Invariant expansions of the radial distribution function for fluids of hard convex bodies

摘要

The radial distribution functions (RDF) for systems consisting of a single nonspherical convex body in a fluid of spheres and for a pure fluid of nonspherical convex bodies are expressed in terms of the minimum surfacehyphen;tohyphen;surface separation and a set of angles derived from the surface normal. The orthogonal function expansion of the anisotropic RDF,g, has the property that the first anisotropic contribution vanishes at zero density and is directly proportional to the nonsphericity of the particle; however, the resulting convex body orthogonal polynomials depend on the surfacehyphen;tohyphen;surface separation. An invariant expansion of the product of the Jacobian and the RDF,S12g, has anisotropic expansion coefficients even at zero density, but the expansion functions are the spherical harmonics (independent of the surfacehyphen;tohyphen;surface coordinate). Monte Carlo simulations are conducted on the two dimensional system consisting of a single convex ellipse in a bath of circular disks. A comparison is made between the centerhyphen;tohyphen;center expansion of the RDF, an expansion based on the orthogonal function expansion, and theS12g(or Kabadindash;Steele) expansion.