WIAS Promovierendenseminar

• Place: Weierstrass-Institute for Applied Analysis and Stochastics
              Mohrenstraße 39, 10117 Berlin
              Erhard-Schmidt Lecture Room (ESH)
  
• Stream: Contact one of the organizers to get access to the credentials of the zoom meeting
• Time: Every second Monday of the month, 2:00PM - 3:00PM
• Organizers: Moritz Ebeling-Rump, Derk Frerichs-Mihov

Creating personal homepages for academics with jekyll

Abstract:
TBA.

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TBA.

The Entropy Method for the Linear Diffusion Equation on the whole real line

Abstract:
In this talk, we investigate the long-time behavior of solutions to the well-studied linear diffusion equation defined on the whole real line with non-homogeneous asymptotic boundary values. In other words, we study solutions that are in equilibria at infinity and answer how they mix these two stable states when time increases. The idea is to use the entropy method in order to prove the convergence towards a steady-state function in parabolic scaling variables. The reason why we use this approach, that works for nonlinear problems as well, comes from our research study as a part of the SFB 910. In project A5 we study the long-time behavior of a nonlinear coupled reaction-diffusion system of mass-action type on the real line and answer a similar question. However, in this talk, we focus on the linear diffusion equation for simplicity.

The direct method and application to poro-visco-elastic materials

Abstract:
In this talk, we show how the direct method of the calculus of variations can be used to prove existence (and uniqueness) of solutions of PDEs. The main idea is to prove that certain functionals have minimizers, and that these minimizers satisfy a PDE. Then, we apply the direct method in combination with a time discretization to prove existence of solutions for poro-visco-elastic materials.

Pricing options under rough volatility

Abstract:
Starting with an introduction of Brownian motion, we discuss the general goals of mathematical finance and explain the intuition behind the Black-Scholes model. After discussing option pricing in this standard framework, we observe some of the shortcomings of the Black-Scholes model. Finally, to overcome these deficiencies, we introduce stochastic volatility and rough volatility models.

Restic - backups done right!

Abstract:
Computers are in severe danger! Humans worldwide drown computers with their beverages, they forget them on the trains and install viruses and other malware. Computers are stolen or hardware problems occur. To prevent you from hearing "No Backup, no mercy" this talks introduces an open-source, effective, secure and cross-platform software called restic with which you can back up your data.
The talk is a hands-on tutorial how to use restic together with WIAS resources. You are going to learn how to install restic, how to back up your data, how to delete old snapshots, useful automations and of course how to restore your data in the worst case. Buckle up and prepare to make data loss a thing of the past.

Version control with "Git"

A Short Introduction to Homogenization

Abstract:
Many fields in mathematics are motivated by physical problems. In our case, we want to model porous/compound materials. Often, only a microscopic description is given (e.g. pore structure), while the macroscopic behaviour is of interest (behaviour of a sponge). The "limiting" procedure where one transitions from the microscopic to the macroscopic scale is difficult to handle and lies in the heart of homogenization theory.
The talk will give a brief overview on the topic as well as the key insights driving the theory.

GENERIC and its applications to geophysical flows.

Abstract:
The GENERIC (acronym for General Equations of Non-Equilibrium for Reversible-Irreversible Coupling) formalism is a modelling tool that uses a variational approach to derive thermodynamically consistent sets of equations for closed systems. I will introduce formally this method while showing simple examples related to fluid mechanics. Secondly, I will discuss transformations that preserve such structure with applications to more sophisticated problems, i.e., FSI (fluid-solid interactions) problems, reactive fluid flows or rock de-hydration processes.

A Conversation about Transition From Science to Data Science

Career Opportunities for WIAS Alumni in IT Security? A Personal Case Study.

Synchronization patterns in globally coupled Stuart-Landau oscillators

Abstract:
We s tudy clusterized states in globally coupled Stuart-Landau oscillators as a paradigmatic model for patterning processes [Kemeth2019].
To study 2-Cluster states we set up a reduced model using collective variables, in which the cluster size ratio [Ott2015] is an additional bifurcation parameter. In the reduced system one can only observe longitudinal instabilities leading to complex 2-Cluster behaviour. By including test oscillators, we can also study instabilities transversal to the 2-Cluster manifold i.e. changes of the cluster type. Using numerical bifurcation analysis, we then find stability regions of cluster solutions of different types. In these, solitary states serve as primary patterns and allow an analytical treatment. The identified instabilities can be seen as building blocks of pathways to complex behaviour such as chimeras [Set2014] and extensive chaos [KM1994] as well as splay states [Politi2019] occuring for varying parameters. With the analytical and numerical approach presented here we identify different transition scenarios from synchrony to complex behaviour by reducing the coupling strength. We locate each of these scenarios in regions in the plane of shear parameters.

