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.

Einladender: Dr. O. Kamps



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 9


Predictive Modelling of Time Series in Neuroscience: The State Space Approach

Dr. Andreas Galka, 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.

Einladender: Prof. Dr. C. Wolters


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.

Einladender: Dr. B. Schmitzer


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.

Einladender: Prof. Dr. U. Thiele


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.

Einladender: Prof. Dr. U. Thiele


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.

Einladender:  Dr. O. Kamps


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

Einladender: Prof. Dr. U. Thiele


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.

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.

[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

Einladender: Dr. O. Kamps

11.09.2018 Sonderkolloquium

Prof. Dr. Marcel G. Clerc

Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile

Einladender: Prof. Dr. U. Thiele