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AM Seminar: On the Geometry of Optimal Mass Transport: where Probability, Control, and Physics meet

Speaker Name: 
Tryphon T. Georgiou
Speaker Title: 
Professor
Speaker Organization: 
University of California, Irvine
Start Time: 
Monday, February 3, 2020 - 4:00pm
End Time: 
Monday, February 3, 2020 - 5:00pm

Abstract

We will highlight the relevance of Monge-Kantorovich Optimal Mass Transport (OMT) in modeling energy dissipation in stochastic models of thermodynamic ensembles, and focus on quantifying the power that can be drawn from thermodynamic engines operating between two heat baths of unequal temperature. Specifically, classical thermodynamics aimed to quantify the efficiency of thermodynamic engines by bounding the maximal amount of mechanical energy produced compared to the amount of heat required. While this was accomplished early on, by Carnot and Clausius, the more practical problem to quantify limits of power that can be delivered, remained elusive due to the fact that quasi-static processes require infinitely slow cycling, resulting in a vanishing power output. Recent insights, drawn from stochastic models, appear to bridge the gap between theory and practice in that they lead to physically meaningful expressions for the dissipation cost in operating a thermodynamic engine over a finite time window. Building on the framework of stochastic thermodynamics and the geometry of OMT, we derive bounds on the maximal power that can be drawn by cycling an over-damped ensemble of particles via a time-varying potential while alternating contact with heat baths of different absolute temperature (T_c cold, and T_h hot). In particular, constraining the spatial gradient of the controlling potential ("control effort"), we show that the maximal achievable power is proportional to (T_h/T_c-1)/8, and that this bound can be reached to within a factor of (T_h/T_c-1)/(T_h/T_c+1).
 
The talk is based on joint works with Rui Fu (UCI), Amir Taghvaei (UCI) and Yongxin Chen (GaTech). Research funding by NSF and AFOSR is gratefully acknowledged.
 

Bio

Tryphon T. Georgiou was educated at the National Technical University of Athens, Greece, and the University of Florida, Gainesville (PhD 1983). He is currently a Distinguished Professor of Mechanical and Aerospace Engineering at the University of California, Irvine. He is also Professor Emeritus at the University of Minnesota, where he held the Hermes-Luh Chair (2002-2016) and served as a co-director (together with Gary Balas) of the Control Science and Dynamical Systems Center (1990-2016). Dr. Georgiou has received the George S. Axelby award of the IEEE Control Systems Society (in 1992, 1999, 2003, 2017), he is a Fellow of the IEEE, IFAC, and a Foreign Member of the Royal Swedish Academy of Engineering Sciences (IVA). 
Event Type: 
Event