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Dr. Holmes works on nonlinear dynamics and differential equations, developing qualitative and analytical methods for studying mathematical models of solid, fluid, and biological systems. He has contributed to the mathematical foundations and applications of dynamical systems or 'chaos theory,' and has used these ideas to better understand the dynamics of coherent structures in turbulent flows, pattern formation in chemical reactions over thin catalysts, nonlinear modes in optical waveguides, and constrained buckling of elastic rods. His current interests focus on the neuromechanics of legged locomotion and swimming (or why it's hard to catch cockroaches and lampreys), and modeling cognitive processes. His work has important technological implications for the design of vehicles and turbomachinery and the development of new materials and devices, including smart and nimble robots, and it requires the posing and solution of beautiful problems in neuroscience, cognitive psychology, mechanics and mathematics. He is co-author, with John Guckenheimer, of a textbook on dynamical systems; with John L. Lumley and Gahl Berkooz, of a monograph on low dimensional models of turbulence; with Florin Diacu, of Celestial Encounters: an historical account of the people and ideas at the roots of 'chaos theory,' and, with Robert Ghrist and Michael Sullivan, of a monograph on knotted orbits in three-dimensional flows. The second edition of "Turbulence, Coherent Structures, Dynamical Systems and Symmetry," with an additional chapter by Clarence W. Rowley, appeared in 2012.
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ULTRASONICS (2024): 107158-107158
Ultrasound in medicine & biologyno. 9 (2023): 1979-1995
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICAno. 3 (2023): A241-A241
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Journal of the Acoustical Society of Americano. 3_supplement (2023): A266-A266
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