When does coarsening occur in the dynamics of one-dimensional fronts ?
arXiv:cond-mat/0307072 · doi:10.1103/PhysRevLett.92.090601
Abstract
Dynamics of a one-dimensional growing front with an unstable straight profile are analyzed. We argue that a coarsening process occurs if and only if the period λof the steady state solution is an increasing function of its amplitude A. This statement is rigorously proved for two important classes of conserved and nonconserved models by investigating the phase diffusion equation of the steady pattern. We further provide clear numerical evidences for the growth equation of a stepped crystal surface.
4 pages. Corrected one mistake in the phase diffusion coefficient, Eq.(11). Accepted for publication in Physical Review Letters
References in corpus (3)
Cited by in corpus (23)
- Self-Organized Ordering of Nanostructures Produced by Ion-Beam Sputtering
- Aeolian sans ripples: experimental study of saturated states
- Phase-space geometry of mass-conserving reaction-diffusion dynamics
- Wavelength selection by interrupted coarsening in reaction-diffusion systems
- Pattern formation by turbulent cascades
- Nonlinear dynamics in one dimension: On a criterion for coarsening and its temporal law
- Short-range stationary patterns and long-range disorder in an evolution equation for one-dimensional interfaces
- Generic equations for pattern formation in evolving interfaces
- Coarsening and wavelength selection far from equilibrium: a unifying framework based on singular perturbation theory
- Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations
- Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation
- Nonlinear wavelength selection in surface faceting under electromigration
- From the conserved Kuramoto-Sivashinsky equation to a coalescing particles model
- State selection in the noisy stabilized Kuramoto-Sivashinsky equation
- Phase instability and coarsening in two dimensions
- Asymptotic and effective coarsening exponents in surface growth models
- Weakly versus highly nonlinear dynamics in 1D systems
- 1D Cahn-Hilliard equation: Ostwald ripening and modulated phase systems
- Drift-Induced Step Instabilities Due to the Gap in the Diffusion Coefficient
- Self-organisation of Protein Patterns
- Free surface instability in a confined suspension jet
- Modified Kuramoto-Sivashinsky equation: stability of stationary solutions and the consequent dynamics
- Step Growth and Meandering in a Precursor-Mediated Epitaxy with Anisotropic Attachment Kinetics and Terrace Diffusion