The Lattice

Boltzmann Equation for Fluid Dynamics and Beyond, Series Numerical Mathematics and Scientific Computation, Clarendon Press, Oxford, 2001.

capsule) dynamics and the fluid dynamics by using the immersed boundary method and calculates the incompressible viscous power-law fluid motion by solving the lattice

Boltzmann equation.

A manifestly covariant relativistic

boltzmann equation for the evolution of a system of events.

Viscous flow computations with the method of lattice

Boltzmann equations.

A stable discretization of the lattice

Boltzmann equation for simulation of incompressible two-phase flows at high density ratio.

The solutions of the

Boltzmann equation problem, beyond current computational capabilities, describe the location of gas molecules probabilistically and predict the likelihood that a molecule will reside at any particular location and have a particular momentum at any given time in the future.

The discrete

Boltzmann equation (1) for the distribution function [f.

That last step was "really a breakthrough from my point of view," comments Roberto Benzi of the University of Rome Tor Vergata, a pioneer in the use of the

Boltzmann equation for fluid flows.

In particular, the

Boltzmann equation is well known to model the transport of neutrons/photons.

j] relationship to the

Boltzmann equation yielded [V.

First there were the grave difficulties incumbent on trying to reconcile the reversible, recurrent dynamics of the micro-components with the irreversible, monotonic approach to equilibrium described by the

Boltzmann equation and the H-Theorem.

Classical

Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations.

The aim is then twofold: to advance the understanding of basic equations in kinetic theory, such as the

Boltzmann equation, and to employ known or newly developed techniques in this field to the rigorous treatment of models in the above mentioned areas, such as the Becker-Doring equation for nucleation, the growth-fragmentation model for cell populations, or individual-based models for collective behaviour.