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We study numerically some discrete growth models belonging to the class of the nonlinear molecular beam epitaxy equation, or Villain-Lai-Das Sarma (VLDS) equation. The conserved restricted solid-on-solid model (CRSOS) with maximum heights…

Statistical Mechanics · Physics 2009-11-10 Fabio D A Aarao Reis

We study the scaling properties of self-flattening surfaces under global suppression on surface fluctuations. Evolution of self-flattening surfaces is described by restricted solid-on-solid type monomer deposition-evaporation model with…

Statistical Mechanics · Physics 2009-11-07 Yup Kim , S. Y. Yoon , Hyunggyu Park

The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different…

Statistical Mechanics · Physics 2013-04-23 Tiago J. Oliveira , Sidiney G. Alves , Silvio C. Ferreira

We show that a 2+1 dimensional discrete surface growth model exhibiting Kardar-Parisi-Zhang (KPZ) class scaling can be mapped onto a two dimensional conserved lattice gas model of directed dimers. In case of KPZ height anisotropy the dimers…

Statistical Mechanics · Physics 2014-01-21 Geza Odor , Bartosz Liedke , Karl-Heinz Heinig

We study a $(2+1)$-dimensional stochastic interface growth model, that is believed to belong to the so-called Anisotropic KPZ (AKPZ) universality class [Borodin and Ferrari, 2014]. It can be seen either as a two-dimensional interacting…

Probability · Mathematics 2017-04-24 Martin Legras , Fabio Lucio Toninelli

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

We consider discrete models of kinetic rough interfaces that exhibit space-time scale-invariance in height-height correlation. A generic scaling theory implies that the dynamical structure factor of the height profile can uniquely…

Statistical Mechanics · Physics 2023-10-06 Rahul Chhimpa , Avinash Chand Yadav

There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting…

Probability · Mathematics 2012-10-29 Ivan Corwin , P. L. Ferrari , S. Peche

We considered the Edwards-Wilkinson model on a small-world network. We studied the finite-size behavior of the surface width by performing exact numerical diagonalization for the underlying coupling matrix. We found that the spectrum…

Statistical Mechanics · Physics 2007-05-23 B. Kozma , G. Korniss

We have characterized the scaling behavior of the first-passage percolation (FPP) model on two types of discrete networks, the regular square lattice and the disordered Delaunay lattice, thereby addressing the effect of the underlying…

Statistical Mechanics · Physics 2018-07-09 Pedro Córdoba-Torres , Silvia N. Santalla , Rodolfo Cuerno , Javier Rodríguez-Laguna

We perform a systematic study of several models that have been proposed for the purpose of understanding the motion of driven interfaces in disordered media. We identify two distinct universality classes: (i) One of these, referred to as…

Condensed Matter · Physics 2009-10-28 L. A. N. Amaral , A. -L. Barabasi , H. A. Makse , H. E. Stanley

Circular KPZ interfaces spreading radially in the plane have GUE Tracy-Widom (TW) height distribution (HD) and Airy$_2$ spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as…

Statistical Mechanics · Physics 2019-04-03 I. S. S. Carrasco , T. J. Oliveira

We use the optimal fluctuation method to evaluate the short-time probability distribution $\mathcal{P}\left(H,L,t\right)$ of height at a single point, $H=h\left(x=0,t\right)$, of the evolving Kardar-Parisi-Zhang (KPZ) interface…

Statistical Mechanics · Physics 2018-02-15 Naftali R. Smith , Baruch Meerson , Pavel Sasorov

We introduce a set of statistical measures that can be used to quantify non-equilibrium surface growth. They are used to deduce new information about spatiotemporal dynamics of model systems for spinodal decomposition and surface…

Statistical Mechanics · Physics 2009-11-10 Girish Nathan , Gemunu Gunaratne

When a nonequilibrium growing interface in the presence of a wall is considered a nonequilibrium wetting transition may take place. This transition can be studied trough Langevin equations or discrete growth models. In the first case, the…

Statistical Mechanics · Physics 2010-08-24 Andre Cardoso Barato

Recent theoretical studies have gradually deepened our understanding of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class even in the large deviation regime, but numerical methods for studying KPZ large deviations remain…

Statistical Mechanics · Physics 2026-02-09 Yuta Yanagibashi , Kazumasa A. Takeuchi

We introduce the generalized spatial discretization of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. We solve exactly the steady state probability density function for the discrete heights of the interface, for any…

Other Condensed Matter · Physics 2012-09-21 R. C. Buceta

The numerical integration of stochastic growth equations on non-Euclidean networks presents unique challenges due to the nonlinearities that occur in many relevant models and of the structural constraints of the networks. In this work, we…

Statistical Mechanics · Physics 2025-09-05 J. M. Marcos , J. J. Meléndez , R. Cuerno , J. J. Ruiz-Lorenzo

We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height…

Statistical Mechanics · Physics 2009-10-28 M. Praehofer , H. Spohn

We study the directed transport of bosons along a one dimensional lattice in a dissipative setting, where the hopping is only facilitated by coupling to a Markovian reservoir. By combining numerical simulations with a field-theoretic…

Statistical Mechanics · Physics 2025-09-12 Y. Minoguchi , J. Huber , L. Garbe , A. Gambassi , P. Rabl