Having a gas with the mechanics of fluids

One of the really hard problems in classical physics is to unveil the physics hidden in the Navier-Stokes equations of hydrodynamics. The traditional approach is to solve numerically the equations for a specific set of boundary conditions -which is computationally very demanding. Or, one can attempt to simulate the motion of all the individual molecules of the fluid and from that extract the macroscopic behaviour of the fluid -but because one will have to calculate the trajectories of an enormous number of molecules, this approach is limited to short time spans. A third approach is to follow the motion of the individual particles, with the important simplification that the particles are only allowed to move on a discrete lattice, a type of model known as a lattice gas. The usefulness of this approach has been studied for about 15 years, and the research is described in Lattice Gas Hydrodynamics .

It is a pleasure to read the book. Equations, of which there are many, are carefully composed and easily deciphered. The text is well written and comprehensible, covering an immense amount of material.

The overall aim is twofold. First, to present the mathematics and physics of lattice-gas models. Second, to demonstrate, as rigorously as possible, that despite the simplified nature of these models, they nevertheless exhibit the macroscopic behaviour, as described by the Navier-Stokes equations, that is found in real fluids. The authors achieve their aim beautifully with a formal and detailed mathematical treatment. At the same time, they make sure the physical picture is kept clear and used as a guidance throughout their presentation.

The basic conceptual ideas are presented in the first chapter, then the mathematical formalism is set up in chapter two. There are also chapters on the equilibrium statistical mechanics of lattice gases and a description of how the macroscopic dynamical behaviour is derived from the microscopic. Four chapters describe thoroughly the hydrodynamics of lattice-gas models. The main motivation for introducing lattice gases was to be able to do affordable numerical simulations, and a chapter describes how this is done.

Advanced students of physics, mathematics and, probably, engineering, will find this book useful. My single frustration is that I would have liked a little about the limitations of lattice-gas models and to what extent they are able to capture the physics of turbulence.

Henrik Jeldtoft Jensen is professor of mathematical physics, Imperial College, London.