Distance distribution function

It is conventional to express tlie stmctiiral infomiation in temis of a pair distance distribution function, or PDDF [5], which is defined by p(r) = p-P(r). Using this, equation (Bl.8.10 becomes... 

Classical Analysis. The classical analytical methods are even applicable for polydisperse samples and rest on the CLD (Sect. 8.5.3) and on Vonk s [189] distance distribution function (DDF) ([189-191] [101] p. 168)... 

Figure 8.35. The homogeneous sphere of radius R. Radial correlation function, ys (r), distance distribution function (DDF) ps (r) and chord length distribution (CLD) gs (r)...

Cantor, C. R., and Pechukas, P. (1971). Determination of distance distribution functions by singlet-singlet energy transfer. Proc. Natl. Acad. Sci. USA 68, 2099-2101. 

Fio. 9. Normalized distance distribution function of the polar coordinate r for all protein atom-aromatic ring contacts as defined by the coordinate system depicted in Pig. 8 (< 10 A). Each value of the distance distribution function was normalized for sample size by dividing the observed frequency by r2. 

Let us denote by V the interaction potential for planar bilayers. Assuming that the fluctuations of adjacent bilayers are totally uncorrelated, and using locally the planar approximation, the free energy per unit area can be written in terms of the distance distribution function... 

Recent Monte Carlo simulations of bilayer fluctuations17 revealed that the distance distribution function is asymmetric. While this result is expected, since it implies that the correlation between fluctuating bilayers decreases... 

The variational method proposed earlier by the authors relied on Monte Carlo simulations to select an intermembrane distance distribution function.8 The purpose of this paper is to present a new approach, in which the interaction between two membranes, in the presence of thermal fluctuations, is calculated directly by employing a suitable approximate partition function. Thus, the asymmetry of the distance distributions results in a natural manner from the calculation. 

Fig. 2 WAXD profiles (a) and the distance distribution functions P(R) (b) of PET as a function of annealing time at 115 °C. M.Q. Melt-quenched sample [6]...

However, the RDF(CM) is not appropriate when the solute is an elongated molecule, as it was discussed before, for the case of (3-carotene in several solvents [47] and benzophenone in water [50], In these cases of elongated solutes, an appropriate function is the minimum-distance distribution function (MDDF), where the histogram used to calculate the distribution function is not the distance between the CMs of solute-solvent, but the minimum distance between them. The MDDF is defined as... 

Figure 7-5. The RDF between the center of mass (dashed line) and the minimum-distance distribution function (solid line) between the benzophenone (shown in the inset) and the water molecules...

Ideal behaviour for chain conformation is represented by a Gaussian distribution W(r) of end-to-end distances. Excluded volume effects give a much different end distance distribution function. Figure 1, with the biggest differences operating on chains which happen to have their chain ends in proximity (4). 

Figure 1. A plot of the end-distance distribution function W(0) vs. the ratio of the end separation divided by Rg for a...

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