Lefschetz Center for Dynamical Systems Seminar
Abstract: Classical bifurcation theory studies dynamical systems, that depend on parameters. Frequently, trivial equilibria are assumed to exist. In an extended phase space, they form manifolds with a trivial transverse foliation. In contrast, we consider vector fields with equilibrium manifolds that are not induced by any parameters. We address the failure of normal hyperbolicity in absence of any transverse flow-invariant foliation. We call our emerging theory "bifurcation without parameters". Applications include coupled oscillators, traveling wave profiles in systems of hyperbolic balance laws, population dynamics, fluid mechanics, and many more. Motivated by several examples, we will present a variety of bifurcation scenarios. We will discuss their dynamic properties and compare them with classical transcritical, Hopf, or Bogdanov-Takens bifurcations.
Brown University Center for Statistical Sciences Seminar
University of Rochester School of Medicine and Dentistry | |
1st Floor Conference Room 106 (Refreshments at 3:45 p.m.) |
Abstract: Longitudinal data are collected from a number of subjects along the time in biomedical longitudinal studies. In some biomedical applications, the biological mechanisms are well studied and the mathematical representations of the biomedical systems are available. The questions that we are concerned include (1) how to estimate the parameters in the longitudinal dynamic systems which are usually described by a set of differential or difference equations; (2) how to forecast the future outcomes for both individual subjects and for the whole population using the identified models; and (3) how to "borrow the strength" across the subjects under the setup of longitudinal dynamic systems. In this talk, I will present two different models for HIV dynamic systems from AIDS clinical trials. One model is a deterministic model with a set of differential equations and another model is a state-space model. In both models, we consider the important features of longitudinal data such as within-subject variation and between-subject variation as well as within-subject correlations. The hierarchical mixed-effects modeling idea is used in both models. The hierarchical Bayesian approach is proposed to estimate the parameters in the deterministic dynamic models and several methods such as a two-stage method, MLE and Bayesian approach are studied under the state-space model setup. Applications to AIDS clinical data will be presented to illustrate the methodologies. Some open questions in this area will be posed.
Brown University
Joint Materials/Solid Mechanics Seminar Series
Abstract: Free-standing or supported thin-films are in widespread use in industry. Many MEMS devices such as pressure sensors and optical switches use thin film membranes that are nanometers thick and microns wide. Nanometer-sized coatings of diamond-variants (diamond-like carbon, ultrananocrystalline diamond) are used as wear protection coatings on roller bearings, hard disks etc. In all these cases, it is important to accurately and nondestructively measure the mechanical properties of the film. Current methods for obtaining mechanical properties and residual stresses include nano-indentation, bulge tests, and resonance tests. Unfortunately these techniques are often destructive. Furthermore, they depend critically on knowledge of how the films are supported, and are therefore usually carried out on structures with simple well-defined geometries. High-frequency ultrasonic techniques can therefore play an important role for non-destructive, in-situ characterization of the mechanical properties of structures of complex geometry.
In this talk, I will describe recent efforts at Northwestern University in the area of ultrasonic characterization of the mechanical properties of thin films and coatings. Three ultrasonic characterization techniques are used: conventional contact acoustic microscopy, guided-wave photo-acoustic (laser ultrasonic) microscopy, and bulk-wave photo-acoustics using a femtosecond laser pump-probe technique. Experiments on unsupported thin films of aluminum/silicon-nitride and gold are performed using guided wave photo-acoustic microscopy to obtain elastic moduli and residual stresses. The elastic moduli of coatings of diamond-variants are obtained using all three techniques. The measurements are compared with results from standard nano-indentation tests.
Center for Fluid Mechanics Seminar
Abstract: Surfactants are surface active molecules that consist of a hydrophilic head group and a hydrophobic tail. When dissolved in water they can spontaneously form several different types of self-assembling aggregates. The size and shape of the resulting aggregate morphology depends on surfactant and counterion concentration. Under the proper conditions wormlike micelles, resembling slender rods, can entangle and impart viscoelasticity to the fluid. The behavior of wormlike micelles solutions is similar to that of polymer solutions. The primary difference being that, unlike a covalently bonded polymer backbone, micelles are in a state of thermodynamic equilibrium with the solvent and are continuously breaking and reforming under Brownian fluctuations. This leads to a broad and dynamic distribution of micelle lengths which can change under an imposed shear or extensional flow. Surfactant solutions are used extensively as rheological and surface tension modifiers in many consumer products and applications.In this presentation, I will discuss the behaviour of a series of wormlike micelle solutions in several extensional flows and describe several newly observed flow instabilities unique to these fluids. The experiments were performed using a series of wormlike micelle solutions of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) dissolved in deionized water. In the first part of the talk, I will describe the behavior of these fluids in pure extensional flows. A filament stretching rheometer was used to follow the evolution in the tensile force and the flow induced birefringence of a wormlike micelle solution experiencing an uniaxial elongation flow. The wormlike micelle solutions demonstrate significant strain hardening and a failure of the stress-optical. At a critical stress, nearly independent of strain rate, the wormlike micelle solutions filaments were found to fail through a dramatic rupture near the axial midplane. This filament failure is not the result of elastocapillary thinning as is commonly observed in the filament stretching of weakly strain hardening polymer solutions. Instead, I believe that the filament failure stems from the local scission of individual wormlike micelle chains. The energy of wormlike micelle chain scission can be calculated and was found to be roughly 4 kBT for all the solutions tested. For the extension rates tested, this scission energy was found to be nearly independent of both the imposed extension rate and the concentration of the surfactant and the salt. In the second part of the talk, I will describe how the extensional rheology of these wormlike micelle solutions can affect the flow past a falling sphere. Experimental measurements of terminal velocity, particle image velocimetry and flow induced birefringence for a wide range of Deborah numbers will be presented. At a critical Deborah number, a new flow instability was observed resulting in dramatic fluctuations in the sedimentation velocity of the sphere are observed. I will present evidence that suggests this instability is directly related to the filament rupture observed in the pure extensional flows.
