{"id":{"repo_id":"must-thes","oai_identifier":"oai:scholarsmine.mst.edu:doctoral_dissertations-3067"},"canonical_url":"https://search.dev.ndltd.org/etd/must-thes/oai:scholarsmine.mst.edu:doctoral_dissertations-3067","repository":{"repo_id":"must-thes","name":"Missouri University of Science and Technology","base_url":"https://scholarsmine.mst.edu/do/oai/"},"display":{"title":"Cell model of a fluid with hard-core repulsive long-range attractive potential","abstract":"\"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.","abstract_html":""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.","abstract_has_math":false,"creators":["Tross, Ralph G."],"institution":"University of Missouri at Rolla","degree_name":"Ph. D. in Physics","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-10T08:00:00Z","date_published":"2016-02-10T08:00:00Z","updated_at":"2026-07-24T03:18:43Z","subjects":["Physics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/2065","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Tross, Ralph G."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-10T08:00:00Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Physics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri at Rolla"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/2065"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"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."]},{"key":"dc:title","label":"Title","values":["Cell model of a fluid with hard-core repulsive long-range attractive potential"]}]}],"canonical_facts":{"dc:creator":["Tross, Ralph G."],"dc:date.available":["2016-02-10T08:00:00Z"],"dc:description.abstract":["\"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."],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/2065"],"dc:subject":["Physics"],"dc:title":["Cell model of a fluid with hard-core repulsive long-range attractive potential"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Physics"],"thesis:institution_name":["University of Missouri at Rolla"]},"updated_at":"2026-07-24T03:18:43Z"}