Application of cellular automata to N-body systems

Thermodynamics from three-dimensional many-body fragmentation simulations on a cellular automaton model

The thermal equilibrium of many-body systems subject to finite range interactions is investigated numerically, by means of a multipurpose 3D cellular automaton dynamic model developed by the authors. The numerical experiments, carried out at fixed number of bodies, volume and energy, demonstrate the formation of an equilibrium among 3D aggregates of bodies. The distribution of the aggregates against size obeys a power law of (negative) exponent tau approximately 2.2 (against 1.3 in 2D). Our experiments, indicating that the exponent is insensitive to the precise parameter values and the precise parametrization of the interactions, are consistent with the idea of the existence of a universality class corresponding to the thermal equilibrium. The numerical value for the exponent tau is in agreement with the theoretical thermal equilibrium analyses based on various other approaches, numerical and semianalytical, indicating that the cellular automaton approach provides an adequate methodology to investigate thermal equilibria. In this paper, as an illustration of this method, we refer to the problem of formation of clusters of nucleons in heavy ion collisions of nuclei leading on to fragmentation. The theoretical tau value, however, corresponding to the thermal equilibrium among the aggregation clusters, is 15 percent lower than the empirical value ( approximately 2.6 ) , as measured in laboratory nuclear fragmentation experiments induced by collision. There is then only a very approximate correspondence between the experimental and the thermal equilibrium value. On the basis of the results of this paper and of a previous paper of this series, we conjecture that the approximate agreement is due to a partial establishment of a thermodynamic equilibrium during the collision of the nuclei. The thermal equilibrium gives the main contribution to the observed tau value; the deviation from this possibly universal value is largely the consequence of the lack of full thermal equilibrium in actual laboratory experiments. This conjecture is extended to interpret the observed ubiquity of power laws of exponents exceeding 2.2, which refer to the distribution of various types of matter in 3D space.

Dynamics of many-particle fragmentation in a cellular automaton model

A three-dimensional cellular automaton model developed by the authors to deal with the dynamics of N-body interactions has been adapted to investigate the head-on collision of two identical bound clusters of particles, and the ensuing process of fragmentation. The range of impact energies is chosen low enough, to secure that a compound bound cluster can be formed. The model is devised to simulate the laboratory set-up of fragmentation experiments as monitored by 4 pi detectors. The particles interact via a Lennard-Jones potential. At low impact energies the numerical experiments following the dynamics of the individual particles indicate a phase of energy sharing among all the particles of the compound cluster. Fragments of all sizes are then found to evaporate from the latter cluster. The cluster sizes, measured in our setup by simulated 4 pi detectors, conform to a power law of exponent approximately 2.6. In an attempt to duplicate the laboratory caloric curves related, in particular, to nuclear fragmentation processes, we introduce several temperature parameters (kinetic temperature of nucleons, kinetic temperature of fragments, reaction equilibrium temperatures). Theoretical caloric curves are then constructed for those temperature parameters, we regard as physically most relevant. Our results show that different temperature definitions generate different curve patterns, indicating that the fragmentation system remains far from thermodynamic equilibrium. The pattern of the laboratory caloric curve for Au-Au collision experiments as derived from a recent analysis [NuPECC Report, 1997 (unpublished)] is reproduced qualitatively by our reaction temperatures.