相关论文: Phase-field systems for grain boundary motions und…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
A nonstandard system of differential equations describing two-species phase segregation is considered. This system naturally arises in the asymptotic analysis recently done by Colli, Gilardi, Krejci and Sprekels as the diffusion coefficient…
This paper presents the first thermodynamic assessment of binary and pseudo-binary phase diagrams in the Ba--La--S and Ga--La--S systems by means of the CALPHAD method. Experimental phase diagram equilibrium data and thermodynamic…
The classical Stefan problem is reduced as the singular limit of phase-field equations. These equations are for temperature $u$ and the phase-field $\varphi$, consists of a heat equation: $$ u_t+\ell\varphi_t=\Delta u, $$ and a…
This paper studies how solute segregation and its relationship to grain boundary energy in binary alloys is captured in the phase field crystal (PFC) formalism, a continuum method that incorporates atomic scale elasto-plastic effects on…
This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a…
In this paper we deal with a singular nonlocal phase field system with inertial term. The system has the logarithm of the absolute temperature $\theta$ under time derivative. Although the system has a difficult mathematical point caused by…
Grain growth in polycrystals is often simulated using orientation-field models, which employ a field to represent the local orientation of the crystal lattice. These models can be challenging to represent a realistic misorientation…
We review our recent modeling of crystal nucleation and polycrystalline growth using a phase field theory. First, we consider the applicability of phase field theory for describing crystal nucleation in a model hard sphere fluid. It is…
We prove well-posedness results for the solution to an initial and boundary-value problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic…
Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a…
We minimized the interface diffuseness in the phase-field models by introducing the parabolic double-well potential and localizing the solute redistribution (or latent heat release) into a narrow region within the phase-field interface. In…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
A vector order parameter phase field model derived from a grand potential functional is presented as a new approach for modeling polycrystalline solidification of alloys. In this approach, the grand potential density is designed to contain…
Phase field models are widely used to describe multiphase systems. Here a smooth indicator function, called phase field, is used to describe the spatial distribution of the phases under investigation. Material properties like density or…
Solidification, coupled with melt flow, plays a critical role in determining the microstructure and properties of materials in several manufacturing processes. Phase-field models coupled with the Navier-Stokes equations are widely used to…
Phase field models are powerful tools to tackle free boundary problems. For phase transformations involving diffusion, the evolution of the non conserved phase field is coupled to the evolution of the conserved diffusion field. Introducing…
We consider the Cauchy-problem for the following parabolic equation: \begin{equation*} \displaystyle u_t = \Delta u+ f(u,|x|), \end{equation*} where $x \in \mathbb{R}^n$, $n >2$, and $f=f(u,|x|)$ is either critical or supercritical with…
We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear,…
Phase transitions impose topological constraints on thermodynamic state variables, masking energetic fluctuations at the phase boundary. This constraint is most apparent in melting systems, where temperature remains pinned despite continued…