WIAS PhD Group
Apes together strong.
Welcome to the website of the self-organized seminar of the doctoral researchers at WIAS. The seminar provides a platform for the doctoral researchers of the WIAS, alumni and fellows to give talks on their research, present themselves and their work to colleagues, and to connect and interchange among one another. Furthermore, the seminar is also open for minicourses on math, science and tutorials on scientific software packages. You are cordially invited to contribute to the WIAS PhD seminar! Please do not hesitate to contact one of the organizers.
The seminar is generally conducted offline, but we can also offer a hybrid format. Please contact one of the organizers to set up a Zoom session if you like.
Location: Weierstrass-Institute for Applied Analysis and Stochastics,
Möhrenstraße 39, 10117 Berlin
Erhard-Schmidt Lecture Hall (ESH)
Time: Every second Monday of the month, 02:00-03:00PM
Stream: Please contact one of the organizers to get access to the credentials of the zoom meeting.
Organizers: Willem van Oosterhout, César Zarco Romero
Recordings: Selected recordings of some talks are stored in the cloud. Please contact the organizers for login credentials.
| Date | Contribution |
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| 25.11.2024 Main building, room 406! | Marwa Zainelabdeen (RG 3) Augmenting the grad-div stabilization for Taylor-Hood finite elements with a vorticity stabilization Abstract: We consider the linear and stationary Oseen equations, which can be viewed as an extension of the Stokes equations by adding convection and reaction terms. Finite element discretization is applied using the Taylor-Hood pair of spaces. To address the lack of pressure robustness in Taylor-Hood finite elements, the so-called grad-div stabilization is added to the discrete problem. Furthermore, the least squares vorticity stabilization (LSVS) proposed in Ahmed et al. (2020) https://doi.org/10.1137/20M1351230 for the Scott-Vogelius finite elements is incorporated for convection stabilization. An error analysis of the stabilized scheme is presented, and convection-robust error bounds are proved. Numerical studies support the analytical results and demonstrate that the LSVS-grad-div method can lead to notable error reductions compared to the standard grad-div method. You can find the results in WIAS preprint 3055 https://doi.org/10.1515/jnma-2023-0118 for topic familiarity prior to the talk. |
| Date | Contribution |
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| 21.10.2024 Main building, room 406! | Moritz Gau (WG 3) Dimension Reduction of a Thermo-visco-elastic Problem at Small Strains Abstract: The derivation of dimension-reduced models is a classical problem in continuum mechanics. In this talk, we consider a thermodynamically consistent nonlinear thermo-visco-elastic model at small strains for thin domains. The system of PDEs consists of the linear momentum equation (without inertia terms) for the displacement, coupled to the heat equation for the temperature. We discuss the rigorous derivation of an effective two-dimensional model for isotropic materials as the thickness of the plate tends to zero, extending results by Blanchard-Francfort 1987 and Licht 2013, who considered only linearised thermo-elasticity and visco-elasticity, respectively. By rescaling the domain to a fixed thickness, we prove suitable a priori estimates to ex- tract converging subsequences and pass to the limit. Since the viscous dissipation in the heat equation is only L1-integrable, the derivation of a priori estimates utilises appropriate nonlinear tests as invented by Boccardo-Gallou ̈et 1989. In the limit, the temperature becomes constant in the vertical direction and the displacement is of Kirchhoff–Love type, so that, in a certain sense, the limits only depend on the two-dimensional cross-section of the plate. The limiting model consists of three equations: the heat equation, and the mechanical equation splits into a membrane and a fourth-order flexural equation. Due to the viscous effects, the out-of-plane parts of the rescaled linearised strains (κbij) become solutions of ODEs in the limit. Especially κb33 obtains a more complex structure compared to elastic and thermo-elastic models, and it appears as in additional coupling in all three equations. This is a joint work with Matthias Liero (WIAS). |
| 18.09.2024 PhD Rehearsal Main building, room 406! | Luisa Plato (RG 4) Cross-Diffusion in Population Dynamics and Electrokinetics Abstract: In this talk I will present the results of my Phd thesis. I will introduce two PDE models including cross-diffusion. Firstly, a predator-prey model with prey-taxis is considered and the existence and weak-strong uniqueness of generalized solutions in all space dimensions as well as the local-in-time existence of classical solutions in space dimension three is shown. Secondly, an anisotropic electrokinetic flow model is considered and the existence and weak-strong uniqueness of suitable weak solutions in dimension three is shown. The talk will focus on the main ideas for the proofs and gives some insight into the technical challenges. |
