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We consider the influence of a power-law deviation from the critical coupling such that the system is critical at its surface. We develop a scaling theory showing that such a perturbation introduces a new length scale which governs the…

Statistical Mechanics · Physics 2009-10-06 Mario Collura , Dragi Karevski , Loïc Turban

We carry out an exact analysis of the average frequency $\nu_{\alpha x_i}^+$ in the direction $x_i$ of positive-slope crossing of a given level $\alpha$ such that, $h({\bf x},t)-\bar{h}=\alpha$, of growing surfaces in spatial dimension $d$.…

Statistical Mechanics · Physics 2009-11-11 A. Bahraminasab , M. Sadegh Movahed , S. D. Nassiri , A. A. Masoudi , Muhammad Sahimi

We study a stochastic Laplacian growth model, where a set $\mathbf{U}\subseteq\mathbb{R}^{\mathrm{d}}$ grows according to a reflecting Brownian motion in $\mathbf{U}$ stopped at level sets of its boundary local time. We derive a scaling…

Probability · Mathematics 2024-11-11 Amir Dembo , Kevin Yang

The scaling behavior of cyclical growth (e.g. cycles of alternating deposition and desorption primary processes) is investigated theoretically and probed experimentally. The scaling approach to kinetic roughening is generalized to cyclical…

Statistical Mechanics · Physics 2009-11-07 Subhadip Raychaudhuri , Yonathan Shapir , David G. Foster , Jacob Jorne

Equilibrium and nonequilibrium states of matter can exhibit fundamentally different behavior. A key example is the Kardar-Parisi-Zhang universality class in two spatial dimensions (2D KPZ), where microscopic deviations from equilibrium give…

We study a new kind of phase ordering phenomenon in coarse-grained depth (CD) models of the hill-valley profile of fluctuating surfaces with zero overall tilt, and for hard-core particles sliding on such surfaces under gravity. For…

Statistical Mechanics · Physics 2007-05-23 Dibyendu Das , Mustansir Barma , Satya N. Majumdar

How does a steady state with strong intermittency develop in time from an initial state which is statistically random? For passive sliders driven by various fluctuating surfaces, we show that the approach involves an indefinitely growing…

Statistical Mechanics · Physics 2018-02-07 Tapas Singha , Mustansir Barma

The Family-Vicsek relation is a seminal universal relation obtained for the global roughness at the interface of two media in the growth process. In this work, we revisit the scaling analysis and, through both analytical and computational…

Statistical Mechanics · Physics 2025-03-18 Evandro A. Rodrigues , Edwin E. Mozo Luis , Thiago A. de Assis , Fernando A. Oliveira

We investigate the average frequency of positive slope $\nu_{\alpha}^{+} $, crossing the height $\alpha = h- \bar h$ in the surface growing processes. The exact level crossing analysis of the random deposition model and the…

Condensed Matter · Physics 2009-11-07 F. Shahbazi , S. Sobhanian , M. Reza Rahimi Tabar , S. Khorram , G. R. Frootan , H. Zahed

We investigate non-linear scaling relations for two-dimensional gravitational collapse in an expanding background using a 2D TreePM code and study the strongly non-linear regime ($\bar\xi \leq 200$) for power law models. Evolution of these…

Astrophysics · Physics 2007-05-23 S. Ray , J. S. Bagla , T. Padmanabhan

I report on an extensive numerical investigation of various discrete growth models describing equilibrium and nonequilibrium interfaces on a substrate of a finite Bethe lattice. An unusual logarithmic scaling behavior is observed for the…

Statistical Mechanics · Physics 2013-07-23 Abbas Ali Saberi

Statistical behavior and scaling properties of iso-height lines in three different saturated two-dimensional grown surfaces with controversial universality classes are investigated using ideas from Schramm-Loewner evolution (SLE$_\kappa$).…

Statistical Mechanics · Physics 2010-08-10 A. A. Saberi , H. Dashti-Naserabadi , S. Rouhani

One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a scaling limit, so that the limit is…

Probability · Mathematics 2022-11-30 Sourav Chatterjee

Clusters formed by fluctuations of two-dimensional (2D) directed interfaces around a threshold level have been extensively studied at equilibrium and in nonequilibrium steady states, but their coarsening dynamics remain poorly understood.…

Statistical Mechanics · Physics 2026-01-21 Renan A. L. Almeida , Tiago J. Oliveira , Jeferson J. Arenzon , Leticia F. Cugliandolo

A growth model which describes the deposition of particles (or the growth of a rigid crystal) on a disordered substrate is investigated. The dynamic renormalization group is applied to the stochastic growth equation using the Martin, Sigga,…

Condensed Matter · Physics 2009-10-22 Yan-Chr Tsai , Yonathan Shapir

We assess the dependence on substrate dimensionality of the asymptotic scaling behavior of a whole family of equations that feature the basic symmetries of the Kardar-Parisi-Zhang (KPZ) equation. Even for cases in which, as expected from…

Statistical Mechanics · Physics 2015-06-15 Matteo Nicoli , Rodolfo Cuerno , Mario Castro

DIS data from HERA show a striking regularity as \sigma^{\gamma^* p} is a function of the ratio \tau=Q^2/Q_s^2(x) only. The scaling function shows a break at \tau ~ 1, which has been taken as an indication for saturation. However, besides…

High Energy Physics - Phenomenology · Physics 2014-11-18 Emil Avsar , Gosta Gustafson

Long-range spatiotemporal correlations may play important roles in nonequilibrium surface growth process. In order to investigate the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we perform extensive…

Statistical Mechanics · Physics 2021-08-11 Tianshu Song , Hui Xia

We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete…

Statistical Mechanics · Physics 2007-05-23 A. Kolakowska , M. A. Novotny

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