English
Related papers

Related papers: Short-time scaling behavior of growing interfaces

200 papers

The short-time evolution of a growing interface is studied analytically and numerically for the Kadar-Parisi-Zhang (KPZ) universality class. The scaling behavior of response and correlation functions is reminiscent of the ``initial slip''…

Statistical Mechanics · Physics 2009-10-30 M. Krech

The short time behavior of the 1+1 dimensional KPZ growth equation with a flat initial condition is obtained from the exact expressions of the moments of the partition function of a directed polymer with one endpoint free and the other…

Statistical Mechanics · Physics 2012-11-13 Thomas Gueudre , Pierre Le Doussal , Alberto Rosso , Adrien Henry , Pasquale Calabrese

The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree.…

Statistical Mechanics · Physics 2023-12-25 Côme Fontaine , Francesco Vercesi , Marc Brachet , Léonie Canet

We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the…

Materials Science · Physics 2009-02-01 A. Kolakowska , M. A. Novotny , P. S. Verma

We study the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) interfaces growing inward from ring-shaped initial conditions, experimentally and numerically, using growth of a turbulent state in liquid-crystal electroconvection and an…

Statistical Mechanics · Physics 2017-08-14 Yohsuke T. Fukai , Kazumasa A. Takeuchi

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 $\alpha$, $\beta$,…

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and…

Statistical Mechanics · Physics 2014-01-28 Matteo Nicoli , Rodolfo Cuerno , Mario Castro

We simulated a growth model in 1+1 dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with…

Statistical Mechanics · Physics 2009-11-07 Anna Chame , Fabio D. A. Aarao Reis

We present an analytical method, rooted in the non-perturbative renormalization group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all…

Statistical Mechanics · Physics 2015-05-28 Léonie Canet , Hugues Chaté , Bertrand Delamotte , Nicolás Wschebor

We study effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modelled by the well-known Kardar--Parisi--Zhang model. The turbulent advecting velocity…

Statistical Mechanics · Physics 2015-11-06 N. V. Antonov , P. I. Kakin

A novel algorithm is envisaged to extract the coupling parameters of the Kardar-Parisi-Zhang (KPZ) equation from experimental data. The method hinges on the Fokker-Planck equation combined with a classical least-square error procedure. It…

Statistical Mechanics · Physics 2009-10-31 Achille Giacometti , Maurice Rossi

We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the KPZ dynamics with a noise featuring smooth spatial correlations of characteristic range $\xi$. We employ Non-perturbative Functional…

Statistical Mechanics · Physics 2017-03-21 Steven Mathey , Elisabeth Agoritsas , Thomas Kloss , Vivien Lecomte , Léonie Canet

The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally…

Condensed Matter · Physics 2016-08-31 Michael Lassig

We consider a large class of $1+1$-dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf-Cole solutions to the KPZ equation.

Mathematical Physics · Physics 2015-12-25 Martin Hairer , Jeremy Quastel

We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate…

Statistical Mechanics · Physics 2014-01-14 Silvia N. Santalla , Javier Rodriguez-Laguna , Rodolfo Cuerno

For stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class in 1+1 dimensions, fluctuations grow as t^{1/3} during time t and the correlation length at a fixed time scales as t^{2/3}. In this note we discuss the scale of time…

Mathematical Physics · Physics 2008-11-01 Patrik L. Ferrari

Scale-invariant fluctuations of growing interfaces are studied for circular clusters of an off-lattice variant of the Eden model, which belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. Statistical properties of…

Statistical Mechanics · Physics 2012-05-15 Kazumasa A. Takeuchi

Recent experimental works on one-dimensional (1D) circular Kardar-Parisi-Zhang (KPZ) systems whose radii decrease in time have reported controversial conclusions about the statistics of their interfaces. Motivated by this, we investigate…

Statistical Mechanics · Physics 2018-07-25 Ismael S. S. Carrasco , Tiago J. Oliveira

The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions $d=1$ and $d=2$. Scaling arguments…

Statistical Mechanics · Physics 2014-06-27 T. A. de Assis , F. D. A. Aarão Reis

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
‹ Prev 1 2 3 10 Next ›