Veranstaltungen
- Montag, 15.07.2024, 10:00 Uhr (Berlin Mitte)
- MATH+ Thematic Einstein Semester on “Mathematics for Quantum Technologies”
Prof. Ulf Leonhardt, Weizmann Institute of Science, Israel:
First advanced lecture of the series “Forces of the quantum vacuum” .
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Berlin Mitte
Abstrakt
Topic: Setting the scene
Quantization of the electromagnetic field in media and in space-time
Normal modes and harmomic oscillators
Zero-point energy
Casimir's cavity: 1D case, zeta-function renormalization
Casimir's cavity: 3D case, Casimir's renormalization
Veranstalter
WIAS Berlin
Einstein Foundation Berlin
- Dienstag, 16.07.2024, 10:00 Uhr (Berlin Mitte)
- MATH+ Thematic Einstein Semester on “Mathematics for Quantum Technologies”
Prof. Ulf Leonhardt, Weizmann Institute of Science, Israel:
Second advanced lecture of the series “Forces of the quantum vacuum” .
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Berlin Mitte
Abstrakt
Topic: Lifshitz theory
The need for a theory in dispersive and dissipative media
Point-splitting method
Fluctuation-dissipation theorem
Kubo-Martin-Schwinger relation
Lifshitz formula in planar, piece-wise homogenous media
Veranstalter
WIAS Berlin
Einstein Foundation Berlin
- Dienstag, 16.07.2024, 13:30 Uhr (WIAS-ESH)
- Seminar Numerische Mathematik
Nishant Ranwan, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala, Indien:
Existence of a weak solution to the fluid-structure interaction problem of blood flow in coronary artery
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
This work is dedicated to proving the existence of a weak solution to the nonlinear coupled fluid-structure interaction (FSI) problem arising in modeling the blood flow through the coronary artery. Considering blood as a homogeneous, incompressible, Newtonian fluid, the $3D$ Navier--Stokes equations model the flow. We adopt the St. Venant--Kirchhoff elasticity model for the arterial wall. With the help of dynamic and kinematic boundary conditions, we define the fluid-structure coupling (two-way) at the interface. Using the operator splitting approach, we split the coupled problem into two parts: the structure sub-problem (SSP) in the Galerkin framework and the piece-wise stationary fluid sub-problem (FSP). In order to establish the existence of a weak solution, the initial step is to tackle the SSP. Following this, the fluid domain is updated through the Harmonic Extension of the structural displacement. Subsequently, the focus shifts to solving the coupled Navier--Stokes equations within the updated fluid domain.
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Seminar Numerische Mathematik
Veranstalter
WIAS Berlin
- Dienstag, 16.07.2024, 15:15 Uhr (FU-140)
- Oberseminar Nonlinear Dynamics
Dr. Sören von der Gracht, Universität Paderborn:
Exploring exotic symmetries to explain exotic behavior of network dynamical systems (hybrid talk)
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Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Hinterhaus, Raum: 140
Abstrakt
Many dynamical systems models of real world processes exhibit the structure of a network consisting of nodes with connections between them. The specific interaction structure of a network can produce remarkable dynamics beyond that of the individual nodes. Prominent examples include synchronization and highly complex branching behavior in bifurcations, phenomena that are not found in dynamical systems without the structure of a network. Network dynamical systems are not well understood mathematically, which makes it hard to quantify and control their behavior. The reason is that most of the established machinery of dynamical systems theory fails to distinguish between networks and general dynamical systems. Several mathematical tools that are tailor-made for network problems have been proposed recently. Strikingly, they have one thing in common: they exploit the algebraic nature of networks. In this talk, I will give an overview over some recent results regarding the question which dynamical behavior and generic bifurcations are dictated by the network structure of a system. In particular, I will illustrate how structural and algebraic properties culminate in symmetries of the governing equations and how these can be exploited for (partial) answers. This includes classical symmetries but also more exotic concepts such as monoid and quiver representations.
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Oberseminar Nonlinear Dynamics
Veranstalter
Freie Universität Berlin
WIAS Berlin
- Dienstag, 16.07.2024, 16:30 Uhr (FU-140)
- Oberseminar Nonlinear Dynamics
Prof. Hans Engler, Georgetown University, USA:
The Lorenz System of 1996 (hybrid talk)
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Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Hinterhaus, Raum: 140
Abstrakt
The meteorologist and applied mathematician Edward Lorenz is famous for discovering chaotic behavior in dynamical systems in 1963. In 1996, Lorenz introduced a dynamical system that describes very simple "weather" on a cartoon planet: a scalar quantity evolves on a circular array of N sites, undergoing radiative forcing, dissipation, and nonlinear advection. Lorenz proposed this system as a test bed for numerical weather prediction. Since then, it has found much use as a test case in data assimilation. Related systems have been studied by other authors earlier. Mathematically, this is an nonlinear N-dimensional dynamical system that is invariant under rotating the sites. There is a single parameter, namely forcing strength. For small forcing strength, there is no "weather": the only possible stable solutions are constant in space and time. As the strength of the forcing increases, periodic wave patterns appear that move around the circle of sites. These periodic patterns are not unique - the same forcing strength may be associated with stable patterns that are qualitatively different, depending on the system's initial state. For even larger forcing, the motion becomes chaotic. Regular wave patterns are replaced by moving irregular wave trains that are short-lived, similar to changing weather systems that move across a landscape. The talk will introduce the main properties of this and of related systems. The appearance of periodic solutions can be explained with bifurcation theory for all these versions. By using the discrete Fourier transform and explicit computation of normal form coefficients, the stability of bifurcating periodic solutions and the coexistence of multiple such solutions for the same radiative forcing can be understood. The system also shows delayed transition to instability as the forcing parameter increases slowly.