Brown Analysis Seminar
Brown University Center for Statistical Sciences Seminar
During the second part of this talk, I will discuss two approaches for the marginal regression analysis of multilevel binary data when clusters are not necessarily nested: a GEE method that relies on a working independence assumption coupled with a three-step method for obtaining empirical standard errors, and a likelihood-based method implemented using Bayesian computational techniques. Implications of time-varying endogenous covariates are addressed. The methods are illustrated with two examples. The first uses data from the BCSC to estimate mammography accuracy from a repeatedly screened population. The second combines state- and national-level survey data to estimate longitudinal screening trends.
Electrical Sciences and Computer Engineeering Seminar
California Institute of Technology, Pasadena, California | |
Abstract: Space robotics is most often thought of as Mars science exploration and orbital attached robotic servicing. These venues will greatly expand and enrichen in the decades ahead. Future scenarios include more global surface, aerial and subsurface autonomous robotic science exploration on-and-near the Moon, Mars, Venus, outer planet moons, and small bodies. Analogously, lower orbit affixed spacecraft servicing will be elevated to higher orbit free-flying assembly, inspection and maintenance of far larger structures and instruments. Tasks will thus significantly increase in physical scale, complexity and duration, advancing ultimately to a sustained and networked robotic presence in space. Some such scenarios will require explicit human and robot cooperation at the worksite from the outset: others may utilize autonomous robots or robot teams as precursors to eventual in situ human-robotic exploration and operations. With this enrichment of space robotics come many technological and operational challenges that span topics from long range autonomous robotic navigation & localization, to highly cooperative mobile-manipulative interactions of heterogeneous robotic systems, to dexterous in-space robotic operations with minimal force restraint and maximal disturbance rejection, time- and-space-scaled telerobotic control, and more. We will outline some future mission concepts and requirements, their operational and technological implications, a few aspects of our recent related research, and illustrative open problems that accompany such new space robotics applications.
Speaker Biography: Dr. Paul S. Schenker is Manager, Mobility & Robotics Systems Section, Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena. As such, he is the line individual responsible for JPL R&D at large in planetary robotics and related terrestrial technology applications. His personal research includes topics in robotic perception, robot control architectures, telerobotics and teleoperation, multi-sensor fusion, and most recently, multi-robot cooperation, areas to which he has contributed about 140 peer review publications as well as a number of recent keynote and plenary technical conference presentations. He has led the development of robotic systems that include the Field Integrated Design & Operations Rover (FIDO), Planetary Dexterous Manipulator (MarsArm, microArm), Robot Assisted Microsurgery System (RAMS), Robotic Work Crew (RWC), and All Terrain Explorer (ATE/Cliff-bot), with resulting technology contributions to NASA missions including the currently operative Mars Exploration Rovers (MER). Dr. Schenker is active in the AAAI, IEEE, OSA, and SPIE. He has served as an elected Board member and 1999 President of the last; he currently serves as an elected member of the National Academy of Sciences/United States Advisory Committee to the International Commission for Optics.
Special Center for Fluid Mechanics Seminar
Please Note Change in Day and Time for this Seminar Only |
Abstract: It's morning. You pour cereal in your bowl, shake the orange juice, fill your glass, and pour milk over your cereal. Why did you shake the orange juice and not the milk? Why do you pour cereal? These are just some everyday examples of complex fluids -- materials that often behave like water or air, but just as often display quite different behavior. Many complex fluids are in the form of particles dispersed in a host liquid or gas, and it is the particle-level interactions that give rise to interesting macroscopic phenomena, such as shear thinning and thickening, viscoelasticity and structure formation. This talk will discuss the micromechanics of particulate dispersions and how the interplay of colloidal, Brownian and hydrodynamic forces set the material's microstructure and determine its macroscopic properties. So why did you shake the orange juice and not the milk?
Comments: PLEASE NOTE CHANGE IN DAY AND TIME FOR THIS SEMINAR ONLY
Special Joint Department of Mathematics Colloquium/PDE Seminar
Abstract: A problem formulated by I.M. Gelfand in the 1950s is to reconstruct the metric tensor of a compact Riemannian manifold with boundary, from data on the spectrum of its Laplace operator, with the Neumann boundary condition, and the behavior at the boundary of the normalized eigenfunctions.
The first ingredient that goes into the resolution of such an ``inverse problem'' is a uniqueness theorem, but further work beyond establishing uniqueness is required. This arises because of the ``ill posedness'' associated with inverse problems. That is, various ``large'' perturbations of the unknown region can yield small perturbations of the observed data. The key to stabilizing an ill-posed inverse problem is to have appropriate a priori knowledge of the unknown domain so that a search for the solution can be confined to a ``compact'' family of possible domains. In this context, the suitable notion is that of Gromov compactness, and one key to stabilizing Gelfand's inverse problem involves establishing such compactness. This is done under fairly weak hypotheses on the geometry of the unknown domain, including bounds on its curvature (to be precise, its Ricci tensor) and on the curvature of its boundary. Estimates for solutions to a naturally occuring elliptic boundary value problem for the metric tensor play a central role.
The speaker will discuss some of these matters, which have been treated in joint work with M. Anderson, A. Katsuda, Y. Kurylev, and M. Lassas.
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