Nonlinear self-adapting wave patterns

David A. Kessler, Herbert Levine

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We propose a new type of traveling wave pattern, one that can adapt to the size of physical system in which it is embedded. Such a system arises when the initial state has an instability for a range of wavevectors, k, that extends down to k = 0, connecting at that point to two symmetry modes of the underlying dynamical system. The Min system of proteins in E. coli is such a system with the symmetry emerging from the global conservation of two proteins, MinD and MinE. For this and related systems, traveling waves can adiabatically deform as the system is increased in size without the increase in node number that would be expected for an oscillatory version of a Turing instability containing an allowed wavenumber band with a finite minimum.

Original languageEnglish
Article number122001
JournalNew Journal of Physics
Issue number12
StatePublished - Dec 2016

Bibliographical note

Funding Information:
This work was supported by the US National Science Foundation Physics Frontier Center program grant no. PHY-1427654, the National Science Foundation Molecular and Cellular Biology (MCB) Division Grant MCB- 1241332 and the US-Israel Binational Science Foundation Grant no. 2015619.Wegratefully acknowledge the hospitality of the Aspen Center for Physics, where this work was started.

Publisher Copyright:
© 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.


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