PHASE SPACE CONTRACTION OF DEGENERATELY DAMPED RANDOM SPLITTINGS
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2025-01-01
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When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics must transfer the energy from the excited modes to the dissipative directions. The precise mechanisms underlying this transfer are of particular interest and are the topic of this paper. We explore a class of randomly switched models introduced by Agazzi, Mattingly, and Melikechi (2022; 2023) and provide some of the first results showing that minimal damping is sufficient to stabilize the system in a fluids model.
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Herzog, DP, and JC Mattingly (2025). PHASE SPACE CONTRACTION OF DEGENERATELY DAMPED RANDOM SPLITTINGS. Probability and Mathematical Physics, 6(3). pp. 733–775. 10.2140/pmp.2025.6.733 Retrieved from https://hdl.handle.net/10161/34293.
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Jonathan Christopher Mattingly
Jonathan Christopher Mattingly grew up in Charlotte, NC, where he attended Irwin Avenue 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 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, the AMS, SIAM and AAAS. He was awarded the Defender of Freedom award by Common Cause for his work on Quantifying Gerrymandering.
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