Lattice Statistics.

The objective of this research is to develop the mathematical formalism necessary to treat correlative statistics for lattice spaces. Toward that goal the investigators are considering 1 the composite kth neighbor degeneracy problem for indistinguishable particles distributed on one dimensional rectangular lattice space 2 the occupational degeneracy for dumbbells and lambda-bell particles on saturated and unsaturated, rectangular lattice spaces of higher dimensionality here they are considering dumbbells that may have either indistinguishable or distinguishable ends 3 the nearest neighbor degeneracy problem for simple, indistinguishable particles distributed on rectangular lattice spaces of higher dimensionality. A secondary objective is to exploit the results of the foregoing research by investigating the consequences of this formalism to chemical and physical systems. Most notably they are considering adsorption processes. The investigators have developed set theoretic arguments that hold the promise of treating successfully a number of problems concerning correlative statistics for lattice spaces. Utilizing this technique they have been able to describe exactly the occupational degeneracy for correlated particles such as dumbbells and lambda-bell particles distributed on lattice spaces of two and three dimensions. The investigators have also utilized these set theoretic arguments to obtain recursion relations that yield exactly the composite nearest, next nearest and third nearest neighbor degeneracies for simple particles distributed on rectangular lattice spaces of higher dimensionality. Author