self-organization with Musical Instruments and Music Perception**Prof. Dr. Rolf Bader, Institut für Systematische Musikwissenschaft, Universität Hamburg

(Einladender: Dr. O. Kamps)**Nonlinear Light Bullets in Discrete Media**

Falk Eilenberger, Friedrich-Schiller-Universität Jena, Institut für Angewandte Physik, Nano-Optik

(Einladender: Prof. Dr. C. Fallnich)**Can we eliminate dengue with Wolbachia? – A critical evaluation by mathematical modeling and data analysis**

Prof. Dr. Arndt Telschow, Institut für Evolution und Biodiversität, Universität Münster

(Einladender: Prof. Dr. M. Ohlberger)