相关论文: Stochastic and statistical stability of the classi…
A simple analytical model for a turbulent flow is proposed, which considers the flow as a collection of localized spatial structures that are composed of elementary "cells" in which the state of the particles (atoms or molecules) is…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with…
We investigate the stability of self-propelled particle flocks in the Taylor-Green vortex, a steady vortical flow. We consider a model where particles align themselves to a combination of the orientation and the acceleration of particles…
Using a Lattice Boltzmann hydrodynamic computational modeler to simulate relativistic fluid systems we explore turbulence in two-dimensional relativistic flows. We first a give a pedagogical description of the phenomenon of turbulence and…
Structured on the paradigmatic Navier-Stokes flow model, we study a stochastically forced Taylor-Couette system in the narrow gap limit, in order to analyze the simultaneous impact of a non-conserved (Gaussian) force and a nonlinear…
We consider the nonlinear Klein Gordon Maxwell system on four dimensional Minkowski space-time. For appropriate nonlinearities the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons…
We present stability and recurrence results for a class of stochastic hybrid dynamical systems with oscillating flow maps. These results are developed by introducing averaging tools that parallel those already existing for ordinary…
Periodically forced, oscillatory fluid flows have been the focus of intense research for decades due to their richness as a nonlinear dynamical system and their relevance to applications in transportation, aeronautics, and energy…
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz '63 model. Specifically, we prove that when damping is absent in one of the temperature components, the system possesses a unique invariant…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
We study the averaging method for flows perturbed by a dynamical system preserving an infinite measure. Motivated by the case of perturbation by the collision dynamic on the finite horizon $\mathbb Z$-periodic Lorentz gas and in view of…
We adapt the statistical mechanics of the shallow-water equations to the case where the flow is forced at small scales. We assume that the statistics of forcing is encoded in a prior potential vorticity distribution which replaces the…
We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a…
Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamical…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be…
We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…