Pair distribution function time-dependent

The correlation functions G are the same functions which Oppenheimer and Bloom introduced in their theory of nuclear spin relaxation [304], The function has been called the time-dependent pair distribution function it should not, however, be confused with the van Hove correlation function which is often referred to by the same name. The name time-dependent intermolecular correlation function (TDICF) has, therefore, been proposed for G [71]. 

In interacting systems the optical and orientation factors in a are no longer separable quantities. The induced optical effect is determined both by the single particle scattering [form factor P q)] and by the pair distribution function [structure factor 5( )], the latter being direction-dependent [42]. Since in addition to orientation the electric field causes particle translation, even for spherical particles the radial distribution function g q, /) and the "static" structure factor attain time-dependent induced anisotropy. The deformed surface potential also contributes to this effect. 

In the discussion of the structure of samples we employed the pair distribution function g r). This notion can be generalized to include also the dynamics, by introducing the time dependent pair distribution function g(r,t). Per definition, the product... 

As we can see, dynamic scattering experiments carried out under variation of the scattering vector and the frequency provide a Fourier-analysis of the time dependent pair distribution function. 

The discussion on the distorted fluid microstructure demonstrates the utility of NEMD as a practical tool and as a means to get an insight into the physics of viscous phenomena. The shear-rate dependent non-Newtonian properties of a liquid can be calculated from the appropriate steady-state averages, but the mechanical transport properties can be obtained indirectly from the nonequilibrium pair distribution function using equation (9.49), and a more physical picture of the behavior of a nonequilibrium fluid is obtained. As an example, the phenomenological theory of Hanley et al. (1987,1988) is outlined where the functionals are evaluated from a relaxation time approximation. The... 

Time-dependent correlation functions. Similar pair and triplet distributions, which describe the time evolution of a system, are also known [318]. These have found interesting uses for the theory of virial expansions of spectral line shapes, pp. 225 ff. below [297, 298],... 

The important feature in the final result (13.45) is the fact that all the needed dynamical information is associated with the time course of a single collision event. To calculate the correlation function that appears here it is sufficient to consider a single binary collision with thermal initial conditions. The result is given in terms of the function B, a two-body property that depends only on the relative position of the particles (the initial configuration for the collision event) and the temperature. The host structure as determined by the V-body force enters only through the configurational average that involves the pair distribution g(r). 

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