Related papers: Phase-field simulations of solidification in binar…
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…
This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The interaction between the bulk and surface media is characterized…
This paper presents an efficient and quantitative phase-field model for elastically heterogeneous alloys that ensures the two mechanical compatibilities$\unicode{x2014}$static and kinematic, in conjunction with chemical equilibrium within…
Ni coarsening in Ni-yttria stabilized zirconia (YSZ) solid oxide fuel cell anodes is considered a major reason for anode degradation. We present a predictive, quantative modeling framework based on the phase-field approach to systematically…
We extend the nested sampling algorithm to simulate materials under periodic boundary and constant pressure conditions, and show how it can be used to determine the complete equilibrium phase diagram, for a given potential energy function,…
Dewetting of a binary alloy thin film is studied using a continuum many-parameter model that accounts for the surface and bulk diffusion, the bulk phase separation, the surface segregation and the particles formation. Analytical solution is…
By means of molecular-dynamics simulations, temperature driven diffusionless structural phase transitions in equi- and nearly equiatomic ordered nickel-titanium alloys were investigated. For this purpose, a model potential from the…
In this work, a ternary phase-field model for two-phase flows in complex geometries is proposed. In this model, one of the three components in the classical ternary Cahn-Hilliard model is considered as the solid phase, and only one…
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 precise domain triangulation is recognized as indispensable for the accurate numerical approximation of differential operators within collocation methods, leading to a substantial reduction in discretization errors. An efficient finite…
We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite…
Substitutions of the zirconium and tin ions along with the indium-niobium and iron-niobium complexes for titanium in the barium modified NBT solid solutions impact the formation of phases in the process of the solid state synthesis and the…
The accurate determination of magnetic phase transitions in electronic systems is an important task of solid state theory. While numerically exact results are readily available for model systems such as the half-filled 3D Hubbard model, the…
Conservative and non-conservative phase-field models are considered for the numerical simulation of lateral phase separation and coarsening in biological membranes. An unfitted finite element method is devised for these models to allow for…
Results are presented from numerical experiments aiming at the computation of stochastic phase-field models for phase transformations by coarse-graining molecular dynamics. The studied phase transformations occur between a solid crystal and…
The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation…
We consider a sharp interface formulation for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling. The flow is characterized by a cluster of surfaces evolving such that the total surface energy plus a weighted sum…
We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of…
We address a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains. Formulated within the variational setting of {\it generalized standard materials}, the constitutive model results…
The precipitate shape, size and distribution are crucial factors which determine the properties of several technologically important alloys. Elastic interactions between the inclusions modify their morphology and align them along…