Lattice Statistics.

Abstract

The objective of this research was to develop the mathematical formalism necessary to treat a number of unsolved problems in lattice statistics. Toward that end the investigators have considered the following problems: (1) The occupational degeneracy of particles of various shapes on lattice spaces of various dimensionalities and structures. (2) The nearest neighbor degeneracy for various kinds of particles on lattice spaces of various dimensionalities and structures. (3) The kth neighbor problem for simple particles on a one dimensional, rectangular lattice space. Utilizing set theoretic arguments they have been able to construct shift operator matrices that, in principle, permit them to establish recursion relations that describe exactly the occupational degeneracy for any shape particle on a lattice space of any dimensionality and structure. Similar techniques allow the investigators to determine the composite nearest neighbor degeneracy for simple particles, dumbbells and lambda-bell particles on quasi-two dimensional rectangular lattices. They have utilized the forgoing formalism to treat the thermodynamics (canonical and grand partition functions) for such systems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 30, 1984
Accession Number
ADA146862

Entities

People

  • R. B. Mcquistan

Organizations

  • University of Wisconsin–Milwaukee

Tags

DTIC Thesaurus Topics

  • Adsorption
  • Air Force
  • Chemical Phenomena
  • Classification
  • Composite Materials
  • Computer Programming
  • Computers
  • Crystal Growth
  • Mathematics
  • Phase Transformations
  • Physics
  • Polynomials
  • Security
  • Statistics
  • Thermodynamics
  • Transitions
  • Two Dimensional

Readers

  • Aerosol Science/Aerosol Physics
  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space