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## Three-dimensional, fully adaptive simulations of phase-field fluid models

## "Simulações de escoamentos tridimensionais bifásicos empregando métodos adaptativos e modelos de campo fase"; "Simulations of 3D two-phase flows using adaptive methods and phase field models"

## Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys

## The effect of adding boron in solidification microstructure of dilute iron-carbon alloy as assessed by phase-field modeling

## Microsegregation in Fe-C-P ternary alloys using a phase-field model

## Numerical simulation of the solidification of pure melt by a phase-field model using an adaptive computation domain

## Grain Growth in Thin Films with a Fibre Texture Studied by Phase-Field Simulations and Mean Field Modelling

## Phase field model for precipitates in crystals

## Viscous Fingering In Complex Magnetic Fluids: Weakly Nonlinear Analysis, Stationary Solutions And Phase-field Models

## The effect of adding boron in solidification microstructure of dilute iron-carbon alloy as assessed by phase-field modeling

## Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys

## Simulation of the solidification of pure nickel via the phase-field method

## A Dynamic Multiscale Phase-field Model for Structural Transformations and Twinning: Regularized Interfaces with Transparent Prescription of Complex Kinetics and Nucleation

## Interface kinetics in phase field models: isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy

## A Stochastic Phase-Field Model Computed From Coarse-Grained Molecular Dynamics

## Thermodynamic consistency and fast dynamics in phase field crystal modeling

## Derivation of the phase field crystal model for colloidal solidification

## Phase field equation in the singular limit of the Stefan problem

## Adaptive Spline-based Finite Element Method with Application to Phase-field Models of Biomembranes

Interfaces play a dominant role in governing the response of many biological systems and they pose many challenges to traditional finite element. For sharp-interface model, traditional finite element methods necessitate the finite element mesh to align with surfaces of discontinuities. Diffuse-interface model replaces the sharp interface with continuous variations of an order parameter resulting in significant computational effort. To overcome these difficulties, we focus on developing a computationally efficient spline-based finite element method for interface problems.

A key challenge while employing B-spline basis functions in finite-element methods is the robust imposition of Dirichlet boundary conditions. We begin by examining weak enforcement of such conditions for B-spline basis functions, with application to both second- and fourth-order problems based on Nitsche's approach. The use of spline-based finite elements is further examined along with a Nitsche technique for enforcing constraints on an embedded interface. We show that how the choice of weights and stabilization parameters in the Nitsche consistency terms has a great influence on the accuracy and robustness of the method. In the presence of curved interface...

## Modeling Microdomain Evolution on Giant Unilamellar Vesicles using a Phase-Field Approach

The surface of cell membranes can display a high degree of lateral heterogeneity. This non-uniform distribution of constituents is characterized by mobile nanodomain clusters called rafts. Enriched by saturated phospholipids, cholesterol and proteins, rafts are considered to be vital for several important cellular functions such as signalling and trafficking, morphological transformations associated with exocytosis and endocytosis and even as sites for the replication of viruses. Understanding the evolving distribution of these domains can provide significant insight into the regulation of cell function. Giant vesicles are simple prototypes of cell membranes. Microdomains on vesicles can be considered as simple analogues of rafts on cell membranes and offer a means to study various features of cellular processes in isolation.

In this work, we employ a continuum approach to model the evolution of microdomains on the surface of Giant Unilamellar Vesicles (GUVs). The interplay of species transport on the vesicle surface and the mechanics of vesicle shape change is captured using a chemo-mechanical model. Specifically, the approach focuses on the regime of vesicle dynamics where shape change occurs on a much faster time scale in comparison to species transport...