Granular statistical mechanics: Volume-stress phase space, equipartition and equations of state

2013 ◽  
Author(s):  
Raphael Blumenfeld ◽  
Joe F. Jordan ◽  
Sam F. Edwards
Keyword(s):  
Phase Space ◽  
Statistical Mechanics ◽  
Equations Of State ◽  
Volume Stress

The theory of rubber elasticity

1976 ◽  
Vol 351 (1666) ◽  
pp. 397-406 ◽  
Keyword(s):  
Equation Of State ◽  
Statistical Mechanics ◽  
Equations Of State ◽  
Rubber Elasticity ◽  
Elastic Behaviour ◽  
Excluded Volume ◽  
Simple Pattern ◽  
Dynamical Approach ◽  
Equilibrium Approach ◽  
The Future

It is argued that since statistical mechanics has developed in two ways, the dynamical approach of Boltzmann and the equilibrium approach of Gibbs, both should be valuable in rubber elasticity. It is shown that this is indeed the case, and the generality of these approaches allows one to study the problem in greater depth than hitherto. In particular, damping terms in the elastic behaviour of rubber can be calculated, and also the effect of entanglements and excluded volume on the equation of state. It is noticeable that although the calculated equations of state are quite complex, they do not fit into a simple pattern of invariants. The future for these developments is briefly discussed.

scholarly journals Themis: A Software to Assess Association Free Energies via Direct Estimative of Partition Functions

2020 ◽  
Author(s):  
Felippe Mariano Colombari ◽  
Asdrubal Lozada-Blanco ◽  
Kalil Bernardino ◽  
Weverson Gomes ◽  
André Farias de Moura
Keyword(s):  
Phase Space ◽  
Statistical Mechanics ◽  
Excited States ◽  
Surface Adsorption ◽  
Chiral Discrimination ◽  
Partition Functions ◽  
Computer Implementation ◽  
Free Energies ◽  
Electronic Excited States ◽  
Discrete Grid

<div>We present the program <i>Themis</i> - a computer implementation of a standard statistical mechanics framework to compute free energies, average energies and entropic contributions for association processes of two atom-based structures. The partition functions are computed analytically using a discrete grid in the phase space, whose size and degree of coarseness can be controlled to allow efficient calculations and to achieve the desired level of accuracy. With this strategy, applications ranging from molecular recognition, chiral discrimination, surface adsorption and even the interactions involving molecules in electronic excited states can be handled.</div>

Phase Space Reconstruction

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Dynamical Systems ◽  
Statistical Mechanics ◽  
State Space ◽  
Phase Plane ◽  
Material Point ◽  
The Other ◽  
Straight Line ◽  
Mathematical Construction

In this chapter we introduce an important concept concerning the study of both discrete and continuous dynamical systems, the concept of phase space or “state space”. It is an abstract mathematical construction with important applications in statistical mechanics, to represent the time evolution of a dynamical system in geometric shape. This space has as many dimensions as the number of variables needed to define the instantaneous state of the system. For instance, the state of a material point moving on a straight line is defined by its position and velocity at each instant, so that the phase space for this system is a plane in which one axis is the position and the other one the velocity. In this case, the phase space is also called “phase plane”. It is later applied in many chapters of the book.

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