Grain boundary pinning and glassy dynamics in stripe phases

Abstract

We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the non-adiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value $R_g\sim {\lambda }_0{\epsilon }^{-1/2}\exp (|a|/\sqrt{\epsilon })$, where $\epsilon \ll 1$ is the dimensionless distance away from threshold, ${\lambda }_0$ the stripe wavelength, and $a$ a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.

arXiv comment17 pages, 8 figures. Corrected version with one new figure

References in corpus (14)

• Theory of Phase Ordering Kinetics
• Stripe glasses: self generated randomness in a uniformly frustrated system
• Glassy dynamics and aging in an exactly solvable spin model
• Metastability in Fluctuation Driven First-order Transitions: Nucleation of Lamellar Phases
• Charge Segregation, Cluster Spin-Glass and Superconductivity in La1.94Sr0.06CuO4
• Domain Coarsening in Systems Far from Equilibrium
• Pattern Dynamics of Rayleigh-Benard convective rolls and weakly segregated diblock copolymers
• Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation
• Ordering kinetics of stripe patterns
• Dynamical Scaling Behavior of the Swift-Hohenberg Equation Following a Quench to the Modulated State
• Domain Coarsening in Electroconvection
• Adiabatic reduction near a bifurcation in stochastically modulated systems
• Comment on ``Stripe Glasses: Self-Generated Randomness in a Uniformly Frustrated System''
• Grain boundary motion in layered phases

Cited by in corpus (33)

• Morphologies and flow patterns in quenching of lamellar systems with shear
• Scaling and hydrodynamic effects in lamellar ordering
• Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt
• Defect Structures in the Growth Kinetics of the Swift-Hohenberg Model
• Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry
• Phase behavior and dynamics of a micelle-forming triblock copolymer system
• Defect kinetics and dynamics of pattern coarsening in a two-dimensional smectic-A system
• Dynamics and Melting of Stripes, Crystals, and Bubbles with Quenched Disorder
• Scale coupling and interface pinning effects in the phase-field-crystal model
• Numerical study of domain coarsening in anisotropic stripe patterns
• Anisotropic velocity statistics of topological defects under shear flow
• Complex-tensor theory of simple smectics
• Coordinated optimization of visual cortical maps (II) Numerical studies
• Dislocation Dynamics in an Anisotropic Stripe Pattern
• Defect formation in the Swift-Hohenberg equation
• Thermal and hydrodynamic effects in the ordering of lamellar fluids
• Defect dynamics in active smectics induced by confining geometry and topology
• Grain boundary dynamics in stripe phases of non potential systems
• Coarsening in potential and nonpotential models of oblique stripe patterns
• Smectic Layering: Landau theory for a complex-tensor order parameter
• Coarsening of Topological Defects in Oscillating Systems with Quenched Disorder
• Shear induced grain boundary motion for lamellar phases in the weakly nonlinear regime
• Pattern formation of phase-separated lipid domains in bilayer membranes
• A Model for Striped Growth
• Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach
• Glassy behavior of two-dimensional stripe-forming systems
• Dependence of Striped Domain Growth on Background Wavenumber
• Numerical scheme for solving the nonuniformly forced cubic and quintic Swift-Hohenberg equations strictly respecting the Lyapunov functional
• Superlattice Patterns in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing
• Active smectics on a sphere
• Uncovering liquid-substrate fluctuation effects on crystal growth and disordered hyperuniformity of two-dimensional materials
• Activated vortex lattice transition in a superconductor with combined sixfold and twelvefold anisotropic interactions
• Early time evolution of Freedericks patterns generated from states of electroconvection