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

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

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

Colloquium Summer Term 2021

Colloquium Winter Term 2020/2021

Colloquium Winter Term 2018/2019

Colloquium Summer Term 2018

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.