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September 23, 2015

Title: Towards numerical evidence for - or against - Yakhot's conjecture

Lennaert van Veen, University of Ontario Institute of Technology
Abstract: The Kardar-Parisi-Zhang model describes the growth of interfaces with a semilinear stochastic differential equation.
In particular, it predicts the value of universal exponents for roughness and growth. These exponents have been found in a number of numerical and laboratory experiments, and several discrete statistical models for particle deposition have been shown to fall in the KPZ universality class.  In 1981, Yakhot showed that the Kuramoto-Sivashinsky equation can be linked to the KPZ model by (somewhat murky) renormalization arguments. The high wave number fluctuations in the deterministic KS equation then play the role of stochastic forcing. The statement that the KS dynamics fall into the KPZ universality class is now referred to as "Yakhot's conjecture". In this joint work with Kazumasa Takeuchi, we try to produce accurate numerical data to either support or refute the conjecture. The first step is to consider the stochastically forced KS initial-boundary value problem in the limit of vanishing amplitude of the forcing.