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We show that driven dislocation assemblies exhibit a set of dynamical phases remarkably similar to those of driven systems with quenched disorder such as vortices in superconductors, magnetic domain walls, and charge density wave materials.…

Materials Science · Physics 2017-12-06 C. Zhou , C. Reichhardt , C. J. Olson Reichhardt , I. J. Beyerlein

In this work, a new class of vector-valued phase field models is presented, where the values of the phase parameters are constrained by a convex set. The generated phase fields feature the partition of the domain into patches of distinct…

Analysis of PDEs · Mathematics 2023-11-03 Orestis Vantzos

We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model,…

Pattern Formation and Solitons · Physics 2018-07-24 Michael H. Köpf , Uwe Thiele

We introduce a new measure of coarseness for characterizing phase separation processes such as those described by Cahn--Hilliard equations. An advantage of our measure is that it remains consistent throughout the evolution, including for…

Analysis of PDEs · Mathematics 2026-01-22 Peter Howard , Adam Larios , Quyuan Lin

The Cahn-Hilliard equation is one of the most common models to describe phase separation processes in mixtures of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…

Numerical Analysis · Mathematics 2023-01-23 Stefan Metzger

We investigate the dynamics of a nonequilibrium interface between coexisting phases in a system described by a Cahn-Hilliard equation with an additional driving term. By means of a matched asymptotic expansion we derive equations for the…

patt-sol · Physics 2009-10-30 Claude A. Laberge , Sven Sandow

In this paper, we present a novel solution strategy for the Cahn-Hilliard-Biot model, a three-way coupled system that features the interplay of solid phase separation, fluid dynamics, and elastic deformations in porous media. It is a…

Numerical Analysis · Mathematics 2026-02-02 Cedric Riethmüller , Erlend Storvik

The kinetic separation of repulsive active Brownian particles into a dense and a dilute phase is analyzed using a systematic coarse-graining strategy. We derive an effective Cahn-Hilliard equation on large length and time scales, which…

Soft Condensed Matter · Physics 2014-06-02 Thomas Speck , Julian Bialké , Andreas M. Menzel , Hartmut Löwen

This article examines the dynamic phase transitions and pattern formations attributed to binary systems modeled by the Cahn-Hilliard equation. In particular, we consider a two-dimensional lattice structure and determine how different…

Analysis of PDEs · Mathematics 2025-11-25 Jared Grossman , Evan Halloran , Shouhong Wang

Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…

Numerical Analysis · Mathematics 2020-05-29 Paweł Dłotko , Thomas Wanner

Many developmental processes in biology utilize Notch-Delta signaling to construct an ordered pattern of cellular differentiation. This signaling modality is based on nearest-neighbor contact, as opposed to the more familiar mechanism…

Molecular Networks · Quantitative Biology 2020-07-14 Eial Teomy , David A. Kessler , Herbert Levine

We use numerical simulations to examine two-dimensional particle mixtures that strongly phase separate in equilibrium. When the system is externally driven in the presence of quenched disorder, plastic flow occurs in the form of meandering…

Statistical Mechanics · Physics 2009-11-13 A. Libal , C. Reichhardt , C. J. Olson Reichhardt

In recent years, nonreciprocally coupled systems have received growing attention. Previous work has shown that the interplay of nonreciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We…

Pattern Formation and Solitons · Physics 2024-04-23 Fridtjof Brauns , M. Cristina Marchetti

Phase separation in the Hubbard model is investigated with the dynamical cluster approximation. We find that it is present in the paramagnetic solution for values of filling smaller than one and at finite temperature when a positive…

Strongly Correlated Electrons · Physics 2007-05-23 A. Macridin , M. Jarrell , Th. Maier

We study a diffuse-interface model for thermally driven phase separation in viscous incompressible mixtures. The system couples a convective Cahn-Hilliard equation for the order parameter with a Stokes subsystem for the velocity-pressure…

Analysis of PDEs · Mathematics 2026-04-24 Maria Deliyianni , Boris Muha , Andrej Novak

We study the pattern formation in a lattice of coupled phase oscillators with quenched disorder. In the synchronized regime concentric waves can arise, which are induced and increase in regularity by the disorder of the system. Maximal…

Disordered Systems and Neural Networks · Physics 2009-11-11 Bernd Blasius , Ralf Toenjes

We obtain new integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous interface problems for the linearized Cahn-Hilliard equation with arbitrary initial data on the…

Analysis of PDEs · Mathematics 2026-05-20 Andreas Chatziafratis , Alain Miranville , Tohru Ozawa

Using the advective Cahn-Hilliard equation as a model, we illuminate the role of advection in phase-separating binary liquids. The advecting velocity is either prescribed, or is determined by an evolution equation that accounts for the…

Fluid Dynamics · Physics 2008-05-12 Lennon O Naraigh

The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…

Analysis of PDEs · Mathematics 2021-04-27 Patrik Knopf , Kei Fong Lam , Chun Liu , Stefan Metzger

This paper studies a polymer chain in the vicinity of a linear interface separating two immiscible solvents. The polymer consists of random monomer types, while the interface carries random charges. Both the monomer types and the charges…

Probability · Mathematics 2015-06-05 Frank den Hollander , Alex A. Opoku