ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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An Expository Talk on Theory of Bifurcations with Numerical Examples

Barry Bernstein
Department of Mathematics, Illinois Institute of Technology

Friday, May 3, 2002 15:00-16:00,
Room 145, NIST North (820)
Friday, May 3, 2002 13:00-14:00,
Room 4550

Abstract: Some elementary notions of the theory of bifurcation of equilibrium solutions of evolution problems governed by nonlinear differential equations are presented. In view of the existence of a huge variety of applications of bifurcation theory in engineering, biology, chemistry, physics, economics, etc., and for ease of presentation and motivation, we choose to discuss in this talk only examples of steady-state solutions in one- and two-dimensions. More specifically, we shall discuss the numerical solution of three bifurcation problems, namely, (a) a rigid hoop hangs from the ceiling with a small bead attached in the loop and resting in the bottom of the hoop, (b) the buckling of an elastic plate, and (c) the flow of a viscous, incompressible, homogeneous fluid between two long, coaxial cylinders which are rotating.

Speaker Bio: Dr. Bernstein was educated at the City College of New York (B.S. mathematics, 1951), and Indiana University (M.A., mathematics and mechanics, 1954; Ph.D., mathematics and mechanics, 1956). He began his research career at the U.S. Naval Research Laboratory (1951-52; '56-'61) and the U.S. National Bureau of Standards (1961-65), and combined research with teaching at Purdue University (1965-66), Illinois Institute of Technology (1966-present), Flinders University, Adelaide, Australia (1988), and Louis Pasteur University, Strasbourg, France (1988-89). With more than seventy papers in journals and conference proceedings, he is known internationally for his pioneering work in nonlinear mathematics, fluid and solid mechanics, polymer science, and non-equilibrium thermodynamics. One of his papers (J. Research NBS, 68B, 103-113 (1964)) was cited in the Centennial Volume in commemoration of the 100th anniversary of the founding of the National Institute of Standards and Technology (formerly known as NBS).

Contact: J. T. Fong

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