Datum Vortrag




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.

Einladender: Dr. O. Kamps


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.

Einladender: Dr. O. Kamps


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.

Einladender: Prof. B. Wirth


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.

Einladender: Dr. O. Kamps

12.12.2017 Adaptive mesh-refinement for nonconforming finite element methods

Prof. Dr. Mira Schedensack
Angewnadte 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.

Einladender: Dr. O. Kamps


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.

09.01.2018 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.