Lefschetz Center for Dynamical Systems Seminar
Abstract: I will describe a set of equations that describe rotating fluid flows dominated by body forces. Two types of instabilities are present in such flows, the so-called ``modal stall'' and ``spike stall'', distinguished by the time-scales of their evolution. The dynamics of the system of equations resembles closely the dynamics of reaction-diffusion systems and I will discuss the parallels. The simplest model is a one-dimensional non-local reaction-diffusion equation for which the standard existence and uniqueness results can be shown. The extensions involve two and three-dimensional equations in an annular domain and I will present numerical simulations of the dynamics. The issue of control of instabilities becomes important when application to turbomachinery (axial compressors) is considered. I'll present both linear and nonlinear control strategies, compare them and discuss the issues of (finite-dimensional) implementation. In particular, I'll discuss the issue of the so-called control spillover in this nonlinear problem - a phenomenon when finite-dimensional control stabilizes some modes but destabilizes others.
Center for Fluid Mechanics Seminar
University of Illinois at Chicago
Abstract: Hydrothermal multi-wall closed-end carbon nanotubes contain an encapsulated multi-phase aqueous fluid, thus offering an attractive test platform for in-situ nanofluidic experiments in the vacuum of the transmission electron microscope. These nanotubes are at least by two orders of magnitude smaller than the finest capillaries used in other dynamic fluidic experiment so far. The excellent wettability of the graphitic inner tube walls by the aqueous fluid and the mobility of this liquid in the nanotubes are observed with nanometer-scale resolution. Complex interface dynamic behavior is induced by means of heating via electron irradiation. The presence of thin wetting layers transporting fluid along the nanotube walls is also demonstrated. The documented phenomena in this study demonstrate the potential of implementing such tubes in future nanofluidic devices.
Brown Analysis Seminar
Special LCDS Seminar/Applied Mathematics Colloquium
Abstract: Mixing is important in many areas of science involving fluids, and can be produced by either chaotic advection or weak turbulence. In this talk, the two processes are compared and contrasted. We study transient mixing in thin fluid layers of which one half is initially labeled by a fluorescent dye. In the chaotic case (time-periodic velocity field), the scalar evolves to a complex recurrent pattern that subsequently decays without change of form, as first noted in a numerical simulation by Pierrehumbert. The pattern simply decays slowly like the grin on the Cheshire Cat. The typical path length per cycle of the forcing and the Reynolds number are shown to govern the decay rate, but the dependence is strikingly non-monotonic in these variables. The time evolution of various statistical measures of the scalar field provides a quantitative description of the interplay between stretching and molecular diffusion. It is surprising to note that diffusion does not broaden the striations of the scalar field. We have explored the effects of many flow variables including periodic and nonperiodic forcing in both space and time. Particle tracking over long periods of time is also used to study the transient mixing process. Weakly turbulent flows (obtained by reducing the viscosity) are shown to mix much more efficiently than chaotic flows in the same geometry.
Abstract: The human brain is a highly convoluted surface with many folds and fissures that vary considerably from person to person, making it difficult to compare functional activity across individuals. Most of the functional activity of the brain occurs on the surface, called the ``grey matter''. Visual stimuli elicit visual evoked scalp potentials (VEPs) which can be recorded from electrodes attached to the surface of the scalp. These VEPs are generated by current sources located in the brain. The location of these neural sources can be estimated when a source is modeled as a dipole and the head is modeled as three concentric spherical shells representing the scalp, skull and neural tissue. I will present results using this model that illustrates the mapping between the visual field and visual cortex when a stimulus is presented in various positions in the visual field. I will also discuss a novel technique that I have developed which uses the Riemann Mapping Theorem and circle packings to create quasi-conformal flat maps of the surface of the brain. These maps can be produced in the Euclidean and hyperbolic planes and on a sphere. I will demonstrate how these maps are being used to elucidate new information about the human brain.
Joint Pattern Theory/Stochastic Systems Seminar
Cambridge University, UK
***** Note Special Day/Time *****
Abstract: We present new results concerning information-theoretic convergence in the Central Limit Theorem. In joint work with Barron, we present a simplified proof, which also provides an explicit rate of convergence, using so -called Poincare inequalities. We also present techniques which can provide a proof in certain dependent cases, under either a Rosenblatt-style mixing condition, or for FKG systems.
Department of Mathematics Colloquium
***NEW, REVISED SPEAKER INFORMATION
<--- 2001 Index
DAM Home Page