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We present a comprehensive analysis of a linear growth model, which combines the characteristic features of the Edwards--Wilkinson and noisy Mullins equations. This model can be derived from microscopics and it describes the relaxation and…

Condensed Matter · Physics 2009-10-28 S. Majaniemi , T. Ala--Nissila , J. Krug

We present a simple one dimensional stochastic model with three control parameters and a surprisingly rich zoo of phase transitions. At each (discrete) site $x$ and time $t$, an integer $n(x,t)$ satisfies a linear interface equation with…

Statistical Mechanics · Physics 2023-04-21 Peter Grassberger , Deepak Dhar , P. K. Mohanty

We investigate, using the noise reduction technique, the asymptotic universality class of the well-studied nonequilibrium limited mobility atomistic solid-on-solid surface growth models introduced by Wolf and Villain (WV) and Das Sarma and…

Statistical Mechanics · Physics 2009-11-07 S. Das Sarma , P. Punyindu Chatraphorn , Z. Toroczkai

We investigate numerically the effects of long-range temporal and spatial correlations based on the rescaled distributions of the squared interface width $W^2(L,t)$ and the interface height $h(x,t)$ in the (1+1)-dimensional…

Statistical Mechanics · Physics 2025-02-25 Zhichao Chang , Hui Xia

We consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold. In particular, we study simple discrete ``forest fire'' lattice models through Monte Carlo simulations in two and…

Statistical Mechanics · Physics 2009-10-31 M. -P. Kuittu , M. Haataja , N. Provatas , T. Ala-Nissila

Building on an analogy between the ageing behaviour of magnetic systems and growing interfaces, the Arcetri model, a new exactly solvable model for growing interfaces is introduced, which shares many properties with the kinetic spherical…

Statistical Mechanics · Physics 2015-09-01 Malte Henkel , Xavier Durang

We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the…

Statistical Mechanics · Physics 2009-11-10 Francesco Ginelli , Haye Hinrichsen

We study an anomalous behavior of the height fluctuation width in the crossover from random to coherent growths of surface for a stochastic model. In the model, random numbers are assigned on perimeter sites of surface, representing pinning…

Statistical Mechanics · Physics 2009-10-28 K. Park , B. Kahng

A competitive growth model (CGM) describes aggregation of a single type of particle under two distinct growth rules with occurrence probabilities $p$ and $1-p$. We explain the origin of scaling behaviors of the resulting surface roughness…

Statistical Mechanics · Physics 2009-11-11 L. A. Braunstein , Chi-Hang Lam

We carried out a finite-size scaling analysis of the restricted solid-on-solid version of a recently introduced growth model that exhibits a roughening transition accompanied by spontaneous symmetry breaking. The dynamic critical exponent…

Statistical Mechanics · Physics 2009-10-31 J. Ricardo G. de Mendonca

Domains of attraction are identified for the universality classes of one-point asymptotic fluctuations for the Kardar-Parisi-Zhang (KPZ) equation with general initial data. The criterion is based on a large deviation rate function for the…

Probability · Mathematics 2020-10-15 Jeremy Quastel , Daniel Remenik

Many models of one-dimensional local random growth are expected to lie in the Kardar-Parisi-Zhang (KPZ) universality class. For such a model, the interface profile at advanced time may be viewed in scaled coordinates specified via…

Probability · Mathematics 2019-12-03 Jacob Calvert , Alan Hammond , Milind Hegde

We propose a simple discrete model to study the nonequilibrium fluctuations of two locally coupled 1+1 dimensional systems (interfaces). Measuring numerically the tilt-dependent velocity we construct a set of stochastic continuum equations…

Condensed Matter · Physics 2009-10-22 Albert-László Barabási

We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one--dimensional integer lattice and grows in discrete time: (1) the height above the site $x$…

Probability · Mathematics 2007-05-23 Janko Gravner , Craig A. Tracy , Harold Widom

We define a stochastic lattice model for a fluctuating directed polymer in $d\geq 2$ dimensions. This model can be alternatively interpreted as a fluctuating random path in 2 dimensions, or a one-dimensional asymmetric simple exclusion…

Statistical Mechanics · Physics 2017-09-20 G. M. Schütz , B. Wehefritz-Kaufmann

We use a lattice gas cellular automata model in the presence of random dynamic scattering sites and quenched disorder in the two-phase immiscible model with the aim of producing an interface dynamics similar to that observed in Hele-Shaw…

Fluid Dynamics · Physics 2015-08-06 R. M. Azevedo , R. R. Montenegro-Filho , M. D. Coutinho-Filho

The Kardar-Parisi-Zhang (KPZ) equation sets the universality class for growing and roughening of nonequilibrium surfaces without any conservation law and nonlocal effects. We argue here that the KPZ equation can be generalized by including…

Statistical Mechanics · Physics 2025-12-01 Debayan Jana , Astik Haldar , Abhik Basu

An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a…

Plasma Physics · Physics 2016-11-30 Johan Anderson , Jonas Johansson

Understanding possible universal properties for systems far from equilibrium is much less developed than for their equilibrium counterparts and poses a major challenge to present day statistical physics. The study of aging properties, and…

Statistical Mechanics · Physics 2017-03-22 Jacopo De Nardis , Pierre Le Doussal , Kazumasa A. Takeuchi

We consider some models in the Kardar-Parisi-Zhang universality class, namely the polynuclear growth model and the totally/partially asymmetric simple exclusion process. For these models, in the limit of large time t, universality of…

Mathematical Physics · Physics 2011-12-22 Patrik L. Ferrari , René Frings