Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.

/pdf/lattice-gas-cellular-automata-and-lattice-boltzmann-models-2kkc77jjx8.pdf

Lattice-Gas Cellular Automata and Lattice Boltzmann Models

The Bonn Meson Exchange Model for the Nucleon Nucleon Interaction

The topic of cosmic strings provides a bridge between the physics of the very small and the very large They are predicted by some unified theories of particle interactions If they exist, they may help to explain some of the largest-scale structures seen in the Universe today They are `topological defects' that may have been formed at phase transitions in the very early history of the Universe, analogous to those found in some condensed-matter systems --- vortex lines in liquid helium, flux tubes in type-II superconductors, or disclination lines in liquid crystals In this review, we describe what they are, why they have been hypothesized and what their cosmological implications would be The relevant background from the standard models of particle physics and cosmology is described in section 1 In section 2, we review the idea of symmetry breaking in field theories, and show how the defects formed are constrained by the topology of the manifold of degenerate vacuum states We also discuss the different types of cosmic strings that can appear in different field theories Section 3 is devoted to the dynamics of cosmic strings, and section 4 to their interaction with other fields The formation and evolution of cosmic strings in the early Universe is the subject of section 5, while section 6 deals with their observational implications Finally, the present status of the theory is reviewed in section 7

Cosmic strings

A no-go theorem for regularizing chiral fermions

Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction

Using Monte Carlo techniques, we evaluate the path integral for the four-dimensional lattice gauge theory with a Z/sub 2/ gauge group. The system exhibits a first-order transition. This is contrary to the implications of the approximate Migdal recursion relations but consistant with mean-field-theory arguments. Our ''data'' agree well with a low-temperature expansion and the exact duality between the high- and low-temperature phases.

Experiments with a Gauge-Invariant Ising System

Monte Carlo computations in lattice gauge theories

By means of a constrained variational calculation we determine the interaction energy of two-vortex configurations in the Ginzburg-Landau theory or, equivalently, in the Abelian Higgs model. The energy is evaluated as a function of the separation between vortices and of the parameter $\ensuremath{\lambda}$, which measures the relative strength of the matter self-coupling and the electromagnetic coupling. Our results provide a precise determination of the inter-vortex potential, attractive for $\ensuremath{\lambda}l1$ and repulsive for $\ensuremath{\lambda}g1$. They also show that for $\ensuremath{\lambda}=1$ the lower bound on the energy which can be then derived is actually reached at all separations and, therefore, that in this case vortices do not interact.

Interaction energy of superconducting vortices

Using Monte Carlo techniques, we study the thermodynamics of four-dimensional Euclidean lattice gauge theories, with gauge groups ${Z}_{N}$ and U(1). For $N\ensuremath{\le}4$ the models exhibit a single first-order phase transition, while for $N\ensuremath{\ge}5$ we observe two transitions of higher order. As $N$ increases, one of these transitions moves toward zero temperature, whereas the other remains at finite temperature and survives in the U(1) limit. The behavior of the Wilson loop factor is also analyzed for the ${Z}_{2}$ and ${Z}_{6}$ models.

Monte Carlo Study of Abelian Lattice Gauge Theories

A quantum Monte Carlo method is developed to treat path integrals at finite temperature and with topological constraints to study a periodic model of a granular superconductor. The results obtained provide strong evidence for a low-temperature first-order reentrant transition induced by zero-point quantum fluctuations.

Laurence Jacobs

Papers

Experiments with a Gauge-Invariant Ising System

Monte Carlo computations in lattice gauge theories

Interaction energy of superconducting vortices

Monte Carlo Study of Abelian Lattice Gauge Theories

First-Order Reentrant Transition in Granular Superconducting Films