Annual Reviews of Computational Physics V

The following sections are included:

• PREFACE

• CONTENTS

The computational aspects of fire in fuel (mostly popularized under the nickname “forest fires”) have been studied through discretized approaches (including percolative cellular automata), partly as a counterpart of ongoing experiments under idealized conditions (simple fuel types, slope or wind controlled spread). Another, substantial body of computer intensive work, has to do with the use of digitized satellite imagery to duplicate or forecast fire scenarios in real topographical situations. Although this has been pursued by discrete automata evolution, a large amount of the more recent studies uses continuous spread algorithms.

This paper describes recent progress in the development and application of Direct Numerical Simulation (DNS) for studying turbulent combustion. The role of DNS within numerical simulation techniques is outlined and currently available DNS methods are summarized. The application areas of DNS and its relevance for practical applications are emphasized. In particular, a DNS approach for reactive flows, which was developed by the author and his coworkers is presented in detail. Studies of premixed and non-premixed combustion performed with this method are reported upon. Investigations of premixed flames by DNS presented in this paper address the issues of flame–vortex interactions, flame dynamics in homogeneous isotropic turbulence, flame ignition and flame–wall interactions. Simplified as well as detailed reaction mechanisms were considered in these simulations. Most of these studies were performed in the framework of flamelet modelling and therefore the impact of DNS on this research activity is emphasized. While simulations of premixed combustion are discussed in more detail, a short overview on investigations of non-premixed combustion is also given. The DNS of the diffusion flames presented here focus on combustion in mixing layers, e.g., auto-ignition processes and the application area of the laminar flamelet assumption. A brief discussion of open issues and ongoing work concludes this review.

This review presents application of molecular dynamics to investigation of the Rayleigh–Taylor instability. A parallel program for simulation of 2-D Lennard–Jones systems with large number of particles (10⁶+) was developed and used. The algorithm is based on the geometric decomposition and it was implemented on networked workstations, CONVEX Exemplar SPP 1×00, TMC CM5, and on Cray T3D under PVM. A broad collection of simulation results for millions of particles and up to half a million of time steps has been obtained and analyzed. Due to thermal fluctuations of a certain wavelength a mixing process can be observed in microscale. The results obtained for different particle–particle interactions, temperatures and computational boxes are compared and discussed. Unlike in macroscale, the patterns observed are created via spontaneous fluctuations in the particle fluid. Two stages of the Rayleigh–Taylor process resulting from long-range correlations are distinguished. Influence of temperature on the speed of mixing and pattern creation is shown.

The properties of adsorbed molecular layers and molecular solids are reviewed in this paper. Phase transitions and time-dependent properties of pure and mixed molecular crystals are analyzed. Phase transitions in adsorbed (2D) fluids and in adsorbed layers of molecules are studied with a combination of path integral Monte Carlo (PIMC), Gibbs ensemble Monte Carlo (GEMC) and finite size scaling techniques. Entropy driven phase transitions in systems with purely repulsive interactions are analyzed as well phase diagrams of fluids with internal quantum states. Adsorbed layers of H₂ molecules at a full monolayer coverage in the structure have a higher transition temperature to the disordered phase compared to the system with the heavier D₂ molecules, this effect is analyzed by PIMC. Linear N₂ molecules adsorbed on graphite show a transition from a high-temperature phase to a low-temperature phase with herringbone ordering of the orientational degrees of freedom, the order of the transition and quantum effects are discussed. Rounding effects of the phase transition in adsorbed layers of (N₂)_x (CO)_1−x for x < 7% are analyzed.

We review some elementary aspects of the critical properties of the series of metal–insulator transitions that constitute the integer quantum Hall effect. Numerical work has proven essential in charting out this phenomenon. Without being complete, we review network models that seem to capture the essentials of this critical phenomenon.

Natural evolution has “created” many parallel cellular systems, in which emergent computation gives rise to impressive computational capabilities. In recent years we are witness to a rapidly growing interest in such complex adaptive systems, addressing, among others, the major problem of designing them to exhibit a specific behavior or solve a given problem. One possible approach, which we explore in this paper, is to employ artificial evolution. The systems studied are based on the cellular automata (CA) model, where a regular grid of cells is updated synchronously in discrete time steps, according to a local, identical interaction rule. We first present the application of a standard genetic algorithm to the evolution of CAs to perform two non-trivial computational tasks, density and synchronization, showing that high-performance systems can be attained. The evolutionary process as well as the resulting emergent computation are then discussed. Next we study two generalizations of the CA model, the first consisting of non-uniform CAs, where cellular rules need not be identical for all cells. Introducing the cellular programming evolutionary algorithm, we apply it to six computational tasks, demonstrating that high-performance systems can be evolved. The second generalization involves non-standard, evolving connectivity architectures, where we demonstrate that yet better systems can be attained. Evolving, cellular systems hold potential both scientifically, as vehicles for studying phenomena of interest in areas such as complex adaptive systems and artificial life, as well as practically, showing a range of potential future applications ensuing the construction of adaptive systems, and in particular ‘evolving ware,’ evolware.

The following sections are included:

• Introduction

• Modeling the Dynamics

• Dynamics of Subsystems of a Given Architecture
  • A pair of idiotype-anti-idiotype clones
  • Central immune system and control of autoreactive clones

• Architecture of Idiotypic Networks
  • Localized memory in idiotypic networks
  • Modeling the architecture on the hypercube
  • Metadynamics

• References