Veranstaltungen

Mittwoch, 09.10.2024, 11:30 Uhr (WIAS-405-406)

Seminar Interacting Random Systems
Christopher Renaud Chan, Université Grenoble Alpes:
Liquid-gas phase transition for Gibbs point process with saturated interaction
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
Gibbs point processes are natural objects to study systems of particles in interaction. In finite volume, the unnormalised density of the Gibbs measure with respect to a Poisson point process with activity $z$ is given by the Boltzmann factor $e^-beta H$, where $beta$ is the inverse temperature and $H$ is the Hamiltonian that encodes the interaction between particles. The infinite volume Gibbs point processes are defined as solutions to the Dobrushin-Lanford-Ruelle equations, which describe the equilibrium of the system. A liquid-gas phase transition occurs when we do not have uniqueness of the infinite volume Gibbs point process and that they have different densities. We explore the occurrence of such phenomenon in the context of saturated interactions. These interactions represent a class of models where the energy cost of adding a point in areas of high particle density is constant. The Quermass interaction exhibits such saturation property. We will present another interesting example: the diluted pairwise interaction. Under some assumptions, we prove the existence of liquid-gas phase transition for saturated interactions using an adaptation of Pirogov-Sinaï-Zahradník theory in the continuous setting.

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Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin

Mittwoch, 09.10.2024, 15:15 Uhr (WIAS-406)

Analysis-Stochastik-Seminar
Prof. Dr. Zhivorad Tomovski, Palacký University Olomouc, Tschechische Republik:
Anomalous and ultraslow diffusion of a particle driven by distributed-order noises
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
We study the generalised Langevin equation (GLE) approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as distributed-order noises that fulfil generalised versions of the fluctuation-dissipation theorem. The mean squared displacement and the normalised displacement correlation function are derived for the different forms of the friction memory kernel. It is shown that such models can be used to describe anomalous diffusion in complex media, giving rise to subdiffusion, superdiffusion, ultraslow diffusion, strong anomaly, and other complex diffusive behaviours.

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Analysis-Stochastik-Seminar

Veranstalter
WIAS Berlin

14. Oktober 2024 (HU Berlin HVP)

Workshop/Konferenz: WIAS Alumni Day 2024
mehr ... Veranstaltungsort
Humboldt-Universität zu Berlin, Hausvogteiplatz 5-7, R. 0007

Abstrakt
The Weierstrass Institute invites to the first WIAS Alumni Day. This event is intended to promote the exchange between current and former WIAS employees and to evolve our alumni program. We are particularly looking forward to contributions from former WIAS members Johannes Neumann and Florian Schmid, who will talk about their career paths and experiences. In addition, we intend to use an open discussion format such as World Café to structure the communication of the participants (which depends on the final composition of the group of participants and will be planned in more detail after the registration deadline). Finally, we are inviting you to a get-together in the rooms of our recently renovated and redesigned library.

Veranstalter
WIAS Berlin

Mittwoch, 16.10.2024, 15:15 Uhr (WIAS-405-406)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Janusz Ginster, WIAS Berlin:
Formation of microstructure for singularly perturbed problems related to helimagnets and shape-memory alloys
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

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Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

Mittwoch, 30.10.2024, 15:15 Uhr (WIAS-405-406)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Tomáš Roubíček, Czech Academy of Sciences, Tschechische Republik:
Time discretization in visco-elastodynamics at large displacements and strains in the Eulerian frame
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
The fully-implicit time discretization (i.e. the backward Euler formula) is applied to compressible nonlinear dynamical models of viscoelastic media in the Eulerian description, i.e. in the actual deforming configuration. The Kelvin--Voigt rheology or also, in the deviatoric part, the Jeffreys (also called anti-Zener) rheology describing a (possibly nonlinear) creep or a rate-dependent plasticity are considered. Both a linearized convective model at large displacements with a convex stored energy and the fully nonlinear large strain variant with a (possibly generalized) polyconvex stored energy are considered. The time-discrete suitably regularized schemes (suggesting an implementable numerical strategy) are devised for both these heavily nonlinear cases. The numerical stability and, considering the multipolar 2nd-grade viscosity, also convergence towards weak solutions are proved, exploiting the convexity of the kinetic energy when written in terms of linear momentum instead of velocity. In the fully nonlinear case, the examples of neo-Hookean and Mooney--Rivlin materials are presented. A comparison with models of viscoelastic barotropic fluids is also made and thermodynamical extension is outlined, too.

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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

Mittwoch, 13.11.2024, 15:15 Uhr (WIAS-405-406)

Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Lukas Abel, Humboldt-Universität zu Berlin:
A scaling law for a model of epitaxial growth with dislocations
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
Epitaxy is a special form of crystal growth and of great importance in modern technology. We consider a crystalline film on a (rigid) substrate. The misfit between the crystal structures of the film and the substrate can lead to dislocations and can have an influence on the morphology of the film. Dislocations are topological defects of the crystallographic lattice. In this talk we will study a variational model from the literature. It is based on linearized elasticity and additionally takes into account the surface energy of the film's free surface as well as the dislocation nucleation energy. In particular we will discuss a new scaling law for the infimum of the energy. This includes a new construction for the upper bound and a new variant of a ball-construction combined with thorough local estimates for the lower bound. The results indicate that in certain parameter regimes, the formation of dislocations is expected. Reference: Preprint arXiv no. 2403.13646, https://arxiv.org/abs/2403.13646

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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin

Dienstag, 19.11.2024, 13:30 Uhr (WIAS-406)

Seminar Materialmodellierung
Angeliki Koutsimpela, Universität Augsburg:
Mean-field limits for interacting particle systems
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Veranstalter
WIAS Berlin