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We consider an effective interface model on a hard wall in (1+1) dimensions, with conservation of the area between the interface and the wall. We prove that the equilibrium fluctuations of the height variable converge in law to the solution…

Probability · Mathematics 2007-11-06 Lorenzo Zambotti

We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a…

Soft Condensed Matter · Physics 2009-10-31 Davide Stelitano , Daniel H. Rothman

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 consider the scaling limits for a one-dimensional random growth model, the weakly asymmetric single step Solid-on-Solid process. We show that the fluctuation field, if considered in an appropriate (long) space-time scale, solves the…

Condensed Matter · Physics 2007-05-23 L. Bertini

We investigate the scaling properties of phase transitions between survival and extinction (active-to-absorbing state phase transition, AAPT) in a model, that by itself belongs to the directed percolation (DP) universality class,…

Statistical Mechanics · Physics 2012-08-22 Niladri Sarkar , Abhik Basu

We study the interface dynamics of a discrete model to quantitatively describe electrochemical deposition experiments. Extensive numerical simulations indicate that the interface dynamics is unstable at early times, but asymptotically…

Statistical Mechanics · Physics 2016-08-15 Mario Castro , Rodolfo Cuerno , Angel S\anchez , Francisco Domínguez-Adame

We investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered…

Other Condensed Matter · Physics 2009-11-11 B. Derrida , C. Enaud , C. Landim , S. Olla

Numerical and analytic results for the exponent \theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear Langevin equations. The models are parametrized by…

Statistical Mechanics · Physics 2009-10-30 J. Krug , H. Kallabis , S. N. Majumdar , S. J Cornell , A. J. Bray , C. Sire

A novel algorithm is envisaged to extract the coupling parameters of the Kardar-Parisi-Zhang (KPZ) equation from experimental data. The method hinges on the Fokker-Planck equation combined with a classical least-square error procedure. It…

Statistical Mechanics · Physics 2009-10-31 Achille Giacometti , Maurice Rossi

The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions $d=1$ and $d=2$. Scaling arguments…

Statistical Mechanics · Physics 2014-06-27 T. A. de Assis , F. D. A. Aarão Reis

In discrete models describing growing rough interfaces of the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time in the monolayer unit. For small systems, we show that it is possible…

Statistical Mechanics · Physics 2026-03-20 Rahul Chhimpa , Avinash Chand Yadav

Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities.…

Disordered Systems and Neural Networks · Physics 2021-07-21 Sebastian Bustingorry , Jill Guyonnet , Patrycja Paruch , Elisabeth Agoritsas

Growth of interfaces during vapor deposition are analyzed on a discrete lattice. Foe a rough surface, relation between the roughness exponent alpha, and corresponding step-step (slope-slope) couplings is obtained in (1+1) and (2+1)…

Soft Condensed Matter · Physics 2007-05-23 S. V. Ghaisas

We study interface fluctuations for the $1$D stochastic Allen-Cahn equation perturbed by half a spatial derivative of the spacetime white noise. This half derivative makes the solution distribution-valued, so that proper renormalization is…

Probability · Mathematics 2025-08-22 Weijun Xu , Shuhan Zhou

We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear…

Statistical Mechanics · Physics 2009-10-31 Z. Toroczkai , G. Korniss , S. Das Sarma , R. K. P. Zia

We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability $S(t)$ in equilibrium step fluctuations described by Langevin equations appropriate for attachment/detachment and…

Statistical Mechanics · Physics 2007-05-23 C. Dasgupta , M. Constantin , S. Das Sarma , Satya N. Majumdar

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

Spatial step edge fluctuations on a multi-component surface of Al/Si(111)-(root3 x root3) were measured via scanning tunneling microscopy over a temperature range of 720K-1070K, for step lengths of L = 65-160 nm. Even though the time scale…

Statistical Mechanics · Physics 2008-10-03 B. R. Conrad , W. G. Cullen , D. B. Dougherty , I. Lyubinetsky , E. D. Williams

In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang equation in (1+1) dimensions is studied by means of numerical simulations, focussing on the two-times evolution of an interface in the absence of any disordered…

Statistical Mechanics · Physics 2009-11-13 Sebastian Bustingorry

We propose a simple discrete model to study the nonequilibrium fluctuations of two locally coupled 1+1 dimensional systems (interfaces). Measuring numerically the tilt-dependent velocity we construct a set of stochastic continuum equations…

Condensed Matter · Physics 2009-10-22 Albert-László Barabási