Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

Autores
Urrutia, I.; Szybisz, L.
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This work is devoted to the exact statistical mechanics treatment of simple inhomogeneous few-body systems. The system of two hard spheres (HSs) confined in a hard spherical pore is systematically analyzed in terms of its dimensionality D. The canonical partition function and the one- and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the D+1 system properties is presented. We analyze in detail both the effect of high confinement, when particles become caged, and the low density limit. Other confinement situations are also studied analytically and several relations between the two HSs in a spherical pore, two sticked HSs in a spherical pore, and two HSs on a spherical surface partition functions are traced. These relations make meaningful the limiting caging and low density behavior. Turning to the system of two HSs in a spherical pore, we also analytically evaluate the pressure tensor. The thermodynamic properties of the system are discussed. To accomplish this statement we purposely focus in the overall characteristics of the inhomogeneous fluid system, instead of concentrate in the peculiarities of a few-body system. Hence, we analyze the equation of state, the pressure at the wall, and the fluid-substrate surface tension. The consequences of new results about the spherically confined system of two HSs in D dimension on the confined many HS system are investigated. New constant coefficients involved in the low density limit properties of the open and closed systems of many HS in a spherical pore are obtained for arbitrary D. The complementary system of many HS which surrounds a HS (a cavity inside of a bulk HS system) is also discussed. © 2010 American Institute of Physics.
Fil:Urrutia, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Szybisz, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
J. Math. Phys. 2010;51(3)
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_00222488_v51_n3_p_Urrutia

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network_name_str Biblioteca Digital (UBA-FCEN)
spelling Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimensionUrrutia, I.Szybisz, L.This work is devoted to the exact statistical mechanics treatment of simple inhomogeneous few-body systems. The system of two hard spheres (HSs) confined in a hard spherical pore is systematically analyzed in terms of its dimensionality D. The canonical partition function and the one- and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the D+1 system properties is presented. We analyze in detail both the effect of high confinement, when particles become caged, and the low density limit. Other confinement situations are also studied analytically and several relations between the two HSs in a spherical pore, two sticked HSs in a spherical pore, and two HSs on a spherical surface partition functions are traced. These relations make meaningful the limiting caging and low density behavior. Turning to the system of two HSs in a spherical pore, we also analytically evaluate the pressure tensor. The thermodynamic properties of the system are discussed. To accomplish this statement we purposely focus in the overall characteristics of the inhomogeneous fluid system, instead of concentrate in the peculiarities of a few-body system. Hence, we analyze the equation of state, the pressure at the wall, and the fluid-substrate surface tension. The consequences of new results about the spherically confined system of two HSs in D dimension on the confined many HS system are investigated. New constant coefficients involved in the low density limit properties of the open and closed systems of many HS in a spherical pore are obtained for arbitrary D. The complementary system of many HS which surrounds a HS (a cavity inside of a bulk HS system) is also discussed. © 2010 American Institute of Physics.Fil:Urrutia, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Szybisz, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00222488_v51_n3_p_UrrutiaJ. Math. Phys. 2010;51(3)reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-29T13:43:09Zpaperaa:paper_00222488_v51_n3_p_UrrutiaInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:43:10.419Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
title Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
spellingShingle Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
Urrutia, I.
title_short Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
title_full Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
title_fullStr Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
title_full_unstemmed Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
title_sort Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
dc.creator.none.fl_str_mv Urrutia, I.
Szybisz, L.
author Urrutia, I.
author_facet Urrutia, I.
Szybisz, L.
author_role author
author2 Szybisz, L.
author2_role author
dc.description.none.fl_txt_mv This work is devoted to the exact statistical mechanics treatment of simple inhomogeneous few-body systems. The system of two hard spheres (HSs) confined in a hard spherical pore is systematically analyzed in terms of its dimensionality D. The canonical partition function and the one- and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the D+1 system properties is presented. We analyze in detail both the effect of high confinement, when particles become caged, and the low density limit. Other confinement situations are also studied analytically and several relations between the two HSs in a spherical pore, two sticked HSs in a spherical pore, and two HSs on a spherical surface partition functions are traced. These relations make meaningful the limiting caging and low density behavior. Turning to the system of two HSs in a spherical pore, we also analytically evaluate the pressure tensor. The thermodynamic properties of the system are discussed. To accomplish this statement we purposely focus in the overall characteristics of the inhomogeneous fluid system, instead of concentrate in the peculiarities of a few-body system. Hence, we analyze the equation of state, the pressure at the wall, and the fluid-substrate surface tension. The consequences of new results about the spherically confined system of two HSs in D dimension on the confined many HS system are investigated. New constant coefficients involved in the low density limit properties of the open and closed systems of many HS in a spherical pore are obtained for arbitrary D. The complementary system of many HS which surrounds a HS (a cavity inside of a bulk HS system) is also discussed. © 2010 American Institute of Physics.
Fil:Urrutia, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Szybisz, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description This work is devoted to the exact statistical mechanics treatment of simple inhomogeneous few-body systems. The system of two hard spheres (HSs) confined in a hard spherical pore is systematically analyzed in terms of its dimensionality D. The canonical partition function and the one- and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the D+1 system properties is presented. We analyze in detail both the effect of high confinement, when particles become caged, and the low density limit. Other confinement situations are also studied analytically and several relations between the two HSs in a spherical pore, two sticked HSs in a spherical pore, and two HSs on a spherical surface partition functions are traced. These relations make meaningful the limiting caging and low density behavior. Turning to the system of two HSs in a spherical pore, we also analytically evaluate the pressure tensor. The thermodynamic properties of the system are discussed. To accomplish this statement we purposely focus in the overall characteristics of the inhomogeneous fluid system, instead of concentrate in the peculiarities of a few-body system. Hence, we analyze the equation of state, the pressure at the wall, and the fluid-substrate surface tension. The consequences of new results about the spherically confined system of two HSs in D dimension on the confined many HS system are investigated. New constant coefficients involved in the low density limit properties of the open and closed systems of many HS in a spherical pore are obtained for arbitrary D. The complementary system of many HS which surrounds a HS (a cavity inside of a bulk HS system) is also discussed. © 2010 American Institute of Physics.
publishDate 2010
dc.date.none.fl_str_mv 2010
dc.type.none.fl_str_mv info:eu-repo/semantics/article
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info:ar-repo/semantics/articulo
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dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_00222488_v51_n3_p_Urrutia
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dc.language.none.fl_str_mv eng
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dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J. Math. Phys. 2010;51(3)
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
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collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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