Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators

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2007-09-01

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Abstract

We study a system of stochastically forced infinite-dimensional coupled harmonic oscillators. Although this system formally conserves energy and is not explicitly dissipative, we show that it has a nontrivial invariant probability measure. This phenomenon, which has no finite dimensional equivalent, is due to the appearance of some anomalous dissipation mechanism which transports energy to infinity. This prevents the energy from building up locally and allows the system to converge to the invariant measure. The invariant measure is constructed explicitly and some of its properties are analyzed. © 2007 Springer Science+Business Media, LLC.

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10.1007/s10955-007-9351-8

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Mattingly, JC, TM Suidan and E Vanden-Eijnden (2007). Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators. Journal of Statistical Physics, 128(5). pp. 1145–1152. 10.1007/s10955-007-9351-8 Retrieved from https://hdl.handle.net/10161/21354.

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Mattingly

Jonathan Christopher Mattingly

Kimberly J. Jenkins Distinguished University Professor of New Technologies

Jonathan Christopher  Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day.  He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and Computational Mathematics in 1998. After 4 years as a Szego assistant professor at Stanford University and a year as a member of the IAS in Princeton, he moved to Duke in 2003. He is currently a Professor of Mathematics and of Statistical Science.

His expertise is in the longtime behavior of stochastic system including randomly forced fluid dynamics, turbulence, stochastic algorithms used in molecular dynamics and Bayesian sampling, and stochasticity in biochemical networks.

Since 2013 he has also been working to understand and quantify gerrymandering and its interaction of a region's geopolitical landscape. This has lead him to testify in a number of court cases including in North Carolina, which led to the NC congressional and both NC legislative maps being deemed unconstitutional and replaced for the 2020 elections. 

He is the recipient of a Sloan Fellowship and a PECASE CAREER award.  He is also a fellow of the IMS and the AMS. He was awarded the Defender of Freedom award by  Common Cause for his work on Quantifying Gerrymandering.



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