Modeling, theory and numerics for PDEs (kinetic and hyperbolic systems)

Liste des Contributions

31. Linear and Non Linear Stability for the kinetic plasma sheath on a bounded interval

M. Mehdi Badsi

08/10/2024 09:00

Plasma sheaths are inhomogeneous equilibrium that form when a plasma is in contact with an absorbing wall. We prove linear and non linear stability of a kinetic sheath equilibrium for a Vlasov-Poisson type system in a bounded interval. Notably, in the linear setting, we obtain exponential decay of the fluctuation provided the rate of injection of particles at equilibrium is smaller that the...

29. Long-time behavior for Vlasov-Fokker-Planck with general potentials

M. Maxime Herda

08/10/2024 09:50

In this presentation, I will talk about the well-posedness, steady states and long time behavior of solutions to Vlasov-Fokker-Planck equation with external confinement potential and self-consistent interactions. Compared to previous works on this topic, our results allow for large, singular and non-symmetric interactions. As a corollary of our main results, we show exponential decay of...

36. On the quadratic stability of asymmetric Hermite basis and application to plasma physics

M. Ruiyang Dai

08/10/2024 11:10

We analyze why the discretization of linear transport with asymmetric Hermite basis functions can be instable in quadratic norm. The main reason is that the finite truncation of the infinite moment linear system looses the skew-symmetry property with respect to the Gram matrix. Then we propose an original closed formula for the scalar product of any pair of asymmetric basis functions. It makes...

48. Linear / nonlinear approaches for the approximation of convection-diffusion equations

Mme Claire Chainais-Hillairet

08/10/2024 13:45

47. Sub-exponential tails in biased run and tumble equations with unbounded velocities

M. Luca Ziviani

08/10/2024 14:35

In this talk we are going to present some recent results about the Run and Tumble equations, a kinetic model for the movement of bacteria subjected to the presence of a chemotactic substance. Unlike many previous articles, in this work in collaboation with Emeric Bouin and Josephine Evans, we consider the Run and Tumble equation when the set velocities is the whole space. The distribution M of...

50. On the stability of numerical schemes for linear transport with boundary

M. Nicolas Seguin

08/10/2024 15:55

The goal is the study the stability of explicit finite difference schemes for the one-dimensional advection equation with an inflow boundary condition, the outflow case being rather well understood. We reformulate the so-called strong stability by introducing the intrinsic Kreiss-Lopatinskii determinant, which possesses the same regularity as the vector bundle of discrete stable solutions. In...

52. A multi-dimensional staggered scheme for the diffusive limit in the radiative transfer equation

M. Khaled Saleh

08/10/2024 16:45

The radiative transfer equation is a kinetic PDE modelling the specific radiation intensity carried by a population of photons described by a statistical description, i.e. a transport equation on the fraction of photons travelling in a given direction. It is well known that as the Knudsen number (which is the ratio of the mean free path length to a representative physical length scale) goes to...

34. TBA

M. Frédéric Hérau

09/10/2024 09:00

32. Hyperbolic approximation of parabolic systems : hypocoercivity and harmonic analysis

M. Timothée Crin-Barrat

09/10/2024 09:50

39. Spectral scheme for the linear Boltzmann BGK equation on the real line

M. Bastien Grosse

09/10/2024 11:10

We present a fully spectral scheme in both space and velocity for an inhomogeneous kinetic equation on the real axis. The collision operator admits several conservation laws, and their number depends on the harmonicity of the potential phi. Our scheme is based upon a projection on Hermite polynomials in velocity and on orthonormal polynomials with respect to the weight exp(-phi) in space. For...

28. Transport and semi-Lagrangian particles

M. Georges-Henri Cottet

10/10/2024 09:00

37. Conservative cascade schemes for Vlasov type equations

M. Michel Mehrenberger

10/10/2024 09:50

The conservative cascade method permits to replace a complex multi-dimensionnal conservative remapping with a sequence ("cascade") of 1D conservative remappings. It shares some features with splitting schemes (in particular the 1D feature permits to ease the parallelization), but it has also some differences, as it remains based on multi-dimensionnal characteristics, which can be more...

49. Numerical simulation of Vlasov-Poisson system with strong external magnetic field

M. Kim Han Trinh

10/10/2024 11:10

44. Particle-Free-Lagrange methods for transport equations

M. Bruno Desprès

10/10/2024 13:45

33. Hydrodynamic limit of elastic kinetic equations by a spectral approach

M. Pierre Gervais

10/10/2024 14:35

[FRANÇAIS] Limite hydrodynamique d'équations cinétiques conservatives par une approche spectrale Parmi les 23 problèmes listés par D. Hilbert durant le Congrès International des Mathématiciens en 1900, le 6ème concerne la dérivation de descriptions macroscopiques des fluides à partir de leurs descriptions microscopique. Une des stratégies possibles consiste à passer par un niveau de...

38. Optimal control in ferromagnetism: minimal time of magnetization switching

Mme Clémentine Courtes

11/10/2024 09:00

In this talk, we consider an ellipsoidal ferromagnetic material exposed to an external magnetic field. The magnetization of the material is modeled by the Landau-Lifshitz equation. We are interested in the following question: can we reverse the magnetization of the material in minimal time by using the external magnetic field as our control variable? We prove that, depending on the material's...

43. Discontinuous Galerkin methods and basis enrichment using neural networks

M. Laurent Navoret

11/10/2024 09:50

The Discontinuous Galerkin method is a high-order accurate numerical scheme to solve hyperbolic systems. In this talk, we will present a strategy to take advantage of the recent development of neural networks to enhance the method's precision around a parametric family of equilibria. The method is based on introducing a prior solution inside the basis, which can be estimated using Physic...

45. Dynamic metastability in the self-attention model

M. Borjan Geshkovski

11/10/2024 11:10

The pure self-attention model is a simplification of the celebrated Transformer architecture, which neglects multi-layer perceptron layers and includes only a single inverse temperature parameter. Despite its apparent simplicity, the model exhibits a remarkably similar qualitative behavior across layers to that observed empirically in a pre-trained Transformer. Viewing layers as a time...

41. TBA

Emeric Bouin