LCDS Seminars 2006

Monday, November 6, 2006

Lefschetz Center for Dynamical Systems Seminar

Speaker:	Tai-Ping Liu, Academia Sinica-Taipei and Stanford University
Title:	Stationary and Self Similar Gas Flow
Time/Place:	4:00 p.m., B&H 161

Wednesday, May 10, 2006

Special LCDS/PDE Seminar

Speaker:	Shih-Hsien Yu, City University of Hong Kong
Title:	Green's Function for Boltzmann Equation and Its Applications
Time/Place:	1:00 p.m., 182 George Street, Room 110

Abstract: In this talk we will survey the recent mathematical theories for Boltzmann equation, in particular, the Green's functions for Boltzmann equation. There are several highlights in this talk: macro-micro decomposition, positive solution of the Boltzmann shock layer, hydrodynamic limit problem, Boltzmann boundary layer, particle-wave decomposition, mixture lemma, and the Green's functions for both initial value problem and initial-boundary value problems.

Wednesday, April 26, 2006

Special LCDS/PDE Seminar

Speaker:	Hyung Ju Hwang, Trinity College, Ireland
Title:	Some Recent Results on Vlasov Theory
Time/Place:	3:00 p.m., 182 George Street,

Monday, April 17, 2006

Lefschetz Center for Dynamical Systems Seminar

Speaker:	Bruce M. Boghosian, Department of Mathematics, Tufts University
Title:	A Variational Principle for Unstable Periodic Orbits in Dynamical Systems
Time/Place:	4:30 p.m., 182 George Street. Room 110

Abstract: We describe a variational principle for locating periodic orbits of first-order dynamical systems. We introduce a quantity that is a functional of the phase-space orbit and a function of the period, both unknowns, and we demand that its variation with respect to both of these dependencies vanish. The Euler-Lagrange equations corresponding to this variational principle lead to a second-order nonlinear integrodifferential equation that must be satisfied along any periodic orbit. We demonstrate that this variational principle may be used as the basis of a numerical algorithm for locating periodic orbits. We begin by applying the method to a simple model problem possessing an unstable limit cycle. We next apply the method to find unstable periodic orbits of the Lorenz equations. Finally, we show how the method can be adapted to find unstable periodic orbits of the driven, incompressible Navier-Stokes equations of viscous hydrodynamics.

Monday, March 20, 2006

Lefschetz Center for Dynamical Systems Seminar

Speaker:	Jorge Sotomayor, University of Sao Paulo
Title:	Bifurcations in the Watt Governor System
Time/Place:	2 p.m., 182 George Street, Room 110 Please Note Change of Time and Place for This Week Only

Abstract: We consider a differential equation presented by Pontryagin in his ODE's book (1962) to explain the condition for Lyapunov stability of the equilibrium -- representing constant speed performance -- of the Watt centrifugal governor coupled with a steam engine in the model of Maxwell (1868) - Vishnegradskii (1877).

After a discussion of the relevance of the study of this model as a paradigm for automatic control, we determine the values of the parameters (3 in Pontryagin's Equation) where the Lyapunov stability fails and where successive Hopf bifurcations of increasing order appear.

A bifurcation diagram is presented as a qualitative synthesis of the results obtained.

Work done in collaborations with L. Mello and D. Braga.

Monday, March 6, 2006
Lefschetz Center for Dynamical Systems Seminar
***Talk Cancelled Due to Illness

Speaker :	Bruce M. Boghosian, Dynamical Systems, Department of Mathematics, Tufts University
Title :	A Variational Principle for Unstable Periodic Orbits in Dynamical Systems
Time/Place :	4:30 p.m., 182 George Street, Room 110

Monday, February 27, 2006
Special PDE/LCDS Seminar

Speaker :	Gerhard Rein, University of Bayreuth
Title :	Collisionless Matter in General Relativity--- Stability Versus Collapse
Time/Place :	2:00 p.m., 182 George Street, Room 110

Wednesday, February 15, 2006
Special PDE/LCDS Seminar

Speaker :	H. T. Yau, Department of Mathematics, Harvard University
Title :	Dynamics of Bose Gas and the Well-poseness of Nonlinear Schrodinger Equation in Infinite Dimensions
Time/Place :	3:00 p.m., 182 George Street, Room 110

Abstract : Gross and Pitaevskii proposed to model the dynamics of the Bose-Einstein condensate by a cubic nonlinear Schrödinger equation. This equation plays a key role in the theory and experiments of the Bose-Einstein condensation. The fundamental mathematical question is to derive this equation from the first principle physics law, i.e., the many-body Schrödinger equation. In this talk, I shall review the recent progress concerning this problem and the analytic methods developed for quantum dynamics of many-body systems, including a well-poseness theorem of the cubic nonlinear Schrodinger equation in infinite dimensions.

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