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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''…

Statistical Mechanics · Physics 2009-10-30 M. Krech

We revisit the anchored Toom interface and use KPZ scaling theory to argue that the interface fluctuations are governed by the Airy_1 process with the role of space and time interchanged. There is no free parameter. The predictions are…

Mathematical Physics · Physics 2015-06-19 G. T. Barkema , P. L. Ferrari , J. L. Lebowitz , H. Spohn

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

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

Consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half-line $x\geq 0$. The interface is initially flat, $h(x,t=0)=0$, and driven by a Neumann boundary condition $\partial_x…

Statistical Mechanics · Physics 2018-10-03 Baruch Meerson , Arkady Vilenkin

We extend the weak universality of KPZ in [Hairer-Quastel] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on correlations of trigonometric functions of…

Probability · Mathematics 2018-08-27 Martin Hairer , Weijun Xu

While the 1-point height distributions (HDs) and 2-point covariances of $(2+1)$ KPZ systems have been investigated in several recent works for flat and spherical geometries, for the cylindrical one the HD was analyzed for few models and…

Statistical Mechanics · Physics 2023-06-29 Ismael S. S. Carrasco , Tiago J. Oliveira

Stochastic growth processes in dimension $(2+1)$ were conjectured by D. Wolf, on the basis of renormalization-group arguments, to fall into two distinct universality classes, according to whether the Hessian $H_\rho$ of the speed of growth…

Probability · Mathematics 2020-03-25 Sunil Chhita , Fabio Lucio Toninelli

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

We investigate growing interfaces of topological-defect turbulence in the electroconvection of nematic liquid crystals. The interfaces exhibit self-affine roughening characterized by both spatial and temporal scaling laws of the…

Statistical Mechanics · Physics 2010-06-15 Kazumasa A. Takeuchi , Masaki Sano

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

We consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half-line $x\geq0$ with the reflecting boundary at $x=0$. The interface is initially flat, $h(x,t=0)=0$. We focus on the…

Statistical Mechanics · Physics 2019-05-01 Tomer Asida , Eli Livne , Baruch Meerson

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

We consider the relaxation (noise-free) statistics of the one-point height $H=h(x=0,t)$ where $h(x,t)$ is the evolving height of a one-dimensional Kardar-Parisi-Zhang (KPZ) interface, starting from a Brownian (random) initial condition. We…

Statistical Mechanics · Physics 2022-10-21 Naftali R. Smith

The Kardar-Parisi-Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height…

Statistical Mechanics · Physics 2024-03-25 Márcio S. Gomes-Filho , Pablo de Castro , Danilo B. Liarte , Fernando A. Oliveira

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

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 present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved…

Statistical Mechanics · Physics 2013-05-15 Sidiney G. Alves , Tiago J. Oliveira , Silvio C. Ferreira

We study the diffusion-limited reaction A + A <-> A in different spatial dimensions to observe the effect of internal fluctuations on the interface between stable and unstable phases. We find that, similar to what has been observed in d=1…

Statistical Mechanics · Physics 2009-11-07 Esteban Moro

This Letter reports on how the interfaces in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) class undergo, in the course of time, a transition from the flat, growing regime to the stationary one. Simulations of the polynuclear growth model…

Statistical Mechanics · Physics 2013-06-03 Kazumasa A. Takeuchi