Lefschetz Center for Dynamical Systems Seminar
Abstract: One of the classical linear instabilities is that of two fluids of different densities, accelarated towards each other, which is called Rayleigh-Taylor instability. It will be shown in the talk that smooth steady states are indeed nonlinearly unstable in a dynamical setting.
Brown University Center for Statistical Sciences Seminar
Abstract: Many statistical analyses involving multilevel data are non-trivial because of uncontrollable missing data. When missing data exist only for the response variable, standard procedures (e.g. as implemented in HLM or PROC MIXED) can be employed as they allow for imbalance or missing data. These procedures, however, do not accommodate truly multivariate responses and missing covariates, and operate under standard error assumptions of hierarchical linear models. In this paper, we develop a variety of algorithms for creating multiple imputations of missing covariates and responses in multilevel data applications. Our imputation procedures rely on multivariate extensions of the hierarchical linear models. The models used for the purpose of creating multiple imputations are flexible enough to accommodate variety of applications, e.g. multivariate clustered, longitudinal, or longitudinal clustered data. Imputation techniques are based on Markov Chain Monte Carlo simulation techniques. These techniques are illustrated with two applications: growth curve modeling of adolescent alcohol use in a large school-based prevention trial and Seattle crime victimization survey.
Special Lefschetz Center for Dynamical Systems Seminar
Abstract: Transport barriers have been identified in the atmosphere from the existence of sharp discontinuities in chemical composition and potential vorticity separating different regions. One prominent example is the barrier which isolates the polar vortex in the winter stratosphere and plays a significant role in the generation of the ozone hole. It is generally believed that this barrier is a dynamical effect of the layerwise motion of the flow and it is often defined as a potential vorticity contour maximizing the meridional gradient. A consistent characterization from the point of view of dynamical systems is, however, still missing.
In this talk, I will show how hyperbolic lines maximizing the stretching around the Antarctic polar vortex are diagnosed using a method based on finite-size Lyapunov exponents. For the first time with atmospheric data, the exchange mechanism associated with lobe dynamics is identified. The tangling hyperbolic lines suggest a stochastic layer around the vortex. The fluid is expelled from this layer toward the surf zone (mid-latitude region stirred by Rossby waves) but is also injected inward from the surf zone, through a process similar to the turnstile mechanism in lobe dynamics. The vortex edge, defined as the location of the maximum gradient in potential vorticity or tracer, is found to be the southward (poleward) envelope of this stochastic layer. Exchanges with the inside of the vortex are therefore largely decoupled from those, possibly intense exchanges, between the stochastic layer and the surf zone. I will also show applications of a series of diagnostics based on recent rigorous mathematical results obtained by G. Haller which provide necessary or sufficient conditions for the existence of hyperbolic lines over finite-time intervals.
Special Scientific Computing Seminar
Abstract: The Boltzmann-Poisson System is the most reliable model for the flow of charged particles in semiconductors. Due to its high computational cost a deterministic computation of its solution has not been done until recently in 1-D. REal devices in 2-D has not already been simulated by deterministic computations, although it is very well known and general practice for electrical engineers to solve it by DSMC methods. In this talk we focus in a rather easy and fast solver in 1-D for this fourth dimensional time evolution problem. This system reduces to a linear conservation law solved by WENO methods coupled with the Poisson equation for the force field acting on the particles. We will focus on the derivation of the method, simulation results for diodes and comparisons to other classical models in the field. Difficulties to go to 2-D will be discussed. This work has been done in collaboration with I.M. Gamba, A. Majorana and C.-W. Shu
Scientific Computing Seminar
Abstract: We present recent developments in modeling and simulation of small scale flows. Our research thrust has been focused in two main directions: Simulation-methods development and physical modeling. Due to the failure of the continuum description at small scales, the main simulation tool used in this work is a molecular method known as the direct simulation Monte Carlo (DSMC).
On the simulation front, we have shown that DSMC is second order accurate in time. We have also derived explicit expressions for the relative noise to signal ratio in particle algorithms and are currently developing hybrid DSMC-continuum methods.
On the modeling front, we have investigated convective heat transfer in small scale channels and shown the Nusselt number (a non-dimensional measure of the heat transfer) to monotonically decrease with increasing rarefaction. We have also investigated wave propagation in "narrow" channels and derived expressions for the wavelength and attenuation coefficient.
PDE Seminar
<--- 2001 Index