相关论文: Ordering kinetics of stripe patterns
We apply analytical and numerical methods to study the linear stability of stripe patterns in two generalizations of the two-dimensional Swift-Hohenberg equation that include coupling to a mean flow. A projection operator is included in our…
This paper investigates the statistical behavior of two-dimensional grain microstructures during grain growth under anisotropic grain boundary characters. We employ the threshold-dynamics method, which allows for unparalleled computational…
A collection of thin structures buckle, bend, and bump into each-other when confined. This contact can lead to the formation of patterns: hair will self-organize in curls; DNA strands will layer into cell nuclei; paper, when crumpled, will…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced…
The observation of charge stripe order in the doped nickelate and cuprate materials has motivated much theoretical effort to understand the underlying mechanism of the stripe phase. Numerical studies of the Hubbard model show two…
Conventional grain growth is rate-limited by the mobility of grain boundary. To describe similar phenomena limited by the mobility of other grain junctions, we have developed a general theory allowing for size-dependent mobility and its…
Self-assembly of ordered nanometer-scale patterns is interesting in itself, but its practical value depends on the ability to predict and control pattern formation. In this paper we demonstrate theoretically and numerically that engineering…
Unidirectional ("stripe") charge-density-wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high temperature (HT) superconductors, where it generally competes with superconductivity (SC).…
Non-topological defects such as grain boundaries abound in pattern forming systems, arising from local variations of pattern properties such as amplitude, wavelength, orientation, etc. We introduce the idea of treating such non-topological…
Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the…
We study the modulational dynamics of striped patterns formed in the wake of a planar directional quench. Such quenches, which move across a medium and nucleate pattern-forming instabilities in their wake, have been shown in numerous…
In the framework of the rate-independent large-strain Cosserat theory of plasticity we calculate analytically explicit solutions of a two-dimensional shear problem. We discuss two cases where the micro-rotations are stationary solutions of…
We consider the pattern dynamics of the lamellar phases observed in Rayleigh-Benard convection, as described by the Swift-Hohenberg equation, and in the weak segregation regime of diblock copolymers. Both numerical and analytical…
Nonlinear stripe patterns occur in many different systems, from the small scales of biological cells to geological scales as cloud patterns. They all share the universal property of being stable at different wavenumbers $q$, i.e., they are…
We study the motion of a grain boundary separating two otherwise stationary domains of hexagonal symmetry. Starting from an order parameter equation appropriate for hexagonal patterns, a multiple scale analysis leads to an analytical…
We use direct numerical simulations and scaling arguments to study coarsening in binary fluid mixtures with a conserved order parameter in the droplet-spinodal regime -- the volume fraction of the droplets is neither too small nor symmetric…
The problem of pattern selection in absolutely unstable open flow systems is investigated by considering the example of Rayleigh-B\'{e}nard convection. The spatiotemporal structure of convection rolls propagating downstream in an externally…
We consider transversely modulated fronts in a directionally quenched Cahn-Hilliard equation, posed on a two-dimensional infinite channel, with both parameter and source-term type heterogeneities. Such quenching heterogeneities travel…
We examine the dynamics and stripe formation in a system with competing short and long range interactions in the presence of both an applied dc drive and quenched disorder. Without disorder, the system forms stripes organized in a labyrinth…