WIAS Promovierendenseminar

• Place: Online via zoom, contact the organizers for credentials
• Time: Every second Monday of the month, 2:00PM - 3:00PM
• Organizers: Moritz Ebeling-Rump, Derk Frerichs

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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