Asymptotic Behaviors of systems of PDEs arising in physics and biology - 4th edition

Session

Poster session

17 nov. 2021, 16:15

Salle Pasteur (Polytech Lille)

50. A Fick’s law recovering relaxation BGK operator for polyatomic mixtures

Kévin Guillon (Institut Mathématique de Bordeaux)

17/11/2021 16:15

Poster

In this talk, we extend the derivation of the Fick-relaxation BGK model, performed in [BP S12], to a polyatomic setting. The construction of the present model is based on the introduction of relaxation coefficients and by solving an entropy minimisation problem. The distribution functions of each species are described by adding a supplementary continuous variable collecting vibrational and...

58. A thermodinamically consistent reduced model for iron corrosion

Federica Raimondi (CNRS - Univ. Lille - Inria)

17/11/2021 16:15

Poster

In [1] Christian Bataillon et al. have proposed a DPCM (Poisson Coupled Diffusion Model) to describe the corrosion process that occurs on the surface of steel containers in contact with the claystone formation. The model in question focuses on the development of a dense oxide layer in the region of contact between the metal and the claystone. The system formed by the layer, the metal and the...

52. Analysis of a Finite–Volume Scheme for a Single–Species Biofilm Model

Christoph Helmer (TU Wien)

17/11/2021 16:15

Poster

Biofilms are accumulations of microorganisms that can be found on almost every surface, for instance as dental plaque on teeth or as an accumulation of Staphylococcus Aureus on catheters. Based on the biofilm growth model formulated by Eberl, Parker and van Loosdrecht in 2000, we formulate an implicit Euler finite–volume scheme for the degenerate–singular diffusion equation for the biomass...

53. Asymptotic-preserving multilevel Monte Carlo for Kinetic Equations in Plasma Edge Simulations

Emil Loevbak (KU Leuven - FWO)

17/11/2021 16:15

Poster

When designing tokamak fusion reactors, two sets of particles need to be modeled. The electromagnetically constrained plasma, which harbors the reaction, is generally modeled as a fluid. This fluid model is coupled with a kinetic equation modeling neutral particles. When the collision rate of neutrals with the background is high, a well-defined limiting equation exists. High-dimensionality of...

60. Boundary control problem of a water waves system in a tank

Pei Su (Institut de Mathématiques de Bordeaux)

17/11/2021 16:15

Poster

Here we are interested in the boundary control problem of the small-amplitude water waves system in a rectangular tank. The model actually we used here is a fully linear and fully dispersive approximation of Zakharov-Craig-Sulem formulation constrained in a rectangle, in particular, with a wave maker. The wave maker acts on one lateral boundary, by imposing the acceleration of the fluid in the...

59. Compactness property of the linearized Boltzmann operator

Marwa Shahine (University of Bordeaux)

17/11/2021 16:15

Poster

We consider the Boltzmann equation that models a polyatomic gas by taking into account the continuous microscopic internal energy I. In particular, we consider the kinetic system proposed by [2], which is based on the procedure of Borgnakke and Larsen [1]. We linearize the Boltzmann equation around the Maxwellian function, which represents the equilibrium distribution function. Under some...

56. Existence of solutions and localisation limit of a nonlocal cross-diffusion system for multi-species populations

Stefan Portisch (TU Wien)

17/11/2021 16:15

Poster

Population dynamics can be modelled by stochastic interacting any particle systems. However their numerical approximation is time consuming so one prefers to investigate simpler macroscopic models, which are derived from the many particle systems in the mean field limit. When several species are involved, this leads to nonlocal cross-diffusion terms. We investigate a nonlocal cross-diffusion...

54. Long-time behaviour of hybrid finite volume schemes for anisotropic Drift-Diffusion model

Julien Moatti (Inria Lille - Nord Europe)

17/11/2021 16:15

Poster

In this poster, we present a Hybrid Finite Volumes scheme to discretise semiconductors models. This type of finite volumes scheme [1] is devised to handle general polygonal/polyhedral meshes, alongside with anisotropic diffusion tensors. Especially, the scheme introduced here can be used in situations where the semiconductor is immersed in a magnetic field [2].
The scheme is based on the...

49. Modelling and simulation of charge transport in perovskite solar cells

Dilara Abdel (Weierstrass Institute Berlin)

17/11/2021 16:15

Poster

Perovskite solar cells (PSCs) have become one of the fastest growing photovoltaic technologies within the last few years, for example perovskite/silicon tandem cells have become more efficient than single junction silicon solar cells [1]. However, which exact physical operation mechanisms play a fundamental role within such devices is not fully understood yet. Experiments indicate that on the...

51. Nonexistence of radial positive solutions for a class of semilinear elliptic systems in an annulus

Said Hakimi (Polydisciplinary Faculty of Beni Mellal)

17/11/2021 16:15

Poster

Abstract in attachment

55. On deterministic numerical methods for the quantum Boltzmann-Nordheim equation

Alexandre Mouton (Laboratoire Paul Painlevé - CNRS)

17/11/2021 16:15

Poster

Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This equation, modeled on the seminal Boltzmann equation, describes using a statistical physics formalism the time evolution of a gas composed of bosons or fermions....

57. Uniformly accurate scheme for tokamak's plasmas model

Damien Prel (Laboratoire de Mathématiques Jean Leray)

17/11/2021 16:15

Poster