STATISTICAL MECHANICS OF CERTAIN HYDRODYNAMIC DISPERSION PHENOMENA

1965 ◽  
Vol 43 (10) ◽  
pp. 1776-1794 ◽  
Author(s):  
Narayan M. Chaudhari ◽  
Adrian E. Scheidegger
Keyword(s):  
Statistical Mechanics ◽  
Markov Processes ◽  
Irreversible Thermodynamics ◽  
Hydrodynamic Dispersion ◽  
Mechanics Of Solids ◽  
Interaction Function ◽  
Onsager Relations ◽  
Weakly Coupled ◽  
Dispersion Systems ◽  
Mass Dispersion

This paper explores the extent of an analogy postulated earlier between the usual energy-based statistical mechanics and mass-dispersion phenomena. It is shown that in the equilibrium case the interaction function as used in the energy-based statistical mechanics of solids or weakly coupled gases entails a corresponding result in mass-dispersion systems. Examples of specific transport equations are calculated. The analogy can also be extended to irreversible thermodynamics. It is shown that Ziegler's generalized Onsager relations entail corresponding results in the case of mass dispersion.It is shown that an approach based on the theory of Markov processes can also be used for the description of mass-based statistical mechanics. The conditions necessary for the maintenance of canonical invariance are indicated. Applications of the above theory to hydrological problems are indicated.

scholarly journals A holographic superfluid symphony

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Daniel Areán ◽  
Matteo Baggioli ◽  
Sebastian Grieninger ◽  
Karl Landsteiner
Keyword(s):  
Constitutive Relations ◽  
Quasinormal Modes ◽  
Role Reversal ◽  
Hydrodynamic Theory ◽  
Hydrodynamic Dispersion ◽  
Complex Frequency ◽  
Hydrodynamic Modes ◽  
Weakly Coupled ◽  
Reversal Phenomenon ◽  
Theory Framework

Abstract We study the hydrodynamic excitations of backreacted holographic superfluids by computing the full set of quasinormal modes (QNMs) at finite momentum and matching them to the existing hydrodynamic theory of superfluids. Additionally, we analyze the behavior of the low-energy excitations in real frequency and complex momentum, going beyond the standard QNM picture. Finally, we carry out a novel type of study of the model by computing the support of the hydrodynamic modes across the phase diagram. We achieve this by determining the support of the corresponding QNMs on the different operators in the dual theory, both in complex frequency and complex momentum space. From the support, we are able to reconstruct the hydrodynamic dispersion relations using the hydrodynamic constitutive relations. Our analysis rules out a role-reversal phenomenon between first and second sound in this model, contrary to results obtained in a weakly coupled field theory framework.

Statistical mechanics of solids

1975 ◽  
Vol 11 (10) ◽  
pp. 4065-4068 ◽  
Author(s):  
D. Shalitin ◽  
Y. Imry
Keyword(s):  
Statistical Mechanics ◽  
Mechanics Of Solids

Mechano-Chemistry; Interdiffusion in Solid Solutions

2008 ◽  
Vol 277 ◽  
pp. 61-68
Author(s):  
Marek Danielewski ◽  
Bartłomiej Wierzba
Keyword(s):  
Diffusion Processes ◽  
Solid Phase ◽  
Volume Transport ◽  
Momentum Equation ◽  
Irreversible Thermodynamics ◽  
Frame Of Reference ◽  
Mechanics Of Solids ◽  
Centre Of Mass ◽  
Volume Velocity ◽  
Internal Forces

In this work we show that the volume velocity, ρυ , rather than the local centre of mass velocity should be used in continua. We use the volume continuity equation to define the volume frame of reference in the multicomponent, compressible continua. The volume velocity (material velocity) is a unique frame of reference for all internal forces and processes, e.g., the mass diffusion. No basic changes are required in the foundations of linear irreversible thermodynamics except recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in every continuum. The volume fixed frame of reference allows the translation of the Newton’s discrete mass-point molecular mechanics into continuum mechanics and the use of the Cauchy linear momentum equation of fluid mechanics and Navier-Lamé equation of mechanics of solids. Our proposed modifications of Navier-Lamé and energy conservation equations are selfconsistent with the literature for solid-phase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffusive volume transport. We do show that the local diffusion processes do not change the centre of mass of the system and that the internal stress depends on the gradient of the local volume velocity only.

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