相关论文: Velocity selection problem for combined motion of …
We discuss melting of alloys along grain boundaries as a free boundary problem for two moving solid-liquid interfaces. One of them is the melting front and the other is the solidification front. The presence of the triple junction plays an…
The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse…
The process of rapid solidification of a binary mixture is considered in the framework of local nonequilibrium model (LNM) based on the assumption that there is no local equilibrium in solute diffusion in the bulk liquid and at the…
We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large "finite" intervals…
Melting of a bicrystal along the grain boundary is discussed. A triple junction plays a crucial role in the velocity selection problem in this case. In some range of the parameters an entirely analytical solution of this problem is given.…
We discuss a simple model of the melting kinetics along the solid-solid interface in eutectic and peritectic systems. The process is controlled by the diffusion inside the liquid phase and the existence of a triple junction is crucial for…
The problem of velocity selection for reaction fronts has been intensively investigated, leading to the successful marginal stability approach for propagation into an unstable state. Because the front velocity is controlled by the leading…
The understanding of the spreading of liquids on solid surfaces is an important challenge for contemporary physics. Today, the motion of the contact line formed at the intersection of two immiscible fluids and a solid is still subject to…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
Probing the fluid dynamics of thin films is an excellent tool to study the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid due to the fact that the dewetting process, an internal…
In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…
A uniform solidification front undergoes non-trivial deformations when encountering an insoluble dispersed particle in a melt. For solid particles, the overall deformation characteristics are primarily dictated by heat transfer between the…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…
We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The…
In this paper, we mainly consider the speed selection problem for the classical Lotka-Volterra competition system. For the first time, we propose a sufficient and necessary condition for this long-standing problem from a new point of view.…
This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial…
We give a general phenomenological description of the steady state 1D front propagation problem in two cases: the solidification of a pure material and the isothermal solidification of two component dilute alloys. The solidification of a…
We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in…