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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

Stochastic growth models in the Kardar-Parisi-Zhang (KPZ) universality class exhibit remarkable fluctuation phenomena. While a variety of powerful methods have led to a detailed understanding of their typical fluctuations or large…

Mathematical Physics · Physics 2026-02-24 Promit Ghosal , Guilherme L. F. Silva

We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the…

Statistical Mechanics · Physics 2019-02-15 Abbas Ali Saberi , Hor Dashti-N. , Joachim Krug

In systems where deposition rates are high compared to diffusion, desorption and other mechanisms that generate correlations, a crossover from random to correlated growth of surface roughness is expected at a characteristic time t_0. This…

Statistical Mechanics · Physics 2009-11-11 Fabio D. A. Aarao Reis

We analyze the shapes of roughness distributions of discrete models in the Kardar, Parisi and Zhang (KPZ) and in the Villain, Lai and Das Sarma (VLDS) classes of interface growth, in one and two dimensions. Three KPZ models in d=2 confirm…

Statistical Mechanics · Physics 2007-05-23 Fabio D. A. Aarão Reis

We introduce a solid on solid lattice model for growth with conditional evaporation. A measure of finite size effects is obtained by observing the time invariance of distribution of local height fluctuations. The model parameters are chosen…

Soft Condensed Matter · Physics 2009-11-11 S. V. Ghaisas

The restricted solid-on-solid (RSOS) model is a model of continuous-time surface growth characterized by the constraint that adjacent height differences are bounded by a fixed constant. Though the model is conjectured to belong to the KPZ…

Probability · Mathematics 2025-04-22 Timothy Sudijono

The short-time evolution of a growing interface is studied within the framework of the dynamic renormalization group approach for the Kadar-Parisi-Zhang (KPZ) equation and for an idealized continuum model of molecular beam epitaxy (MBE).…

Condensed Matter · Physics 2009-10-28 M. Krech

In a recent work [Phys. Rev. E 109, L042102 (2024)], interesting dimensional crossovers [from two- to one-dimensional (2D to 1D) scaling] were found in the growth of Kardar-Parisi-Zhang (KPZ) interfaces on rectangular substrates, with…

Statistical Mechanics · Physics 2026-05-08 Ismael S. S. Carrasco , Tiago J. Oliveira

We show that the emergence of different surface patterns (ripples, dots) can be well understood by a suitable mapping onto the simplest nonequilibrium lattice gases and cellular automata.Using this efficient approach difficult, unanswered…

Statistical Mechanics · Physics 2014-01-21 Géza Ódor , Bartosz Liedke , Karl-Heinz Heinig , Jeffrey Kelling

We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the…

Materials Science · Physics 2009-02-01 A. Kolakowska , M. A. Novotny , P. S. Verma

We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equation in one and two dimensions in order to study the scaling properties of the interface at the depinning transition. Specifically, the $\alpha$, $\beta$,…

We study height fluctuations of interfaces in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) class, growing at different speeds in the left half and the right half of space. Carrying out simulations of the discrete polynuclear growth…

Statistical Mechanics · Physics 2018-04-18 Yasufumi Ito , Kazumasa A. Takeuchi

The dynamical evolution of the surface height is controlled by either a linear or a nonlinear Langevin equation, depending on the underlying microscopic dynamics, and is often done theoretically using stochastic coarse-grained growth…

Statistical Mechanics · Physics 2025-07-29 Anirban Ghosh , Dipanjan Chakraborty

Tissue growth underpins a wide array of biological and developmental processes, and numerical modeling of growing systems has been shown to be a useful tool for understanding these processes. However, the phenomena that can be captured are…

Soft Condensed Matter · Physics 2023-11-08 Andrew Killeen , Benjamin Partridge , Thibault Bertrand , Chiu Fan Lee

In order to estimate roughness exponents of interface growth models, we propose the calculation of effective exponents from the roughness fluctuation (sigma) in the steady state. We compare the finite-size behavior of these exponents and…

Statistical Mechanics · Physics 2016-08-31 Fabio D. A. Aarao Reis

The short time behavior of the 1+1 dimensional KPZ growth equation with a flat initial condition is obtained from the exact expressions of the moments of the partition function of a directed polymer with one endpoint free and the other…

Statistical Mechanics · Physics 2012-11-13 Thomas Gueudre , Pierre Le Doussal , Alberto Rosso , Adrien Henry , Pasquale Calabrese

We study the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) interfaces growing inward from ring-shaped initial conditions, experimentally and numerically, using growth of a turbulent state in liquid-crystal electroconvection and an…

Statistical Mechanics · Physics 2017-08-14 Yohsuke T. Fukai , Kazumasa A. Takeuchi

For stationary interface growth, governed by the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik-Rains distribution. Recently Chhita et al. [1]…

Statistical Mechanics · Physics 2017-11-22 Baruch Meerson , Johannes Schmidt

The nonequilibrium steady state of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class is studied in-depth by exact solutions, yet no direct experimental evidence of its characteristic statistical properties has been…

Statistical Mechanics · Physics 2020-07-14 Takayasu Iwatsuka , Yohsuke T. Fukai , Kazumasa A. Takeuchi