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We study the distribution and scaling of the extreme height fluctuations for Edwards-Wilkinson-type relaxation on small-world substrates. When random links are added to a one-dimensional lattice, the average size of the fluctuations becomes…

Statistical Mechanics · Physics 2007-05-23 H. Guclu , G. Korniss

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 analyze the scaling of the crack roughness and of avalanche precursors in the two dimensional random fuse model by numerical simulations, employing large system sizes and extensive sample averaging. We find that the crack roughness…

Statistical Mechanics · Physics 2009-11-10 Stefano Zapperi , Phani Kumar V. V. Nukala , Srdan Simunovic

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

We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an…

Numerical Analysis · Mathematics 2026-03-17 Xinran Liu , Zhenyu Zhao , Benxue Gong

The occurrence of strong coupling or nonlinear scaling behavior for kinetically rough interfaces whose dynamics are conserved, but not necessarily variational, remains to be fully understood. Here we formulate and study a family of…

Statistical Mechanics · Physics 2025-11-07 Pedro Gatón-Pérez , Enrique Rodriguez-Fernandez , Rodolfo Cuerno

The competition between local Brownian roughness and global parabolic curvature experienced in many random interface models reflects an important aspect of the KPZ universality class. It may be summarised by an exponent triple…

Probability · Mathematics 2018-11-14 Riddhipratim Basu , Shirshendu Ganguly , Alan Hammond

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 analyse the statistical distribution function for the height fluctuations of brittle fracture surfaces using extensive experimental data sampled on widely different materials and geometries. We compare a direct measurement of the…

The Kardar-Parisi-Zhang universality class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, height correlations should…

Condensed Matter · Physics 2009-10-30 Michael Lassig

While the 1-point height distributions (HDs) and 2-point covariances of $(2+1)$ KPZ systems have been investigated in several recent works for flat and spherical geometries, for the cylindrical one the HD was analyzed for few models and…

Statistical Mechanics · Physics 2023-06-29 Ismael S. S. Carrasco , Tiago J. Oliveira

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

We study the local and global roughness scaling in growth models with grains at the film surfaces. The local roughness, measured as a function of window size r, shows a crossover at a characteristic length r_c, from a rapid increase with…

Statistical Mechanics · Physics 2007-05-23 T. J. Oliveira , F. D. A. Aarao Reis

We have used kinetic Monte Carlo (kMC) simulations of a lattice gas to study front fluctuations in the spreading of a non-volatile liquid droplet onto a solid substrate. Our results are consistent with a diffusive growth law for the radius…

Statistical Mechanics · Physics 2023-11-30 J. M. Marcos , P. Rodríguez-López , J. J. Melendez , R. Cuerno , J. J. Ruiz-Lorenzo

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 investigate the statistics of Iso-height lines of (2+1)-dimensional Kardar-Parisi-Zhang model at different level sets around the mean height in the saturation regime. We find that the exponent describing the distribution of the…

Statistical Mechanics · Physics 2009-03-23 A. A. Saberi , S. Rouhani

Using the linearity property of the Mullins-Herring equation when the velocity is zero with a Gaussian noise, we obtain an analytic form for the global mean-square surface width and height-height correlation function. This can be used to…

Soft Condensed Matter · Physics 2009-11-13 Esmat Darvish , Amir Ali Masoudi

We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments of liquid-crystal turbulence, we determine the universal…

Statistical Mechanics · Physics 2020-02-13 Yohsuke T. Fukai , Kazumasa A. Takeuchi

We investigate the scaling properties of post-mortem fracture surfaces in silica glass and glassy ceramics. In both cases, the 2D height-height correlation function is found to obey Family-Viseck scaling properties, but with two sets of…

Statistical Mechanics · Physics 2016-02-26 Daniel Bonamy , Laurent Ponson , Silke Prades , Elisabeth Bouchaud , Claude Guillot

We describe a directed avalanche model; a slowly unloading sandbox driven by lowering a retaining wall. The directness of the dynamics allows us to interpret the stable sand surfaces as world sheets of fluctuating interfaces in one lower…

Statistical Mechanics · Physics 2009-11-07 Chun-Chung Chen , Marcel den Nijs