On the realizability of pair correlation functions

O.U. Uche, F.H. Stillinger and S. Torquato

Physica A: Statistical Mechanics and its Applications, 2006, vol. 360, issue 1, 21-36

Abstract: The pair correlation function g2(r) provides a basic geometric descriptor for many-particle systems. It must obey two necessary conditions: (i) non-negativity for all distances r, and (ii) non-negativity of its associated structure factor S(k) for all k. Here we utilize an improved stochastic construction algorithm for particle configurations to establish conditions in which (i) and (ii) are also sufficient, i.e., g2(r) is in fact realizable. Two types of target pair correlation functions have been investigated in one, two, and three dimensions for hard-core particles, specifically a unit step function, and a contact δ plus step pair correlation function. Results indicate that the former target function is realizable up to a terminal density set by necessary condition (ii), at which the particle core packing fraction equals 2-d in d dimensions. Furthermore, results are consistent with the proposition that for d>1 the contact δ plus step function is realizable up to a terminal density due to condition (ii) at which the packing fraction of cores is (d+2)/2d+1 [Torquato and Stillinger, J. Phys. Chem. B 106 (2000) 8354, 11406].

Keywords: Pair correlation function; Realizability; Hard spheres and disks (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037843710500484X
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:360:y:2006:i:1:p:21-36

DOI: 10.1016/j.physa.2005.03.058

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().