Time—Correlation—Function Expressions for Linear and Nonlinear Transport Coefficients

1967 ◽  
Vol 47 (9) ◽  
pp. 3161-3169 ◽  
Author(s):  
Frank C. Andrews
Keyword(s):  
Correlation Function ◽  
Transport Coefficients ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Nonlinear Transport ◽  
Linear And Nonlinear

Computer simulation of time correlation functions and matter transport coefficients for a model order–disorder alloy

1998 ◽  
Vol 76 (11) ◽  
pp. 1548-1553
Author(s):  
Ziqiang Qin ◽  
Alan R Allnatt ◽  
E Loftus Allnatt
Keyword(s):  
Correlation Function ◽  
Transition Temperature ◽  
Correlation Functions ◽  
Theoretical Calculations ◽  
Transport Coefficients ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Time Correlation Functions ◽  
Matter Transport ◽  
Phenomenological Coefficients

The time correlation functions associated with the Onsager phenomenological coefficients for isothermal matter transport have been calculated by Monte Carlo simulation for a binary system (A,B) at the equiatomic composition according to the Kikuchi-Sato model of an order-disorder alloy with vacancy transport mechanism. The diagonal (AA) time correlation functions are positive, decay monotonically to zero, and exhibit a long time tail where they vary as t-n where t is time; the exponent n varies weakly with temperature at high temperatures and more rapidly as the temperature is lowered through the order-disorder transition temperature. In the region of short-range order the off-diagonal (AB) time correlation function is negative but otherwise shows similar behaviour to the diagonal one, although as the transition temperature is approached n varies more rapidly. At the transition temperature and below, the off-diagonal time correlation function increases from an initial negative value to a maximum where it is positive and then, at later times, decreases to zero. The implications of these observations for approximate theoretical calculations of the phenomenological coefficients are briefly indicated.Key words: diffusion, non-equilibrium phenomena, statistical mechanics, transport properties.

How to analyse the results

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Transport Coefficients ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Einstein Relation ◽  
Time Correlation Functions ◽  
Practical Guidance

In this chapter, practical guidance is given on the calculation of thermodynamic, structural, and dynamical quantities from simulation trajectories. Program examples are provided to illustrate the calculation of the radial distribution function and a time correlation function using the direct and fast Fourier transform methods. There is a detailed discussion of the calculation of statistical errors through the statistical inefficiency. The estimation of the error in equilibrium averages, fluctuations and in time correlation functions is discussed. The correction of thermodynamic averages to neighbouring state points is described along with the extension and extrapolation of the radial distribution function. The calculation of transport coefficients by the integration of the time correlation function and through the Einstein relation is discussed.

Rate Constants, Reactive Flux

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Correlation Function ◽  
Rate Constant ◽  
Cross Sections ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Exact Expression ◽  
Reaction Cross ◽  
Dividing Surface ◽  
Definition Of ◽  
Reactive Flux

This chapter discusses a direct approach to the calculation of the rate constant k(T) that bypasses the detailed state-to-state reaction cross-sections. The method is based on the calculation of the reactive flux across a dividing surface on the potential energy surface. Versions based on classical as well as quantum mechanics are described. The classical version and its relation to Wigner’s variational theorem and recrossings of the dividing surface is discussed. Neglecting recrossings, an approximate result based on the calculation of the classical one-way flux from reactants to products is considered. Recrossings can subsequently be included via a transmission coefficient. An alternative exact expression is formulated based on a canonical average of the flux time-correlation function. It concludes with the quantum mechanical definition of the flux operator and the derivation of a relation between the rate constant and a flux correlation function.

Two-body dynamics in fluids as probed by interaction-induced light scattering

1981 ◽  
Vol 59 (10) ◽  
pp. 1504-1509 ◽  
Author(s):  
U. Balucani ◽  
R. Vallauri
Keyword(s):  
Correlation Function ◽  
Light Scattering ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Simulation Experiments ◽  
Particle Pairs ◽  
Body Dynamics ◽  
Atomic Fluids ◽  
Relative Dynamics

The relative dynamics of particle pairs in fluids is investigated both theoretically and by simulation experiments. The physical implications of this analysis are important in all interaction-induced phenomena and illustrated in the case of the pair time correlation function relevant to collision-induced light scattering in atomic fluids.

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