相关论文: Phase-field systems for grain boundary motions und…
We propose a two dimensional frame-invariant phase field model of grain impingement and coarsening. One dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed. We are…
The solidification of polycrystalline materials can be modelled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that…
We compare time-dependent solutions of different phase-field models for dendritic solidification in two dimensions, including a thermodynamically consistent model and several ad hoc models. The results are identical when the phase-field…
Three different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches. First, thin-interface limits of two-sided phase-field models are…
The interplay between the diffusion-controlled dynamics of a solidification front and the trajectory of a grain boundary groove at the solid-liquid interface is studied by means of thin-sample directional solidification experiments of a…
The kinetics of an initially undercooled solid-liquid melt is studied by means of a generalized Phase Field model, which describes the dynamics of an ordering non-conserved field phi (e.g. solid-liquid order parameter) coupled to a…
In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an…
In this paper we propose a quaternion formulation for the orientation variable in the three dimensional Kobayashi--Warren model for the dynamics of polycrystals. We obtain existence of solutions to the $L^2$-gradient descent flow of the…
As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition…
Systematic microstructure design requires reliable thermodynamic descriptions of each and all microstructure elements. While such descriptions are well established for most bulk phases, thermodynamic assessment of crystal defects is…
This paper deals with the nonlinear phase field system \begin{equation*} \begin{cases} \partial_t (\theta +\ell \varphi) - \Delta\theta = f & \mbox{in}\ \Omega\times(0, T), \\[1mm] \partial_t \varphi - \Delta\varphi + \xi + \pi(\varphi) =…
An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…
In this paper we study a variational system of two parabolic PDEs, called the Kobayashi-Warren-Carter system, which models the grain boundary motion in a polycrystal. The focus of the study is the existence of solutions to this system which…
In this paper, we consider a class of optimal control problems governed by 1D parabolic state-systems of KWC types with dynamic boundary conditions. The state-systems are based on a phase-field model of grain boundary motion, proposed in…
We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a…
We consider the problem of heterogeneous nucleation and growth. The system is described by a phase field model in which the temperature is included through thermal noise. We show that this phase field approach is suitable to describe…
Time discretizations of phase-field systems have been studied. For example, a time discretization and an error estimate for a parabolic-parabolic phase-field system have been studied by Colli--K. [Commun. Pure Appl. Anal. 18 (2019)]. Also,…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
Grain growth in polycrystals is one of the principal mechanisms that take place during heat treatment of metallic components. This work treats an aspect of the anisotropic grain growth problem. By applying the first principles of…
In this paper we derive, starting from the basic principles of Thermodynamics, an extended version of the nonconserved Penrose-Fife phase transition model, in which dynamic boundary conditions are considered in order to take into account…