Related papers: On the Modified Eguchi-Oki-Matsumura System
We examine the existence and stability of frozen waves in diblock copolymers with local conservation of the order parameter, which are described by the modified Cahn--Hilliard model. It is shown that a range of stable waves exists and each…
We are concerned with the simulation and control of a two phase flow model governed by a coupled Cahn-Hilliard Navier-Stokes system involving a nonsmooth energy potential. We establish the existence of optimal solutions and present two…
The Cahn--Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn--Hilliard equation with an imposed advection term in order to model the stirring and…
Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I…
In this paper, we propose a first order energy stable linear semi-implicit method for solving the Allen-Cahn-Ohta-Kawasaki equation. By introducing a new nonlinear term in the Ohta-Kawasaki free energy functional, all the system forces in…
A system with equation and dynamic boundary condition of Cahn-Hilliard type is considered. This system comes from a derivation performed in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167--247) via an energetic variational approach.…
The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase transitions for binary systems using either the classical…
In this paper, we consider a coupled system, known as Kobayashi--Warren--Carter system, abbreviated as the KWC system. KWC system consists of an Allen--Cahn type equation and a singular diffusion equation, and it was proposed by [Kobayashi…
For the Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg algebra can be found. The inclusion of the standard time evolution symmetry in this algebra…
This work investigates the well-posedness and optimal control of a sixth-order Cahn-Hilliard equation, a higher-order variant of the celebrated and well-established Cahn-Hilliard equation. The equation is endowed with a source term, where…
A high order discontinuous Galerkin method for the material transport of thermodynamic tracers is coupled to a low order mixed finite element solver in the context of the thermal shallow water equations. The coupling preserves the energy…
The Cahn-Hilliard equation is a fundamental model that describes phase separation processes of two-phase flows or binary mixtures. In recent years, the dynamic boundary conditions for the Cahn-Hilliard equation have been proposed and…
The effect of an order-parameter dependent mobility (or kinetic coefficient), on the phase-ordering dynamics of a system described by an n-component vector order parameter is addressed at zero temperature in the large-n limit. We consider…
The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we…
We investigate the effect of order parameter fluctuations in the holographic superconductor. In particular, using a fully backreacted bulk geometry, the intrinsic spectral functions of the order parameter in both the normal and the…
Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm for the evolutionary MHD system in Els\"asser variables. We…
This article is concerned with the existence of traveling wave solutions, including standing waves, to some models based on configurational forces, describing respectively the diffusionless phase transformations of solid materials, e.g.,…
In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based…
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…
The time development of the reduced density matrix for a quantum oscillator damped by coupling it to an ohmic environment is calculated via an identity of the Debye-Waller form. Results obtained some years ago by Hakim and the author in the…