Related papers: Finite-time scaling for kinetic rough interfaces
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
The short-time evolution of a growing interface is studied analytically and numerically for the Kadar-Parisi-Zhang (KPZ) universality class. The scaling behavior of response and correlation functions is reminiscent of the ``initial slip''…
We present analytical results for the finite-size scaling in d--dimensional O(N) systems with strong anisotropy where the critical exponents (e.g. \nu_{||} and \nu_{\perp}) depend on the direction. Prominent examples are systems with…
We numerically study the geometry of a driven elastic string at its sample-dependent depinning threshold in random-periodic media. We find that the anisotropic finite-size scaling of the average square width $\bar{w^2}$ and of its…
We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the…
The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can…
Although scaling phenomena have long been documented in crystalline plasticity, the universality class has been difficult to identify due to the rarity of avalanche events, which require large system sizes and long times in order to…
The effects of a randomly moving environment on a randomly growing interface are studied by the field theoretic renormalization group analysis. The kinetic growth of an interface (kinetic roughening) is described by the Kardar-Parisi-Zhang…
Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…
The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree.…
The occurrence of strong coupling or nonlinear scaling behavior for kinetically rough interfaces whose dynamics are conserved, but not necessarily variational, remains to be fully understood. Here we formulate and study a family of…
We introduce a systematic method for extracting multivariable universal scaling functions and critical exponents from data. We exemplify our insights by analyzing simulations of avalanches in an interface using simulations from a driven…
We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments of liquid-crystal turbulence, we determine the universal…
We analyze the continuum limit of a thresholding algorithm for motion by mean curvature of one dimensional interfaces in various space-time discrete regimes. The algorithm can be viewed as a time-splitting scheme for the Allen-Cahn equation…
Statistical topography of two-dimensional interfaces in the presence of quenched disorder is studied utilizing combinatorial optimization algorithms. Finite-size scaling is used to measure geometrical exponents associated with contour loops…
In the continuum theory the time evolution of surfaces eroded by ion bombardment is modelled by stochastic partial differential equations (SPDEs). These determine the scaling regimes and universality classes of the evolving surfaces.…
We study the scaling properties of a one-dimensional interface at equilibrium, at finite temperature and in a disordered environment with a finite disorder correlation length. We focus our approach on the scalings of its geometrical…
We demonstrate the non-universal behavior of finite size scaling in (1+1) dimension of a nonlinear discrete growth model involving extended particles in generalized point of view. In particular, we show the violation of the universal nature…
The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…
We study the standard three-dimensional driven diffusive system on a simple cubic lattice where particle jumps along a given lattice direction are biased by an infinitely strong field, while those along other directions follow the usual…