Doctoral Dissertations


"A model of a one-dimensional fluid is investigated in which the praticles [sic] are embedded in a cellular space grid and interact with a modified Lennart-Jones potential. It is shown that with an appropriate change in the potential function the model is also suitable for a two- or three-dimensional fluid with more restricted interactions. The man-fermion-like nature of the system resulting from the hard-rod repulsive part of the modified Lennard-Jones potential makes possible an isomorphism between occupation numbers (number operators) and spin states (spin operators) of an Ising ferromagnet, permitting a convenient mathematical formulation of the problem in terms of the Ising model formalism. While the spinor-algebraic method of Onsager and Kaufman is seen not to lead to a solution of this problem, a method is found for linearizing the partition function which results in a useful series solution. The validity of the solution is first proved by applying it to a one-dimensional model with nearest-neighbor interactions for which the exact partition function is known in closed form. The series solution is shown to offer a convenient and unified method for obtaining, algebraically, correct low-temperature expansions of the partition function for two- and three-dimensional fluids with nearest-neighbor interactions and similar potentials incorporating only a limited number of bonds. Application of the solution to several infinite systems produced consistent and realistic results in various limits and leas to a correct picture of a phase transition under certain conditions without recourse to the Maxwell construction. A numerical evaluation and analysis of the series solution, by means of high-speed computer, for small one-, two-, and three-dimensional systems shows realistic thermodynamic behavior and confirms other estimates of the critical temperature of the three-dimensional system"--Abstract, pages ii-iii.


Lund, Louis H., 1919-1998

Committee Member(s)

Rivers, Jack L.
Willett, Joseph E.



Degree Name

Ph. D. in Physics


Page iv was omitted in numbering sequence.


University of Missouri at Rolla

Publication Date



xi, 334 pages

Note about bibliography

Includes bibliographical references (pages 279-281).


© 1968 Ralph Gunter Tross, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Matrix analytic methods

Thesis Number

T 2066

Print OCLC #


Electronic OCLC #


Included in

Physics Commons