People

While many become mired in the details of the construction of complex models, Professor Holmes' research largely focuses on the stripping away of detail to better reveal the underlying structure of a complicated system. Much of his work is on the analysis of nonlinear dynamics and differential equations as he develops methods for better understanding the overall qualitative behaviors of these systems. This has led to significant contributions to the development of chaos theory, showing that seemingly random systems exhibit some degree of predictability and order. Holmes' research has also contributed to the understanding of turbulent flows, elastic buckling, pattern formation in chemical reactions over thin catalysts, and nonlinear modes in optical waveguides.

A current area of interest is the study of running cockroaches. Even in the face of random perturbations, insects have a remarkable ability to maintain relatively constant headings. Holmes' research has lent insight into the mechanism by which this stability is achieved, and his seemingly simple models have proven very robust. In a synthesis of biology, mathematics, neuroscience, and basic Newtonian mechanics, this work is leading to an integrative understanding of legged motion. In related work in neuromechanics he studies the hydrodynamic forces in swimming of lampreys. Holmes; research has far-reaching applications from flight-vehicle design to robotics.

Professor Holmes, a native of England, was trained as an engineer, receiving his Ph.D. from Southampton University in 1974. It wasn’t long, however, before his interest changed from engineering to the underlying mathematics of engineering, and soon after graduating he began working on engineering problems from a mathematical point of view. In 1977 he accepted a position at Cornell where he taught both engineering and math for 17 years. In 1994 he came to Princeton as a professor of Mechanical and Aerospace Engineering and as a core member of PACM. Prof. Holmes is an editor for 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. He still finds time to write poetry and has published four collections.

Professor Holmes serves as a professor in the MAE Department and in PACM. He teaches both undergraduates and graduate students and also conducts seminars in PACM. He was jointly responsible for the creation of the Math Alive course. Prof. Holmes currently advises 5 Ph.D. students and 4 postdoctoral fellows.

PACM Students advised: Philip Eckhoff