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Related papers: Dynamic scaling of growing interfaces

200 papers

Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance…

Statistical Mechanics · Physics 2015-05-13 Carlos Escudero

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 study the atypically large deviations of the height $H \sim {{\cal O}}(t)$ at the origin at late times in $1+1$-dimensional growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. We present exact results for the…

Statistical Mechanics · Physics 2016-05-04 Pierre Le Doussal , Satya N. Majumdar , Gregory Schehr

We model the ascent of warm, moist air in the Earth's atmosphere by turbulent convection and expansion with the KPZ equation, familiar in the physics literature on surface growth. Clouds form in domains where the interface between the…

ao-sci · Physics 2008-02-03 Jon D. Pelletier

We define a new model of interface roughening which has the property that the minimum of interface height is conserved locally during the growth. This model corresponds to the limit $q \to \infty$ of the q-color dimer deposition-evaporation…

Statistical Mechanics · Physics 2008-02-03 Hari M. Koduvely , Deepak Dhar

We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed non-perturbative renormalization for self-affine surface dynamics. Within this framework, we…

Statistical Mechanics · Physics 2009-10-31 C. Castellano , A. Gabrielli , M. Marsili , M. A. Munoz , L. Pietronero

Domains of attraction are identified for the universality classes of one-point asymptotic fluctuations for the Kardar-Parisi-Zhang (KPZ) equation with general initial data. The criterion is based on a large deviation rate function for the…

Probability · Mathematics 2020-10-15 Jeremy Quastel , Daniel Remenik

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…

Physics and Society · Physics 2015-06-12 Misako Takayasu , Hayafumi Watanabe , Hideki Takayasu

Numerical simulations are essential tools for exploring the dynamic scaling properties of the nonlinear Kadar-Parisi-Zhang (KPZ) equation. Yet the inherent nonlinearity frequently causes numerical divergence within the strong-coupling…

Computational Physics · Physics 2023-12-25 Tianshu Song , Hui Xia

Critical wetting transitions under nonequilibrium conditions are studied numerically and analytically by means of an interface-displacement model defined by a Kardar-Parisi-Zhang equation, plus some extra terms representing a limiting,…

Statistical Mechanics · Physics 2009-11-13 Elvira Romera , Francisco de los Santos , Omar Al Hammal , Miguel A. Munoz

We show that d+1-dimensional surface growth models can be mapped onto driven lattice gases of d-mers. The continuous surface growth corresponds to one dimensional drift of d-mers perpendicular to the (d-1)-dimensional "plane" spanned by the…

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

The Kardar-Parisi-Zhang (KPZ) equation is a paradigmatic model of nonequilibrium low-dimensional systems with spatiotemporal scale invariance, recently highlighting universal behavior in fluctuation statistics. Its space derivative, namely…

Statistical Mechanics · Physics 2020-05-27 E. Rodriguez-Fernandez , R. Cuerno

The Kardar-Parisi-Zhang (KPZ) equation is a celebrated non-linear stochastic equation featuring non-equilibrium scaling. Although in one dimension, its statistical properties are very well understood, a new scaling regime has been reported…

Statistical Mechanics · Physics 2025-12-04 Liubov Gosteva , Nicolás Wschebor , Léonie Canet

We study the coupled dynamics of the displacement fields in a one dimensional coupled-field model for drifting crystals, first proposed by R.Lahiri and S.Ramaswamy [{\em Phys. Rev. Lett.} {\bf 79}, 1150 (1997)]. We present some exact…

Condensed Matter · Physics 2009-11-07 Dibyendu Das , Abhik Basu , Mustansir Barma , Sriram Ramaswamy

Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…

Probability · Mathematics 2019-03-22 F. L. Toninelli

We study two-component growth that mixes random deposition (RD) with a correlated growth process that occurs with probability p. We find that these composite systems are in the universality class of the correlated growth process. For RD…

Materials Science · Physics 2007-05-23 A. Kolakowska , M. A. Novotny , P. S. Verma

We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho and the spatial dimension d. By means of a stochastic Cole-Hopf transformation, the…

Statistical Mechanics · Physics 2009-10-31 Erwin Frey , Uwe C. T"auber , Hans-Karl Janssen

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling…

Statistical Mechanics · Physics 2020-02-05 Alexander K. Hartmann , Alexandre Krajenbrink , Pierre Le Doussal

The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev-Petviashvili (KP) equation. This is derived algebraically from a Fredholm…

Probability · Mathematics 2023-04-26 Jeremy Quastel , Daniel Remenik

It is shown that an alternative approach for the characterization of growing branched patterns consists of the statistical analysis of frozen structures, which cannot be modified by further growth, that arise due to competitive processes…

Other Condensed Matter · Physics 2009-11-11 C. M. Horowitz , M. A. Pasquale , E. V. Albano , A. J. Arvia