Anna T. Lawniczak

LATTICE GAS AUTOMATA FOR REACTIVE SYSTEMS

Reactive lattice gas automata provide a microscopic approach to the dynamics of spatially-distributed reacting systems. An important virtue of this approach is that it offers a method for the investigation of reactive systems at a mesoscopic level that goes beyond phenomenological reaction-diffusion equations. After introducing the subject within the wider framework of lattice gas automata (LGA) as a microscopic approach to the phenomenology of macroscopic systems, we describe the reactive LGA in terms of a simple physical picture to show how an automaton can be constructed to capture the essentials of a reactive molecular dynamics scheme. The statistical mechanical theory of the automaton is then developed for diffusive transport and for reactive processes, and a general algorithm is presented for reactive LGA. The method is illustrated by considering applications to bistable and excitable media, oscillatory behavior in reactive systems, chemical chaos and pattern formation triggered by Turing bifurcations. The reactive lattice gas scheme is contrasted with related cellular automaton methods and the paper concludes with a discussion of future perspectives.

Performance of data networks with random links

We investigate simplified models of computer data networks and examine how the introduction of additional random links influences the performance of these networks. In general, the impact of additional random links on the performance of the network strongly depends on the routing algorithm used in the network. Significant performance gains can be achieved if the routing is based on ‘geometrical distance’ or shortest path reduced table routing. With shortest path full table routing degradation of performance is observed.

Reactive lattice gas automata

Abstract A probabilistic lattice gas cellular automaton model of a chemically reacting system is constructed. Microdynamical equations for the evolution of the system are given; the continuous and discrete Boltzmann equations are developed and their reduction to a generalized reaction-diffusion equation is discussed. The microscopic reactive dynamics is consistent with any polynomial rate law up to the fourth order in the average particle density. It is shown how several microscopic CA rules are consistent with a given rate law. As most CA systems, the present one has spurious properties whose effects are shown to be unimportant under appropriate conditions. As an explicit example of the general formalism a CA dynamics is constructed for an autocatalytic reactive scheme known as the Schlogl model. Simulations show that in spite of the simplicity of the underlying discrete dynamics the model exhibits the phase separation and wave propagation phenomena expected for this system. Because of the microscopic nature of the dynamics the role of internal fluctuations on the evolution process can be investigated.

Individual-based lattice model for spatial spread of epidemics

We present a lattice gas cellular automaton (LGCA) to study spatial and temporal dynamics of an epidemic of SIR (susceptible-infected-removed) type. The automaton is fully discrete, i.e., space, time and number of individuals are discrete variables. The automaton can be applied to study spread of epidemics in both human and animal populations. We investigate effects of spatial inhomogeneities in initial distribution of infected and vaccinated populations on the dynamics of epidemic of SIR type. We discuss vaccination strategies which differ only in spatial distribution of vaccinated individuals. Also, we derive an approximate, mean-field type description of the automaton, and discuss differences between the mean-field dynamics and the results ofLGCA simulation.

Reactive dynamics in a multispecies lattice-gas automaton

A multispecies reactive lattice‐gas automaton model is constructed and used to study chemical oscillations and pattern formation processes in a spatially distributed two‐dimensional medium. Both steady state and oscillatory dynamics are explored. Nonequilibrium spatial structures are also investigated. The automaton simulations show the formation of rings of chemical excitation, spiral waves, and Turing patterns. Since the automaton model treats the dynamics at a mesoscopic level, fluctuations are included and nonequilibrium spatial structures can be investigated at a deeper level than reaction–diffusion equation descriptions.

Building blocks of a simulation environment of the OSI network layer of packet-switching networks

This paper describes the main building blocks of a simulation environment of the OSI network layer of packet-switching networks. The need for such a tool is presented and pitfalls of previous solutions are described. Remedies provided by the most recent solution are discussed. Architecture, organisation, and architectural decisions are explained.

Computational intelligence based architecture for cognitive agents

Abstract We discuss some limitations of reflexive agents to motivate the need to develop cognitive agents and propose a hierarchical, layered, architecture for cognitive agents. Our examples often involve the discussion of cognitive agents in highway traffic models. A cognitive agent is an agent capable of performing cognitive acts, i.e. a sequence of the following activities: “ Perceiving ” information in the environment and provided by other agents, “ Reasoning ” about this information using existing knowledge, “ Judging ” the obtained information using existing knowledge, “ Responding ” to other cognitive agents or to the external environment, as it may be required, and “ Learning ”, i.e. changing (and, hopefully augmenting) the existing knowledge if the newly acquired information allows it. We describe how computational intelligence techniques (e.g., fuzzy logic, neural networks, genetic algorithms, etc) allow mimicking to a certain extent the cognitive acts performed by human beings. The order with which the cognitive actions take place is important and so is the order with which the various computational intelligence techniques are applied. We believe that a hierarchical layered model should be defined for the generic cognitive agents in a style akin to the hierarchical OSI 7 layer model used in data communication. We outline in broad sense such a reference model.

Development and performance of cellular automaton model of OSI network layer of packet-switching networks

We present a cellular automaton model of the OSI network layer. Our focus is on parameters that can affect flow and congestion in the network, such as randomly inserted additional links, used to model additional wired and wireless connections in LANs and WANs. We present selected simulation results and observe, in accordance with other models, that throughput is maximal at the critical load of the network. Further, the addition of links increases the critical load of a network if queueing costs are taken into account in routing decisions for packets.

OSI Network‐layer Abstraction: Analysis of Simulation Dynamics and Performance Indicators

The Open Systems Interconnection (OSI) reference model provides a conceptual framework for communication among computers in a data communication network. The Network Layer of this model is responsible for the routing and forwarding of packets of data. We investigate the OSI Network Layer and develop an abstraction suitable for the study of various network performance indicators, e.g. throughput, average packet delay, average packet speed, average packet path‐length, etc. We investigate how the network dynamics and the network performance indicators are affected by various routing algorithms and by the addition of randomly generated links into a regular network connection topology of fixed size. We observe that the network dynamics is not simply the sum of effects resulting from adding individual links to the connection topology but rather is governed nonlinearly by the complex interactions caused by the existence of all randomly added and already existing links in the network. Data for our study was gathe...

Fourier analysis of Turing-like pattern formation in cellular automaton models

Abstract The novelty of this paper is the study of emergence of diffusion-induced (Turing-like) patterns from a microscopic point of view, namely, in terms of cellular automata. Formally, the cellular automaton model is described in lattice-gas terminology [H. Bussemaker, A. Deutsch, E. Geigant, Phys. Rev. Lett. 78 (1997) 5018–5021]. The automaton rules capture in abstract form the essential ideas of activator–inhibitor interactions of biological systems. In spite of the automaton’s simplicity, self-organised formation of stationary spatial patterns emerging from a randomly perturbed uniform state is observed. Fourier analysis of approximate mean-field kinetic difference equations [J.P. Boon, D. Dab, R. Kapral, A.T. Lawniczak, Phys. Rep. 273 (1996) 55–147] yields a critical wave length and a “Turing condition” for the onset of pattern formation.