[KM1994] N. Nakagawa and Y. Kuramoto, Physica D: Nonlinear Phenomena, 75, Issues 1-3 (1994).
[Set2014] G. Sethia and A. Sen, Phys. Rev. Lett. 112 144101 (2014).
[Ott2015] W. L. Ku, M. Girvan, E. Ott, Chaos 25 , 123122 (2015).
[Kemeth2019] Kemeth, Felix P., Sindre W. Haugland, and Katharina Krischer. Chaos: An Interdisciplinary Journal of Nonlinear Science 29.2 (2019): 023107.
[Politi2019] P. Clusella and A. Politi, Phys. Rev. E 99, 062201 (2019).
[Kemeth2021] Kemeth, Felix P., et al. Journal of Physics: Complexity 2.2 (2021): 025005.

Modelling electrolytes with the Poisson-Nernst-Planck-equation

Abstract:
The capacity of batteries is one of their central quantities and hence of major interest. In order to calculate it, modelling the behaviour of electrolytes is necessary. We give a short introduction into some of the most important concepts in thermodynamics and chemistry, and finally talk about a state-of-the-art model using the Poisson-Nernst-Planck-equation.

Bifurcations and Instabilities of Temporal Dissipative Solitons in DDE-systems with large delay

Abstract:
We study different bifurcation scenarios and instabilities of Temporal Dissipative Solitons in systems with time-delayed feedback and large delay. As these solitons can be described as homoclinic orbits in the profile equation under the reappearance map, we use homoclinic bifurcation theory for our comprehension of their bifurcations and instabilities. We demonstrate our results with the examples of the FitzHugh-Nagumo system and Morris-Lecar model with time-delayed feedback.

Three months with ParMooN

Abstract:
What does it mean for a research group to implement its own software library? During my internship at WIAS I discovered the huge world of ParMooN, a C++ finite element library of the institute. Even if sometimes it is quite painful to surf through the hundreds of header and source files of the library, it is somehow fascinating to have an idea of its complex architecture and of how it can help us to solve quantitatively problems from the real world. The application of my code is the simulation of the mechanical behaviour of an elastic material embedded with a thin vasculature.
In my presentation, I will introduce the physical problem and the library; then I will show the numerical results I have obtain until now.

Sophie Luisa Plato (RG 4)

Biological pest control - Analysis and numerics for a spatial-temporal predator-prey system.

Abstract:
In the production of ornamental plants, as for example roses, it is desirable to reduce the use of chemical pesticides in order to protect the environment and the people involved in the production process. This can be achieved by releasing natural enemies of the pest involved, which do not harm the plants. A typical example of such a predator-prey pair is the two-spotted spider mite and the predatory mite.
In this talk we consider a system of two coupled evolution equations modelling this predator-prey interaction. The first part of the talk is devoted to the proof of the existence of weak solutions to this model and in the second part we present our numerical approximations of these solutions.

A glimps into doing a Ph.D. in the Leibniz Association

Abstract:
Data is the best way to start a discussion. We, in the Leibniz PhD Network, regularly discuss with Leibniz policy and politicians on how to improve the situation of doctoral researchers. Surprisingly, there is a significant lack of knowledge on how their situation really is. Therefore, we started the working group survey in 2017. This kicked of the biennial cycle in which we now survey you: 2017, 2019 and we are currently finishing the development of the 2021 questionnaire. Since 2017, the survey and its results have been the basis of our work.
Here, you will be presented with the data of the 2019 survey and a perspective on what to expect of the 2021 survey.

Lasse Ermoneit (RG 2)

Semi-analytical approach to determine the timing jitter of a mode-locked laser with opto-electronic feedback

Abstract:
Passively mode-locked lasers are an important device among semiconductor lasers and are used to generate high-frequency regular pulses. Their mathematical description can be done via delay differential equations to avoid the more complex consideration with partial differential equations. Since any laser system is usually subject to noise due to quantum effects, this is incorporated into the system of equations and a nonlinear differential equation with delay and stochastic white noise is obtained.. The timing jitter is the measure for the irregularity of the pulses of the laser: It corresponds to the standard deviation of the noise influenced pulses to an external clock.
Here, an approach is presented that makes it possible to shortcut a large part of the fully numerical non-parallelizable computations in order to get to this key quantity, the timing jitter.

Modelling charge transport in perovskite solar cells: Potential-based and limiting ion depletion

Abstract:
Perovskite solar cells (PSCs) have become one of the fastest growing photovoltaic technologies within the last few years. However, their commercialization is still in its early stages and several challenges need to be overcome. For this reason it is paramount to understand the charge transport in perovskites better via improved modelling and simulation. Unfortunately, there is a discrepancy in the adequate modeling of the additional ionic transport within the perovskite material with drift-diffusion equations. Thus, we present a new charge transport model which is, unlike other models in the literature, based on quasi Fermi potentials instead of densities. This allows to easily include nonlinear diffusion (based on for example Fermi-Dirac, Gauss-Fermi or Blakemore statistics) as well as limit the ion depletion (via the Fermi-Dirac integral of order -1). We present numerical finite volume simulations to underline the importance of limiting ion depletion.

