Veranstaltungen

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Dienstag, 24.05.2022, 15:15 Uhr (WIAS-ESH)
Oberseminar Nonlinear Dynamics
Dr. Oleksandr A. Burylko, Institute of Mathematics NAS of Ukraine and Potsdam Institute for Climate Impact Research:
Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators (hybrid talk)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coupled identical units do not allow solutions where distinct oscillators are frequency-unlocked?a necessary condition for the emergence of chimeras. Thus, forced symmetry breaking is necessary to observe chimera-type solutions. Here, we consider the bifurcations that arise when full permutational symmetry is broken for the network to consist of coupled populations. We consider the smallest possible network composed of four phase oscillators and elucidate the phase space structure, (partial) integrability for some parameter values, and how the bifurcations away from full symmetry lead to frequency-unlocked weak chimera solutions Since such solutions wind around a torus they must arise in a global bifurcation scenario. Moreover, periodic weak chimeras undergo a period doubling cascade leading to chaos. The resulting chaotic dynamics with distinct frequencies do not rely on amplitude variation and arise in the smallest networks that support chaos

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Oberseminar Nonlinear Dynamics

Veranstalter
WIAS Berlin
Freie Universität Berlin
Mittwoch, 25.05.2022, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Joachim Rehberg, WIAS Berlin:
On non-autonomous and quasilinear parabolic systems (hybrid talk)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

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Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Dienstag, 31.05.2022, 13:30 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Gabriel R. Barrenechea, University of Strathclyde, GB:
Divergence-free finite element methods for an inviscid fluid model
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In this talk I will review some recent results on the stabilisation of linearised incompressible inviscid flows (or, with a very small viscosity).
The partial differential equation is a linearised incompressible equation similar to Euler's equation, or Oseen's equation in the vanishing viscosity limit. In the first part of the talk I will present results on the well-posedeness of the partial differential equation itself. From a numerical methods' perspective, the common point of the two parts is the aim of proving the following type of estimate:
u - _h^ _L^2^ leq C h^k+frac12 u _H^k+1^
where u is the exact velocity and u_h^ is its finite element approximation. In the estimate above, the constant C is independent of the viscosity (if the problem has a viscosity), and, more importantly, independent of the pressure. This estimate mimicks what has been achieved for stabilised methods for the convection-diffusion equation in the past. Nevertheless, up to the best of our knowledge, this is the first time this type of estimate is obtained in a pressure-robust way.
I will first present results of discretisations using H(div)-conforming spaces, such as Raviart-Thomas, or Brezzi-Douglas-Marini where an estimate of the type eqrefmain-estimate is proven (besides an optimal estimate for the pressure). In the second part of the talk I will move on to H^1-conforming divergence-free elements, with the Scott-Vogelius element as the prime example. In this case, due to the H^1-conformity, extra control on the convective term needs to be added. After a (very brief) review of the idea of vorticity stabilisation, I will present very recent results on CIP stabilisation where a discussion on the type, and number, of jump terms will be presented. The method is independent of the pressure gradients, which makes it pressure-robust and leads to pressure-independent error estimates such as eqrefmain-estimate.
Finally, some numerical results will be presented and the present approach will be compared to the classical CIP method.
This work is a collaboration with E. Burman (UCL, UK), and E. Caceres and J. Guzmán (Brown, USA).

Veranstalter
WIAS Berlin
Mittwoch, 01.06.2022, 12:30 Uhr (WIAS-405-406)
Seminar Interacting Random Systems
Francesca Cottini, Università degli Studi di Milano-Bicocca, Italien:
Gaussian Limits for Subcritical Chaos
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
In this talk I will present a general and novel criterion to show the convergence towards a Gaussian limit for polynomial chaos, that is a multi-linear polynomial of independent random variables. This result is motivated by the study of 2d directed polymers in the subcritical regime and of the related 2d Stochastic Heat Equation, for which many convergence results were proved in recent years. Our criterion allows us to recover these results in a simpler way and, furthermore, to obtain novel results. I will focus on two main new Gaussian limits, for a singular product between the partition function and the disorder, and for the logarithm of the partition function, through an explicit chaos expansion. This is a joint work with Francesco Caravenna.

