Related papers: The analyticity region of the hard sphere gas. Imp…
This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.
Extended gas haloes around galaxies are a ubiquitous prediction of galaxy formation scenarios. However, the density profiles of this hot halo gas is virtually unknown, although various profiles have been suggested on theoretical grounds. In…
We study a one dimensional gas of needle-like objects as a testing ground for a formalism that relates the thermodynamic properties of "hard" potentials to the probabilities for contacts between particles. Specifically, we use Monte Carlo…
Mathematically rigorous derivation of the hadron matter equation of state within the induced surface and curvature tensions approach is worked out. Such an equation of state allows one to go beyond the Van der Waals approximation for the…
We study the generic volume rigidity of $(d-1)$-dimensional simplicial complexes in $\mathbb R^{d-1}$, and show that the volume rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
A method for taking into account the long-range potential of atoms in the framework of the hard-sphere model is proposed. It is shown that thermodynamic quantities can be represented as a sum of three contribution: that of an ideal gas, the…
Here I present results from individual galaxy studies and galaxy surveys in the Local Universe with particular emphasis on the spatially resolved properties of neutral hydrogen gas. The 3D nature of the data allows detailed studies of the…
The thickness of isothermal gaseous layers and their midplane volume densities \rho_{gas}(R) were calculated for several spiral and LSB galaxies by solving the self-consistent equilibrium equations for gaseous discs embedded into a stellar…
A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established…
An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structural properties, they yield a thermodynamically…
We obtain analytic expressions for the time correlation functions of a liquid of spherical particles, exact in the limit of high dimensions $d$. The derivation is long but straightforward: a dynamic virial expansion for which only the first…
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…
Consider a non-negative number $t$ and a hyperplane $H$ of $\mathbb{R}^d$ whose distance to the center of the hypercube $[0,1]^d$ is $t$. If $t$ is equal to $0$ and $H$ is orthogonal to a diagonal of $[0,1]^d$, it is known that the…
We present a novel concept of proportional gas amplification for the read-out of the spherical proportional counter. The standard single-ball read-out presents limitations for large diameter spherical detectors and high pressure operations.…
The classical (i.e. non-quantum) equilibrium statistical mechanics of a two-dimensional one-component plasma (a system of charged point-particles embedded in a neutralizing background) living on a pseudosphere (an infinite surface of…
Hard-sphere colloids are popular as models for testing fundamental theories in condensed matter and statistical physics, from crystal nucleation to the glass transition. A single parameter, the volume fraction (phi), characterizes an ideal,…
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
We compute the area of a generic d-sphere in a Snyder geometry.
We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method…