One-dimensional Kardar-Parisi-Zhang and Kuramoto-Sivashinsky universality class: Limit distributions

Roy, D and Pandit, R (2020) One-dimensional Kardar-Parisi-Zhang and Kuramoto-Sivashinsky universality class: Limit distributions. In: Physical Review E, 101 (3).

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Abstract

Tracy-Widom and Baik-Rains distributions appear as universal limit distributions for height fluctuations in the one-dimensional Kardar-Parisi-Zhang (KPZ) stochastic partial differential equation (PDE). We obtain the same universal distributions in the spatiotemporally chaotic, nonequilibrium, but statistically steady state of the one-dimensional Kuramoto-Sivashinsky (KS) deterministic PDE, by carrying out extensive pseudospectral direct numerical simulations to obtain the spatiotemporal evolution of the KS height profile h(x,t) for different initial conditions. We establish, therefore, that the statistical properties of the one-dimensional (1D) KS PDE in this state are in the 1D KPZ universality class. © 2020 American Physical Society.

Item Type:	Journal Article
Publication:	Physical Review E
Publisher:	American Physical Society
Additional Information:	Copyright of this article belongs to American Physical Society
Keywords:	Stochastic systems, Initial conditions; Kuramoto-Sivashinsky; Pseudospectral direct numerical simulation; Spatiotemporal evolution; Statistical properties; Statistically steady state; Stochastic partial differential equation; Universality class, Partial differential equations, article
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics Division of Physical & Mathematical Sciences > Physics
Date Deposited:	06 Apr 2021 07:33
Last Modified:	06 Apr 2021 07:34
URI:	http://eprints.iisc.ac.in/id/eprint/65296

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