Minimum action method for the Kardar-Parisi-Zhang equation

Abstract

We apply a numerical minimum action method derived from the Wentzell-Freidlin theory of large deviations to the Kardar-Parisi-Zhang equation for a growing interface. In one dimension we find that the switching scenario is determined by the nucleation and subsequent propagation of facets or steps, corresponding to moving domain walls or growth modes in the underlying noise driven Burgers equation. The transition scenario is in accordance with recent analytical studies of the one dimensional Kardar-Parisi-Zhang equation in the asymptotic weak noise limit. We also briefly discuss transitions in two dimensions.

26 pages (revtex) and 18 figures (eps)

Cited by in corpus (29)

• The instanton method and its numerical implementation in fluid mechanics
• Large Deviations of Surface Height in the Kardar-Parisi-Zhang Equation
• Dynamical phase transition in large deviation statistics of the Kardar-Parisi-Zhang equation
• Large deviations of surface height in the $1+1$-dimensional Kardar-Parisi-Zhang equation: exact long-time results for $\lambda H<0$
• Anomalous scaling of dynamical large deviations
• Short-time height distribution in 1d KPZ equation: starting from a parabola
• Instanton filtering for the stochastic Burgers equation
• Statistics of large currents in the Kipnis-Marchioro-Presutti model in a ring geometry
• Landau theory of the short-time dynamical phase transitions of the Kardar-Parisi-Zhang interface
• Computation of rare transitions in the barotropic quasi-geostrophic equations
• Height distribution tails in the Kardar-Parisi-Zhang equation with Brownian initial conditions
• Discretization-related issues in the KPZ equation: Consistency, Galilean-invariance violation, and fluctuation--dissipation relation
• Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Exact short-time height distribution for the flat Kardar-Parisi-Zhang interface
• Arclength parametrized Hamilton's equations for the calculation of instantons
• Optimal paths of non-equilibrium stochastic fields: the Kardar-Parisi-Zhang interface as a test case
• Finite-size effects in the short-time height distribution of the Kardar-Parisi-Zhang equation
• Large fluctuations of a Kardar-Parisi-Zhang interface on a half-line
• Gell-Mann-Low criticality in neural networks
• Large fluctuations of a Kardar-Parisi-Zhang interface on a half-line: the height statistics at a shifted point
• Time-averaged height distribution of the Kardar-Parisi-Zhang interface
• Nonequilibrium Steady State of a Weakly-Driven Kardar-Parisi-Zhang Equation
• Local average height distribution of fluctuating interfaces
• Convergence analysis of a finite element approximation of minimum action methods
• Invited review: KPZ. Recent developments via a variational formulation
• First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions
• Exact short-time height distribution and dynamical phase transition in the relaxation of a Kardar-Parisi-Zhang interface with random initial condition
• The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime
• Combined use of mixed and hybrid finite elements method with domain decomposition and spectral methods for a study of renormalization for the KPZ model