On the thermophoresis of a spheroidal solid aerosol particle

The steady motion of a spheroidal aerosol particle with inner nonuniformly distributed heat sources (sinks) that is placed in an external temperature gradient is theoretically studied in the Stokes approximation. The mean temperature of the particle surface is assumed to differ slightly from that of the gaseous environment. An analytic expression for the force and rate of thermophoresis are found by solving the gas-dynamic equations in view of the motion of the environment.     

Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.     

Growth of 1-Periodic Graphs

A new class of graphs is introduced: 1-periodic graphs. A problem on the form of the growth of these graphs is stated. For certain classes of graphs, a self-similar growth in the form of a polygon is proved. Certain general conjectures on the form of the growth are stated. Bibliography: 1 title.     

Subgroup separability of graphs of abelian groups

In the present paper we give necessary and sufficient conditions for the subgroup separability of the fundamental group of a finite graph of groups with finitely generated abelian vertex groups.

     

The role of As2O3 on the stability and some physical properties of PbO-Sb2O3 glasses

PbO-Sb₂O₃ glasses added with different concentrations of As₂O₃ (10-55 mol%) were prepared to understand their IR spectra, elastic properties (Young's modulus E, Shear modulus G, microhardness H), optical absorption and dielectric properties (constant ε, loss tan δ, ac conductivity σ_ac over a moderately wide range of frequency and temperature and breakdown strength in air medium at room temperature). Results have indicated that the structure of the PbO-Sb₂O₃-As₂O₃ glass is more rigid when the concentration of As₂O₃ is around 40 mol%.     

On the factors governing the minimum size of light beams during self-focusing

The final stage of self-focusing of 500-ps pulses of a neodymium laser in silicate and phosphate glasses and in the nonlinear liquids perfluorooctane, benzene, and toluene is studied theoretically and experimentally. The formation of spatial solitons, which are stable due to the nonlinearity saturation, is demonstrated. It is found that the intensity of the nonlinearity saturation is close to that of the threshold breakdown for glasses and the role of stimulated Raman scattering is significant for liquids.     

Effect of superfluidity on the structure of the inner crust of neutron stars

A self-consistent, completely quantum calculation of the structure of the inner crust of neutron stars is carried out in the Wigner-Seitz approximation with a realistic phenomenological nuclear energy functional, where pair correlations of neutrons and protons are included in the explicit form. It has been shown that the superfluidity of neutrons and protons affects the structure of the ground state of the crust.     

Deformed Quantum Calogero-Moser Problems and Lie Superalgebras

The deformed quantum Calogero-Moser-Sutherland problems related to the root systems of the contragredient Lie superalgebras are introduced. The construction is based on the notion of the generalized root systems suggested by V. Serganova. For the classical series a recurrent formula for the quantum integrals is found, which implies the integrability of these problems. The corresponding algebras of the quantum integrals are investigated, the explicit formulas for their Poincare series for generic values of the deformation parameter are presented.     

Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions

Journal of Statistical Physics - We study high-energy asymptotics of the steady velocity distributions for model kinetic equations describing various regimes in dilute granular flows. The main...