Related papers: Global stability and $H$-theorem in lattice models…
Sometimes the dynamics of a physical system is described by non-Hamiltonian equations of motion, and additionally, the system is characterized by long-range interactions. A concrete example is that of particles interacting with light as…
We analyze the stability of stationary solutions of a singular Vlasov type hydrodynamic equation (HE). This equation was derived (under suitable assumptions) as the hydrodynamical scaling limit of the Hamiltonian evolution of a system…
The lattice Boltzmann equation can be viewed as a discretization of the continuous Boltzmann equation. Because of this connection it has long been speculated that lattice Boltzmann algorithms might obey an H-theorem. In this letter we prove…
Although the Vlasov equation is used as a good approximation for a sufficiently large $N$, Braun and Hepp have showed that the time evolution of the one particle distribution function of a $N$ particle classical Hamiltonian system with long…
A Traveling Maxwellian $\mathcal{M} = \mathcal{M}(t, x, v)$ represents a traveling wave solution to the Boltzmann equation in the whole space $\R^3_x$(for the spatial variable). The primary objective of this study is to investigate the…
A Collision-Avoiding flocking particle system proposed in [8] is studied in this paper. The global wellposedness of its corresponding Vlasov-type kinetic equation is proved. As a corollary of the global stability result, the mean field…
We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within…
We complete the kinetic theory of inhomogeneous systems with long-range interactions initiated in previous works. We use a simpler and more physical formalism. We consider a system of particles submitted to a small external stochastic…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…
Long-range interacting N-particle systems get trapped into long-living out-of-equilibrium stationary states called quasi-stationary states (QSS). We study here the response to a small external perturbation when such systems are settled into…
In this paper, we consider the spatially inhomogeneous diffusively driven inelastic Boltzmann equation in different cases: the restitution coefficient can be constant or can depend on the impact velocity (which is a more physically relevant…
We complete the existing literature on the kinetic theory of systems with long-range interactions. Starting from the BBGKY hierarchy, or using projection operator technics or a quasilinear theory, a general kinetic equation can be derived…
We present a kinetic theory for inhomogeneous systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a closed kinetic equation describing the relaxation of the…
Empirically defining some constant probabilistic orbits of f(x) and g(x) iterated high-order functions, the stability of these functions in possible entangled interaction dynamics of the environment through its orbit's connectivity (open…
Dynamics of many-body Hamiltonian systems with long range interactions is studied, in the context of the so called $\alpha-$HMF model. Building on the analogy with the related mean field model, we construct stationary states of the…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
The Vlasov equation is well known to provide a good description of the dynamics of mean-field systems in the $N \to \infty$ limit. This equation has an infinity of stationary states and the case of {\it homogeneous} states, for which the…
In this work we revisit the existence, stability and dynamics of unstable traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an $\alpha$-Fermi-Pasta-Ulam type with the additional feature…
Time-dependent density functional theory, proposed recently in the context of atomic diffusion and non-equilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the…