Global branching for discontinuous problems
Global existence and extinction of weak solutions to a class of semiconductor equations with fast diffusion terms.
Global existence for the discrete diffusive coagulation-fragmentation equations in L1.
Global existence versus blow up for some models of interacting particles
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and Debye-Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.
Global solutions for a problem modeling the dynamics of a system of self-gravitating Brownian particles
Results on the global existence and uniqueness of variational solutions to an elliptic-parabolic problem occurring in statistical mechanics are provided.
Global solutions to vortex density equations arising from sup-conductivity
Global strong solutions of Vlasov's equation---necessary and sufficient conditions for their existence
Graph weights arising from Mayer's theory of cluster integrals.
Gravitational collapse of a Brownian gas
We investigate a model describing the dynamics of a gas of self-gravitating Brownian particles. This model can also have applications for the chemotaxis of bacterial populations. We focus here on the collapse phase obtained at sufficiently low temperature/energy and on the post-collapse regime following the singular time where the central density diverges. Several analytical results are illustrated by numerical simulations.
Green's function method approach to electron configuration of superlattices.
Ground state incongruence in 2D spin glasses revisited.
Growth and accretion of mass in an astrophysical model
We study asymptotic behavior of radial solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles. In particular, we consider stationary solutions in balls and in the whole space, self-similar solutions defined globally in time, blowing up self-similar solutions, and singularities of solutions that blow up in a finite time.
Growth and accretion of mass in an astrophysical model, II
Radially symmetric solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles in a bounded container are studied. Conditions ensuring either global-in-time existence of solutions or their finite time blow up are given.
Growth fluctuations in a class of deposition models
H1/2 maps with values into the circle : minimal connections, lifting, and the Ginzburg–Landau equation
Hard balls gas and Alexandrov spaces of curvature bounded above.
Harmonic measures versus quasiconformal measures for hyperbolic groups
We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.
Heat kernel for random walk trace on ℤ3 and ℤ4
We study the simple random walk X on the range of simple random walk on ℤ3 and ℤ4. In dimension four, we establish quenched bounds for the heat kernel of X and max0≤k≤n|Xk| which require extra logarithmic correction terms to the higher-dimensional case. In dimension three, we demonstrate anomalous behavior of X at the quenched level. In order to establish these estimates, we obtain several asymptotic estimates for cut times of simple random walk and asymptotic estimates for loop-erased random walk,...
Hermite basis diagonalization for the non-cutoff radially symmetric linearized Boltzmann operator
We provide some new explicit expressions for the linearized non-cutoff radially symmetric Boltzmann operator with Maxwellian molecules, proving that this operator is a simple function of the standard harmonic oscillator. A detailed article is available on arXiv [15].
Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation
This work is devoted to the numerical simulation of the Vlasov equation using a phase space grid. In contrast to Particle-In-Cell (PIC) methods, which are known to be noisy, we propose a semi-Lagrangian-type method to discretize the Vlasov equation in the two-dimensional phase space. As this kind of method requires a huge computational effort, one has to carry out the simulations on parallel machines. For this purpose, we present a method using patches decomposing the phase domain, each patch being...