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This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…

Computational Physics · Physics 2021-06-04 Tim Wallis , Philip T. Barton , Nikolaos Nikiforakis

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

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

In this paper we present PDE and finite element analyses for a system of partial differential equations (PDEs) consisting of the Darcy equation and the Cahn-Hilliard equation, which arises as a diffuse interface model for the two phase…

Numerical Analysis · Mathematics 2013-04-26 Xiaobing Feng , Steven Wise

We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model…

Materials Science · Physics 2022-10-26 Vidar Skogvoll , Marco Salvalaglio , Luiza Angheluta

We propose in this paper a new multiphase Cahn-Hilliard model with doubly degenerate mobilities. We prove by a formal asymptotic analysis that it approximates with second order accuracy the multiphase surface diffusion flow with mobility…

Numerical Analysis · Mathematics 2023-04-19 Elie Bretin , Roland Denis , Simon Masnou , Arnaud Sengers , Garry Terii

We analyze a Navier-Stokes-Cahn-Hilliard model for viscous incompressible two-phase flows where the mechanisms of chemotaxis, active transport and reaction are taken into account. The evolution system couples the Navier-Stokes equations for…

Analysis of PDEs · Mathematics 2024-06-03 Jingning He , Hao Wu

Pair interactions between active particles need not follow Newton's third law. In this work we propose a continuum model of pattern formation due to non-reciprocal interaction between multiple species of scalar active matter. The classical…

Statistical Mechanics · Physics 2020-10-21 Suropriya Saha , Jaime Agudo-Canalejo , Ramin Golestanian

We study a diffuse interface model describing the motion of two viscous fluids driven by the surface tension in a Hele-Shaw cell. The full system consists of the Cahn-Hilliard equation coupled with the Darcy's law. We address the physically…

Analysis of PDEs · Mathematics 2019-03-12 Andrea Giorgini

It is shown how the combination of atomic deposition and nonlinear diffusion may lead, below a critical temperature, to the growth of nonuniform layers on a substrate. The dynamics of such a system is of the Cahn-Hilliard type, supplemented…

Pattern Formation and Solitons · Physics 2013-07-22 Daniel Walgraef

In this paper we report on 2D numerical simulations concerning linear and nonlinear evolution of surface-tension-driven instability in two-fluid systems heated from below using classical and phase-field models. In the phase-field formalism,…

Pattern Formation and Solitons · Physics 2015-06-26 Rodica Borcia , Domnic Merkt , Michael Bestehorn

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…

Analysis of PDEs · Mathematics 2014-01-15 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

The paper is concerned with dynamics of multi-phase media consisting of a solid permeable material and a compressible Newtonian fluid. Governing macroscopic equations are derived starting from the space-averaged microscopic mass and…

Fluid Dynamics · Physics 2007-05-29 Vyacheslav S. Borisov

We consider two-phase fluid deformable surfaces as model systems for biomembranes. Such surfaces are modeled by incompressible surface Navier-Stokes-Cahn-Hilliard-like equations with bending forces. We derive this model using the…

Numerical Analysis · Mathematics 2023-08-03 Elena Bachini , Veit Krause , Ingo Nitschke , Axel Voigt

We study a model for the deformation of a visco-elasto-plastic material that is nearly incompressible. It originates from geophysics, is given in the Eulerian description and combines a Kelvin-Voigt rheology in the spherical part with a…

Analysis of PDEs · Mathematics 2025-12-22 Thomas Eiter

We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a…

Analysis of PDEs · Mathematics 2017-01-03 Helmut Abels , Dominic Breit

The Cahn-Hilliard equation is a widely used model for describing phase separation processes in a binary mixture. In this paper, we investigate the viscous Cahn-Hilliard equation with a degenerate, phase-dependent mobility. We define the…

Analysis of PDEs · Mathematics 2024-09-04 Toai Luong

This study presents a Eulerian theory to elucidate the molecular kinematics in polymer networks and their connection to continuum deformation, grounded in fundamental statistical physics and thermodynamics. Three key innovations are…

Soft Condensed Matter · Physics 2025-07-16 Siyu Wang , Heng Xiao , Lin Zhan

Implicit-Explicit methods have been widely used for the efficient numerical simulation of phase field problems such as the Cahn-Hilliard equation or thin film type equations. Due to the lack of maximum principle and stiffness caused by the…

Analysis of PDEs · Mathematics 2020-08-11 Dong Li , Tao Tang

This work begins by applying peridynamics and phase-field modeling to predict 1-d interface motion with inertia in an elastic solid with a non-monotone stress-strain response. In classical nonlinear elasticity, it is known that subsonic…

Analysis of PDEs · Mathematics 2021-11-24 Janel Chua , Vaibhav Agrawal , Timothy Breitzman , George Gazonas , Kaushik Dayal