Holmes
Philip Holmes, Eugene Higgins Professor of Mechanical & Aerospace Engineering
Fellow of the American Physical Society
Member, American Academy of Arts and Sciences
Ph.D. Southampton (1973)
Profile
Since 1994 he has been Professor of Mechanics and Applied Mathematics at Princeton University, where he directed the Program in Applied and Computational Mathematics until 1997. He is an associate faculty member in the Department of Mathematics.
In 1981 he was a Visiting Scholar in the Department of Mathematics at the University of California , Berkeley. From 1981-86 he was Director of the Center for Applied Mathematics at Cornell. In 1985-86 he held the Chaire Aisenstadt of the Centre de Recherches Mathematiques, Universite de Montreal; in 1988-89 he was a Sherman Fairchild Distinguished Scholar at the California Institute of Technology and, in 1993-94, a John Simon Guggenheim Memorial Fellow. He was elected a Fellow of the American Academy of Arts and Sciences in 1994. In January 2000 he held a Visiting Professorship at the Paul Erdōs Mathematical Center, Budapest, Hungary, and in 2001 he was elected an Honorary Member of the Hungarian Academy of Sciences. Dr Holmes teaches courses at all levels from freshman to advanced graduate, and conducts seminars in dynamics and applied mathematics. He helped Ingrid Daubechies develop 'Math Alive:' an applied mathematics course for non-science majors. He has published over 200 papers, articles and reviews. He has supervised 30 PhD. and 3 MSc theses, mentored 17 postdoctoral fellows, and he currently has five PhD students and four postdoctoral fellows working with him.
Research Interests
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 modelling 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 neurobiology, cognitive psychology, mechanics and mathematics.
He is co-author, with John Guckenheimer, of a textbook on dynamical systems; with John L. Lumley and Gal 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. He serves on the editorial boards of the Journal of Nonlinear Science, Regular and Chaotic Motion, the SIAM Journal on Applied Dynamical Systems, Applied Mathematics Research eXpress, and the Springer Verlag Applied Mathematical Sciences and Texts in Applied Mathematics book series. Recent examples of his pedagogical work appear on the web-based peer-reviewed Scholarpedia; see:
Dr. Holmes' research is currently sponsored by the National Science Foundation, the National Institutes of Health and of Mental Health, and the Air Force Office of Scientific Research.
Selected Recent Publications
(see links at right for full publication list in CV, and for downloadable papers)
* F. Cirak, J. Cisternas, A.M. Cuitino, G. Ertl, P. Holmes, I.G. Kevrekidis, M. Ortiz, H.H. Rotermund, M. Schunack and J. Wolff (2003) Science 300, 1932-1936. Oscillatory thermo-mechanical instability of an ultrathin catalyst.
* R. Goodman, P. Holmes, and M.I. Weinstein (2004) Physica D 192 (3-4), 215-248. Strong NLS soliton-defect interactions.
* R.M. Ghigliazza and P. Holmes (2004) SIAM J. on Applied Dynamical Systems 3 (4), 636-670 and 671-700}. Minimal models of bursting neurons: How multiple currents, conductances and timescales affect bifurcation diagrams, and A minimal model of a central pattern generator and
motoneurons for insect locomotion.
* T.R. Smith, J. Moehlis and P. Holmes (2005) J. Fluid Mech. 538, 71-110. Low-dimensional models for turbulent plane Couette flow in a minimal flow unit.
* T. McMillen and P. Holmes (2006) J. Math. Biol. 53, 843-866. An elastic rod model for anguilliform swimming.
* J.E. Seipel and P. Holmes (2006) Int. J. Robotics Research 25 (9), 889-902. Three-dimensional translational dynamics and stability of multi-legged runners.
* R. Bogacz, E. Shea-Brown, J. Moehlis, P. Holmes and J.D. Cohen (2006) Psychological Review 113 (4), 700 - 765. The physics of optimal decison making: A formal analysis of performance in two-alternative forced choice tasks.
* P. Holmes, R.J. Full, D. Koditschek and J. Guckenheimer (2006) SIAM Review 48 (2), 207-304. Dynamics of legged locomotion: Models, analysis, and challenges.
* R. Kukillaya and P. Holmes (2007) Biological Cybernetics 97 (5-6), 379-395. A hexapedal jointed-leg model for insect locomotion in the horizontal plane.
* J. Gao and P. Holmes (2007) J. Computational Neurosci. 22, 39-61. On the dynamics of electrically-coupled neurons with inhibitory synapses.
* Y.S. Liu, P. Holmes and J.D. Cohen (2008) Neural Computation 20 (2), 345-373. A neural network model of the Eriksen task: Reduction, analysis, and data fitting.
* P. Eckhoff, P. Holmes, C. Law, P.M. Connolly and J.I. Gold (2008) New J. of Physics 10, doi: 1367-2630/10/1/015006. On diffusion processes with variable drift rates as models for decision making during learning.
* P. Varkonyi, P. Holmes, T. Keimel, K. Hoffman and A.H. Cohen (2008) J. Computational Neurosci. 25 (2), 245-261. On the derivation and tuning of phase oscillator models for lamprey central pattern generators.
* T. McMillen, T.L. Williams and P. Holmes (2008) PLoS Computational Biology 4 (8),doi: 10.1371/ journal.pcbi.1000157. Nonlinear muscles, passive viscoelasticity and body taper conspire to create neuro-mechanical phase lags in anguilliform swimmers.
* S. Feng, P. Holmes, A. Rorie and W.T. Newsome (2009) PLoS Computational Biology 5 (2), doi: 10.1371/journal.pcbi.1000284. Can monkeys choose optimally when faced with noisy stimuli and unequal rewards?
* P. Eckhoff, K-F. Wong-Lin and P. Holmes (2009) J. Neurosci. 29 (13), 4301-4311. Optimality and robustness of a biophysical decision-making model under nonepinephrine modulation.
* J. Gao, K.F. Wong-Lin, P. Holmes, P. Simen and J.D. Cohen (2009) Neural Computation 21 (9), 2407-2436. Sequential effects in two-choice reaction time tasks: Decomposition and synthesis of mechanisms.
* R. Kukillaya, J. Proctor and P. Holmes (2009) CHAOS: An Interdisciplinary Journal of Nonlinear Science 19 (2), 026107. Neuro-mechanical models for insect locomotion: Stability, maneuverability,
and proprioceptive feedback.