Proof of the De Gennes formula for the superheating field in the weak κ limit
Properties of the solution map for a first order linear problem.
Qualitative investigation of the three-phase solutions of the sine-Laplace equation
Quantum Euler-Poisson systems: Existence of stationary states
A one-dimensional quantum Euler-Poisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly non-convex or non-monotone) pressure-density functions under a “subsonic” condition, i.e. assuming sufficiently small current densities. The proof is based on a reformulation of the dispersive third-order equation for the electron...
Quantum graph spectra of a graphyne structure
We study the dispersion relations and spectra of invariant Schrödinger operators on a graphyne structure (lithographite). In particular, description of different parts of the spectrum, band-gap structure, and Dirac points are provided.
Quantum integrable 1D anyonic models: construction through braided Yang-Baxter equation.
Quantum-dot-based photon emission and media conversion for quantum information applications.
Quasicrystallographic groups on Minkowski spaces.
Quasi-neutral limit for a viscous capillary model of plasma
Quelques applications de la positivité en théorie du transport
Quenched limits for transient, ballistic, sub-gaussian one-dimensional random walk in random environment
We consider a nearest-neighbor, one-dimensional random walk {Xn}n≥0 in a random i.i.d. environment, in the regime where the walk is transient with speed vP>0 and there exists an s∈(1, 2) such that the annealed law of n−1/s(Xn−nvP) converges to a stable law of parameter s. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible. In particular we show that there exist sequences {tk} and {tk'} depending on the environment only, such that a quenched...
Random hysteresis loops
Dynamical hysteresis is a phenomenon which arises in ferromagnetic systems below the critical temperature as a response to adiabatic variations of the external magnetic field. We study the problem in the context of the mean-field Ising model with Glauber dynamics, proving that for frequencies of the magnetic field oscillations of order , the size of the system, the “critical” hysteresis loop becomes random.
Random matrices, non-colliding processes and queues
Random walks in a Dirichlet environment.
Reconstruction des phases en cristallographie par maximum d'entropie
Reduced resistive MHD in Tokamaks with general density
The aim of this paper is to derive a general model for reduced viscous and resistive Magnetohydrodynamics (MHD) and to study its mathematical structure. The model is established for arbitrary density profiles in the poloidal section of the toroidal geometry of Tokamaks. The existence of global weak solutions, on the one hand, and the stability of the fundamental mode around initial data, on the other hand, are investigated.
Reduced resistive MHD in Tokamaks with general density
The aim of this paper is to derive a general model for reduced viscous and resistive Magnetohydrodynamics (MHD) and to study its mathematical structure. The model is established for arbitrary density profiles in the poloidal section of the toroidal geometry of Tokamaks. The existence of global weak solutions, on the one hand, and the stability of the fundamental mode around initial data, on the other hand, are investigated.
Régularité de la solution des équations cinétiques en physique des plasmas
Regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system
We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in . It is proved that if the velocity field in the Besov space satisfies some integral property, then the solution keeps its smoothness.
Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors
This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in , we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into...