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In the first part of this work the classical and statistical aspects of the dynamics of an inextensible chain in three dimensions are investigated. In the second part the special case of a chain admitting only fixed angles with respect to…

Statistical Mechanics · Physics 2009-05-22 Franco Ferrari , Jaroslaw Paturej , Thomas A. Vilgis

We identify the key features of Kardar-Parisi-Zhang universality class in the fluctuations of the wave density logarithm, in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit…

Disordered Systems and Neural Networks · Physics 2024-04-24 Sen Mu , Jiangbin Gong , Gabriel Lemarié

We consider the scaling limits for a one-dimensional random growth model, the weakly asymmetric single step Solid-on-Solid process. We show that the fluctuation field, if considered in an appropriate (long) space-time scale, solves the…

Condensed Matter · Physics 2007-05-23 L. Bertini

Dynamical universality classes are distinguished by their dynamical exponent $z$ and unique scaling functions encoding space-time asymmetry for, e.g. slow-relaxation modes or the distribution of time-integrated currents. So far the…

Statistical Mechanics · Physics 2019-11-20 Jan de Gier , Andreas Schadschneider , Johannes Schmidt , Gunter M. Schütz

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 Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic surface roughening) with turbulent motion of the environment taken into account is studied by the field theoretic renormalization group approach. The turbulent…

Statistical Mechanics · Physics 2020-07-14 N. V. Antonov , N. M. Gulitskiy , P. I. Kakin , M. M. Kostenko

We study a generalized Kardar-Parisi-Zhang (KPZ) equation [Jana et al., Phys. Rev. E 109, L032104 (2024)] that sets the paradigm for universality in roughening of growing nonequilibrium surfaces without any conservation laws but with…

Statistical Mechanics · Physics 2025-07-29 Debayan Jana , Abhik Basu

We simulate the Kardar-Parisi-Zhang equation in 2+1 dimensions. The Hopf-Cole transformation is used in order to obtain a stable numerical scheme. The two relevant critical exponents are precisely measured. (2 PostScript figures available…

High Energy Physics - Lattice · Physics 2009-10-22 Matteo Beccaria , Giuseppe Curci

While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting…

Soft Condensed Matter · Physics 2022-08-30 Kirill E. Polovnikov , Sergei K. Nechaev , Alexander Y. Grosberg

We discuss the features of nonequilibrium growth problems, their scaling description and their differences from equilibrium problems. The emphasis is on the Kardar-Parisi-Zhang equation and the renormalization group point of view. Some of…

Statistical Mechanics · Physics 2007-05-23 Sutapa Mukherji , Somendra M. Bhattacharjee

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

The one dimensional Kardar-Parisi-Zhang universality class is believed to describe many types of evolving interfaces which have the same characteristic scaling exponents. These exponents lead to a natural renormalization/rescaling on the…

Statistical Mechanics · Physics 2020-10-15 Ivan Corwin , Jeremy Quastel , Daniel Remenik

We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out…

Disordered Systems and Neural Networks · Physics 2009-10-31 Christophe Texier , Alain Comtet

We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this…

Statistical Mechanics · Physics 2024-08-29 Francesco Vercesi , Susie Poirier , Anna Minguzzi , Léonie Canet

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

The controversy whether or not he Kardar-Parisi-Zhang (KPZ) equation has an upper critical dimension (UCD) is going on for quite a long time. Some approximate integral equations for the two-point function served as an indication for the…

Materials Science · Physics 2008-04-21 Eytan Katzav , Moshe Schwartz

A growing interface subject to noise is described by the Kardar-Parisi-Zhang equation or, equivalently, the noisy Burgers equation. In one dimension this equation is analyzed by means of a weak noise canonical phase space approach applied…

Statistical Mechanics · Physics 2014-10-07 Hans C Fogedby

Integrable probability has emerged as an active area of research at the interface of probability/mathematical physics/statistical mechanics on the one hand, and representation theory/integrable systems on the other. Informally, integrable…

Mathematical Physics · Physics 2014-03-28 Ivan Corwin

This paper concerns the multi-component coupled Kardar-Parisi-Zhang (KPZ) equation and its two types of approximations. One approximation is obtained as a simple replacement of the noise term by a smeared noise with a proper…

Probability · Mathematics 2017-03-30 Tadahisa Funaki , Masato Hoshino

This paper concerns the existence of global weak solutions \`a la Leray for compressible Navier-Stokes equations with a pressure law that depends on the density and on time and space variables $t$ and $x$. The assumptions on the pressure…

Analysis of PDEs · Mathematics 2021-08-11 Didier Bresch , Pierre Emmanuel Jabin , Fei Wang