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Related papers: Finite time corrections in KPZ growth models

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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…

Statistical Mechanics · Physics 2009-11-25 Pradipta Kumar Mandal , Debnarayan Jana

We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model…

Statistical Mechanics · Physics 2013-04-01 Amit K. Chattopadhyay

We have studied front dynamics for the discrete $A+A \leftrightarrow A$ reaction-diffusion system, which in the continuum is described by the (stochastic) Fisher-Kolmogorov-Petrovsky-Piscunov equation. We have revisited this discrete model…

Statistical Mechanics · Physics 2023-11-30 B. G. Barreales , J. J. Melendez , R. Cuerno , J. J. Ruiz-Lorenzo

We consider the early time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions in curved (or droplet) geometry. We show that for short time $t$, the probability distribution $P(H,t)$ of the height $H$ at a given point $x$…

Statistical Mechanics · Physics 2017-04-26 Pierre Le Doussal , Satya N. Majumdar , Alberto Rosso , Gregory Schehr

Scale-invariant fluctuations of growing interfaces are studied for circular clusters of an off-lattice variant of the Eden model, which belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. Statistical properties of…

Statistical Mechanics · Physics 2012-05-15 Kazumasa A. Takeuchi

In discrete models describing growing rough interfaces of the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time in the monolayer unit. For small systems, we show that it is possible…

Statistical Mechanics · Physics 2026-03-20 Rahul Chhimpa , Avinash Chand Yadav

We assess the dependence on substrate dimensionality of the asymptotic scaling behavior of a whole family of equations that feature the basic symmetries of the Kardar-Parisi-Zhang (KPZ) equation. Even for cases in which, as expected from…

Statistical Mechanics · Physics 2015-06-15 Matteo Nicoli , Rodolfo Cuerno , Mario Castro

We consider the scaling limits for a one-dimensional random growth model, the weakly asymmetric single step Solid-on-Solid process. We show that the fluctuation field, if considered in an appropriate (long) space-time scale, solves the…

Condensed Matter · Physics 2007-05-23 L. Bertini

We study the kinetic roughening of the single-step (SS) growth model with a tunable parameter $p$ in $1+1$ and $2+1$ dimensions by performing extensive numerical simulations. We show that there exists a very slow crossover from an…

Statistical Mechanics · Physics 2020-06-09 E. Daryaei

The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an overarching paradigm for the scaling of nonequilibrium, spatially extended, classical and quantum systems with strong correlations. Recent analytical solutions have…

Statistical Mechanics · Physics 2022-08-31 Enrique Rodriguez-Fernandez , Silvia N. Santalla , Mario Castro , Rodolfo Cuerno

We simulated a growth model in 1+1 dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with…

Statistical Mechanics · Physics 2009-11-07 Anna Chame , Fabio D. A. Aarao Reis

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…

Statistical Mechanics · Physics 2020-02-13 Yohsuke T. Fukai , Kazumasa A. Takeuchi

Recent theoretical studies have gradually deepened our understanding of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class even in the large deviation regime, but numerical methods for studying KPZ large deviations remain…

Statistical Mechanics · Physics 2026-02-09 Yuta Yanagibashi , Kazumasa A. Takeuchi

We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have…

Probability · Mathematics 2012-01-25 M. Balázs , J. Komjáthy , T. Seppäläinen

A generalization of the simple exclusion asymmetric model is introduced. In this model an arbitrary mixture of molecules with distinct sizes $s = 0,1,2,...$, in units of lattice space, diffuses asymmetrically on the lattice. A related…

Statistical Mechanics · Physics 2009-10-31 F. C. Alcaraz , R. Z. Bariev

We argue that while fluctuating fronts propagating into an unstable state should be in the standard KPZ universality class when they are {\em pushed}, they should not when they are {\em pulled}: The universal $1/t$ velocity relaxation of…

Statistical Mechanics · Physics 2009-10-31 Goutam Tripathy , Wim van Saarloos

The Kardar-Parisi-Zhang (KPZ) equation defines the main universality class for nonlinear growth and roughening of surfaces. But under certain conditions, a conserved KPZ equation (cKPZ) is thought to set the universality class instead. This…

Statistical Mechanics · Physics 2018-07-18 Fernando Caballero , Cesare Nardini , Frederic van Wijland , Michael E. Cates

We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in 1+1 and 2+1 dimensions using an Euler discretization scheme and the replacement of ${(\nabla h)}^2$ by exponentially decreasing functions of that quantity to suppress…

Statistical Mechanics · Physics 2009-11-13 Vladimir G. Miranda , F. D. A. Aarao Reis

One-dimensional interacting particle systems, 1+1 random growth models, and two-dimensional directed polymers define 2d height fields. The KPZ universality conjecture posits that an appropriately scaled height function converges to a…

Probability · Mathematics 2022-07-21 Jinho Baik

We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all…

Statistical Mechanics · Physics 2014-12-23 I. S. S. Carrasco , K. A. Takeuchi , S. C. Ferreira , T. J. Oliveira