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Schmuck, M.; Pradas, M.; Pavliotis, G. A. and Kalliadasis, S.
(2015).
DOI: https://doi.org/10.1093/imamat/hxt041
Abstract
Consider the generalized Kuramoto–Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction–diffusion systems, to interface motion of viscous film flows. Our aim is to develop a systematic and rigorous low-dimensional representation of the gKS equation. For this purpose, we approximate it by a renormalization group equation which is qualitatively characterized by rigorous error bounds. This formulation allows for a new stochastic mode reduction guaranteeing optimality in the sense of maximal information entropy. Herewith, noise is systematically added to the reduced gKS equation and gives a rigorous and analytical explanation for its origin. These new results would allow one to reliably perform low-dimensional numerical computations by accounting for the neglected degrees of freedom in a systematic way. Moreover, the presented reduction strategy might also be useful in other applications where classical mode reduction approaches fail or are too complicated to be implemented.
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About
- Item ORO ID
- 44653
- Item Type
- Journal Item
- ISSN
- 1464-3634
- Keywords
- generalized Kuramoto–Sivashinsky equation; renormalization group method; stochastic mode reduction
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2013 The Authors
- Depositing User
- Marc Pradas