Related papers: Computationally efficient phase-field models with …
We optimize a numerical time-stabilization routine for the phase-field crystal (PFC) models of solidification. By numerical experiments, we showcase that our approach can improve the accuracy of underlying time integration schemes by a few…
We consider a system of two coupled parabolic PDEs introduced in [1] to model motility of eukaryotic cells. We study the asymptotic behavior of solutions in the limit of a small parameter related to the width of the interface in phase field…
Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to…
We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a regularization to the objective functional and relax the…
We introduce a phase-field method for continuous modeling of cracks with frictional contacts. Compared with standard discrete methods for frictional contacts, the phase-field method has two attractive features: (1) it can represent…
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…
We consider a system of two PDEs arising in modeling of motility of eukariotic cells on substrates. This system consists of the Allen-Cahn equation for the scalar phase field function coupled with another vectorial parabolic equation for…
A phase-field crystal model based on the density-field approach incorporating high-order interparticle direct correlations is developed to study vapor-liquid-solid coexistence and transitions within a single continuum description.…
Phase-field models have recently had great success in describing the dynamic morphologies and motility of eukaryotic cells. In this work we investigate the minimal phase-field model introduced in [Berlyand, Potomkin, Rybalko (2017)].…
Modelling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of…
We develop a phase-field model for evaporation from a porous medium by explicitly considering a vapor component together with the liquid and gas phases in the system. The phase-field model consists of the conservation of mass (for phases…
In the last two decades, many phase-field models for solid-state sintering have been published. Two groups of models have emerged, with and without the contribution of rigid body motion. This paper first describes the previously published…
An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large…
This work overviews a new, recent success of phase-field modelling: its application to predicting the evolution of the corrosion front and the associated structural integrity challenges. Despite its important implications for society,…
We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first…
In the present work we introduce a novel graded-material design based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material…
We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the…
Phase field fracture models have seen widespread application in the last decade. Among these applications, its use to model the evolution of fatigue cracks has attracted particular interest, as fatigue damage behaviour can be predicted for…
Exact characterization of phase transitions requires sufficient configurational sampling, necessitating efficient and accurate potential energy surfaces. Molecular force fields with computational efficiency and physical interpretability are…
This paper presents an overview of the theories and computer implementation aspects of phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches to fracture is that PFM can elegantly simulate complicated…