| 16.09.2024 Main building, room 406! | Lasse Ermoneit (RG 2) Berry Phase of the Spatially Coupled, Anisotropic 2D Quantum Harmonic Oscillator Abstract: In this seminar talk, I will introduce the concept of the Berry phase and discuss its significance in quantum systems. Building on recent findings of a topological Berry phase in our Si/SiGe quantum bus shuttles, I explore this phenomenon using a toy model: a spatially coupled, anisotropic 2D quantum harmonic oscillator. Through this model, I aim to demonstrate how spatial coupling and anisotropy give rise to a Berry phase in a relatively basic quantum mechanical system. |
| 20.06.2024 | Helia Shafigh (RG 5) Überlebenswahrscheinlichkeit eines Hasen unter Wölfen Abstract: In diesem Vortrag (der sich an Schüler richtet) geht es um einen einsamen Hasen, der in einer Welt voller Wölfe möglichst lange zu überleben versucht (random walk among obstacles). Wir besprechen drei verschiedene Modelle (1. unbewegliche Wölfe, 2. ein herumlaufender Wolf, 3. viele herumlaufende Wölfe), in denen wir uns für die (asymptotische) Überlebenswahrscheinlichkeit des Hasen bis zu einer festen Zeit interessieren. Die Neuigkeit dieser Modelle ist die, dass der Hase die Möglichkeit hat, sich in eine Höhle zurückzuziehen und in den Schlaf zu fallen, was ihn für die Wölfe unsichtbar macht (dormancy). |
| 13.05.2024 Takes place at 10:00! | César Zarco Romero (RG 5) Huge networks, random graphs and analysis. Abstract: From microbiological applications to modern combinatorics, very large networks are undoubtedly ubiquitous. This talk is an invitation to Graph Limit Theory, the mathematical theory of large networks. We will introduce three random graph models and present the replica symmetry breaking for an interesting double phase transition. Some thoughts around large deviations, the theory of rare events in probability, for a new spatial approach will be discussed. |
| 15.04.2024 Moved from 08.04.! | Wilfried Kenmoe Nzali (RG 6) Volatile Electricity Markets and Battery Storage Abstract: In this work, we model a volatile electricity market in combination with a Stationary Battery Storage Device (SBSD) to reduce consumer costs. We use stochastic optimal control to manage charging and discharging of the SBSD. Our goal is a mathematical tool for consumers to cut energy expenses by integrating battery storage where we assume no market-wide impact. Initially, we focus on formulating a stochastic optimal control problem for continuous charging and discharging, considering factors like electricity prices and battery conditions. |
| 18.03.2024 Moved from 11.03.! | Qi Wang (RG 8) Robust Multilevel Training of Artificial Neural Networks Abstract: In this talk, we will introduce a multilevel optimizier for training of an artificial neural network. We are particularly interested in nerual networks to learn the hidden physical law or nonlinear mapping from the given data using algebraic multigrid strategies. And we would like to give some further insight into the potential of multilevel optimization methods in the end. |
| 12.02.2024 | Zeina Amer (LG 5) Opto-Electronic Coupling in Laser Simulations Abstract: In this talk, I will introduce the drift-diffusion model and the Helmholtz equation, representing the electrodynamic and optical wave propagation components, respectively, in a laser simulation model. The discussion will focus on the numerical solution of these equations and the coupling mechanisms between them, illustrated through a benchmark example. |
| 06.02.2024 13:00, ESH Defense Rehearsal! | Dilara Abdel (LG 5) Modeling and simulation of vacancy-assisted charge transport in innovative semiconductor devices Abstract: In response to the climate crisis, there is a need for technological innovations to reduce the escalating CO emissions. Two promising semiconductor technologies in this regard, perovskite-based solar cells and memristive devices based on two-dimensional layered transition metal dichalcogenide (TMDC), can potentially contribute to the expansion of renewable energy sources and the development of energy-efficient computing hardware. Within perovskite and TMDC materials, ions dislocate from their ideal position in the semiconductor crystal and leave void spaces. So far, the precise influence of these vacancies and their dynamics on device performance remain underexplored. Therefore, this talk is dedicated to comprehensively examining the impact of vacancy-assisted charge transport in innovative semiconductor devices through a theoretical approach by modeling and simulating systems of partial differential equations. We start by deriving drift-diffusion equations using thermodynamic principles. Particular attention is directed towards accurately limiting vacancy accumulation. Furthermore, we formulate drift-diffusion models to describe charge transport in perovskite solar cells and TMDC memristors. We discretize the transport equations via the finite volume method and establish the existence of discrete solutions using the entropy method. Our study concludes with simulations conducted with an open source software tool developed in the programming language Julia. These simulations explore the influence of volume exclusion effects on charge transport in perovskite solar cells and compare our simulation results with experimental measurements found in literature for TMDC-based memristive devices. |
