Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
School of Public Health, University of Minnesota | |
*Sponsored by The Charles K. Colver Lectureships Fund |
Abstract: A spatial cumulative distribution function (SCDF) gives the proportion of a spatial domain $D$ having the value of some response variable less than a particular level $w$. In this paper we provide a fully hierarchical approach to SCDF modeling, using a Bayesian framework implemented via Markov chain Monte Carlo (MCMC) methods. The approach generalizes the SCDF to accommodate block-level variables, possibly utilizing a spatial change of support model within an MCMC algorithm. We then extend our approach to allow covariate weighting of the SCDF estimate. Such an extension is particularly natural in assessments of environmental justice, where it is important to determine if a particular natural in assessments of environmental justice, where it is important to determine if a particular sociodemographic group is being excessively exposed to harmful levels of certain pollutants. We then further generalize the framework to the bivariate random process setting, which allows simultaneous modeling of both the responses and the weights. Once again MCMC methods (combined with a convenient Kronecker structure) enable straightforward estimates of weighted, bivariate, and conditional SCDFs. We illustrate our methods with two air pollution data sets, one concerning ozone exposure and race in Atlanta, GA, and the other recording both NO and NO$_{2}$ ambient levels at 67 monitoring sites in central and southern California.
NOTE: This work is joint with Ms. Margaret Short of the Division of Biostatistics, University of Minnesota, and Dr. Alan E. Gelfand of the Institute of Statistics and Decision Sciences, Duke University.
Brown University
Joint Materials/Solid Mechanics Seminar Series
Abstract: The phase-field approach is applied to the plating of a metal from an electrolyte. A free energy functional that includes chemical, electrostatic and gradient energies is used to derive governing equations for the phase field, electrostatic potential and the concentrations. The system of derived PDEs is solved in I-D for stationary (equilibrium) and moving interfaces. The solution for the equilibrium interface, properly predicts the charge separation associated with the double layer at the electrochemical interface and its extent in the electrolyte as a function of electrolyte concentration, as well as the surface energy vs. reference potential ("electrocapillary") curves. The dynamic solutions show the development of the resistance (ohmic), diffusion and activation overpotentials. The model is being developed for future application to non-planar plating geometries used in the microelectronic industry.
Brown University Mathematics Department Geometry Seminar
Abstract: We look at some properties of the equation $\Delta u = 1/u$ and search for singular solutions, which are nonnegative and achieve the value zero on a domain in space.
Scientific Computing Seminar
Abstract: In this talk, a procedure for the placement and scheduling of actuators in distributed parameter systems is proposed. In addition to the already established measures of actuator selection based on enhanced controllability and performance improvement employed in the last 30+ years, a method that also considers the spatial effects of disturbances is introduced. The ultimate goal is to ensure that actuators, whether mobile or stationary, are placed in locations that provide a certain robustness with respect to the "worst" spatial distribution of distrubances. Even further, a way to address the spatiotemporal variations of disturbances on the closed loop performance, is to schedule the actuators by employing the actuator (or actuator groups) that are located spatially "closer" to local-in-space disturbances. An overview of the various approaches and measures for the placement of actuators will be summarized and a two different measures for actuator scheduling will be presented. Variants of the above scenarios, are the case of a single actuating device capable of moving within the spatial domain and of multiple actuating devices that exhibit linear dynamics for certain time duration before reverting to a nonlinear mapping or becoming incapacitated. The former duplicates the case of multiple available actuators with only one being active over a certain time interval and with the remaining ones kept dormant, while the latter scenario attempts to employ the actuators while in their linear regime and then switch to healthy ones. Both numerical and experimental results for a thermal processing of materials problem and of vibration suppression in flexible structures will be presented. Chris Hallstro
PDE Seminar
Department of Mathematics Colloquium
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