ON THE TWO-POINT CORRELATION FUNCTION FOR DISPERSIONS OF NONOVERLAPPING SPHERES

1998 ◽  
Vol 08 (02) ◽  
pp. 359-377 ◽  
Author(s):  
KONSTANTIN Z. MARKOV ◽  
JOHN R. WILLIS
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Characteristic Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Integral Formula ◽  
Probability Densities ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Point Level

Random dispersions of spheres are useful and appropriate models for a wide class of particulate random materials. They can be described in two equivalent and alternative ways — either by the multipoint moments of the characteristic function of the region, occupied by the spheres, or by the probability densities of the spheres' centers. On the "two-point" level, a simple and convenient integral formula is derived which interconnects the radial distribution function of the spheres with the two-point correlation of the said characteristic function. As one of the possible applications of the formula, the behavior of the correlation function near the origin is studied in more detail and related to the behavior of the radial distribution function at the "touching" separation of the spheres.

SQUARE-WELL FLUID AT LOW DENSITIES

1967 ◽  
Vol 45 (12) ◽  
pp. 3959-3978 ◽  
Author(s):  
J. A. Barker ◽  
D. Henderson
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Critical Temperature ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Virial Coefficients ◽  
Hard Core ◽  
Direct Correlation Function ◽  
Virial Series ◽  
Square Well

Values for the radial distribution function and the direct correlation function at low densities and for the first five virial coefficients are obtained for a fluid of molecules interacting according to the square-well potential when the width of the attractive well is half the radius of the hard core. It is found that the higher-order coefficients are surprisingly large and, as a result, the virial series fails to converge even at temperatures and volumes significantly greater than the critical temperature and volume. Comparisons of these exact virial coefficients with those given by several approximate theories are made. Values are also given for the first five virial coefficients when the width of the attractive well is equal to the radius of the hard core.

The total and direct correlation function in the interface of the lattice gas in two dimensions

1985 ◽  
Vol 400 (1819) ◽  
pp. 263-287 ◽  
Keyword(s):  
Computer Simulation ◽  
Distribution Function ◽  
Correlation Function ◽  
Lattice Gas ◽  
Fourier Transforms ◽  
Two Dimensions ◽  
Direct Correlation Function ◽  
Point Distribution ◽  
Point Correlation ◽  
Point Correlation Function

The interface between two co-existing phases of a lattice gas in two dimensions in a certain non-zero external potential is studied by a computer simulation, which produces numerically accurate results by the use of a transfer matrix which is constructed numerically. Strips of dimensions 7 x ∞ and 11 x ∞ were studied at T ≼0.5 T c . The two-point distribution function, the two-point correlation function, the direct correlation function of Ornstein–Zernike and their Fourier transforms were computed and are shown and discussed.

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.

The Influence of Hydrogen atoms on the Performance of Radial Distribution Function Based Descriptors in the Chemoinformatic Studies of HIV-1 Prote-ase Complexes with Inhibitors.

2020 ◽  
Vol 17 ◽  
Author(s):  
Jurica Novak ◽  
Maria A. Grishina ◽  
Vladimir A. Potemkin
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Current Model ◽  
Direct Interaction ◽  
Hydroxyl Group ◽  
Linear Regression Method ◽  
Hydrogen Atoms ◽  
Protease Enzyme ◽  
Hiv 1

: In this letter the newly introduced approach based on the radial distribution function (RDF) weighted by the number of va-lence shell electrons is applied for a series of HIV-1 protease enzyme and its complexes with inhibitors to evaluate the influ-ence of hydrogen atoms on the performance of the model. The multiple linear regression method was used for the selection of the relevant descriptors. Two groups of residues having dominant contribution to the RDF descriptor are identified as relevant for the inhibition. In the first group are residues like Arg8, Asp25, Thr26, Gly27 and Asp29, which establish direct interaction with the inhibitor, while the second group consists of the amino acids at the interface of the two homodimer sub-units or with the solvent. The crucial motif pointed out by our approach as the most important for inhibition of the enzyme’s activity and present in all inhibitors is hydroxyl group that establish hydrogen bond with Asp25 side chain. Additionally, the comparison to the model without hydrogen showed that both models are of similar quality, but the downside of the current model is the need for the determination of residues’ protonation states.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

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