| 02.02.2024 11:00, ESH Defense Rehearsal! | Dilara Abdel (LG 5) Solving differential equations using physics-informed deep operator networks Abstract: Differential equations are fundamental in science and engineering and are typically addressed using classical numerical techniques. However, modifying parameters or input functions in classical discretizations requires re-executing simulations, posing computational challenges. Recently, deep operator networks (DeepONets) were introduced as an innovative neural network architecture to address this challenge. However, in their conventional form, DeepONets operate as purely data-driven methods. In response, physics-informed DeepONets were formulated as an alternative, ensuring network predictions align with the underlying physics encoded by the differential equation, even without specific real-world measurements. This talk aims to describe the basic concepts of neural networks, deep operator networks, and the integration of a priori known physical knowledge within a neural network framework. |
| Date | Contribution |
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| 16.10.2023 Moved from 09.10.! | Luca Pelizzari (RG 6) (Rough) path signatures and applications. Abstract: In this talk, we provide an elementary introduction to the notion of (rough) path signatures and discuss some of its principal properties. These properties motivate its prominent role in various applications, most notably in machine learning and mathematical finance. In the second part, we demonstrate an application in the so-called optimal stopping problem—a classical problem in stochastic analysis—based on recent work with C. Bayer and J. Schoenmakers. |
| 23.10.2023 Defense Test Run! | Derk Frerichs-Mihov (RG 3) Decrypting classically encrypted messages using Shor's algorithm - How quantum computers outperform even Sherlock Holmes Abstract: One of nowadays widely used public-key cryptography schemes is the RSA method, which is so secure that even Sherlock Holmes could not break it. Unfortunately, this encryption is in danger: Shor's algorithm and quantum computers make it easy to decrypt data like passwords, patents, and research results encrypted with the RSA scheme. This talk explains how prime factorization of large numbers can be conducted on quantum computers using Shor's algorithm and how it can be utilized to break the RSA encryption method. |
| 27.10.2023 At 11:00! | Derk Frerichs-Mihov (RG 3) On slope limiting and deep learning techniques for the numerical solution to convection-dominated convection-diffusion problems Abstract: Convection-diffusion problems describe the distribution of a scalar quantity like mass or energy inside a flowing medium. When the convection is orders of magnitude stronger than the diffusion, usually the solution to these problems possesses layers, which are small regions where the solution has a steep gradient. Unfortunately, many classical numerical methods used to approximate the solution fail in accurately resolving these layers. Their numerical solutions are polluted by unphysical values, so-called spurious oscillations. In my PhD phase at WIAS, I've investigated several paths to generate physically consistent solutions summarized in my PhD thesis. This talk presents the results of my thesis in which I've investigated so-called slope-limiting techniques for discontinuous Galerkin methods and techniques from deep learning. |
| 11.09.2023 | Leonie Schmeller (RG 7) Multi-Phase Dynamic Systems at Finite-Strain Elasticity Abstract Dynamic multi-phase systems coupled with non-linear elasticity form the fundamental model system for describing various phenomena in soft matter physics and biology, including the wetting of soft substrates, phase separation processes, and swelling of hydrogels. We develop a model framework that couples phase fields with mechanical deformations, which yields a natural formulation of realistic scenarios and at the same time enables rigorous analytical considerations as well as the systematic development of numerical implementations. |
| 19.06.2023 Moved from 12.05.! | Camilla Belponer (RG 3) Topic: Modeling Vascularised Tissues Abstract The interest in efficient simulation of vascularized tissues is motivated by the solution of inverse problems in the context of tissue imaging, where available medical data (such as those obtained via Magnetic Resonance Elastography) have a limited resolution, typically at the scale of an effective - macro scale - tissue, and cannot resolve the microscale of quantities of interests related, for instance, to the tissue vasculature. Our model is based on a geometrical multiscale 3D (elastic) -1D (fluid) formulation combined with an immersed method. At the elastic-fluid immersed boundary Γ we impose a trace-averaged boundary condition whose goal is to impose only a local Dirichlet boundary condition on the tissue-vessel interface allowing the enforcement of a pure normal displacement at the fictional vessel boundary. In order to decouple the discretization of the elastic tissue from the vessel boundary, the boundary condition on Γ is imposed via a Lagrange multiplier, modeling the fluid vessels as immersed singular sources for the elasticity equation. Next, to efficiently handle the multiscale nature of the problem, the problem is formulated as a mixed-dimensional PDE in the framework of reduced Lagrange multipliers on a space of co-dimension 2. |
