On the spatiotemporal correlations in a linear stochastic field generated by non-interacting particles: Theory.

Many of the physical macroscopic quantities could be explained as the result of a collection of microscopic particles which act independent of each-other, in a linear fashion. Since the physical laws of the interaction of these particles with their surrounding medium are non-deterministic, one could think of these particles as the generators of a linear stochastic field. In this paper, we have introduced a derivation which has yielded an equation for the spatiotemporal correlations in such a field. The derivation is simple and extendable to include the behavior of many physical particles. A simple numerical algorithm has been devised to solve the obtained initial value integrodifferential equation and a computer program has been developed accordingly. The temporal correlations in four benchmark problems, i.e. a three dimensional one group fissile cube, two multi-region one group slabs and a two-group multi-region slab, have been obtained and compared with direct Monte Carlo simulations which show the accuracy of the method. Finally, these benchmarks show some possible applications of this formulation, e.g. generalizing the Rossi-alpha formula and extraction of the average neutron velocity in a steady-state reactor core. [ABSTRACT FROM AUTHOR]