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Related papers: Interface dynamics from experimental data

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We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the KPZ dynamics with a noise featuring smooth spatial correlations of characteristic range $\xi$. We employ Non-perturbative Functional…

Statistical Mechanics · Physics 2017-03-21 Steven Mathey , Elisabeth Agoritsas , Thomas Kloss , Vivien Lecomte , Léonie Canet

We present results from extensive numerical integration of the KPZ equation in $1 + 1$ dimensions aimed to check the long-time behavior of the dynamical structure factor of that system. Over a number of decades in the size of the structure…

Statistical Mechanics · Physics 2008-04-21 Eytan Katzav , Moshe Schwartz

We apply a number of schemes which variationally improve perturbation theory for the Kardar-Parisi-Zhang equation in order to extract estimates for the dynamic exponent z. The results for the various schemes show the same broad features,…

Condensed Matter · Physics 2009-10-28 T. Blum , A. J. McKane

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

In this paper we discuss the well known Kardar Parisi Zhang (KPZ) equation driven by temporally correlated noise. We use a self consistent approach to derive the scaling exponents of this system. We also draw general conclusions about the…

Statistical Mechanics · Physics 2008-04-21 Eytan Katzav , Moshe Schwartz

We consider a system of infinitely many interacting Brownian motions that models the height of a one-dimensional interface between two bulk phases. We prove that the large scale fluctuations of the system are well approximated by the…

Probability · Mathematics 2017-08-02 Joscha Diehl , Massimiliano Gubinelli , Nicolas Perkowski

The probabilities $P_\pm(t_0,t)$ that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval $(t_0, t)$ are shown numerically to decay as $P_\pm \sim (t_0/t)^{\theta_\pm}$ with $\theta_+ = 1.18…

Statistical Mechanics · Physics 2009-10-31 Harald Kallabis , Joachim Krug

We determine the exact short-time distribution $-\ln \mathcal{P}_{\text{f}}\left(H,t\right)= S_{\text{f}} \left(H\right)/\sqrt{t}$ of the one-point height $H=h(x=0,t)$ of an evolving 1+1 Kardar-Parisi-Zhang (KPZ) interface for flat initial…

Statistical Mechanics · Physics 2018-05-16 Naftali R. Smith , Baruch Meerson

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

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

Tracking the sign of fluctuations governed by the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) universality class, we show, both experimentally and numerically, that its evolution has an unexpected link to a simple stochastic model called…

Statistical Mechanics · Physics 2016-08-17 Kazumasa A. Takeuchi , Takuma Akimoto

We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a…

Statistical Mechanics · Physics 2009-11-13 Hans C. Fogedby

We apply a numerical minimum action method derived from the Wentzell-Freidlin theory of large deviations to the Kardar-Parisi-Zhang equation for a growing interface. In one dimension we find that the switching scenario is determined by the…

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

Using the optimal fluctuation method, we evaluate the short-time probability distribution $P (\bar{H}, L, t=T)$ of the spatially averaged height $\bar{H} = (1/L) \int_0^L h(x, t=T) \, dx$ of a one-dimensional interface $h(x, t)$ governed by…

Statistical Mechanics · Physics 2023-12-12 Timo Schorlepp , Pavel Sasorov , Baruch Meerson

Recently, a variational approach has been introduced for the paradigmatic Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together with the functional Taylor expansion that the KPZ nonequilibrium potential (NEP) admits.…

Statistical Mechanics · Physics 2014-01-27 Horacio S. Wio , Roberto R. Deza , Carlos Escudero , Jorge A. Revelli

We demonstrate and explain that conventional finite difference schemes for direct numerical integration do not approximate the continuum Kardar-Parisi-Zhang (KPZ) equation due to microscopic roughness. The effective diffusion coefficient is…

Statistical Mechanics · Physics 2008-02-03 Chi-Hang Lam , F. G. Shin

A model for kinetic roughening of one-dimensional interfaces is presented within an intrinsic geometry framework that is free from the standard small-slope and no-overhang approximations. The model is meant to probe the consequences of the…

Statistical Mechanics · Physics 2011-06-02 Javier Rodriguez-Laguna , Silvia N. Santalla , Rodolfo Cuerno

Stochastic motion of a point -- known as Brownian motion -- has many successful applications in science, thanks to its scale invariance and consequent universal features such as Gaussian fluctuations. In contrast, the stochastic motion of a…

Statistical Mechanics · Physics 2011-08-11 Kazumasa A. Takeuchi , Masaki Sano , Tomohiro Sasamoto , Herbert Spohn

The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally…

Condensed Matter · Physics 2016-08-31 Michael Lassig

The Kardar-Parisi-Zhang (KPZ) equation is accepted as a generic description of interfacial growth. In several recent studies, however, values of the roughness exponent alpha have been reported that are significantly less than that…

Statistical Mechanics · Physics 2016-08-31 R. A. Blythe , M. R. Evans