Discrete one-dimensional quasi-periodic Schroedinger operators with

Speaker: 

Silvius Klein

Institution: 

UCLA

Time: 

Thursday, January 15, 2004 - 2:00pm

Location: 

MSTB 254

We consider the discrete one-dimensional quasi-periodic
Schroedinger operator with potential defined by a Gevrey-class function.
We show - in the perturbative regime - that the operator satisfies
Anderson localization and that the Lyapunov exponent is positive and
continuous for all energies. We also mention a partial nonperturbative
result valid for some particular Gevrey classes. These results extend
some recent work by J. Bourgain, M. Goldstein, W. Schlag to a more general
class of potentials.

A generalized variational principle for the Sherrington-Kirkpatrick spin glass model

Speaker: 

Dr. Shannon Starr

Institution: 

McGill University

Time: 

Thursday, February 19, 2004 - 11:00am

Location: 

MSTB 254

Recently Michael Aizenman, Bob Sims and I formulated a
generalized variational principle (GVP) for the SK model and its
relatives. Our result is based on the recent developments of F. Guerra and
F. Toninelli, but is equally well motivated by the physicists' approach as
in the book by Parisi, Mezard and Virasoro. In this talk, I will give an
introduction to the SK model, describe the Parisi ansatz, and show how an
elementary, but little-known, fact about Gaussian processes implies the
GVP almost trivially. I will end with a brief description of some special
Poisson-Kingman distributions, called Poisson-Dirichlet processes,
$\textrm{PD}(\alpha,0)$ for $0

Multiscale Analysis of Nonlinear Waves

Speaker: 

Prof. J. Xin

Institution: 

U. of Texas

Time: 

Tuesday, February 17, 2004 - 3:00pm

Location: 

MSTB 254

Multiscale asymptotic analysis is a particularly useful tool for studying nonlinear waves when exact solutions are not available. This is demonstrated in concrete problems: reaction diffusion front speeds in random shear flows, and localized propagating pulses in nonlinear scalar wave equations, both in two space dimensions. Complementary numerical results will also be shown.

Surfactant Effects in Interfacial Fluid Dynamics

Speaker: 

Prof. Ashley James

Institution: 

Dept Aero and Mech., UMN

Time: 

Monday, February 9, 2004 - 4:00pm

Location: 

MSTB 254

A numerical method to simulate interfacial surfactant mechanics within a volume of fluid method has been developed. Two important features of this new method are that it conserves surfactant mass exactly and the form of the equation of state is not restricted, i.e. the relation between surfactant concentration and surface tension can be linear or nonlinear. To conserve surfactant, the surfactant mass and the interfacial surface area are tracked as the interface evolves, and then the surfactant concentration is reconstructed. The algorithm is coupled to an incompressible Navier-Stokes solver that uses a continuum method to incorporate both the normal and tangential components of the surface tension force into the momentum equation.

Numerical simulations demonstrate the effect of surfactant on the dynamics of several problems by comparison to surfactant-free simulations. First, the buoyant rise of a bubble is examined. Next, the evolution of a drop in an extensional flow is studied. Finally, the motion of a drop through a constriction is investigated. In each of these problems surfactant accumulation allows high interface curvature and the formation of small secondary drops or bubbles.

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