Lefschetz Center for Dynamical Systems Seminar
Abstract: We show that for Smale solenoids the fractal (Hausdorff or box) dimensions of all stable slices are the same. Our approach should lead to a proof that the fractal dimension of hyperbolic sets can be computed by adding those of their stable and unstable slices.
Brown University
Joint Materials/Solid Mechanics Seminar Series
Department of Mechanical Engineering, University of Delaware | |
Abstract: Multi-scale multi-phenomena modeling of the structure- property-function relations for carbon nanotubes and their composites requires a consideration of modeling hierarchy bridging the lengths from nano- to micro- to macro-scale. The first part of this presentation focuses on a micromechanical approach for predicting the nanocomposite elastic behavior as a function of the constituent properties, reinforcement geometry and nanotube structure. The experimental characterization results of a model composite system of aligned multi-walled carbon nanotubes embedded in a polystyrene matrix highlight the structure/size influence of the nanotube reinforcement on the properties of the nanocomposite. Crucial to accurate modeling of nanocomposite properties is the knowledge of the nanoscale structure and interaction, which is the focus of the second part of the presentation. Here, the atomistic modeling of carbon nanotube behavior is based upon a molecular structural mechanics approach. Using this approach, we have simulated nanotube static and dynamic properties, and the application of nanotube-based mechanical sensors are discussed. Also, thermal properties of carbon nanotubes, such as specific heat and thermal expansion, are studied by quantizing the vibrational modes of carbon nanotubes. The presentation concludes with a few brief remarks on key areas for future research.
Cognitive & Linquistic Sciences
Spring 2005 Colloquium and CG233 Speakers
Center for Fluid Mechanics Seminar
Cambridge, Massachusetts | |
Abstract: New Scientific missions call for emerging propulsion technologies capable of fine tuning a satellite's relative position and canceling small disturbances. One candidate technology that holds promise for these type of missions are colloidal thrusters. These thrusters are liquid electrostatic accelerators, which do not rely on gas ionization (plasma), are intrinsically small, and operate at low power levels, while having small plume divergence angles to avoid spacecraft (S/C) contamination problems.
Colloid thrusters deliver low thrust (0.1 microN/emitter, Isp = 500-7000 s) which can be multiplied many times over by integrating them in microfabricated arrays. We present a numerical simulation of a colloid thruster in an effort to complement experimental and analytical research in the area. The goal of this project has been to create a flexible numerical tool to compute single-emitter current, jet size, velocity, electric field strengths for a given geometry, fluid, flow rate, and voltage. Results are presented and compared to experimental data and analytical approximations.
Stochastic Systems Seminar
Abstract: Many important examples in a variety of statistical applications naturally lead to the study of the distribution of the sum of a finite number of random variables with values on the nonnegative integers. Often, this distribution is well approximated by a Poisson or compound Poisson law. We consider the problem of obtaining quantitative, nonasymptotic bounds for the accuracy of this approximation, with respect to the relative entropy "distance". In the course of exploring this question, we obtain the following results, all of which use information-theoretic ideas: (a) New, general and explicit relative entropy bounds for compound Poisson approximation. (b) Under certain conditions, we obtain tighter compound Poisson approximation bounds in terms of the total variation distance, which in certain cases are optimal or near-optimal. (c) A simple, new proof of a logarithmic Sobolev inequality for compound Poisson distributions. This leads -- by an extension of the so-called "entropy method" -- to a hierarchy of results about the tails of Lipschitz functions of compound Poisson random variables. In particular, these tails are Poisson-like, exponential, or decaying by a power law, according to whether the corresponding Levy measure has bounded support, finite exponential moments or finite polynomial moments. The talk is based on joint work with Ioannis Kontoyiannis at Brown University.
**Special Informal Brown Analysis Seminar
***Special Colloquium*** Department of Mathematics
PDE Seminar
Department of Mathematics Colloquium
See Special Colloquium on Wednesday, March 23, 2005
<--- 2005 Index