English
Related papers

Related papers: On a diffuse interface model for diblock copolymer…

200 papers

Dynamic density functionals (DDFs) are popular tools for studying the dynamical evolution of inhomogeneous polymer systems. Here, we present a systematic evaluation of a set of diffusive DDF theories by comparing their predictions with data…

Soft Condensed Matter · Physics 2018-02-07 Shuanhu Qi , Friederike Schmid

This paper is concerned with quasilinear parabolic reaction-diffusion-advection systems on extended domains. Frameworks for well-posedness in Hilbert spaces and spaces of continuous functions are presented, based on known results using…

Dynamical Systems · Mathematics 2013-05-17 Martin Meyries , Jens D. M. Rademacher , Eric Siero

We present the second of two articles on the small volume fraction limit of a nonlocal Cahn-Hilliard functional introduced to model microphase separation of diblock copolymers. After having established the results for the sharp-interface…

Analysis of PDEs · Mathematics 2010-04-27 Rustum Choksi , Mark A. Peletier

The motion of two contiguous incompressible and viscous fluids is described within the diffuse interface theory by the so-called Model H. The system consists of the Navier-Stokes equations, which are coupled with the Cahn-Hilliard equation…

Analysis of PDEs · Mathematics 2024-12-10 Andrea Giorgini , Alain Miranville , Roger Temam

We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…

Analysis of PDEs · Mathematics 2025-10-10 Monica Conti , Stefania Gatti , Andrea Giorgini , Giulio Schimperna

We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interfaces between stable homogeneous rest states. In many example…

Analysis of PDEs · Mathematics 2022-12-28 Paul Carter , Arjen Doelman , Kaitlynn Lilly , Erin Obermayer , Shreyas Rao

We discuss two doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion. Degeneracy is introduced in both the mobility function and a restriction function associated to the chemical potential. Our computational results…

Numerical Analysis · Mathematics 2020-12-17 Marco Salvalaglio , Axel Voigt , Steven M. Wise

In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities \cite{Lowengrub1998}. Under minor reformulation of the system, we show…

Mathematical Physics · Physics 2015-06-18 Zhenlin Guo , Ping Lin , John S. Lowengrub

We consider the initial-boundary value problem of a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities in a bounded domain $\Omega\subset\mathbb{R}^3$. Our first aim is to study…

Analysis of PDEs · Mathematics 2026-03-30 Harald Garcke , Maoyin Lv , Hao Wu

The Cahn-Hilliard-Navier-Stokes system is based on a well-known diffuse interface model and describes the evolution of an incompressible isothermal mixture of binary fluids. A nonlocal variant consists of the Navier-Stokes equations…

Analysis of PDEs · Mathematics 2015-05-30 Sergio Frigeri , Maurizio Grasselli

We consider the numerical approximations of a two-phase hydrodynamics coupled phase-field model that incorporates the variable densities, viscosities and moving contact line boundary conditions. The model is a nonlinear, coupled system that…

Numerical Analysis · Mathematics 2017-02-15 Haijun Yu , Xiaofeng Yang

We consider the impingement of a droplet onto a wall with high impact speed. To model this process we favour a diffuse-interface concept. Precisely, we suggest a compressible Navier--Stokes--Allen--Cahn model. Basic properties of the model…

Fluid Dynamics · Physics 2019-09-30 Lukas Ostrowski , Christian Rohde

Reactions at a strongly segregated interface of a symmetric binary polymer blend are investigated via Monte Carlo simulations. End functionalized homopolymers of different species interact at the interface instantaneously and irreversibly…

Statistical Mechanics · Physics 2009-10-30 Marcus Mueller

A thermodynamically consistent framework able to model either diffusive and displacive phase transitions is proposed. The first law of thermodynamics, the balance of linear momentum equation and the Cahn-Hilliard equation for solute mass…

Materials Science · Physics 2015-03-17 Mirko Maraldi , Luisa Molari , Diego Grandi

A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma dynamics evolves…

Plasma Physics · Physics 2016-06-21 J. Gonzalez , J. M. Donoso , S. P. Tierno

We extend the doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion, which yield more accurate approximations than classical degenerate Cahn-Hilliard (DCH) models, to the anisotropic case. We consider both weak and…

Numerical Analysis · Mathematics 2020-12-17 Marco Salvalaglio , Maximilian Selch , Axel Voigt , Steven M. Wise

We analyze the localized phase of a general model of a directed polymer in the proximity of an interface that separates two solvents. Each monomer unit carries a charge, $\omega_n$, that determines the type (attractive or repulsive) and the…

Probability · Mathematics 2007-05-23 G. Giacomin , F. L. Toninelli

In many interfacial flow systems, variations of surface properties lead to novel and interesting behaviors. In this work a three-dimensional model of flow dynamics for multicomponent vesicles is presented. The surface composition is modeled…

Soft Condensed Matter · Physics 2017-12-07 Prerna Gera , David Salac

We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…

Statistical Mechanics · Physics 2015-06-25 Guido Manzi , Rossana Marra

Many-body long-range interacting systems can remain approximately in a quasi-stationary state far-from-thermodynamic equilibrium. These states are typically characterized by a pair of counter-propagating density clusters, or by a single…

Pattern Formation and Solitons · Physics 2022-12-20 Danilo M. Rivera , Roberto E. Navarro