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Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin
Mittwoch, 01.06.2022, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Melanie Koser, Humboldt-Universität zu Berlin:
Pattern formation in certain frustrated spin systems (hybrid talk)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Weitere Informationen
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 02.06.2022, 14:00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Julien Moatti, Université de Lille, Frankreich:
A structure preserving hybrid finite volume scheme for semi-conductor models on general meshes
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In 1996, Gajewski and Gärtner introduced a model describing semi-conductor devices in presence of an exterior magnetic field and proposed a scheme to discretise it. From a numerical point of view, the main difficulty in dealing with this model is the impact of the magnetic field over the system, which leads to anisotropic diffusion equations. In particular their scheme does not preserve the positivity of the solutions if the magnetic field is too intense.
In this talk, I will introduce a new structure preserving scheme for discretising similar systems of equations. The scheme under study is based on the Hybrid Finite Volume method, which is devised to handle anisotropic diffusion tensors alongside with very general polygonal/polyhedral meshes. It is designed to handle general statistics (including Boltzmann and Blakemore) as well as strong magnetic fields, while ensuring that the computed densities are positive.
The analysis of the scheme relies on the preservation of an entropy structure at the discrete level, which mimics the continuous behaviour of the system. I will explain how we can use this structure to show that there exist positive solutions to the scheme. As a by product, we also establish a "good discrete long-time behaviour" property: the discrete solutions converge towards a discrete thermal equilibrium as time tends to infinity.
Alongside with the theoretical results, I will present numerical results obtained with this scheme in various situations. I will especially focus on the preservation of bounds for the carrier densities and on the long-time behaviour of the solutions.
This is a joint work with Claire Chainais-Hillairet, Maxime Herda and Simon Lemaire.

Veranstalter
WIAS Berlin
Donnerstag, 02.06.2022, 16:00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Fenja Severing, WIAS Berlin:
Instabilities in the context of the Generalized Nonlinear Schrödinger Equation
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Tba

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Forschungsseminar Mathematische Modelle der Photonik

Veranstalter
WIAS Berlin
Mittwoch, 08.06.2022, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Robert Lasarzik, WIAS Berlin:
Energy-variational solutions and their approximation (hybrid talk)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In this talk, energy-variational (EnVar) solutions are introduced for a large class of nonlinear evolution equations. Considering the Ericksen--Leslie equations modelling the evolution of liquid crystals, we observe that EnVar solutions emerge as the limit of a structure-preserving finite element scheme. We can show weak-strong uniqueness of the limit solution and additionally the so-called semi-flow property, which says that concatenations and restrictions of EnVar solutions are EnVar solutions again. Under certain assumptions every EnVar solution implies the existence of a measure-valued solution to the Ericksen--Leslie system. This implies that the EnVar solution concept is finer than the usual measure-valued solution concept. Finally, a time-discretization scheme is introduced via an incremental minimization, which resembles the minimizing movement scheme for gradient flows.

Weitere Informationen
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Montag, 20.06.2022, 15:00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. Maxim A. Olshanskii, University of Houston, USA:
Numerical analysis of surface fluids
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In this talk we focus on numerical analysis for systems of PDEs governing the motion of material viscous surfaces, the topic motivated by continuum-based modeling of lateral organization in plasma membranes. We shall consider several systems of fluid and phase-field equations defined on evolving surfaces and discuss some recent results about well-posedness of such problems. We further introduce a computational approach and numerical analysis for the resulting systems of PDEs. The methods are combined to deliver a computationally tractable and thermodynamically consistent model describing the dynamics of a two-phase viscous layer. The talk closes with an illustration of the model capacity to predict lateral ordering in multicomponent vesicles of different lipid compositions.

Veranstalter
WIAS Berlin