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Philip J. Holmes is going to spend January 2000 as a Paul Erdos Visiting Professor at the Technical University of Budapest, Department of Strength of Materials. The goal of his visit is to deliver lectures and seminars at various institutions, to get in touch with Hungarian scientists and students in the fields of mechanical engineering, theoretical and applied mechanics, applied mathematics and theoretical physics, also, he is going to conduct joint research with Gabor Domokos. You can reach Professor Holmes at pholmes@iit.bme.hu, or at 463-1493 during this period. Below, we provide his brief curriculum vitae, the coordinates of his public appearances and topics abstracts for the talks.

Philip J. Holmes
Philip Holmes was born in Lincolnshire, England in 1945 and educated at the Universities of Oxford and Southampton, obtaining a PhD in engineering in 1973. He taught at Cornell University from 1977 to 1994, where he was latterly the Charles N. Mellowes Professor of Engineering and Professor of Mathematics. 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. Dr Holmes works
in the areas of dynamical systems and nonlinear mechanics. He is concerned
to develop qualitative and analytical methods for studying mathematical
models of both solid and fluid systems. He has supervised 21 PhD. and two
MSc theses, and acted as advisor for nine postdoctoral fellows.
Dr Holmes teaches courses and conducts research seminars in dynamics
and applied mathematics. He has published over 180 papers, articles and
reviews, and has supervised 2 MSc and 21 PhD theses and the work of 10
postdoctoral scholars. 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 Archive for Rational Mechanics and Analysis,
Regular and Chaotic Motion, the Journal of Nonlinear Science and the Springer
Verlag Applied Mathematical Sciences book series, and he is a former editor
of Complex Systems, Proceedings of the Edinburgh Mathematical Society and
the SIAM Journal on Applied Mathematics. In another life, he has published
three collections of
2000 január 11, 14:00, BME Tartószerkezetek Mechanikája Tanszék, Kmf
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I will discuss joint work with Gabor Domokos (Technical University of
Budapest), John Schmitt and Barrie Royce in which we consider elastic buckling
of an inextensible beam confined to the plane and subject to fixed end
displacements, in the presence of rigid, frictionless sidewalls which constrain
overall lateral motions. We formulate the geometrically nonlinear problem,
derive analytical results for special cases including that of line contact
regions, and develop a numerical shooting scheme for general solutions.
We compare these theoretical and numerical results with experiments on
slender steel beams. In contrast to the simple behavior of the unconstrained
problem, we find a rich bifurcation structure, with multiple branches and
concomitant hysteresis in the overall load-displacement curves. My interest
in this problem is in part due to the fact that, in spite of having complete
solutions in terms of elliptic functions, it is remarkably difficult to
extract the geometrical structure of the bifurcation sets.
2000 január 12, 14:00, MTA Székház Kisterem
In 1889, for his paper on Hamiltonian dynamics and the three-body problem
of celestial mechanics, Henri Poincaré was awarded a prize established
to honor the 60th birthday of King Oscar II of Sweden and Norway. As the
paper was being edited for publication in {Acta Mathematica}, a serious
error came to light. In correcting his error, Poincaré discovered the phenomenon
we now call chaos. The resulting 270-page paper [1] is essentially the
first textbook in the modern geometrical theory of dynamical systems. Drawing
on an earlier review article [2], on recently published historical materials
[3], and on a less-technical general account [4], I shall tell the story
of this paper and some of the key contributions to which it led.
[1] H. Poincaré, Sur le probléme des trois corps et les équations de
la dynamique
[2] P. Holmes, Poincaré, celestial mechanics, dynamical-systems theory,
and "chaos"'
[3] J. Barrow-Green, Poincaré and the Three Body Problem
[4] F. Diacu and P. Holmes, Celestial Encounters: The Origins of Chaos
and Stability
2000 január 19,20,21, BME Műszaki Mechanika Tanszék, MG épület
Part 1: Finite-dimensional dynamics. Textbook: J.Guckenheimer and P.Holmes (1983). Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, New York, 1983 (5th corrected printing, 1997). MODELS FOR INSECT LOCOMOTION, OR WHY COCKROACHES
GET AWAY
2000 január 21, 14:00, BME Műszaki Mechanika Tanszék Philip Holmes,
I will discuss joint work with John Schmitt in which we study the dynamics and stability of legged locomotion in the horizontal plane. Inspired by experimental studies of insects due to R.J. Full et al., we develop two and three-degree-of freedom rigid body models with both rigid `peg-legs' and pairs of elastic legs in intermittent contact with the ground. We focus on conservative compliant-legged models, but we also consider prescribed `muscle' forces, leg displacements and combined strategies. The resulting piecewise-holonomic mechanical systems exhibit periodic gaits whose neutral and asymptotic stability characteristics are due to intermittent foot contact, and are largely determined by geometrical criteria. Most strikingly, we show that mechanics alone can confer asymptotic stability in heading and body orientation.We discuss the relevance of our idealised models to recent experiments and simulations on insect running and turning. |