8 papers
Discrete Sobolev and Trudinger inequalities on polyhedral meshes
Maxime Herda, Ariane Trescases, Antoine Zurek
We revisit the derivation of discrete Sobolev and related inequalities on bounded domains for piecewise constant functions on polyhedral meshes. Our results improve the dependence…
Synchronization of Synchrotron Radiation Bursts during a spatio-temporal Instability in accelerator-Based source
C. Evain, A. -A. Diallo, E. Roussel +9
Synchronization is a fundamental phenomenon in dynamical systems, occurring in a wide range of contexts such as mechanical, chemical, biological, and social systems. In this work,…
Fractional hypocoercivity in bounded domains in the anomalous diffusion limit
Maxime Herda, Marc Pegon, Isabelle Tristani
In this paper, we provide quantitative stability results for several dissipative linear kinetic equations with heavy-tailed equilibria in different geometries. Moreover, the approa…
Existence of solutions and uniform bounds for the stationary semiconductor equations with generation and ionic carriers
Dilara Abdel, Alain Blaustein, Claire Chainais-Hillairet +2
We consider a stationary drift-diffusion system with ionic charge carriers and external generation of electron and hole charge carriers. This system arises, among other application…
Numerical analysis and simulation of lateral memristive devices: Schottky, ohmic, and multi-dimensional electrode models
Dilara Abdel, Maxime Herda, Martin Ziegler +3
In this paper, we present the numerical analysis and simulations of a multi-dimensional memristive device model. Memristive devices and memtransistors based on two-dimensional (2D)…
A finite volume scheme for the local sensing chemotaxis model
Maxime Herda, Ariane Trescases, Antoine Zurek
In this paper we design, analyze and simulate a finite volume scheme for a cross-diffusion system which models chemotaxis with local sensing. This system has the same Lyapunov func…
Charge transport systems with Fermi-Dirac statistics for memristors
Maxime Herda, Ansgar Jüngel, Stefan Portisch
An instationary drift-diffusion system for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a bounded do…
Well-posedness and long-time behavior for self-consistent Vlasov-Fokker-Planck equations with general potentials
Pierre Gervais, Maxime Herda
We study the well-posedness, steady states and long time behavior of solutions to Vlasov-Fokker-Planck equation with external confinement potential and nonlinear self-consistent in…