English
Related papers

Related papers: Stochastic growth in time dependent environments

200 papers

We study atypically large fluctuations of height $H$ in the 1+1-dimensional Kardar-Parisi-Zhang (KPZ) equation at long times $t$, when starting from a "droplet" initial condition. We derive exact large deviation function of height for…

Statistical Mechanics · Physics 2017-06-13 Pavel Sasorov , Baruch Meerson , Sylvain Prolhac

We study the spatiotemporal dynamics of random spatially distributed noninfinitesimal perturbations in one-dimensional chaotic extended systems. We find that an initial perturbation of finite size $\epsilon_0$ grows in time obeying the…

Chaotic Dynamics · Physics 2009-11-10 Juan M. Lopez , Cristina Primo , Miguel A. Rodriguez , Ivan G. Szendro

We study the one-dimensional Bak-Sneppen model for the evolution of species in an ecosystem. Of particular interest are the temporal fluctuations in the fitness variables. We numerically compute the power spectral density and apply the…

Statistical Mechanics · Physics 2023-06-16 Abha Singh , Rahul Chhimpa , Avinash Chand Yadav

This article reviews recent developments in statistical field theory far from equilibrium. It focuses on the Kardar-Parisi-Zhang equation of stochastic surface growth and its mathematical relatives, namely the stochastic Burgers equation in…

Condensed Matter · Physics 2015-06-25 Michael Lassig

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

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

We conjecture the universal probability distribution at large time for the one-point height in the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality class, with initial conditions interpolating from any one of the three main…

Statistical Mechanics · Physics 2017-06-07 Pierre Le Doussal

We investigate the infinite-dimensional limit of nonequilibrium surface growth by numerically integrating stochastic growth equations on a fully connected graph. In particular, we study the Edwards-Wilkinson (EW), Kardar-Parisi-Zhang (KPZ),…

Statistical Mechanics · Physics 2026-03-04 J. M. Marcos , J. J. Meléndez , R. Cuerno , J. J. Ruiz-Lorenzo

Consider a deterministically growing surface of any dimension, where the growth at a point is an arbitrary nonlinear function of the heights at that point and its neighboring points. Assuming that this nonlinear function is monotone,…

Probability · Mathematics 2021-09-07 Sourav Chatterjee

We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models. We show…

Mathematical Physics · Physics 2014-04-24 Patrik L. Ferrari , Alexei Borodin

We obtain several exact results for universal distributions involving the maximum of the Airy$_2$ process minus a parabola and plus a Brownian motion, with applications to the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality…

Disordered Systems and Neural Networks · Physics 2017-12-13 Pierre Le Doussal

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

A perturbative method is developed to calculate the finite size corrections of the low lying energies of the asymmetric XXZ hamiltonian near the stochastic line. The crossover from isotropic to anisotropic, Kardar-Parisi-Zhang (KPZ) scaling…

Condensed Matter · Physics 2008-02-03 Doochul Kim

A nonperturbative weak noise scheme is applied to the Kardar-Parisi-Zhang equation for a growing interface in all dimensions. It is shown that the growth morphology can be interpreted in terms of a dynamically evolving texture of localized…

Statistical Mechanics · Physics 2014-10-07 Hans C. Fogedby

This paper concerns the multi-component coupled Kardar-Parisi-Zhang (KPZ) equation and its two types of approximations. One approximation is obtained as a simple replacement of the noise term by a smeared noise with a proper…

Probability · Mathematics 2017-03-30 Tadahisa Funaki , Masato Hoshino

We define a stochastic lattice model for a fluctuating directed polymer in $d\geq 2$ dimensions. This model can be alternatively interpreted as a fluctuating random path in 2 dimensions, or a one-dimensional asymmetric simple exclusion…

Statistical Mechanics · Physics 2017-09-20 G. M. Schütz , B. Wehefritz-Kaufmann

Universal behavior in far-from-equilibrium systems is driven by interactions between transport processes and noise structure. The Kardar-Parisi-Zhang (KPZ) framework predicts that extensions incorporating conserved currents or temporally…

We have considered three different "one-body" statistical systems involving Brownian excursions, which possess for fluctuations Kardar-Parisi-Zhang scaling with the critical exponent $\nu=\frac{1}{3}$. In all models imposed external…

Statistical Mechanics · Physics 2020-05-07 Alexander Gorsky , Sergei Nechaev , Alexander Valov

Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal…

Statistical Mechanics · Physics 2009-11-07 M. Myllys , J. Maunuksela , M. Alava , T. Ala-Nissila , J. Merikoski , J. Timonen

A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit non-equilibrium phase transitions, which…

Condensed Matter · Physics 2015-06-24 Miguel A. Munoz , F. de los Santos , A. Achahbar