Related papers: Weak Stefan Formulation for Bulk Crystal Growth wi…
We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have finite velocities until the contact. Under these assumptions, we construct a smooth…
We consider the problem of heat conduction with phase change, that is essential for permafrost modeling in Land Surface Models and Dynamic Global Vegetation Models. These models require minimal computational effort and an extremely robust…
In this article it is proved the existence of similarity solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity and a Robin condition at the fixed face. The temperature distribution is obtained through a…
The aim of this paper is to prove the existence of weak solution for a quasi-static evolution of thermo-visco-elastic model with Norton-Hoff law of plasticity. The dependence on temperature occurs both in the elastic constitutive equations…
The one-dimensional (1D) Stefan problem is a prototypical heat and mass transfer problem that analyzes the temperature distribution in a material undergoing phase change. In addition, it describes the evolution of the phase change front…
An attempt is made to review the heat transfer and the related problems encountered in the simulation of single crystal growth. The peculiarities of conductive, convective and radiative heat transfer in the different melt, solution, and…
In this article we consider a mathematical model of an initial stage of closure electrical contact that involves a metallic vaporization after instantaneous exploding of contact due to arc ignition with power $P_0$ on fixed face $z=0$ and…
This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…
We study the supercooled Stefan problem in arbitrary dimensions. First, we study general solutions and their irregularities, showing generic fractal freezing and nucleation, based on a novel Markovian gluing principle. In contrast, we then…
In this paper we consider two different Stefan problems for a semi-infinite material for the non classical heat equation with a source which depends on the heat flux at the fixed face x = 0. One of them (with constant temperature on x = 0)…
We present a finite-element approximation for the one-sided Stefan problem and the one-sided Mullins--Sekerka problem, respectively. The problems feature a fully anisotropic Gibbs--Thomson law, as well as kinetic undercooling. Our…
In this contribution tracking control designs using output feedback are presented for a two-phase Stefan problem arising in the modeling of the Vertical Gradient Freeze process. The two-phase Stefan problem, consisting of two coupled free…
The mathematical model describing the dynamics of closed contact heating which involves vaporization of the metal when instantaneous explosion of micro-asperity occurs is presented through a Stefan type problem. The temperature field for…
In this article we study a mathematical model of the heat transfer in semi infinite material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component is…
The non-local in space two-phase Stefan problem (a prototype in phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admits a unique weak solution. This formulation makes Stefan…
In this study, we propose a parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions. This model describes the energy-driven motion of a surface cluster whose distributional solution was studied by…
This paper presents results for the sampled-data boundary feedback control to the Stefan problem. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's temperature profile…
We introduce a notion of viscosity solutions for the two-phase Stefan problem, which incorporates possible existence of a mushy region generated by the initial data. We show that a comparison principle holds between viscosity solutions, and…
This work expands on our recently introduced low Mach enthalpy method [1] for simulating the melting and solidification of a phase change material (PCM) alongside (or without) an ambient gas phase. The method captures PCM's volume change…
Using harmonic and anharmonic force constants extracted from density-functional calculations within a supercell, we have developed a relatively simple but general method to compute thermodynamic and thermal properties of any crystal. First,…