Lefschetz Center for Dynamical Systems Seminar
Abstract: In this talk, we will give a brief survey of the problem of the relation between bifurcations and stability of traveling waves. When the equation of travelling waves undergoes a homoclinic/hetroclinic bifurcations, this naturally corresponds to emergence of a new travelling wave. The question is "How the stability of the wave is related to the `geometry' of the bifurcation?" We will give some overview of this problem.
Brown University Center for Statistical Sciences Seminar
Abstract: Over the last decade, substantial evidence has been developed to support an association between exposure to particulate air pollution and daily mortality in U.S. cities. The evidence for an effect of short-term (acute) exposures has derived from time series analyses. The combined effects of chronic and acute exposures have been estimated from cohort studies that give estimates that are an order of magnitude greater than the time series results. In this talk, we will review the statistical models used for estimating health effects of air pollution focusing on spatial time series models. We will then connect the time series and cohort methodoligies to ask what we can learn about the total effects (acute plus chronic) from time series data. The methods will be illustrated with analyses of data from the National Morbidity and Mortality Air Pollution Study (NMMAPS).
Center for Fluid Mechanics Seminar
University of Pennsylvania, Philadelphia | |
Abstract: We study the use of electric and magnetic fields to propel and stir liquids and particles in microfluidic devices as well as the effects of the flow fields on biological interactions. Following a brief introduction, most of the talk will focus on the use of Lorentz forces to pump and stir liquids in micro fluidic networks consisting of individually controlled branches. The networks' basic building blocks are conduits equipped with two electrodes along two opposing walls. When a prescribed potential difference is applied across each electrode pair, it induces current in the liquid (assumed to be a weak electrolyte solution). The entire device is either subjected to an external uniform magnetic field or fabricated within a magnetic material. By judicious application of the potential differences at various network branches, one can direct liquid flow along any desired path without any mechanical pumps or valves. Ideas of linear network theory are extended to allow one to determine the flow rates in various branches as functions of the applied fields and to determine the control variables needed to achieve desired flow paths. By equipping network branches with centrally located electrodes, the branches can double as stirrers capable of inducing chaotic advection. Prototype devices were fabricated with low temperature, co-fired ceramic tapes (LTCC). LTCC provide a rapid, low-cost prototyping medium for the fabrication of micro-fluidic systems and components.
Special Analysis Seminar
Stochastic Systems Seminar
Abstract: We shall describe a Large Deviation Principle for the usual empirical measure (based on i.i.d. sample) under a topology based on functions having only some exponential moments. In this case, the rate function differs from the usual relative entropy and involves linear forms which are no longer measures. Basic techniques from Orlicz spaces theory appear to be a powerful tool.
A Gibbs Conditioning Principle (GCP) is then derived with the help of the previous result. Besides a rather direct proof, the main improvements with respect to already published GCP's are the following: Convergence holds in situation where the underlying log-Laplace transform (the pressure) may not be steep and the constraints are built on energy functions admitting only some finite exponential moments.
Brown Analysis Seminar
Applied Mathematics Colloquium
Special Stochastic Seminar
Abstract: In an occupancy experiment, $r$ balls are placed at random into $n$ urns, with each ball independently equally likely to enter each urn. Closed form expressions can be obtained for the probability of various events of interest, such as the event that at least $m$ urns are empty, or that less than half of the balls are in singly occupied urns. However, unless $n$ is small or the event of interest is very simple, the closed form expressions can be unwieldy.
In this talk, I will discuss a large deviations approximation to general occupancy problems which becomes exact as $r$ and $n$ tend to infinity, and which has a simple expression in terms of relative entropy. We approach the problem indirectly by first characterizing the large deviations behavior of sequential occupancy experiments, in which the balls are thrown one at a time, and one is interested in the entire evolution of the occupancy state. Once this is done, the original problem follows via the contraction principle.
I will also briefly apply the general results to investigate the need for wavelength conversion in a wavelength multiplexed optical packet switch.
This is a joint work with Paul Dupuis and Phil Whiting.
Scientific Computing Seminar
Abstract: In this talk, we will discuss some recent results in solving Maxwell equations in nonhomogeneous media. First, we will discuss a new upwind embedded boundary method with finite difference methods to solve time dependent Maxwell equation in media with material interfaces; secondly, a high order spectral approximation of a global boundary condition will be presented for time harmonic Maxwell equations in layered media; lastly, we will present a fast solver for integral equations of Maxwell equation in layered media.
Department of Mathematics Colloquium
PDE Seminar
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