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Mr Mehdi Badsi10/8/24, 9:00 AM
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...
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Mr Maxime Herda10/8/24, 9:50 AM
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...
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Mr Ruiyang Dai10/8/24, 11:10 AM
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...
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Mrs Claire Chainais-Hillairet10/8/24, 1:45 PM
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Mr Luca Ziviani10/8/24, 2:35 PM
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...
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Mr Nicolas Seguin10/8/24, 3:55 PM
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...
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Mr Khaled Saleh10/8/24, 4:45 PM
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...
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Mr Frédéric Hérau10/9/24, 9:00 AM
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Mr Timothée Crin-Barrat10/9/24, 9:50 AM
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Mr Bastien Grosse10/9/24, 11:10 AM
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...
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Mr Georges-Henri Cottet10/10/24, 9:00 AM
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Mr Michel Mehrenberger10/10/24, 9:50 AM
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...
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Mr Kim Han Trinh10/10/24, 11:10 AM
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Mr Bruno Desprès10/10/24, 1:45 PM
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Mr Pierre Gervais10/10/24, 2:35 PM
[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...
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Mrs Clémentine Courtes10/11/24, 9:00 AM
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...
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Mr Laurent Navoret10/11/24, 9:50 AM
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...
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Mr Borjan Geshkovski10/11/24, 11:10 AM
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...
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Emeric Bouin
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