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Topological defects shape the material and transport properties of physical systems. Examples range from vortex lines in quantum superfluids, defect-mediated buckling of graphene, and grain boundaries in ferromagnets and colloidal crystals,…

Soft Condensed Matter · Physics 2018-03-23 Norbert Stoop , Jörn Dunkel

Mass conservation in chemical species appears in a broad class of reaction-diffusion systems (RDs) and is known to bring about coarsening of the pattern in chemical concentration. Recent theoretical studies on RDs with mass conservation…

Statistical Mechanics · Physics 2021-06-16 Michio Tateno , Shuji Ishihara

Interplay between kinetic roughening and phase ordering is studied in a growth SOS model with two kinds of particles and Ising-like interaction by Monte Carlo simulations. We found that, for a sufficiently large coupling, growth is strongly…

Materials Science · Physics 2009-10-31 M. Kotrla , M. Predota , F. Slanina

The Kardar-Parisi-Zhang (KPZ) equation sets the universality class for growing and roughening of nonequilibrium surfaces without any conservation law and nonlocal effects. We argue here that the KPZ equation can be generalized by including…

Statistical Mechanics · Physics 2025-12-01 Debayan Jana , Astik Haldar , Abhik Basu

In a recent work [Phys. Rev. E 109, L042102 (2024)], interesting dimensional crossovers [from two- to one-dimensional (2D to 1D) scaling] were found in the growth of Kardar-Parisi-Zhang (KPZ) interfaces on rectangular substrates, with…

Statistical Mechanics · Physics 2026-05-08 Ismael S. S. Carrasco , Tiago J. Oliveira

We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson…

Statistical Mechanics · Physics 2009-11-07 T. J. da Silva , J. G. Moreira

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

Monte Carlo simulations are employed to investigate the surface growth generated by deposition of particles of different sizes on a substrate, in one and two dimensions. The particles have a linear form, and occupy an integer number of…

Statistical Mechanics · Physics 2011-11-17 F. L. Forgerini , W. Figueiredo

Revealing universal behaviors is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces, of interfaces in bacterial colonies, and spin transport in quantum magnets all belong to the same…

We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang equation and the Lai-Das Sarma equation) and related atomistic models of epitaxial growth…

Condensed Matter · Physics 2009-10-28 C. Dasgupta , J. M. Kim , M. Dutta , S. Das Sarma

We propose a unified moving boundary problem for surface growth by electrochemical and chemical vapor deposition, which is derived from constitutive equations into which stochastic forces are incorporated. We compute the coefficients in the…

Statistical Mechanics · Physics 2009-11-07 Rodolfo Cuerno , Mario Castro

We study a stochastic PDE model for an evolving set $\mathbb{M}(t)\subseteq\mathbb{R}^{\mathrm{d}+1}$ that resembles a continuum version of origin-excited or reinforced random walk. We show that long-time fluctuations of an associated…

Probability · Mathematics 2025-07-16 Amir Dembo , Kevin Yang

We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equation in one and two dimensions in order to study the scaling properties of the interface at the depinning transition. Specifically, the $\alpha$, $\beta$,…

Pattern formation in a two-dimensional system of rod-like particles has been simulated using a lattice approach. Rod-like particles were modelled as linear $k$-mers of two mutually perpendicular orientations ($k_x$- and $k_y$-mers) on a…

Statistical Mechanics · Physics 2018-12-27 Yuri Yu. Tarasevich , Valeri V. Laptev , Valentiva V. Chirkova , Nikolai I. Lebovka

In systems where deposition rates are high compared to diffusion, desorption and other mechanisms that generate correlations, a crossover from random to correlated growth of surface roughness is expected at a characteristic time t_0. This…

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

Tissue growth underpins a wide array of biological and developmental processes, and numerical modeling of growing systems has been shown to be a useful tool for understanding these processes. However, the phenomena that can be captured are…

Soft Condensed Matter · Physics 2023-11-08 Andrew Killeen , Benjamin Partridge , Thibault Bertrand , Chiu Fan Lee

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

The main purpose of the present paper is to establish a link between quadrature surfaces (potential theoretic concept) and sandpile dynamics (Laplacian growth models). For this aim, we introduce a new model of Laplacian growth on the…

Analysis of PDEs · Mathematics 2017-03-23 Hayk Aleksanyan , Henrik Shahgholian

Anomalous behavior of correlation functions of tagged particles are studied in generalizations of the one dimensional asymmetric exclusion problem. In these generalized models the range of the hard-core interactions are changed and the…

Statistical Mechanics · Physics 2009-11-07 Anderson A. Ferreira , Francisco C. Alcaraz

By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is…

Mathematical Physics · Physics 2026-04-16 Dionisios Margetis