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

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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 d...

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Autores principales:	Urrutia, I., Szybisz, L.
Formato:	Artículo publishedVersion
Publicado:	2010
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00222488_v51_n3_p_Urrutia http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v51_n3_p_Urrutia_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_00222488_v51_n3_p_Urrutia_oai
record_format	dspace
spelling	I28-R145-paper_00222488_v51_n3_p_Urrutia_oai2020-10-19 Urrutia, I. Szybisz, L. 2010 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00222488_v51_n3_p_Urrutia info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Phys. 2010;51(3) Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v51_n3_p_Urrutia_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
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.
format	Artículo Artículo publishedVersion
author	Urrutia, I. Szybisz, L.
spellingShingle	Urrutia, I. Szybisz, L. Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
author_facet	Urrutia, I. Szybisz, L.
author_sort	Urrutia, I.
title	Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension
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
publishDate	2010
url	http://hdl.handle.net/20.500.12110/paper_00222488_v51_n3_p_Urrutia http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v51_n3_p_Urrutia_oai
work_keys_str_mv	AT urrutiai statisticalmechanicsoftwohardspheresinasphericalporeexactanalyticresultsinddimension AT szybiszl statisticalmechanicsoftwohardspheresinasphericalporeexactanalyticresultsinddimension
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Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

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