This is joint work with John Kerin, a former Georgetown University undergraduate student.
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Oberseminar Nonlinear Dynamics
Veranstalter
Freie Universität Berlin
WIAS Berlin
- Mittwoch, 17.07.2024, 14:15 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Daniel Matthes, Technische Universität München:
Covariance modulated optimal transport: Geometry and gradient flows
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
This talk is about a novel variant of optimal mass transport in which particles move with a global linear but anisotropic mobility depending on the covariance of the ensemble density. This gives rise to a novel kind of Wasserstein metric that provides a rigorous gradient flow formulation of the mean-field limit for the ensemble Kalman sampling. In combination with the abstract machinery of metric gradient flows, the new metric is an effective tool to study the rate of convergence of these methods. I shall present several analytic results about the modulated Wasserstein metric. The first is the splitting representation, which allows to write the modulated metric as the sum of two simpler metrics, one measuring the distance in terms of first and second moments, the other one measuring in terms of shapes. The second result is about geodesic convexity and the related rates of convergence in gradient flows. Specifically, we prove exponential equilibration in linear Fokker-Planck equations with Gaussian steady states at a rate that does not depend on the covariance of the Gaussian. The third and only partial result is about geodesics, that we prove to exist for sufficiently close densities, or densities with multiple reflection symmetries. We also characterize geodesics in terms of particle trajectories, that are no longer straight line as in the genuine Wasserstein metric, but follow more complicated curves that satisfy second order ordinary differential equations. This is joint work with Andre Schlichting, Matthias Erbar, Franca Hoffmann, and Martin Burger.
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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Donnerstag, 18.07.2024, 10:00 Uhr (Berlin Mitte)
- MATH+ Thematic Einstein Semester on “Mathematics for Quantum Technologies”
Prof. Ulf Leonhardt, Weizmann Institute of Science, Israel:
Third advanced lecture of the series “Forces of the quantum vacuum” .
mehr ... Veranstaltungsort
Berlin Mitte
Abstrakt
Topic: Applications
Imaginary frequencies for capturing the broad band of quantum forces
Thermal Casimir effect
Perfectly conducting cavity
Magnetic mirror and Casimir repulsion
Permittivity hierarchy and repulsive Casimir forces
Negative refraction and quantum levitation
Engineering in the imaginary part of the spectrum
Veranstalter
WIAS Berlin
Einstein Foundation Berlin
- Donnerstag, 18.07.2024, 15:00 Uhr (WIAS-406)
- Seminar Materialmodellierung
Prof. Dr. Jan Giesselmann, Technische Universität Darmstadt:
A posteriori error estimates for systems of hyperbolic conservation laws modeling compressible flows
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstrakt
Hyperbolic conservation laws are a class of PDEs that have many applications, most notably in compressible fluid flows when viscosity is neglected. While these equations are successfully used by engineers in simulations, there are many open questions regarding their mathematical study. These are mostly driven by to the non-uniqueness of entropy solutions in multiple space dimensions but even in one space dimensions stability of solutions is challenging if one is to go beyond initial data that are small in BV.
The challenges in the mathematical analysis have lead to a situation where a variety of sophisticated numerical schemes exists and is successfully used in practice but the mathematical foundations of these methods are not as substantial as one would hope. This issue has been addressed by several authors in recent years and we plan plan to present what has been achieved in the field of a posteriori error estimates, i.e. explicit bounds for the error of the numerical solution that can be computed from the numerical solution.
A fundamental building block of a posteriori error estimates are stability theories that allow to relate certain norms of residuals, i.e. quantities measuring by how much an approximate solution fails to satisfy the PDE, to certain norms of the error, i.e. the difference between numerical and exact solution. Examples of such stability theories include the classical relative entropy framework, the theory of shifts developed by Vasseur and coworkers and recent results by Bressan and coworkers.
We will describe these stability results and discuss how they have been used to derive a posteriori error estimates for hyperbolic conservation laws.
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Seminar Materialmodellierung
Veranstalter
WIAS Berlin
- Freitag, 19.07.2024, 10:00 Uhr (Berlin Mitte)
- MATH+ Thematic Einstein Semester on “Mathematics for Quantum Technologies”
Prof. Ulf Leonhardt, Weizmann Institute of Science, Israel:
Fourth advanced lecture of the series “Forces of the quantum vacuum” .
mehr ... Veranstaltungsort
Berlin Mitte
Abstrakt
Topic: Outlook
The quantum vacuum seen by accelerated observers (relativistic acceleration, Rindler coordinates, Unruh effect)
Entanglement in the quantum vacuum
Classical analogue of the Unruh effect
The case for a Casimir cosmology
Veranstalter
WIAS Berlin
Einstein Foundation Berlin