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The Landau-Lifshitz fluctuating hydrodynamics is used to study the statistical properties of the linearized Kolmogorov flow. The relative simplicity of this flow allows a detailed analysis of the fluctuation spectrum from near equilibrium…
The modification of the Vlasov equation, in its standard form describing a charged particle distribution in the six-dimensional phase space, is derived explicitly within a formal Hamiltonian approach for arbitrarily curved spacetime. The…
In this paper we use the theory of viscosity solutions for Hamilton-Jacobi equations to study propagation phenomena in kinetic equations. We perform the hydrodynamic limit of some kinetic models thanks to an adapted WKB ansatz. Our models…
In Physica A vol 387(24) (2008) pp6079-6094 [1], a kinetic equation for gas flows was proposed that leads to a set of four macroscopic conservation equations, rather than the traditional set of three equations. The additional equation…
We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
We introduce a general class of stochastic lattice gas models, and derive their fluctuating hydrodynamics description in the large size limit under a local equilibrium hypothesis. The model consists in energetic particles on a lattice…
Triggered by the fact that, in the hydrodynamic limit, several different kinetic equations of physical interest all lead to the same Navier-Stokes-Fourier system, we develop in the paper an abstract framework which allows to explain this…
Vlasov kinetic theory is extended by adopting an extra one particle distribution function as an additional state variable characterizing the micro-turbulence internal structure. The extended Vlasov equation keeps the reversibility, the…
The hydrodynamic interpretation of quantum mechanics treats a system of particles in an effective manner. In this work, we investigate squeezed coherent states within the hydrodynamic interpretation. The Hamiltonian operator in question is…
We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to the description of the evolution of systems whose dynamics is…
We use the extended relaxation time approximation for the collision kernel, which incorporates a particle-energy dependent relaxation time, to derive second-order viscous hydrodynamics from the Boltzmann equation for a system of massless…
Kinetic and hydrodynamic theories are widely employed for describing the collective behaviour of active matter systems. At the fluctuating level, these have been obtained from explicit coarse-graining procedures in the limit where each…
Hydrodynamic behavior is a general feature of interacting systems with many degrees of freedom constrained by conservation laws. To date hydrodynamic scaling in relativistic quantum systems has been observed in many high energy settings,…
We complete the kinetic theory of two-dimensional (2D) point vortices initiated in previous works. We use a simpler and more physical formalism. We consider a system of 2D point vortices submitted to a small external stochastic perturbation…
We prove the hydrodynamic limit for a one dimensional harmonic chain with a random flip of the momentum sign. The system is open and subject to two thermostats at the boundaries and to an external tension at one of the endpoints. Under a…
We consider a stochastic model of the two-dimensional chemostat as a diffusion process for the concentration of substrate and the concentration of biomass. The model allows for the washout phenomenon: the disappearance of the biomass inside…
A quasi-two-dimensional system of hard spheres strongly confined between two parallel plates is considered. The attention is focussed on the macroscopic self-diffusion process observed when the system is looked from above or from below. The…
We study a hydrodynamic limit of a system of coupled kinetic and fluid equations under a strong local alignment force and a strong Brownian motion. More precisely, we consider the Vlasov-Fokker-Planck type equation and compressible…
The derivation of shallow water models from Navier-Stokes equations is revisited yielding a class of two-layer shallow water models.An improved velocity profile is proposed, based on the superposition of an ideal fluid and a viscous layer…