PhD defense rehearsal

Coarse-graining for gradient systems and Markov processes

Abstract:
Coarse-graining is a well-established tool in mathematical and natural sciences for reducing the complexity ofa physical system and for deriving effective models. In the talk, we consider several examples that originate from interacting particle systems and describe reaction and reaction diffusion systems. The aim is twofold: first,provide mathematically rigorous results for physical coarse-graining. Secondly, the so derived systems can be formulated in a mathematically equivalent way, which provides new modelling insights.

Phase-field model with nonlinear elasticity (Modelling and Numerical aspects)

Abstract:
In this talk, I will present a phase field model for a Neo-Hookian (nonlinear) elastic material, which is then coupled to formulate a Cahn-Hillard type dynamic system. After introducing the individual components of the problem, a coupling is discussed. We set up a weak formulation and show a strategy to implement and solve the problem numerically.

Instead of 08.03.2021

Inhomogeneous Random Graphs: A large deviations result for their cluster sizes and its implications.

Abstract:
An inhomogeneous random graph consists of a fixed number of vertices that are connected via random edges. The edge probabilities depend on an additional parameter that we call the vertex type. We want to study how such a random graph decomposes into its connected components. In particular, we want to understand conditions for the existence of macroscopic components, whose size is proportional to the total number of vertices. Once the model parameters surpass a certain threshold, a (unique) macroscopic component appears with high probability. I will explain how this phase transition can be studied via large deviations theory which reformulates the probabilistic calculus of the model into an optimization problem for a certain function.
I will also discuss in which ways the inhomogeneous random graph model can be linked to models of coagulation that I will only briefly sketch.

Dynamic Programming Approach for Robust Receding Horizon Control in Continuous Systems

Abstract:
There is still little connection in the literature between the field of Model-based Reinforcement Learning (MB-RL) and the field of Continuous Optimal Control. In Continuous Optimal Control, the ODE model, describing a real physical process, is usually regarded as ground truth. This may lead to catastrophic failures when the resulting control is applied to the real system, due to errors in the model. In MB-RL, this issue is often addressed by keeping and continuously updating a posterior over model parameters, but successful applications so far are mostly limited to Markov Decision Processes which are discrete in time. We propose a model-based decision-time planning agent for continuous optimal control problems of arbitrary horizon length. Continuous updates of the model parameters during the online phase enable handling of complex unknown dynamics even with simple linear models. During planning, robust feedback-control laws are computed in a Dynamic Programming sense by utilizing Bellman's principle.

Spin systems and random loops

Abstract:
Random loop models are systems of statistical mechanics whose configurations can be viewed as collections of closed loops living in higher dimensional space. They are interesting objects on its own and further have a close connection to other important statistical mechanics models such as spin systems. In this talk, I will introduce random loop models, discuss a conjecture about the occurrence of macroscopic loops and explain its role as alternative formulation of spin systems.

Topology Optimization subject to a Local Volume Constraint

Abstract:
The industry sector of additive manufacturing has shown remarkable growth in previous years and is predicted to continue growing at a rate of 15% in the coming years. It progressed from prototyping to actual production. Topology Optimization and Additive Manufacturing have been called a "match made in heaven", because Topology Optimization can aid engineers to take advantage of the newfound design freedom. Commonly a perimeter term is incorporated which avoids checker-boarding, but also counteracts the desired creation of infill structures. By incorporating a local volume constraint mesoscale holes are introduced. Analytically, the existence of unique solutions is shown. Apart from better cooling properties and a larger resilience to local material damage, these structures demonstrate an improved nonlinear material behavior. One observes an increased critical buckling load - a potentially catastrophic failure mode that would not be taken into account if only considering linear elasticity.

The very basics of numerical analysis - or what am I doing here when I'm not drinking coffee?

Abstract:
When we drink coffee, caffeine spreads in our body through our blood. The flow of particles inside a media, e.g. the caffeine inside the blood, can be described with the so called convection-diffusion-reaction equations that are often approximated using numerical algorithms. In this talk the basic concepts of numerical analysis are explained with the help of a conforming Courant finite element discretization of the convection-diffusion-reaction equations. Afterwards a short outlook is given that explains my current research activities.
Numerical examples round up the presentation.

