Nonlinear Waves Seminar
Lefschetz Center for Dynamical Systems Seminar
Abstract: Constrained or projected ODE appear in problems from queueing theory, communication, manufacturing, economics, and elsewhere. Natural constraints in the state space of the model (e.g., non-negativity constraints in queueing problems) lead to ODEs with discontinuous right hand sides and a state space that is a convex polytope. These ODE cannot be analyzed either by standard methods or the theory developed by Fillipov for ODEs with discontinuities. In this talk we will show how such equations arise by using one or two simple examples, show how basic qualitative results can be proved using a device called the Skorokhod Problem, and discuss stability theory for the simplest class of such equations. If time permits a few remarks will be made on connections with Neumann boundary conditions for PDE and variational inequalities.
Brown University Center for Statistical Sciences Seminar
Sponsored by: The Bruce M. Bigelow Class of 1955 Lecture Series, The Charles K. Colver Lectureships and Publication Fund and the Department of Diagnostic Imaging at Brown University and Rhode Island Hospital/Lifespan |
Abstract: Elicitation of expert opinion to help determine the value of medical care is becoming more common as consumers and purchasers of health care demand to know what they are getting for the money they spend on health care. For example, medical practice guidelines are increasingly utilized to understand variations in the delivery of many medical and surgical procedures. The most common approach to developing guidelines is to elicit judgements from a multi-disciplinary panel of experts regarding treatment efficacy within distinct clinical strata. In this talk, I will discuss an application of utilization of such judgements in order to measure the effectiveness of acute treatment of major depressive disorder in large insured populations in the United States. The elicitation of the judgements amount to specifying priors for effectiveness parameters in a hierarchical model.
This is joint work with Richard G. Frank, Tom G. McGuire, Howard H. Goldman, Marcela Horvitz-Lenon, Susan Busch, and Anupa Bir supported by Grant 97-49667A-HE from the John D. & Catherine T. MacArthur Foundation.
Center for Fluid Mechanics Seminar
Abstract: The motion of contact lines (the locus of intersection of a two-fluid interface with a bounding solid) has, due to the multitude of length scales involved, been one of the few problems that have defied conclusive theoretical analysis over the years. It has long been concluded that continuum hydrodynamics is not adequate for the description of the physics involved in the vicinity of the contact angle, which is predominantly molecular kinetic. Continuum numerical simulation techniques have enjoyed limited success because of the ad hoc assumptions (in the form of boundary conditions close to the contact line) required to achieve agreement with experimental data.
We present a new hybrid simulation technique that allows the use of molecular dynamics to provide the correct physics in the vicinity of the contact line. The molecular dynamics solution is matched to a continuum ``far field'' solution using the well known Schwarz Alternating method - a domain decomposition technique. A finite element simulation technique providing the continuum ``far field'' solution has also been developed and is presented here.
The new hybrid technique is quite general: it can be used in other situations where molecular information is required or is of interest. By limiting the molecular treatment to the regions where it is needed, this hybrid method allows the simulation of complex fluid mechanical phenomena which require modelling on the microscale without the associated astronomical cost of a fully molecular solution.
Brown University Graduate School Dissertation Defense
Stochastic Control Seminar
Brown Analysis Seminar
Brown University Graduate School Dissertation Defense
Department of Mathematics Colloquium
Scientific Computing Seminar
Abstract: The seminar presents a method for computational aeroacoustics, primarily aimed at computing sound propagation in, and radiation from, turbofan inlets. The physics of sound propagation is modeled by the system of partial differential equations that describe conservation of mass, momentum and energy in inviscid flows. The equations are solved numerically in the time domain as an initial and boundary value problem to obtain the time-dependent acoustic pressure in the flow field, from which sound pressure levels are obtained by integration.
A multidomain spectral method is used to discretize the space terms. Complex geometries are handled by the use of unstructured grids of non-overlapping hexahedra that may have curved boundaries. An isoparametric mapping is used to transform each hexahedron on the master element, on which an efficient collocation spectral approximation can be defined by the use of tensor products. Continuity of the solution in space is enforced as part of the solution process by the use of a set of staggered grids that do not involve the element corners.
A set of Runge-Kutta methods optimized for wave propagation and with minimal storage requirements are developed for integration in time. Several radiation boundary conditions are implemented and tested, and possible ways to construct the spectral grids within the elements are discussed. Numerical results that validate the methodology are presented for several test cases representative of the fan noise problem. An account is given of a simple modification that allows computation of noise superposed on a mean flow known from other sources, such as experiments, and its application to turbulent mixing noise from a supersonic jet.
Brown University Graduate School Dissertation Defense
PDE Seminar
Abstract: There is widespread interest, and major experimental programs underway, for the design and construction of electromechanical "machines" at nanometer to millimeter scale. This work is proceeding largely without guidance from mathematical theory. The building blocks for such machines currently are thin films, nanotubes and nanorods, objects with at least one nanoscale or microscale dimension but also one or more relatively large dimensions.
Using a macroscale--to--microscale approach, we describe a direct derivation of a theory of single crystal thin films, starting from three dimensional nonlinear elasticity including a term for interfacial energy. The derivation relies on $\Gamma$--convergence arguments, and yields a frame--indifferent Cosserat membrane theory. We highlight some predictions that are specifically linked to size and have no bulk analogs. We construct simple energy minimizing deformations --- tents and tunnels --- which could be the basis of simple microactuators or micropumps.
Alternatively, beginning at the atomic level, we face the presence of at least one large dimension, which frustrates purely atomic scale approaches, but which provides a glimmering opportunity for analysis. We present a scheme for the direct passage from atomic to continuum scale, applicable to cases in which one or two dimensions remain at atomic scale. The scheme is based on 1) limited distortion of unit cells 2) many atoms in certain directions. It gives rise to weak convergence problems. The continuum theories that emerge are completely nonstandard.
Joint work with Kaushik Bhattracharya and Gero Friesecke.
<--- 1999 Index