Related papers: The analyticity region of the hard sphere gas. Imp…
We present three-dimensional solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make…
Cosmic gas cycles in and out of galaxies, but outside of galaxies it is difficult to observe except for the absorption lines that circumgalactic clouds leave in the spectra of background quasars. Using photoionization modeling of those…
We develop a cavity-based method which allows to extract thermodynamic properties from position information in hard-sphere/disk systems. So far, there are 'available-volume' and 'free-volume' methods. We add a third one, which we call…
An equation of state for a multicomponent mixture of non-additive hard spheres in $d$ dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard…
The asymptotic form of the energy density for a gas of particles surrounding a sphere of mass $M$ and radius $R$ is studied using Einstein's equations. It is shown that if the pressure of the gas $p$ varies linearly with the energy density…
Granular gas mixtures modeled as systems of inelastic and rough particles, either hard disks on a plane or hard spheres, are considered. Both classes of systems are embedded in a three-dimensional space ($d=3$) but, while in the hard-sphere…
While hard-sphere models form the foundation of theoretical condensed matter physics, real systems often exhibit some degree of softness. We present a theoretical and numerical study of a class of nearly hard-sphere systems, generalized…
Time-accurate simulation of gas dynamic structures resulting in viscous, heat conducting and radiating gas flows through localized heat release areas is performed. Cases of intensive heat release in to air at atmospheric pressure are…
We calculate a collective number of thermodynamic quantities in a one-dimensional gas of hard elongated objects (such as needles) whose centers mobile on a line. Our formalism uses an approximation for the probabilities of contact between…
Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions…
We obtain sharp lower bounds on the radii of inscribed balls for strictly convex isoperimetric domains lying in a 2-dimensional Alexandrov metric space of curvature bounded below. We also characterize the case when such bounds are attained.
The manuscript provides formulas for the volume of a body defined by the intersection of a solid cone and a solid sphere as a function of the sphere radius, of the distance between cone apex and sphere center, and of the cone aperture…
A family of potential-density pairs that represent spherical shells with finite thickness is obtained from the superposition of spheres with finite radii. Other families of shells with infinite thickness with a central hole are obtained by…
The ground state energy for a dilute hard "sphere" Bose gas in various dimensions is studied theoretically.
The depletion force and depletion potential between two in principle unequal "big" hard spheres embedded in a multicomponent mixture of "small" hard spheres are computed using the Rational Function Approximation method for the structural…
A new kinetic approach is developed and a quasi-practical gas is defined to which the new approach can be applied. One of the advantages of this new approach over the standard one is direct calculability in terms of today's computational…
The pressure function is a fundamental object in various areas of mathematics. Its regularity is studied to derive insights into phase transitions in certain physical systems or to determine the Hausdorff dimension of self-affine sets. In…
Advances in instrumentation have recently extended detailed measurements of gas kinematics to large samples of high-redshift galaxies. Relative to most nearby, thin disk galaxies, in which gas rotation accurately traces the gravitational…
This paper is concerned with the cubic Szeg\H{o} equation $$ i\partial_t u=\Pi(|u|^2 u), $$ defined on the $L^2$ Hardy space on the one-dimensional torus $\mathbb T$, where $\Pi: L^2(\mathbb T)\rightarrow L^2_+(\mathbb T)$ is the Szeg\H{o}…
The square-well fluid with hard-sphere diameters is studied within the framework of Thermodynamic Geometry (TG). Coexistence and spinodal curves, as well as the Widom line for ranges $\lambda^{*} = 1.25, 1.5, 2.0, 3.0$ for this fluid are…