Entropy methods for quantum and classical evolution equations

Post-quantum cryptography and the first quantum-safe digital signature scheme

Abstract:
In May 2018 news spread far beyond the cryptologist community: a group of German, Dutch and American computer scientists had published the first quantum-resilient digital signature scheme as an internet standard (RFC 8391), thus taking a major step towards arming digital signature against future attacks with quantum computers. The proposed XMSS scheme (eXtended Merkle Signature Scheme) makes use of cryptographic hash functions, which are considered quantum-safe. In this talk we want to lead the audience towards an understanding of the importance and mode of operation of digital signature schemes, the threat that quantum computers might in the near future pose to them, and how the newly standardized scheme offers resilience against quantum computer attacks. We will start with a general introduction of digital signature and an explanation of a basic version of the widespread RSA algorithm and its major weaknesses, focusing on factorization attacks. Then we will introduce the basics of quantum computing, show how Shor's algorithm enables them to very efficiently perform factorization attacks, thus breaking RSA, and finally introduce XMSS and give an explanation for why it is supposed to be safe against quantum-aided attacks. Code examples and examples of quantum computations performed with a prototypical 5-qubit processor (IBM Q Experience) will be included in the talk.

Working with Wasserstein gradient flows

Abstract:
This talk explains what the Wasserstein distance is, how it generates a gradient flow for the heat equation and how to pass to the limit in a sandwich model with thin plates.

starts at 1:00 PM

On approximations of solutions of evolution equations using semigroups

Abstract:
In the talk, some results of my master thesis will be discussed. We approximate the solution of a non-autonomous linear evolution equation in the operator-norm topology. The approximation is derived using the Trotter product formula and can be estimated. As an example, we consider the diffusion equation perturbed by a time dependent potential.

starts at 11:00 AM

A mixed stochastic-numeric algorithm for transported interacting particles

Abstract:
A coupled system of population balance and convection-diffusion equations is solved numerically, employing stochastic and finite element techniques in combination. While the evolution of the particle population is modelled as a Markov jump process and solved with a stochastic simulation algorithm, transport of temperature and species concentration are subject to a finite element approximation. We want to briefly introduce both the stochastic and the deterministic approach and discuss some difficulties to overcome when combining them. A proof of concept simulation of a flow crystallizer in 2D is presented.

An atomistically informed phase-field model for describing the solid-liquid interface kinetics in silicon

Abstract:
An atomistically informed parametrization of a phase-field model for describing the anisotropic mobility of liquid-solid interfaces in silicon is presented. The model is derived from a consistent set of atomistic data and thus allows to directly link molecular dynamics and phase field simulations. Expressions for the free energy density, the interfacial energy and the temperature and orientation dependent interface mobility are systematically fitted to data from molecular dynamics simulations based on the Stillinger-Weber interatomic potential. The temperature-dependent interface velocity follows a Vogel-Fulcher type behavior and allows to properly account for the dynamics in the undercooled melt.
Our three dimensional simulations reproduce the expected physical behavior of a silicon crystal in a melt, e.g. the critical nucleation radius and the experimentally observed equilibrium shape.

The phase field approach for topology optimization

Abstract:
In this talk I will present an approach on topology optimization based on the phase field model from [Blank et. al., 2014] which utilizes the Allan-Cahn gradient flow. This method natively includes changes to the topology during the optimization and replaces sharp interfaces with boundary layers for smoothness. Instead of the prime-dual active set method a Lagrangian approach is considered.

A Walk to a Random Forest

Talk on professional experience in the field of data science

Einfluss dynamischer Resonanzen auf die Wechselwirkung optischer Femtosekunden-Pulse mit transparenten Dielektrika

starts at 4:00 PM

Analysis for Dissipative Maxwell-Bloch Type Models

A structure-preserving finite difference scheme for the Cahn-Hilliard equation

Analysis of periodic solutions of the Mackey-Glass equation

Abstract:
The Mackey-Glass equation is the nonlinear time delay differential equation, which describes the formation of white blood cells. We study the possibility of simultaneous existence of several stable attractors (periodic solutions) in this equation. As a research method we use method of uniform normalization.

(Evolutionary) Gamma-Convergence and micro-macro limits

Two-scale homogenization of systems of nonlinear parabolic equations

Abstract:
We consider two different classes of systems of nonlinear parabolic equations, namely, reaction-diffusion systems and Cahn-Hilliard-type equations. While the latter class admits a gradient structure, the former does in general not admit one. The equation's coefficients are periodically oscillating with a period which is proportional to the characteristic microscopic length scale. Using the method of two-scale convergence, we rigorously derive effective (upscaled or homogenized) equations for the limit of smaller and smaller periods. Therefore, depending on the class of systems under consideration, we use either suitable Gronwall-type estimates (for Lipschitz continuous reaction terms) or Gamma-convergence (for energy functionals).

Bootstrap confidence sets under model misspecification

starts at 10:00 AM (Erhard-Schmidt lecture room)

Delay Induced Multistability and Zigzagging of Laser Cavity Solitons

starts at 2:30 PM

An Assessment of Solvers for Saddle Point Problems Emerging from the Incompressible Navier-Stokes equations