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A set of one dimensional interfaces involving attachment and detachment of $k$-particle neighbors is studied numerically using both large scale simulations and finite size scaling analysis. A labeling algorithm introduced by Barma and Dhar…

Statistical Mechanics · Physics 2007-05-23 M. D. Grynberg

Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our contribution we export these insights to the case…

Statistical Mechanics · Physics 2016-10-24 Patrik L. Ferrari , Tomohiro Sasamoto , Herbert Spohn

The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev-Petviashvili (KP) equation. This is derived algebraically from a Fredholm…

Probability · Mathematics 2023-04-26 Jeremy Quastel , Daniel Remenik

We give a brief overview of the seminal paper which introduced the Kardar-Parisi-Zhang equation as a paradigmatic model for random growth in 1986. We describe some of the developments to which it gave rise in mathematics and physics over…

Disordered Systems and Neural Networks · Physics 2025-07-14 Pierre Le Doussal

We prove that two half-space models in the KPZ universality class, exponential last-passage percolation and a family of Poisson-avoiding metrics generalizing colored TASEP, converge to a common scaling limit. This scaling limit is the…

Probability · Mathematics 2026-05-11 Duncan Dauvergne , Lingfu Zhang

With Monte Carlo methods, we investigate the relaxation dynamics of a domain wall in the two-dimensional random-field Ising model with a driving field. The short-time dynamic behavior at the depinning transition is carefully examined, and…

Statistical Mechanics · Physics 2012-02-10 N. J. Zhou , B. Zheng , Y. Y. He

The statistics of the average height fluctuation of the one-dimensional Kardar-Parisi-Zhang(KPZ)-type surface is investigated. Guided by the idea of local stationarity, we derive the scaling form of the characteristic function in the…

Statistical Mechanics · Physics 2009-11-11 Deok-Sun Lee , Doochul Kim

We show that in a broad class of directed abelian sandpile models that had been expected to have the same exponents as the Dhar-Ramaswamy model, the avalanche exponent depends upon the details of the interaction, calling into question the…

Condensed Matter · Physics 2007-05-23 Rick Tully , George Reiter

The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different…

Statistical Mechanics · Physics 2013-04-23 Tiago J. Oliveira , Sidiney G. Alves , Silvio C. Ferreira

A stochastic partial differential equation along the lines of the Kardar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as radially symmetric solutions…

Statistical Mechanics · Physics 2015-06-25 M. T. Batchelor , B. I. Henry , S. D. Watt

In this work, an approach to generate radial interfaces is presented. A radial network recursively obtained is used to implement discrete model rules designed originally for the investigation in flat substrates. In order to test the…

Statistical Mechanics · Physics 2019-02-11 Sidiney G. Alves

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

Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…

We review recent progress on the study of the Kardar-Parisi-Zhang (KPZ) equation in a periodic setting, which describes the random growth of an interface in a cylindrical geometry. The main results include central limit theorems for the…

Probability · Mathematics 2025-01-22 Yu Gu , Tomasz Komorowski

Growth of interfaces during vapor deposition is analyzed on a discrete lattice. It leads to finding distribution of local heights, measurable for any lattice model. Invariance in the change of this distribution in time is used to determine…

Soft Condensed Matter · Physics 2016-08-31 S. V. Ghaisas

We use the optimal fluctuation method to evaluate the short-time probability distribution $\mathcal{P}\left(H,L,t\right)$ of height at a single point, $H=h\left(x=0,t\right)$, of the evolving Kardar-Parisi-Zhang (KPZ) interface…

Statistical Mechanics · Physics 2018-02-15 Naftali R. Smith , Baruch Meerson , Pavel Sasorov

With Monte Carlo simulations, the nonsteady dynamics properties of a domain wall have been systematically investigated for the thermally activated creep state under an alternating driving field. Taking the driven random-field Ising model in…

Statistical Mechanics · Physics 2014-07-11 N. J. Zhou , B. Zheng

We study the synchronization physics of 1D and 2D oscillator lattices subject to noise and predict a dynamical transition that leads to a sudden drastic increase of phase diffusion. Our analysis is based on the widely applicable…

Statistical Mechanics · Physics 2017-08-02 Roland Lauter , Aditi Mitra , Florian Marquardt

The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree.…

Statistical Mechanics · Physics 2023-12-25 Côme Fontaine , Francesco Vercesi , Marc Brachet , Léonie Canet

We introduce a new class of growth models, with a surface restructuring mechanism in which impinging particles may dislodge suspended particles, previously aggregated on the same column in the deposit. The flux of these particles is…

Statistical Mechanics · Physics 2013-03-14 J. S. Oliveira Filho , T. J. Oliveira , J. A. Redinz
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