English
Related papers

Related papers: Upscaled phase-field models for interfacial dynami…

200 papers

We study the well-posedness of a modified degenerate Cahn-Hilliard type model for surface diffusion. With degenerate phase-dependent diffusion mobility and additional stabilizing function, this model is able to give the correct sharp…

Analysis of PDEs · Mathematics 2022-04-19 Xiaohua Niu , Yang Xiang , Xiaodong Yan

We develop coarse-grained particle approaches for studying the elastic mechanics of vesicles with heterogeneous membranes having phase-separated domains. We perform simulations both of passive shape fluctuations and of active systems where…

Soft Condensed Matter · Physics 2023-02-28 David A. Rower , Paul J. Atzberger

The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…

Analysis of PDEs · Mathematics 2023-07-28 Chun Liu , Hao Wu

We consider a phase-field model for the incompressible flow of two immiscible fluids. This model extends widespread models for two fluid phases by including a third, solid phase, which can evolve due to e.g. precipitation and dissolution.…

Analysis of PDEs · Mathematics 2022-05-18 Lars von Wolff , Iuliu Sorin Pop

We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium. The system of equations consists of a Brinkman equation for…

Analysis of PDEs · Mathematics 2025-09-15 Pierluigi Colli , Patrik Knopf , Giulio Schimperna , Andrea Signori

The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…

Statistical Mechanics · Physics 2009-11-10 E. V. L. de Mello , Otton Teixeira da Silveira Filho

In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that our two-step scheme is unconditionally energy stable and…

Numerical Analysis · Mathematics 2014-11-20 Amanda E. Diegel , Cheng Wang , Steven M. Wise

In this work, we propose a new model for flow through deformable porous media, where the solid material has two phases with distinct material properties. The two phases of the porous material follow a Cahn-Hilliard type evolution, with…

Mathematical Physics · Physics 2021-09-09 Erlend Storvik , Jakub Wiktor Both , Jan Martin Nordbotten , Florin Adrian Radu

In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving…

Mathematical Physics · Physics 2015-07-10 Alpha Albert Lee , Andreas Münch , Endre Süli

A phase field model which describes the formation of protein-RNA complexes subject to phase segregation is analyzed. A single protein, two RNA species, and two complexes are considered. Protein and RNA species are governed by coupled…

Analysis of PDEs · Mathematics 2023-02-08 Maurizio Grasselli , Luca Scarpa , Andrea Signori

In this paper, we develop a general framework for multicontinuum homogenization in perforated domains. The simulations of problems in perforated domains are expensive and, in many applications, coarse-grid macroscopic models are developed.…

Numerical Analysis · Mathematics 2024-04-29 Wei Xie , Yalchin Efendiev , Yunqing Huang , Wing Tat Leung , Yin Yang

In the present work, we address a class of Cahn-Hilliard equations characterized by a nonlinear diffusive dynamics and possibly containing an additional sixth order term. This model describes the separation properties of oil-water mixtures,…

Analysis of PDEs · Mathematics 2012-06-26 Giulio Schimperna , Irena Pawlow

Variational models of phase transitions take into account double-well energies singularly perturbed by gradient terms, such as the Cahn-Hilliard free energy. The derivation by $\Gamma$-convergence of a sharp-interface limit for such energy…

Analysis of PDEs · Mathematics 2025-06-12 Giuseppe Cosma Brusca , Davide Donati , Margherita Solci

This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…

Materials Science · Physics 2020-05-11 Arne Claus Hansen-Dörr , Franz Dammaß , René de Borst , Markus Kästner

We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions.…

Applied Physics · Physics 2019-03-27 Rudy J. M. Geelen , Yingjie Liu , Tianchen Hu , Michael R. Tupek , John E. Dolbow

This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which associates the classical Cahn--Hilliard energy with two…

Analysis of PDEs · Mathematics 2020-07-09 Elie Bretin , Simon Masnou , Arnaud Sengers , Garry Terii

The Cahn--Hilliard equation is one of the most common models to describe phase segregation processes in binary mixtures. In recent times, various dynamic boundary conditions have been introduced to model interactions of the materials with…

Analysis of PDEs · Mathematics 2021-10-12 Patrik Knopf , Andrea Signori

We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The…

Analysis of PDEs · Mathematics 2013-12-04 Thi Trang Nguyen , Michel Lenczner , Matthieu Brassart

This paper investigates a Cahn-Hilliard-Swift-Hohenberg system, focusing on a three-species chemical mixture subject to physical constraints on volume fractions. The resulting system leads to complex patterns involving a separation into…

Analysis of PDEs · Mathematics 2024-10-02 Harald Garcke , Kei Fong Lam , Robert Nürnberg , Andrea Signori

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…

Mesoscale and Nanoscale Physics · Physics 2019-10-23 Petri Hirvonen , Vili Heinonen , Haikuan Dong , Zheyong Fan , Ken R. Elder , Tapio Ala-Nissila