| 08.05.2023 | Dr. Alexander Vibe, Julius von Falkenhausen, Thomas Rupp (EDAG Group) Topic: Career Paths for Mathematicians in Industry |
| 12.04.2023 Moved from 03.04.! | Daniel Runge (RG 3) Topic: A Reduced Basis Approach for Convection-Diffusion Systems with Non-Linear Boundary Reactions Abstract This talk presents an efficient strategy to solve advection-diffusion problems with non-linear boundary conditions as they appear, e.g., in heterogeneous catalysis. Since the non-linearity only involves the degrees of freedom along (a part of) the boundary, a reduced basis ansatz is suggested that computes discrete basis functions for the present advection-diffusion operator such that the global non-linear problem reduces to a smaller problem on the boundary. The computed basis functions are completely independent of the non-linearities. Thus, they can be reused for problems with the same differential operator and geometry. Corresponding scenarios might be inverse problems, but also modeling the effect of different catalysts in the same reaction chamber. The strategy is explained for a mass-conservative finite volume method and demonstrated in a numerical example implemented in the julia language. |
| 13.03.2023 | Nina Kliche (RG 4) Topic: Modeling and simulation of mini-grids under uncertainty Abstract Mini-grids generate and distribute energy locally and offer a reliable solution to ensure access to energy in countries where electrification is slow. Green energy generation, demand and weather naturally introduce uncertainties whereas the installation of a battery energy storage system asks for consideration of battery degradation. As thermal issues can significantly affect battery lifetime, an optimal control problem for the daily operation including thermal battery management under uncertainties is set up and a numerical approach is presented. |
| 13.02.2023 In Room 411 (library, HVP 5-7) | Coffee ☕, snacks 🧁, and open discussion 💬. |
| 09.01.2023 | Julian Kern (RG 5) Topic: Where's the math in biology? Abstract I will discuss how mathematics entered biology through population genetics. At the end of the talk, you will be familiar with some basic models in population genetics and have some general idea about the questions that are being asked as well as a few key ideas on how to answer them. |
| Date | Contribution |
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| 12.12.2022 | Christine Keller (RG 7) Development of an Ion-Channel Model-Framework Abstract: Ion channels are pore-forming proteins in the cell membrane that control a large part of biological processes, e.g., the generation of electrical signals in the nervous and muscle systems. The behavior of ion channels can be studied in the laboratory by measuring the current response to a time-dependent voltage difference. This signal is a unique signature of each channel and its environment, as it varies with the structure of the channel protein and the ion concentration. Its interpretation is therefore of great interest for the development of medications and therapies in medicine. The development of a model-framework can support the interpretation of this current-voltage relation and contribute to a better understanding. In this talk, a model will be presented that describes ion activities in the channel using non-equilibrium thermodynamics and mixing theories. The model accounts for size and correlation phenomena such as space charge competitions and finite volume effects, as well as solvation effects of ions in aqueous electrolytes. |
| 07.11.2022 | Anieza Maltsi (RG 1) A mathematical study of the Darwin-Howie-Whelan equations for Transmission Electron Microscopy Abstract: The Darwin-Howie-Whelan (DHW) equations are commonly used to describe and simulate the scattering of fast electrons in transmission electron microscopy (TEM). While they are a system of infinitely many envelope functions, derived from the Schrödinger equations, only a finite subset is used in simulations. In this talk, mathematical guidelines for optimal choices of the finite set are provided and are justified by exact error estimates. Then a mathematical model and a toolchain for the numerical simulation of TEM images of semiconductor quantum dots (QDs) is described. Finally, symmetries observed in TEM images are investigated with respect to the DHW equations. |
| 10.10.2022 | Fenja Severing (RG 2) Instabilities in the context of the generalized Nonlinear Schrödinger Equation Abstract: Nonlinear waves can be observed in various fields, like water waves or optical waves.They can experience modulation instability as described by the Nonlinear Schrödinger Equation (NLSE). Solved numerically by the Split-Step Method (SSM), not only physical instabilities occur but also unwanted numerical ones. Here, we study how to avoid numerical instabilities for the generalized NLS. |
