Related papers: Solution of the Percus-Yevick equation for hard hy…
Recent values for virial coefficients up to B12, when expressed in powers of density relative to maximum close packing,lead to a closed equation-of-state for the equilibrium fluid. The series obtained converges for all densities;it becomes…
We propose a generalization of the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation from ${\mathbb R}^n$ to an arbitrary Riemannian manifold. Its form is obtained by extending the relation of the WDVV equation with ${\cal N}{=}\,4$…
The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…
We apply second order Andersen-Weeks-Chandler perturbation theory to the one-component sticky-hard-spheres fluid. We compare the results with the mean spherical approximation, the Percus-Yevick approximation, two generalized Percus-Yevick…
We compute the fourth virial coefficient of a binary nonadditive hard-sphere mixture over a wide range of deviations from diameter additivity and size ratios. Hinging on this knowledge, we build up a $y$ expansion [B. Barboy and W. N.…
The invariance for the equation of fast diffusion in the 2D coordinate space has been proved, and its reduction to the 1D (with respect to the spatial variable) analog is demonstrated. On the basis of these results, new exact…
Quantum vortices in superfluids have been an important research area for many decades. Naturally, research on this topic has focused on two and three-dimensional superfluids, in which vortex cores form points and lines, respectively. Very…
The structural properties of fluids whose molecules interact via potentials with a hard core plus two piece-wise constant sections of different widths and heights are presented. These follow from the more general development previously…
New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are…
We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken.…
The study of superfluid quantum vortices has long been an important area of research, with previous work naturally focusing on two-dimensional and three-dimensional systems, where rotation stabilises point vortices and line vortices…
A closed virial equation-of-state for the low density fluid phase of hard disks is obtained from the known virial coefficients. The equation exhibits 6-figure accuracy for the thermodynamic (MD) pressure up to the reduced number density ~…
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…
We continue the study of Confined Vortex Surfaces (\CVS{}) that we introduced in the previous paper. We classify the solutions of the \CVS{} equation and find the analytical formula for the velocity field for arbitrary background strain…
In this paper, for any odd $n$ and any integer $m\geq1$ with $n>4m$, we study the fundamental solution of the higher order Schr\"{o}dinger equation \begin{equation*} \mathrm{i}\partial_tu(x,t)=((-\Delta)^m+V(x))u(x,t),\quad t\in…
This Perspective article provides an overview of some of our analytical approaches to the computation of the structural and thermodynamic properties of single-component and multicomponent hard-sphere fluids. For the structural properties,…
We consider the inhomogeneous div-curl system (i.e.\ to find a vector field with prescribed div and curl) in a bounded star-shaped domain in $\mathbb{R}^3$. An explicit general solution is given in terms of classical integral operators,…
The set of primitive vectors on large spheres in the euclidean space of dimension d>2 equidistribute when projected on the unit sphere. We consider here a refinement of this problem concerning the direction of the vector together with the…
A perturbation series solution is constructed in terms of Airy functions for a nonlinear two-point boundary-value problem arising in an established model of steady electrodiffusion in one dimension, for two ionic species carrying equal and…
We consider the slow flow of a viscous incompressible liquid in a channel of constant but arbitrary cross section shape, driven by non-uniform suction or injection through the porous channel walls. A similarity transformation reduces the…