The Apollonian decay of beer foam bubble size distribution and the lattices of Young diagrams and their correlated mixing functions.
The asymmetric simple exclusion model with multiple shocks
The Bethe lattice spin glass at zero temperature
The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
The existence of solutions to the Cauchy problem for a nonlinear parabolic equation describing the gravitational interaction of particles is studied under minimal regularity assumptions on the initial conditions. Self-similar solutions are constructed for some homogeneous initial data.
The condition of quasiperiodicity in imaginary time as a constraint at the functional integration and the time-dependent -correlator of the Heisenberg magnet.
The entropy principle: from continuum mechanics to hyperbolic systems of balance laws
We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the entropy principle for selecting admissible discontinuous weak solutions and to symmetrize general systems of hyperbolic balance laws. A particular attention is given on the local and global well-posedness of the relative Cauchy problem for smooth solutions....
The integrated density of states for an interacting multiparticle homogeneous model and applications to the Anderson model.
The kinetic transport equation in the case of Compton scattering.
The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited
The mean-field limit for the dynamics of large particle systems
This short course explains how the usual mean-field evolution PDEs in Statistical Physics - such as the Vlasov-Poisson, Schrödinger-Poisson or time-dependent Hartree-Fock equations - are rigorously derived from first principles, i.e. from the fundamental microscopic models that govern the evolution of large, interacting particle systems.
The parabolic Anderson model in a dynamic random environment: Basic properties of the quenched Lyapunov exponent
In this paper we study the parabolic Anderson equation , , , where the -field and the -field are -valued, is the diffusion constant, and is the discrete Laplacian. The -field plays the role of adynamic random environmentthat drives the equation. The initial condition , , is taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump...
The parabolic-parabolic Keller-Segel equation
I present in this note recent results on the uniqueness and stability for the parabolic-parabolic Keller-Segel equation on the plane, obtained in collaboration with S. Mischler in [11].
The relativistic Enskog equation near the vacuum.
The spectral gap for a Glauber-type dynamics in a continuous gas
The structural influence of the forces of the stability of dynamical systems.
The time constant and critical probabilities in percolation models.
The time for a critical nearest particle system to reach equilibrium starting with a large gap.
The use of Laguerre-Sonine polynomials in solving Boltzmann's equation (II).
The Wigner–Poisson–Fokker–Planck system : global-in-time solution and dispersive effects
Theoretical and numerical comparison of some sampling methods for molecular dynamics
The purpose of the present article is to compare different phase-space sampling methods, such as purely stochastic methods (Rejection method, Metropolized independence sampler, Importance Sampling), stochastically perturbed Molecular Dynamics methods (Hybrid Monte Carlo, Langevin Dynamics, Biased Random Walk), and purely deterministic methods (Nosé-Hoover chains, Nosé-Poincaré and Recursive Multiple Thermostats (RMT) methods). After recalling some theoretical convergence properties for the...