Related papers: Scaling and width distributions of parity conservi…
Given the variety of the visual world there is not one true scale for recognition: objects may appear at drastically different sizes across the visual field. Rather than enumerate variations across filter channels or pyramid levels, dynamic…
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 review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a…
When using Laguerre and Hermite spectral methods to numerically solve PDEs in unbounded domains, the number of collocation points assigned inside the region of interest is often insufficient, particularly when the region is expanded or…
We considered the Edwards-Wilkinson model on a small-world network. We studied the finite-size behavior of the surface width by performing exact numerical diagonalization for the underlying coupling matrix. We found that the spectrum…
Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…
Finite-size scaling arguments naturally lead us to introduce a coordinate-dependent diffusion coefficient in a Fokker-Planck description of the late stage dynamics of unbiased polymer translocation through a membrane pore. The solution for…
The one-dimensional contact process with weak to intermediate quenched disorder in its transmission rates is investigated via quasi-stationary Monte Carlo simulation. We address the contested questions of both the nature of dynamical…
We discuss the methods to calculate the roughness exponent alpha and the dynamic exponent z from the scaling properties of the local roughness, which is frequently used in the analysis of experimental data. Through numerical simulations, we…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
We present a detailed study of squared local roughness (SLRDs) and local extremal height distributions (LEHDs), calculated in windows of lateral size $l$, for interfaces in several universality classes, in substrate dimensions $d_s = 1$ and…
A model for kinetic roughening of one-dimensional interfaces is presented within an intrinsic geometry framework that is free from the standard small-slope and no-overhang approximations. The model is meant to probe the consequences of the…
The Family-Vicsek relation is a seminal universal relation obtained for the global roughness at the interface of two media in the growth process. In this work, we revisit the scaling analysis and, through both analytical and computational…
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…
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced.…
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
Persistence probabilities of the interface height in (1+1)- and (2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the…
Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an…
Using stability arguments, this Brief Report suggests that a term that enhances the surface tension in the presence of large height fluctuations should be included in the Kardar-Parisi-Zhang equation. A one-loop renormalization group…
A brief review is presented of the scaling of complex fluids, polymers and polyelectrolytes in solution and in confined geometry, in thermodynamical, structural and rheology properties using equilibrium and nonequilibrium dissipative…