Related papers: Thermal Expansion Puzzles
We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer $k$, we construct a set of codimension $2k$ in…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
In this paper we present a new approach based on the heat equation and extension problems to some intertwining formulas arising in conformal CR geometry.
From two q-summation formulas we deduce certain series expansion formulas involving the q-gamma function. With these formulas we can give q-analogues of series expansions for certain constants.
An introduction to the physics and mathematics of the expanding universe, using no more than high-school level / undergraduate mathematics. Covered are the basics of scale factor expansion, the dynamics of the expanding universe, various…
Various procedures for expressing the multipolar expansion of the electromagnetic field are considered with application to the calculation of the radiated power. Some results from literature are discussed and perspective of developing the…
We consider two optimization problems in thermal insulation: in both cases the goal is to find a thin layer around the boundary of the thermal body which gives the best insulation. The total mass of the insulating material is prescribed..…
We classify ``arithmetic convection equations'' on modular curves, and describe their space of solutions. Certain of these solutions involve the Fourier expansions of the Eisenstein modular forms of weight 4 and 6, while others involve the…
A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a H\"{o}lder continuous function, regularity of the resulting solution is in line…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…
The mean transverse kinetic energies of the fragments formed in the interaction of 1 A GeV Au+C have been determined. An energy balance argument indicates the presence of a collective energy which increases in magnitude with increasing…
Steady progress in the miniaturization of structures and devices has reached a scale where thermal fluctuations become relevant and it is thus important to understand how such fluctuations affect their mechanical stability. Here, we…
Logical and mathematical aspects of the basic concepts of thermodynamics are considered.
The changes of main paradigms on the structure and evolution of the Universe are reviewed. Two puzzles of the modern cosmology, the mean density of matter and the regularity of the Universe on large scales, as well as the possibility to…
Turbulence is a key process in many astrophysical systems. In this work we explore the statistics of thermal and kinetic energy of isothermal, supersonic, turbulent gas. We develop analytic formulas for the PDF of thermal and kinetic…
Assuming a first order phase transition during inflation, a model scenario is described which does not require a tiny coupling constant. Thermal equilibrium is closely maintained as inflation commences. No large scale reheating is…
It is shown that the partial temperatures of a homogeneous multicomponent gas mixture in the thermodynamical equilibrium cannot be equal to each other. New general solutions for equilibrium distribution functions of the multicomponent…
The paper describes a method for measuring the thermal diffusivity of materials having a high thermal conductivity. The apparatus is rather simple and low-cost, being therefore suitable in a laboratory for undergraduate students of…
We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary…
Nuclear caloric curves have been analyzed using an expanding Fermi gas hypothesis to extract average nuclear densities. In this approach the observed flattening of the caloric curves reflects progressively increasing expansion with…