Related papers: Explicit solution for non-classical one-phase Stef…
A review of solutions of solid-state diffusion problems in infinite and semi-infinite bodies is presented. Based on the identified solutions for the semi-infinite body a two-step diffusion problem is discussed in detail with the first step…
The emerging field of phase-coherent caloritronics (from the Latin word "calor", i.e., heat) is based on the possibility to control heat currents using the phase difference of the superconducting order parameter. The goal is to design and…
The paper investigates an inverse problem of recovering the internal source from external temperature measurements in photo-thermal effect. The photo-thermal effect actually involves two physical processes: electromagnetic scattering and…
We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of…
The role of thermal relaxation in nanoparticle melting is studied using a mathematical model based on the Maxwell--Cattaneo equation for heat conduction. The model is formulated in terms of a two-phase Stefan problem. We consider the cases…
We investigate the regularizing behavior of two-phase Stefan problem near initial data. The main step in the analysis is to establish that in any given scale, the scaled solution is very close to a Lipschitz profile in space-time. We…
We develop a high-order energy method to prove asymptotic stability of flat steady surfaces for the Stefan problem with surface tension - also known as the Stefan problem with Gibbs-Thomson correction.
The one-dimensional problem of the nonlinear heat equation is considered. We assume that the heat flow in the origin of coordinates is the power function of time and the initial temperature is zero. Approximate solutions of the problem are…
We consider a many-fermion model which exhibits a transition from a superconducting to a rotational phase with variation of a parameter in its Hamiltonian. The model has analytical solutions in its two limits due to the presence of…
In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving…
This work presents a unified numerical framework for simulating incompressible flows within the coupled fluid-porous-medium system and involving heat and solute transport and phase-changing process. A complete set of governing equations is…
The Stefan problem with surface tension is well known to exhibit discontinuities in the associated moving aggregate (i.e., in the domain occupied by the solid), whose structure has only been understood under translational or radial symmetry…
Let $\Omega$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=\varphi(t)f(x,y)$ with $\varphi$ be given inexactly and $f$ be unknown. The problem is nonlinear and ill-posed. By a…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
An exact analytical solution of the statistical multifragmentation model is found in thermodynamic limit. Excluded volume effects are taken into account in the thermodynamically self-consistent way. The model exhibits a 1-st order phase…
We present analytical formula along with its existence theorem for solution of inverse heat conduction problem of semi-infinite bar, equivalent to a Volterra integral equation of first kind, as an infinite series of fractional derivatives.…
Specific heat measurements have been successfully used to probe unconventional superconducting phases in one-band heavy-fermion and organic superconductors. We extend the method to study successive phase transitions in multi-band materials…
This paper is devoted to the mathematical analysis of a thermomechanical model describing phase transitions in terms of the entropy and order structure balance law. We consider a macroscopic description of the phenomenon and make a…
We present a theoretical study of radiative heat transport in nonlinear solid-state quantum circuits. We give a detailed account of heat rectification effects, i.e. the asymmetry of heat current with respect to a reversal of the thermal…
We prove existence and uniqueness of strong solutions to the two-phase Stefan problem with Gibbs-Thomson law where the free interface forms a ninety degree contact angle with the fixed boundary. We also discuss existence of global solutions…