Lefschetz Center for Dynamical Systems Seminar
Abstract: Inertial manifolds are a modern tool in the qualitative theory of partial differential equations. They contain the global attractor and allow for a reduction to a finite-dimensional system. In this talk we give an introduction and present a geometric approach to inertial manifolds for nonautonomous dynamical systems. We present a new application to time-dependent evolution equations.
Brown University Center for Statistical Sciences Seminar
Division of Cancer Epidemiology and Genetics, National Cancer Institute | |
1st Floor Conference Room |
Abstract: Family studies is identify disease-related genes frequently collect only families with multiple cases. It is often desirable to determine if risk factors that are known to influence disease risk in the general population also play a role in the study families. If so, these factors should be incorporated into the genetic analysis to control for confounding. We propose a two level mixed-effects model that allows us to incorporate a genetic component accounting for the different genetic correlations among family members and to adjust for ascertainment. Conditional maximum likelihood analysis based on this model is performed. For rare diseases, a simple approximation to the model is given. We show that standard conditional logistic regression of case-control data with matching on family that conditions on the number of cases in the family, can yield biased estimates of exposure effects if genetic correlations are ignored. Conditions under which the conditional logistic approach remains applicable are given. The robustness of the proposed model with respect to various misspecifications of the genetic random effects is assessed in simulations, and the model is applied to a data from a family study on nasopharyngeal carcinoma in Taiwan.
Stochastic Systems Seminar
Department of Mathematical Science, Pittsburgh, PA 15213 | |
Abstract: Although the governing laws of evolution of real-world networks vary with time, much of the study of stochastic networks has focused on stationary models. While stationary models may serve as reasonable approximations for slowly varying systems, they fail to capture many important time-dependent phenomena such as rush hour, periodicity and sudden network failures. In this talk we introduce and characterize directional derivatives of the multi-dimensional reflection map and show how they may be used to shed insight into the behaviour of a large class of non-stationary networks. (This is joint work with Avi Mandelbaum.)
Brown University Mathematics Department Special Geometry Seminar
Brown University Mathematics Department Geometry Seminar
Brown Applied Mathematics Pattern Theory and Vision Seminar
Brown Analysis Seminar
Center for Fluid Mechanics Seminar
School of Oceanography | |
Flow Past Topography
| |
Abstract: Stratified flow past topography has applications that include the forecasting of severe downslope winds, clear air turbulence and drag induced by mountain ranges which accounts for about 50% of the resistance felt by atmospheric circulation. Topographic effects are also thought to be a significant source of mixing in the abyssal ocean. For nearly half a century Long's model, along with related numerical simulations provided the framework for interpreting these phenomena. Validation of theoretical predictions has been limited by the great difficulty of acquiring comprehensive measurements of geophysical flows at high Reynolds numbers. Direct comparison has recently become possible with the advent of new technical approaches, which are providing insights on small scale mechanisms neglected in prior studies.
Measurements of tidally forced stratified flow over a sill are used to illustrate the importance of mixing, entrainment and boundary layer separation and the influence these processes have on the time dependent response. Separation of the accelerated current at the sill crest forms a jet which inhibits development of the downslope flow. Instability and small scale mixing above the jet then create a nearly stationary layer which generates an asymmetric response and favorable pressure gradient, suppressing separation and leading to development of the high drag state. A different mechanism associated with separation from irregular lateral boundaries is also observed. Following separation the shear zone may start as a nearly vertical vortex sheet, but the presence of horizontal density gradients leads to progressive tilting and consequent vortex stretching, creating a region of convective overturning, turbulence, whirlpools and rapid air entrainment.
This is a joint Applied Mathematics/Geology/Engineering
Seminar
Scientific Computing Seminar
Abstract:
Over the past decade the rapid increase in computer power
and the advent of inexpensive parallel computers based on
off-the-shelf processors, able to handle three-dimensional
unsteady computations using multi-million point grids,
resulted in a renewed interest in the large-eddy
simulation (LES) approach, as a tool to study turbulent
and transitional flows in complex geometrical configurations.
In the present seminar computational algorithms suitable for
LES around complex dynamically moving boundaries will be
discussed. The main features of the approach are as
follows:
1. the equations governing the dynamics of the
large scales are solved on fixed Cartesian or
Cylindrical coordinate grids;
2. the interface between the fluid and a stationary
or moving solid boundary is tracked as a discontinuity
using highly accurate interface tracking methodologies
devised for solidification and multiphase flow problems;
3. the imposition of proper boundary conditions in the
vicinity of the interface is done using local multidimensional
reconstructions that are applicable to complex bodies and
do not involve special treatments;
4. issues related to the filtering operations and the
subsequent computation of the subgrid-scale (SGS) eddy
viscosity in the vicinity of immersed interfaces will
also be discussed. A variety of examples that establish
the formal accuracy and range of applicability of the
method will be given.
PDE Seminar
Department of Mathematics Colloquium
<--- 2003 Index