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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.
Curriculum vitae of
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. 
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 Mathématiques, Université de Montréal; 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. 

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 
poetry; the second won an Eric Gregory Award (UK Society of Authors) in 1975 and the third was a Poetry Book Society Recommendation for 1986. He is currently completing a fourth collection. 

2000 január 11 14:00 BME Tartószerkezetek Mechanikája Tanszék Kmf 35 CONSTRAINED EULER BUCKLING
2000 január 12 14:00 MTA Székház Kisterem POINCARÉ'S MISTAKE AND THE ORIGINS OF "CHAOS THEOR" IN SCIENCE AND TECHNOLOGY
2000 január 
19,20,21
BME Műszaki Mechanika Tanszék MG épület Minicourse 
NONLINEAR DYNAMICS SHORT COURSE
2000 január 21 14:00 BME Műszaki Mechanika Tanszék MG épület MODELS FOR INSECT LOCOMOTION, OR WHY COCKROACHES GET AWAY

Részletes program


CONSTRAINED EULER BUCKLING

2000 január 11, 14:00, BME Tartószerkezetek Mechanikája Tanszék, Kmf 35 
 

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. 
 
 
 

POINCARÉ'S MISTAKE AND THE ORIGINS OF "CHAOS THEORY'' IN SCIENCE AND TECHNOLOGY

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 
Acta Mathematica 13, 1-270, 1890. 

[2] P. Holmes, Poincaré, celestial mechanics, dynamical-systems theory, and "chaos"' 
Physics Reports 193(3), 137-163, 1990. 

[3] J. Barrow-Green, Poincaré and the Three Body Problem 
American Mathematical Society / London Mathematical Society Publications, Providence RI, 1996. 

[4] F. Diacu and P. Holmes, Celestial Encounters: The Origins of Chaos and Stability 
Princeton University Press, 1996. 
 
 

NONLINEAR DYNAMICS SHORT COURSE

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). 

1.1. Review of linear and planar systems: ODEs and mappings, stable manifold theorem, basic ideas of Poincare maps, limit sets, structural stability. Special prope 
Examples: Duffing and van der Pol oscillators. (1.5-2 hrs) [Chap 1, especially secs 1.1-7.]. 

1.2. Dimension reduction: Center manifolds, local bifucations, normal forms, selected codimension 2 unfoldings. 
Examples: Takens-Bogdanov normal forms, Moore-Greizer compressor model. (3-4 hrs, 2 hrs - computer based exercises) [Chaps 3, secs 3.1-4; Chap 7, secs 7.2-5]. 

1.3. Global bifurcations and chaos: ODEs and iterated maps, Smale horseshoes, symbolic dynamics, strange attractors, homoclinic loops and Silnikov phenomena. 
Examples: Thermosyphons and the Lorenz equation; vibrating strings, beams, and plates. Return to Moore-Greizer model. (2 hrs, computer exercises - 1hr) [Chap 5, secs 5.1-3, 5.7  and Chap 6, secs 6.1, 3]. 

1.4. Perturbation methods, averaging theory, Melnikov's method for detecting homoclinic orbits, singular perturbation theory. 
Examples: Nonlinear oscillators with periodic forcing: pendula, Duffing and van der Pol equations. (3 hrs., analytical/computer exercises 1-2 hrs) [Chap 4, secs 4.1-5]. 

MODELS FOR INSECT LOCOMOTION, OR WHY COCKROACHES GET AWAY

2000 január 21, 14:00, BME Műszaki Mechanika Tanszék 

Philip Holmes, 
Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics, Princeton University. 

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.