Related papers: The analyticity region of the hard sphere gas. Imp…
Hard sphere systems in two dimensions are examined for arbitrary density. Simulation results are compared to the theoretical predictions for both the low and the high density limit, where the system is either disordered or ordered,…
Model of hard sphere system is important part of modern theories of liquids. Radial distribution function of hard sphere fluid represented in form of explicit analytical expression allows to obtain thermodynamic potentials in analytical…
An equation of state of the hard sphere fluid which is not analytical at the freezing density is proposed and tested. The nonanalytical term is based on the the classical nucleation theory and is able to capture the observed ``anomalous…
Due to our vantage point in the disk of the Galaxy, its 3D structure is not directly accessible. However, knowing the spatial distribution, e.g. of atomic and molecular hydrogen gas is of great importance for interpreting and modelling…
The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities $d$ are studied with an analytical approximation method that generalizes the Rational Function Approximation earlier introduced in the…
The equation of state for a two-dimensional hard-sphere gas is difficult to calculate by usual methods. In this paper we develop an approach for calculating the equation of state of hard-sphere gases, both for two- and three-dimensional…
We compute the analytic torsion of a cone over a sphere of dimension 1, 2, and 3, and we conjecture a general formula for the cone over an odd dimensional sphere.
We give a new criterion for a classical gas with a repulsive pair potential to exhibit uniqueness of the infinite volume Gibbs measure and analyticity of the pressure. Our improvement on the bound for analyticity is by a factor $e^2$ over…
The aim of this paper is to review and discuss qualitatively some results on the properties of amorphous packings of hard spheres that were recently obtained by means of the replica method. The theory gives predictions for the equation of…
Few equilibrium --even less so nonequilibrium-- statistical-mechanical models with continuous degrees of freedom can be solved exactly. Classical hard-spheres in infinitely many space dimensions are a notable exception. We show that even…
Mixtures of hard hyperspheres in odd space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called Rational Function Approximation and provides a procedure for evaluating equations of…
We find the complete rational homology for the finite subset spaces of a $d$-dimensional sphere. We also determine the integral homology in top $d$ degrees and obtain a partial description of it in codimension $d$.
When modeling the three-dimensional hydrodynamics of interstellar material rotating in a galactic gravitational potential, it is useful to have an analytic expression for gravitational perturbations due to stellar spiral arms. We present…
We present a general analytical procedure for computing the number density of voids with radius above a given value within the context of gravitational formation of the large scale structure of the universe out of Gaussian initial…
We study the radial distribution of pressure, density, temperature and flow velocity fields at different times in a two dimensional hard sphere gas that is initially at rest and disturbed by injecting kinetic energy in a localized region…
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension $d$ ($1 \leq d \leq 3$) are developed as heuristic interpolations from the knowledge of…
In this work, we use the Casimir effect to probe the existence of one extra dimension. We begin by evaluating the Casimir pressure between two plates in a $M^4\times S^1$ manifold, and then use an appropriate statistical analysis in order…
We present the first 3D hydrodynamical simulations of ram pressure stripping of a disc galaxy orbiting in a galaxy cluster. Along the orbit, the ram pressure that this galaxy experiences varies with time. In this paper, we focus on the…
We consider a classical dipole gas in with low activity and show that the pressure has a limit as the volume goes to infinity. The result is obtained by a renormalization group analysis of the model.
The new mathematical framework based on the free energy of pure classical fluids presented in [R. D. Rohrmann, Physica A 347, 221 (2005)] is extended to multi-component systems to determine thermodynamic and structural properties of…