Exact results are presented for the surface diffusion of small two-dimensional clusters, the constituent atoms of which are commensurate with a square lattice of adsorption sites. Cluster motion is due to the hopping of atoms along the cluster perimeter with various rates. We apply the formalism of Titulaer and Deutch [ J. Chem. Phys. 77, 472 (1982)], which describes evolution in reciprocal space via a linear master equation with dimension equal to the number of cluster configurations. We focus on the regime of rapid hopping of atoms along straight close-packed edges, where certain subsets of configurations cycle rapidly between each other. Each such subset is treated as a single quasiconfiguration, thereby reducing the dimension of the evolution equation, simplifying the analysis, and elucidating limiting behavior. We also discuss the influence of concerted atom motions on the diffusion of tetramers and larger clusters. Exact results are presented for the surface diffusion of small two-dimensional clusters, the constituent atoms of which are commensurate with a square lattice of adsorption sites. Cluster motion is due to the hopping of atoms along the cluster perimeter with various rates. We apply the formalism of Titulaer and Deutch ͓J. Chem. Phys. 77, 472 ͑1982͔͒, which describes evolution in reciprocal space via a linear master equation with dimension equal to the number of cluster configurations. We focus on the regime of rapid hopping of atoms along straight close-packed edges, where certain subsets of configurations cycle rapidly between each other. Each such subset is treated as a single quasiconfiguration, thereby reducing the dimension of the evolution equation, simplifying the analysis, and elucidating limiting behavior. We also discuss the influence of concerted atom motions on the diffusion of tetramers and larger clusters. ͓S0163-1829͑99͒05704-5͔ Disciplines Condensed Matter Physics | Mathematics

A deterministic system of interacting agents is considered as a model for economic dynamics. The dynamics of the system is described by a coupled map lattice with near neighbor interactions. The evolution of each agent results from the competition between two factors: the agent's own tendency to grow and the environmental influence that moderates this growth. Depending on the values of the parameters that control these factors, the system can display Pareto or Boltzmann-Gibbs statistical behaviors in its asymptotic dynamical regime. The regions where these behaviors appear are calculated on the space of parameters of the system. Other statistical properties, such as the mean wealth, the standard deviation, and the Gini coefficient characterizing the degree of equity in the wealth distribution are also calculated on the space of parameters of the system.

An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control term representing the local environmental pressure which avoids an exponential growth. The asymptotic state of the system evolution displays a complex behavior. The distribution of the maps values in this final regime is of power law type. In the model, inequality emerges as a result of the dynamical processes taking place in the microscopic scales.Key words: coupled-maps models, non-equilibrium systems, power law scaling Inequality in the richness distribution is a fact in each economic activity. The origin of such behavior seems to be caused by the interaction of the macro with the microeconomy. Here we propose a simple spatio-temporal model for economy evolution where inequality emerges as a result of the dynamical processes taking only place on the microscopic scale. That is, the microeconomy fully determines the macroeconomic characteristics of the system. The model is composed by N interacting agents representing a company, country or other economic entity. Each agent, identified by an index i = 1 · · · N, is characterized by a real, scalar degree of freedom, x i ∈ [0, ∞] denoting the strength, wealth or richness of the agent. The system evolves in time t synchronously. Each agent updates its x t i value according to its present state and

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