Partial distribution function

Due to the striking difference in the partial distribution functions between molten salts and Lennard-Jones liquid mixtures the structure factors of KrAr... 

The site-site pair distribution function, hf-(r), is related to the partial distribution functions g jp r) = hf j (r) + fiaofipo by the relation,... 

In [6.41-43] we find reports of the experimental investigations of partial distribution functions of atoms in amorphous alloys. The strong LO is discovered in the alloys of the metal-metalloid and metal-metal types. The compositional order is closely (but not always unambiguously) connected with the topological order, so that the presence of the former testifies to the existence of the definite local topological order. 

A first attempt to consider the role of the Debye counterion atmosphere on the transport of a surfactant ion through the DL was made by Mikhailovskij (1976, 1980) (cf. Kortilm 1966, Lyklema 1991). In contrast to a macro-kinetic model, Mikhailovskij derived kinetic equations for a multi-component system under the influence of an external electric field. The basis of this derivation was the set of Bogolubow equations for the partial distribution functions. As the result of the model derivation the following set of electro-diffusion equations is obtained. 

Reduction of the number of independent parameters in the evolution of an indignant system proceeds continuously as a result of parameter synchronization and the determination of the correlative bonds between them. However, taking into account the difference between partial processes and their respective relaxation times, separate states of evolution can be noted, every one of which is described by its own number of independent parameters changing through transition from one state to another. For example, after the finishing time r(/V from the start of a single-component system, a so-called kinetic state of a process takes place [11,12] (ro and V are characteristic size of a particle and heat rate of their moving, respectively is an indication of particle interaction time under collision, in the order of 10" -10s). In this state a state of a system is fully determined by a partial distribution function tU] that rules by the temporary evolution of a system. Multi-partial distribution function and as a result a full one represent a function of (Oil... 

The tetrachloride liquids XCiti (X = C, Si, Ti, V, Ge, Sn etc) make an interesting series for studying aspects of orientational correlation in relation to molecular contours. The various diffraction studies have been surveyed in a paper [253 which uses the reference interaction site model (RISM) to evaluate the partial distribution functions. Data for carbon tetrachloride are particularly instructive as they Illustrate the complementary nature of X-ray and neutron scattering. There are three partial functions gcc( )> weighting factors... 

Figure 6.7.3 Number density of fluoride in molten xThF -(1 -x)MF(M = Li and Na, 0

In the derivation of the Boltzmann equation it is assumed that the distribution function changes only in consequence of completed collisions, i.e., the effect of partial collisions is neglected. We shall, therefore, consider the single-particle distribution function averaged23 over a time r, which will (later) be taken large compared with a collision time ... 

Stochastic equation (A8.7) is linear over SP and contains the operators La and V.co of differentiation over time-independent variables Q and co. Therefore, if we assume that the time fluctuations of the liquid cage axis orientation Z(t) are Markovian, then the method used in Chapter 7 yields a kinetic equation for the partially averaged distribution function P(Q, co, t, E). The latter allows us to calculate the searched averaged distribution function... 

The key to the resolution of the apparent contradiction becomes evident upon re-examining the initial derivation which proceeds from Fig. 68. Finite, or bounded, molecular species are implied in the expression for the probability of a specific x-mev configuration thus fx — 2x + l unreacted ends in addition to the one selected at random are prescribed. An infinite network, on the other hand, is terminated only partially by unreacted end groups the walls of the macroscopic container place the ultimate limitation on its extent. Hence the network fraction is implicitly excluded from consideration, with the result that the distribution functions given above are oblivious of it. Failure of to retain the same value throughout the range in a is a... 

It would be valuable if one could proceed with a reliable free energy calculation without having to be too concerned about the important phase space and entropy of the systems of interest, and to analyze the perturbation distribution functions. The OS technique [35, 43, 44, 54] has been developed for this purpose. Since this is developed from Bennett s acceptance ratio method, this will also be reviewed in this section. That is, we focus on the situation in which the two systems of interest (or intermediates in between) have partial overlap in their important phase space regions. The partial overlap relationship should represent the situation found in a wide range of real problems. 

Note also that Eq. (5.2) is equivalent to the common Laplace transform. A comparison of double-exponential and distributional analyses is represented in Figure 5.1. The distribution function shows width about central values which the double-exponential fit cannot express because of its mathematical form. Here the appearance of central values may partially be a consequence of the model functions assumed in the solution. Nevertheless, width directly... 

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