Perturbation theory with a hard dumbbell reference system. I. Application to liquid nitrogen

1979 ◽  
Vol 71 (10) ◽  
pp. 4128-4131 ◽  
Author(s):  
Friedrich Kohler ◽  
N. Quirke ◽  
J. W. Perram
Keyword(s):  
Perturbation Theory ◽  
Liquid Nitrogen ◽  
Reference System ◽  
Hard Dumbbell

Pair Potential for Liquid Nitrogen in the Perturbation Theory

1971 ◽  
Vol 55 (7) ◽  
pp. 3611-3612
Author(s):  
K. Rajagopal ◽  
T. M. Reed
Keyword(s):  
Perturbation Theory ◽  
Liquid Nitrogen ◽  
Pair Potential

Thermodynamics of a quadrupolar hard diatomic fluid using a perturbation theory with nonspherical reference system

1989 ◽  
Vol 93 (11) ◽  
pp. 4636-4642 ◽  
Author(s):  
M. Lombardero ◽  
C. Martin ◽  
E. Lomba ◽  
J. L. F. Abascal
Keyword(s):  
Perturbation Theory ◽  
Reference System

Perturbation Theory

1984 ◽  
Author(s):  
C. G. Gray ◽  
K. E. Gubbins
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
Reference System ◽  
Pair Correlation ◽  
Perturbation Parameter ◽  
Distribution Functions ◽  
Reference Potential ◽  
Atomic Liquids ◽  
Perturbation Potential ◽  
System Properties

In perturbation theory one relates the properties (e.g. the distribution functions or free energy) of the real system, for which the intermolecular potential energy is u(rN ωN), to those of a reference system where the potential is u0(rNωN), usually by an expansion in powers of the perturbation potential u1 ≡ u — u0. The first-order, second-order, etc. perturbation terms then involve both u1 and the distribution functions for the reference system. In the sections that follow we first briefly discuss the historical background of perturbation theory (§ 4.1). As a simple example we then derive the u-expansion for the free energy (§ 4.2). This is followed by general expansions for the angular pair correlation function (§ 4.3) and the free energy (§ 4.4). The expansions developed in these latter sections are for an arbitrary reference system and arbitrary perturbation parameter. We next consider some particular choices of reference system and perturbation parameter. We first consider the u-expansion (§ 4.5) further, for a potential having both attractive and repulsive parts, and also the f-expansion (§ 4.6) which uses a different reference fluid. This is followed by a description of methods for expanding the system properties for an anisotropic repulsive potential about those for a hard sphere potential (§4.7), and then the expansion for a general potential (attractive and repulsive parts) about a non-spherical reference potential (§ 4.8). We also discuss two approximation methods based on perturbation theory, the effective central potential method (§ 4.9), and generalized van der Waals models (§4.11). Non-additive potential effects are discussed in §4.10. Perturbation theories have been the subject of reviews for both atomic and molecular liquids. Perturbation expansions are closely related to inverse temperature expansions, which have been a standard technique since the earliest days of statistical mechanics. As examples, we mention some early work on gases (virial coefficients, dielectric and Kerr constants), and solids (lattice phonon specific heat, polar lattice thermodynamics, electric and magnetic susceptibility properties, alloy order-disorder transitions, ferromagnetism, and diamagnetism). In considering perturbation theory for liquids it is convenient first to discuss the historical development for atomic liquids.

scholarly journals Nutation and reference frame

1995 ◽  
Vol 10 ◽  
pp. 228-231
Author(s):  
N. Capitaine
Keyword(s):  
Perturbation Theory ◽  
Reference Frame ◽  
Euler Equations ◽  
Coordinate Transformation ◽  
Earth Rotation ◽  
Reference System ◽  
Reference Frames ◽  
Fundamental Importance ◽  
Terrestrial Reference System ◽  
Celestial Reference System

The reference frames are of fundamental importance in all kinds of the precession and nutation studies involving the theory, the coordinate transformation and the observations. The aim of this paper is to review all the frames used in such studies and to lead to a better consistency between them in order that theory and reductions of observations be referred, as close as possible, to the frames to which observables are actually sensitive.The equations of Earth rotation can be expressed either as Euler equations in the Terrestrial Reference System (TRS), or as perturbation theory in the Celestial Reference System (CRS) (Kinoshita 1977). Euler equations are transformed to the CRS in the astronomical approach (Woolard 1953) and solved by the method of variation of the parameters, whereas, in the geophysical approach (Melchior 1971), the solutions, first obtained in the TRS, are transformed to the CRS and then solved by an integration with respect to time.

On the role of the reference system in perturbation theory: An augmented van der Waals theory of simple fluids

2009 ◽  
Vol 279 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Roman Melnyk ◽  
Ivo Nezbeda ◽  
Douglas Henderson ◽  
Andrij Trokhymchuk
Keyword(s):  
Perturbation Theory ◽  
Reference System ◽  
Van Der Waals ◽  
Simple Fluids ◽  
Van Der Waals Theory
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