相关论文: Pattern Selection in a Phase Field Model for Direc…

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around…

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…

A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…

We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [von Pezold et al, Physical Review B 2010; Wei et…

We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…

We consider a phase field crystal modeling approach for binary mixtures of interacting active and passive particles. The approach allows to describe generic properties for such systems within a continuum model. We validate the approach by…

A multiscale scheme combining molecular dynamics (MD) and microscopic phase-field theory is proposed to study the structural phase transformations in solids with inhomogeneous strain field. The approach calculates strain response based on…

We consider the problem of state selection for a stochastic system, initially in an unstable stationary state, when multiple metastable states compete for occupation. Using path-integral techniques we derive remarkably simple and accurate…

The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be…

A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where…

We consider classical hard-core particles moving on two parallel chains in the same direction. An interaction between the channels is included via the hopping rates. For a ring, the stationary state has a product form. For the case of…

We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that…

Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living…

We present a phase field model of solidification which includes the effects of the crystalline orientation in the solid phase. This model describes grain boundaries as well as solid-liquid boundaries within a unified framework. With an…

We present a convergence result for the finite volume method applied to a particular phase field problem suitable for simulation of pure substance solidification. The model consists of the heat equation and the phase field equation with a…

A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the…

A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened…

This paper studies a two-stage model of experimentation, where the researcher first samples representative units from an eligible pool, then assigns each sampled unit to treatment or control. To implement balanced sampling and assignment,…

We describe a class of (2,2) superconformal field theories obtained by fibering a Landau-Ginzburg orbifold CFT over a compact Kaehler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model, our…

The ground-state phase diagram of the asymmetric Hubbard model is studied in one and two dimensions by a well-controlled numerical method. The method allows to calculate directly the probabilities of particular phases in the approximate…