Related papers: Radial distribution function for hard spheres in f…
We derive, from the dimensional cross-over criterion, a fundamental-measure density functional for parallel hard curved rectangles moving on a cylindrical surface. We derive it from the density functional of circular arcs of length $\sigma$…
The continuity conditions of the radial distribution function g(r) and its close relative the cavity function y(r) are studied in the context of the Percus-Yevick (PY) integral equation for 3D square-well fluids. The cases corresponding to…
In this work we present a numerical study, based on molecular dynamics simulations, to estimate the freezing point of hard spheres and hypersphere systems in dimension D = 4, 5, 6 and 7. We have studied the changes of the Radial…
The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly…
We consider dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation and pair distribution function of the disk…
A simple recipe to derive the compressibility factor of a multicomponent mixture of d-dimensional additive hard spheres in terms of that of the one-component system is proposed. The recipe is based (i) on an exact condition that has to be…
Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
A comparison of simulation results with the prediction of the structural properties of square-shoulder fluids is carried out to assess the performance of three theories: Tang--Lu's first-order mean spherical approximation, the simplified…
In various stereological problems an $n$-dimensional convex body is intersected with an $(n-1)$-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the…
The velocity distribution of dark matter near the Earth is important for an accurate analysis of the signals in terrestrial detectors. This distribution is typically extracted from numerical simulations. Here we address the possibility of…
The equation of state for five-dimensional hard hyperspheres arising as a weighted average of the Percus-Yevick compressibility (3/5) and virial (2/5) equations of state is considered. This Carnahan-Starling-like equation turns out to be…
We introduce an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of our recently published averaged pair distribution function at contact which has been shown to accurately…
The simplest bounded potential is that of penetrable spheres, which takes a positive finite value $\epsilon$ if the two spheres are overlapped, being 0 otherwise. In this paper we derive the cavity function to second order in density and…
Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E \textbf{83}, 011201…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
Fracture functions are parton distributions of an initial hadron in the presence of an almost collinear particle observed in the final state. They are important ingredients in QCD factorization for processes where a particle is produced…
Using the first seven known virial coefficients and forcing it to possess two branch-point singularities, a new equation of state for the hard-sphere fluid is proposed. This equation of state predicts accurate values of the higher virial…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
We present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary…
Integral equation of pure liquids, combined with a new "scaling approximation" based on a corresponding states treatment of pair correlation functions, is used to evaluate approximate structure factors for colloidal fluids constituted of…