相关论文: Spectral Closure for the Linear Boltzmann-BGK Equa…
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…
In this paper, we give an overview of the results established in [3] which provides the first rigorous derivation of hydrodynamic equations from the Boltzmann equation for inelastic hard spheres in 3D. In particular, we obtain a new system…
We present a detailed description of the essentially entropic lattice Boltzmann model. The entropic lattice Boltzmann model guarantees unconditional numerical stability by iteratively solving the nonlinear entropy evolution equation. In…
In this paper we consider the incompressible 3D Euler and Navier-Stokes equations in a smooth bounded domain. First, we study the 3D Euler equations endowed with slip boundary conditions and we prove the same criteria for energy…
Exactly solved models provide rigorous understanding of many-body phenomena in strongly correlated systems. In this article, we report a breakthrough in uncovering universal many-body correlated properties of quantum integrable Lieb-Liniger…
The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one…
We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…
The departure of a granular gas in the instable region of parameters from the initial homogeneous cooling state is studied. Results from Molecular Dynamics and from Direct Monte Carlo simulation of the Boltzmann equation are compared. It is…
We use the Boltzmann equation in the relaxation time approximation to study the expansion of a dilute Fermi gas at unitarity. We focus, in particular, on the approach to the hydrodynamic limit. Our main finding are: i) In the regime that…
A recently developed local-density current functional formalism for confined Bose-condensed superfluids requires visco-elastic spectra which are defined through a finite-frequency extension of the dissipative coefficients entering the…
We introduce a mesoscopic three-dimensional Lattice Boltzmann Model which attempts to mimick the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard Lattice Boltzmann…
In this paper, we study the Navier-Stokes equations of compressible, barotropic flow posed in a bounded set in $\mathbb{R}^3$ with different boundary conditions. Specifically, we prove that the local-in-time smooth solution of the…
The dependence of the bulk viscosity with the relativistic parameter $z=kT/mc^{2}$, obtained through the complete Boltzmann equation [1,2], is thoroughly analyzed. A complete and rigorous examination of the relevant non-relativistic and…
We derive hydrodynamic equations from Vicsek-style dry active matter models in three dimensions (3D), building on our experience on the 2D case using the Boltzmann-Ginzburg-Landau approach. The hydrodynamic equations are obtained from a…
We establish the incompressible Navier--Stokes limit for the discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighborhood of the global Maxwellian.…
We combine the theory of slow spectral closure for linearized Boltzmann equations with Maxwell's kinetic boundary conditions to derive non-local hydrodynamics with arbitrary accommodation. Focusing on shear-mode dynamics, we obtain explicit…
Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high…
We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is…
We compute the spectral densities of $T^{\mu\nu}$ and $J^{\mu}$ in high temperature QCD plasmas at small frequency and momentum,\, $\omega,k \sim g^4 T$. The leading log Boltzmann equation is reformulated as a Fokker Planck equation with…
We establish the incompressible low--Mach/high--Reynolds limit for the Boltzmann equation for a broad class of initial data, without recourse to any asymptotic expansion. Exploiting the local Maxwellian manifold and the macro--micro…