English
Related papers

Related papers: The universality class of fluctuating pulled front…

200 papers

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

We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the…

Statistical Mechanics · Physics 2019-02-15 Abbas Ali Saberi , Hor Dashti-N. , Joachim Krug

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 present a (heuristic) theoretical derivation for the scaling of the diffusion coefficient $D_f$ for fluctuating ``pulled'' fronts. In agreement with earlier numerical simulations, we find that as $N\to\infty$, $D_f$ approaches zero as…

Statistical Mechanics · Physics 2007-05-23 Debabrata Panja

This paper is an introductory review of the problem of front propagation into unstable states. Our presentation is centered around the concept of the asymptotic linear spreading velocity v*, the asymptotic rate with which initially…

Soft Condensed Matter · Physics 2015-06-24 Wim van Saarloos

Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal…

Statistical Mechanics · Physics 2009-11-07 M. Myllys , J. Maunuksela , M. Alava , T. Ala-Nissila , J. Merikoski , J. Timonen

We study the diffusion-limited reaction A + A <-> A in different spatial dimensions to observe the effect of internal fluctuations on the interface between stable and unstable phases. We find that, similar to what has been observed in d=1…

Statistical Mechanics · Physics 2009-11-07 Esteban Moro

We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all…

Statistical Mechanics · Physics 2014-12-23 I. S. S. Carrasco , K. A. Takeuchi , S. C. Ferreira , T. J. Oliveira

A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit non-equilibrium phase transitions, which…

Condensed Matter · Physics 2015-06-24 Miguel A. Munoz , F. de los Santos , A. Achahbar

Front propagation into unstable states is often determined by the linearization, that is, propagation speeds agree with predictions from the linearized equation at the unstable state. The leading edge behavior is then a Gaussian tail…

Analysis of PDEs · Mathematics 2025-08-21 Montie Avery , Matt Holzer , Arnd Scheel

The front of a compact bacterial colony growing on a Petri dish is a paradigmatic instance of non-equilibrium fluctuations in the celebrated Eden, or Kardar-Parisi-Zhang (KPZ), universality class. While in many experiments the scaling…

The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion…

Statistical Mechanics · Physics 2020-08-26 Evgeniy Khain , Baruch Meerson , Pavel Sasorov

We investigate the universal fluctuations of localized wavefunction in the Fock space of two interacting particles in one-dimensional disordered systems, focusing on the interplay between random potentials and random long-range…

Disordered Systems and Neural Networks · Physics 2025-07-04 Sen Mu , Gabriel Lemarié , Jiangbin Gong

The determination of the exact exponents of the KPZ class in any substrate dimension $d$ is one of the most important open issues in Statistical Physics. Based on the behavior of the dimensional variation of some exact exponent differences…

Statistical Mechanics · Physics 2022-12-21 Tiago J. Oliveira

We study stationary fluctuations of conserved slow modes in a two-lane model of hardcore particles which are expected to show universal behaviour. Specifically, we focus on the properties of fluctuations at a special umbilic point where the…

Statistical Mechanics · Physics 2025-09-08 Johannes Schmidt , Žiga Krajnik , Vladislav Popkov

The optimal fluctuation approach is applied to study the most distant (non-universal) tails of the free-energy distribution function P(F) for an elastic string (of a large but finite length L) interacting with a quenched random potential. A…

Disordered Systems and Neural Networks · Physics 2009-11-13 I. V. Kolokolov , S. E. Korshunov

Despite similarities between models exhibiting absorbing phase transitions (APTs) and those showing Kardar-Parisi-Zhang (KPZ) growth, the relationship between these universal fluctuations has remained elusive. We numerically study…

Statistical Mechanics · Physics 2026-05-19 Yohsuke T. Fukai , Keiichi Tamai , Tetsuya Hiraiwa

Our understanding of the one-dimensional KPZ equation, \textit{alias} noisy Burgers equation, has advanced substantially over the past five years. We provide a non-technical review, where we limit ourselves to the stochastic PDE and lattice…

Mathematical Physics · Physics 2015-06-24 Jeremy Quastel , Herbert Spohn

We propose a phenomenological description for the effect of a weak noise on the position of a front described by the Fisher-Kolmogorov-Petrovsky-Piscounov equation or any other travelling wave equation in the same class. Our scenario is…

Disordered Systems and Neural Networks · Physics 2009-11-11 E. Brunet , B. Derrida , A. H. Mueller , S. Munier

The Kardar-Parisi-Zhang (KPZ) equation defines the main universality class for nonlinear growth and roughening of surfaces. But under certain conditions, a conserved KPZ equation (cKPZ) is thought to set the universality class instead. This…

Statistical Mechanics · Physics 2018-07-18 Fernando Caballero , Cesare Nardini , Frederic van Wijland , Michael E. Cates