Related papers: Particles-on-Demand for Kinetic Theory
We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation.…
A simple model of the driven motion of interacting particles in a two dimensional random medium is analyzed, focusing on the critical behavior near to the threshold that separates a static phase from a flowing phase with a steady-state…
The dynamical system for inertial particles in fluid flow has both attracting and repelling regions, the interplay of which can localize particles. In laminar flow experiments we find that particles, initially moving throughout the fluid…
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 a new kinetic model and its lattice Boltzmann realization for the simulation of compressible, non-ideal fluid flows. The method employs first-neighbour lattices and introduces a consistent set of correction terms constructed via…
We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…
A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but…
We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different velocity sets, i.e., higher- and lower-order lattices, are consistently and efficiently coupled, allowing us to use the…
We present a new way of quantum kinetic equation derivation. This method appears as a natural generalization of the many-particle quantum hydrodynamic method. Kinetic equations are derived for different system of particles. First of all we…
The hydrodynamic limit of a discrete kinetic equation is intrinsically connected with the symmetry of the lattices used in construction of a discrete velocity model. On mixed lattices composed of standard lattices the sixth-order (and…
Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption that a small set of fields provides a closed description on large space and time scales. Conditions governing the choice for these fields are discussed…
A basic aspect of the kinetic descriptions of incompressible fluids based on an inverse kinetic approaches is the possibility of satisfying an H-theorem. This property is in fact related to the identification of the kinetic distribution…
The maximum speed at which a liquid can wet a solid is limited by the need to displace gas lubrication films in front of the moving contact line. The characteristic height of these films is often comparable to the mean free path in the gas…
We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas,…
We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The dynamics…
We reconsider some fundamental aspects of the fluid mechanics model, and the derivation of continuum flow equations from gas kinetic theory. Two topologies for fluid representation are presented, and a set of macroscopic equations are…
Every physical theory has (at least) two different forms of mathematical equations to represent its target systems: the dynamical (equations of motion) and the kinematical (kinematical constraints). Kinematical constraints are…
Many applications of porous media research involves high pressures and, correspondingly, exchange of thermal energy between the fluid and the matrix. While the system is relatively well understood for the case of non-moving porous media,…
By using the quantum maximum entropy principle we formally derive, from a underlying kinetic description, isothermal (hydrodynamic and diffusive) quantum fluid equations for particles with Fermi-Dirac and Bose-Einstein statistics. A…
Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation.…