Veranstaltungen

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Dienstag, 17.05.2022, 15:15 Uhr (WIAS-ESH)
Oberseminar Nonlinear Dynamics
Leonhard Schülen, Technische Universität Berlin:
The solitary route to chimera states
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit we demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. We demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators

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Oberseminar Nonlinear Dynamics

Veranstalter
WIAS Berlin
Freie Universität Berlin
Mittwoch, 18.05.2022, 10:00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. Zdeněk Hlávka, Charles University, Tschechische Republik:
Testing dependencies in functional time series (hybrid talk)
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We discuss tests of serial independence for a sequence of functional observations and tests of independence between two (or more) time series of functional observations. The tests are based on characteristic functions which are appropriately estimated from functional observations. The limit distribution of the new test statistic is obtained under the null hypothesis, while under alternatives it is shown that the test statistics almost surely diverge as the sample size increases. In a Monte Carlo study, we investigate appropriate resampling methods and we investigate the tests? performance in finite samples. Finally, an application illustrates the use of the method with real data from financial markets, including also cumulative intraday returns of Bitcoin and Ethereum. References: Meintanis, S. G., Hušková, M., & Hlávka, Z. (2022). Fourier-type tests of mutual independence between functional time series. Journal of Multivariate Analysis, 189, 104873. Hlávka, Z., Hušková, M., & Meintanis, S. G. (2021). Testing serial independence with functional data. Test, 30(3), 603-629.

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Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Mittwoch, 18.05.2022, 12:30 Uhr (WIAS-ESH)
Seminar Interacting Random Systems
Richard Kraaij, TU Delft:
Large deviations for weakly coupled slow-fast systems via the comparison principle of an associated Hamilton-Jacobi equation
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In statistical physics many interesting phenomena, e.g. behavior of systems at critical parameters or in the theory of hydrodynamic limits, arise from systems having multiple time-scales. A slow component is influenced by fast components, and as the number of interacting components tends to infinity, limiting results for the slow component are obtained in terms of 'averaged' versions of the fast components. I will consider in my talk the large deviations of coupled Markovian systems with two-time scales. The large deviations can arise from two sources: deviations of the slow process itself, or deviations of the large time averages of the fast process, effectively leading to a competition of two deviation effects. Arguing via the non-linear analogue of the "martingale problem approach" that applies for large deviations of Markov processes, we arrive at a uniqueness problem for a Hamilton-Jacobi-Bellman equation. We establish under mild conditions that this Hamilton-Jacobi-Bellman equation is well-posed, and as a consequence that we have a large deviation principle for a wide class of weakly coupled Markov processes.


Based on joint work with Mikola Schlottke (Eindhoven, The Netherlands)

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Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin

Mittwoch, 18.05.2022, 15:15 Uhr (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
PD Dr. Maria Neuss-Radu, Friedrich-Alexander-Universität Erlangen-Nürnberg:
Effective models for nonlinear drift-diffusion of multiple species in porous media (online talk)
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Online Event

Abstrakt
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's equation for the electric potential. The diffusion terms depend nonlinearly on the concentrations. We consider non-homogeneous Neumann boundary condition for the electric potential. The aim is the rigorous derivation of an effective (homogenized) model in the limit when the scale parameter $epsilon$ tends to zero. This is based on uniform a priori estimates for the solutions of the microscopic model. The crucial result is the uniform $L^infty$-estimate for the concentration in space and time. This result exploits the fact that the system admits a nonnegative energy functional which decreases in time along the solutions of the system. By using weak and strong (two-scale) convergence properties of the microscopic solutions, effective models are derived in the limit $epsilon to 0$ for different scalings of the microscopic model. This is a joint work with Apratim Bhattacharya (Erlangen) and Markus Gahn (Heidelberg).

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Freitag, 20.05.2022, 13:00 Uhr (Online Event)
Forschungsseminar Mathematische Modelle der Photonik
Prof. Andrey Shilnikov, Georgia State University, USA:
Long saga of in-depth modeling of two swim CPGs in two sea slugs (online talk)
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Online Event

Abstrakt
We introduce the concepts underlying the modeling of swim CPGs of two sea slugs in control and under perturbations. The emphasis is put upon the nonlinear dynamics of both interacting cells and synapses and their synergy to produce an emergent network level bursting. We discuss some of its prominent features such feed back loops to maintain stability, including structural, as well resilience to short and long-term perturbations. Our research approaches are rooted in applied dynamical systems, parameter optimization with machine learning elements.

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Forschungsseminar: Mathematische Modelle der Photonik

Veranstalter
WIAS Berlin
Freitag, 20.05.2022, 13:00 Uhr (Online Event)
E-Coffee-Lecture
Alireza Selahi Moghaddam, WIAS:
Creating nice 3d models and animations with Blender
mehr ... Veranstaltungsort
Online Event

Abstrakt
Blender is an open source 3d modeling and animation software, which can easily compete with it's commercial counter-products. Although utilizing the full potential of such a software requires many years of learning, it is surprisingly easy to get nice results with very little effort, which can be used in scientific presentations or papers. With it's Python-interface, Blender even offers a way to fit right into the context of scientific computing.

Veranstalter
WIAS Berlin