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Related papers: Geometry dependence in linear interface growth

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We consider the evolution of interfaces with a diffusive term and a generalized Kardar-Parisi-Zhang (KPZ) non-linearity, which results in a propagation velocity that depends periodically on the tilt of the interface. Using large scale…

Statistical Mechanics · Physics 2022-01-06 Peter Grassberger

Simulations of restricted solid-on-solid growth models are used to build the width-distributions of d=2-5 dimensional KPZ interfaces. We find that the universal scaling function associated with the steady-state width-distribution changes…

Statistical Mechanics · Physics 2009-11-07 E. Marinari , A. Pagnani , G. Parisi , Z. Racz

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…

Probability · Mathematics 2019-03-22 F. L. Toninelli

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

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

We consider the fluctuations in the stochastic growth of a one-dimensional interface of height $h(x,t)$ described by the Kardar-Parisi-Zhang (KPZ) universality class. We study the joint probability distribution function (JPDF) of the…

Disordered Systems and Neural Networks · Physics 2018-09-24 Jacopo de Nardis , Pierre Le Doussal

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 present numerical evidence that there are two distinct universality classes characterizing driven interface roughening in the presence of quenched disorder. The evidence is based on the behavior of $\lambda$, the coefficient of the…

Condensed Matter · Physics 2009-10-22 LAN Amaral , A-L Barabasi , HE Stanley

We report on an extensive numerical investigation of the Kardar-Parisi-Zhang equation describing non-equilibrium interfaces. Attention is paid to the dependence of the growth exponents on the details of the distribution of the noise. All…

Statistical Mechanics · Physics 2009-10-30 T. J. Newman , Michael R. Swift

We study the height distribution of a one-dimensional Edwards-Wilkinson interface in the presence of a stochastic diffusivity $D(t)=B^2(t)$, where $B(t)$ represents a one-dimensional Brownian motion at time $t$. The height distribution at a…

Statistical Mechanics · Physics 2025-06-16 David S. Dean , Satya N. Majumdar , Sanjib Sabhapandit

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 $\alpha$, $\beta$,…

Two-dimensional (2D) KPZ growth is usually investigated on substrates of lateral sizes $L_x=L_y$, so that $L_x$ and the correlation length ($\xi$) are the only relevant lengths determining the scaling behavior. However, in cylindrical…

Statistical Mechanics · Physics 2024-05-06 Ismael S. S. Carrasco , Tiago J. Oliveira

The directed landscape is a prominent model of random geometry which is believed to be the universal scaling limit of all planar random geometries in the Kardar-Parisi-Zhang universality class. It comes equipped with a few different natural…

Probability · Mathematics 2024-04-04 Manan Bhatia

We study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1…

Statistical Mechanics · Physics 2015-05-18 Joachim Rambeau , Gregory Schehr

This work considers the behavior of the height distributions of the equipotential lines in a region confined by two interfaces: a cathode with an irregular interface and a distant flat anode. Both boundaries, which are maintained at…

Computational Physics · Physics 2014-10-08 C. P. de Castro , T. A. de Assis , C. M. C. de Castilho , R. F. S. Andrade

We examine height-height correlations in the transient growth regime of the 2+1 Kardar-Parisi-Zhang (KPZ) universality class, with a particular focus on the {\it spatial covariance} of the underlying two-point statistics, higher-dimensional…

Statistical Mechanics · Physics 2014-03-31 T. Halpin-Healy , G. Palasantzas

Despite similarities between models exhibiting absorbing phase transitions (APTs) and those showing Kardar-Parisi-Zhang (KPZ) growth, the relationship between these universal fluctuations has remained elusive. We numerically study…

Statistical Mechanics · Physics 2026-05-19 Yohsuke T. Fukai , Keiichi Tamai , Tetsuya Hiraiwa

Discrete and continuous models belonging to a universality class share the same linearities and (or) nonlinearities. In this work, we propose a new approach to calculate coarse grained coefficients of the continuous differential equation…

Statistical Mechanics · Physics 2012-11-22 R. C. Buceta , D. Hansmann

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

We study the interface representation of the contact process (CP) at its directed-percolation critical point, where the scaling properties of the interface can be related to those of the original particle model. Interestingly, such a…

Statistical Mechanics · Physics 2024-09-30 B. G. Barreales , J. J. Meléndez , R. Cuerno , J. J. Ruiz-Lorenzo