Decay of pair correlation functions

1977 ◽  
Vol 55 (9) ◽  
pp. 761-766 ◽  
Author(s):  
Yoshio Tago ◽  
William R. Smith
Keyword(s):  
Correlation Function ◽  
Correlation Length ◽  
Correlation Functions ◽  
Pair Correlation Function ◽  
Hard Sphere ◽  
Pair Correlation ◽  
Direct Correlation Function ◽  
Pair Correlation Functions ◽  
Hard Sphere Fluid

The decay equation, which determines the correlation length and the period of the pair correlation function of a fluid at large distances, is discussed using the Ornstein–Zernike equation when the direct correlation function vanishes rapidly at large distances. The decay equation is solved numerically using the exact hard sphere and sticky hard sphere fluid results from the Percus–Yevick approximation. In the case of the hard sphere fluid, oscillatory decay is always obtained. For the sticky hard sphere fluid, we obtain a locus both in the pressure–temperature plane and the density–temperature plane such that the decay is monotonic inside and oscillatory outside the locus.

scholarly journals Spectral analysis of pair-correlation bandwidth: application to cell biology images

2015 ◽  
Vol 2 (2) ◽  
pp. 140494 ◽  
Author(s):  
Benjamin J. Binder ◽  
Matthew J. Simpson
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Pair Correlation Function ◽  
Cell Biology ◽  
Pair Correlation ◽  
Aggregate Size ◽  
Reference Population ◽  
Quantitative Information ◽  
Pair Correlation Functions ◽  
Synthetic Simulation

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

Describing the geometrical packing of gravelly cobble deposits using pair-correlation functions

2001 ◽  
Vol 38 (6) ◽  
pp. 1343-1353
Author(s):  
Zon-Yee Yang ◽  
Shin-Chen Lo
Keyword(s):  
Particle Size ◽  
Correlation Function ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Correlation Functions ◽  
Pair Correlation Function ◽  
Distribution Curve ◽  
Pair Correlation ◽  
Pair Correlation Functions ◽  
Point Field

There is a close correlation between the mechanical behavior of gravelly cobbles and their geometrical fabric. In geotechnical engineering, the particle-size distribution curve is used to describe the particle gradation. However, a group of particles with the same particle-size distribution can result in several packing arrangements due to the different sedimentation processes. The particle-size distribution curve does not distinguish this characteristic. This study attempts to employ the pair-correlation function of point field theory for describing the geometric packing of gravelly cobble deposits. In the point field, a single gravel- or cobble-sized particle is represented by a point of its geometric center. The pair-correlation function can statistically illustrate the characteristics of a geometrical point pattern and is helpful in interpreting the neighborhood relationship between particles, such as the frequency of interpoint distances and the dominant particle sizes in a point process. Some examples based on ideal particle shapes and arrangements are analyzed to illustrate the interpretations from the pair-correlation functions. The characteristics of pair-correlation functions of field examples are also explained. It is shown that the pair-correlation function can provide another approach to understanding the geometrical packing characteristics of a gravelly cobble formation.Key words: gravelly cobble deposit, geometrical packing, interpoint distance, particle-size distribution, pair-correlation function, point field theory.

Solvation force in a hard-sphere fluid

1999 ◽  
Vol 77 (8) ◽  
pp. 585-590 ◽  
Author(s):  
M Moradi ◽  
M Kavosh Tehrani
Keyword(s):  
Correlation Function ◽  
Hard Sphere ◽  
Hard Core ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Direct Correlation Function ◽  
Functional Theory ◽  
Hard Sphere Fluid ◽  
Generalized Mean ◽  
Simulation Results

The solvation force in a hard-sphere fluid is obtained by the denisty functional theory proposed by Rickayzen and Augousti. The direct correlation function (DCF) with the tail introduced by Tang and Lu is used. This DCF (hereafter TL DCF ) is postulated to hold the Yukawa form outside the hard core; and the generalized mean spherical approximation (GMSA) approach has been applied. The results are compared with those obtained by using the Percus-Yevick (PY) DCF. These results are also compared with those of Monte Carlo simulations. At low densities and fairly high densities the results are in agreement. But at high densities there is more oscillation in the solvation force obtained by using TL DCF in comparison with the PY DCF. There are no simulation results at high densities to be compared with these results.PACS No. 61.20

Direct correlation function: Hard sphere fluid

1975 ◽  
Vol 63 (2) ◽  
pp. 601-607 ◽  
Author(s):  
Douglas Henderson ◽  
E. W. Grundke
Keyword(s):  
Correlation Function ◽  
Hard Sphere ◽  
Direct Correlation Function ◽  
Hard Sphere Fluid

scholarly journals Pair correlation functions and limiting distributions of iterated cluster point processes

2018 ◽  
Vol 55 (3) ◽  
pp. 789-809 ◽  
Author(s):  
Jesper Møller ◽  
Andreas D. Christoffersen
Keyword(s):  
Correlation Function ◽  
Markov Chain ◽  
Correlation Functions ◽  
Pair Correlation Function ◽  
Point Processes ◽  
Equilibrium Distribution ◽  
Pair Correlation ◽  
Cluster Process ◽  
Previous State ◽  
Special Case

Abstract We consider a Markov chain of point processes such that each state is a superposition of an independent cluster process with the previous state as its centre process together with some independent noise process and a thinned version of the previous state. The model extends earlier work by Felsenstein (1975) and Shimatani (2010) describing a reproducing population. We discuss when closed-form expressions of the first- and second-order moments are available for a given state. In a special case it is known that the pair correlation function for these type of point processes converges as the Markov chain progresses, but it has not been shown whether the Markov chain has an equilibrium distribution with this, particular, pair correlation function and how it may be constructed. Assuming the same reproducing system, we construct an equilibrium distribution by a coupling argument.

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