| 19.09.2022 | Dr. Matthias Liero (RG 1) Creating personal homepages for academics with jekyll Abstract: Visibility is essential for young researchers to disseminate their research and publications, to highlight achievements and affiliations, and to network and collaborate with others. In this talk, we will discuss what information to include on your personal homepage and how-to create a simple and effective academical personal website using the "static-site generator" jekyll. |
| 11.07.2022 | Maximilian Reiter (RG 4) Numerical approximation of the Ericksen-Leslie equations Abstract: In this talk, we introduce the Ericksen-Leslie equations - a model for the fluid flow of liquid crystals in three dimensions. We introduce a generalized solution concept and propose an implementable, structure-inheriting space-time discretization which converges to the former. Computational studies are shown in order to provide some evidence of the applicability of the proposed algorithm. |
| 09.05.2022 | Stefanie Schindler (RG 1) 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. |
| 11.04.2022 | Willem van Oosterhout (RG 1) 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. |
| 14.03.2022 | Simon Breneis (RG 6) 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. |
| 21.02.2022 | Derk Frerichs-Mihov (RG 3) 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. |
| 07.02.2022 | Alireza Selahi (RG 7) Version control with "Git" |
| 24.01.2022 | Anh Duc Vu (LG 6) 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. |
| Date | Contribution |
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| 13.12.2021 | Andrea Zafferi (WG 1) 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. |
| 22.11.2021 | Dr. Swetlana Giere (felmo GmbH) A Conversation about Transition From Science to Data Science |
| 08.11.2021 | Dr. Clemens Bartsch (genua GmbH: IT Project Manager) Career Opportunities for WIAS Alumni in IT Security? A Personal Case Study. |
| 11.10.2021 | Alexander Gerdes (RG 2) 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. |
| 13.09.2021 | Alireza Selahi Moghaddam (RG 7) 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. |
| 09.08.2021 | Mina Stöhr (RG 2) 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. |
| 12.07.2021 | Lorenzo Scaglione (RG 3) 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. |
| 14.06.2021 | Jacob Gorenflos (FMP/Leibniz PhD Network) A glimpse 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. |
| 10.05.2021 | Dilara Abdel (LG 5) 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. |
| 03.05.2021 PhD Defense Rehearsal | Artur Stephan (RG 1) 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. |
| 12.04.2021 | Leonie Schmeller (RG 7) 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. |
| 15.03.2021 | Heide Langhammer (RG 5) 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. |
| 08.02.2021 | David Sommer (RG 4) 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. |
| 11.01.2021 | Alexandra Quitmann (RG 5) 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. |
| Date | Contribution |
|---|---|
| 07.12.2020 | Moritz Ebeling-Rump (RG 4) 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. |
| 11.11.2020 | Derk Frerichs (RG 3) 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. |
| Date | Contribution |
|---|---|
| 22.11.2018 | Markus Mittnenzweig (RG 1) Entropy methods for quantum and classical evolution equations |
| 27.08.2018 | Clemens Bartsch (RG 3) 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. |
| 19.02.2018 | Thomas Frenzel (RG 1) 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. |
| Date | Contribution |
|---|---|
| 19.06.2017 | Artur Stephan (RG 1) 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. |
| 12.06.2017 | Clemens Bartsch (RG 3) 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. |
| 08.05.2017 | Sibylle Bergmann (RG 7) 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. |
| Date | Contribution |
|---|---|
| 24.10.2016 | Johannes Neumann (RG 4) 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. |
| 10.10.2016 | Swetlana Giere (RG 3) A Walk to a Random Forest |
| 05.09.2016 | Alexander Weiß (GetYourGuide: Data Science Manager) Talk on professional experience in the field of data science |
| 22.08.2016 | Michael Hofmann (RG 2) Einfluss dynamischer Resonanzen auf die Wechselwirkung optischer Femtosekunden-Pulse mit transparenten Dielektrika |
| 27.06.2016 | Florian Eichenauer (RG 1) Analysis for Dissipative Maxwell-Bloch Type Models |
| 20.06.2016 | Paul Helly (Guest of RG 1) A structure-preserving finite difference scheme for the Cahn-Hilliard equation |
| 25.01.2016 | Alena Moriakova (Guest of RG 2) 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. |
| 11.01.2016 | Thomas Frenzel (RG 1) (Evolutionary) Gamma-Convergence and micro-macro limits |
| Date | Contribution |
|---|---|
| 23.11.2015 | Sina Reichelt (RG 1) 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). |
| 09.11.2015 | Dmitry Puzyrev (RG 1) Delay Induced Multistability and Zigzagging of Laser Cavity Solitons |
| 21.09.2015 | Clemens Bartsch (RG 3) An Assessment of Solvers for Saddle Point Problems Emerging from the Incompressible Navier-Stokes equations |
