Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
Abstract: The talk deals with consistent inference using repeated observations on N individuals. When the model involves individual specific parameters -- fixed effects -- maximum likelihood estimators of common parameters are typically inconsistent as N to infinity. This is `the incidental parameters problem' of Neyman and Scott (Econometrica 1948). A strategy to obtain consistent estimators of the common parameters is to reparametrize so that the fixed effects are orthogonal to the common parameters. I shall show that maximizing the marginal posterior density after integrating out the orthogonalized fixed effects yields consistent estimators for a class of dynamic regression models and a class of panel `survival' models. The method is related to use of the modified profile likelihood as discussed by Cox and Reid (JRSS (B) 1987.)
Center for Fluid Mechanics Seminar
Abstract: The first objective of this research was to study the time-evolving velocity field in a two-stream, turbulent, planar free shear layer using a cinematic particle image velocimetry technique. Experimental data obtained by this technique yielded a combined spatial and temporal evolution of the two-dimensional velocity and spanwise vorticity fields. The detailed velocity field structure of the fully-developed shear layer was significantly different from previous lower Reynolds number results in that the classical well-defined eddies and braids were replaced with complex three-dimensional agglomerated vortices of both signs. Additionally, various Lagrangian tracking correlation methods were used to estimate eddy lifetime. When based on vorticity, this time scale significantly increased as expected when the tracking was computed with a second-order Lagrangian tracking technique as compared to a (zeroth-order) Taylor hypothesis approach. However when based on streamwise velocity fluctuations, this time scale did not increase significantly for the higher-order projection methods. The latter result is attributed to occurrences of "reverse correlation" of the instantaneous streamwise velocity fluctuations caused by eddy rotation.
The second objective of this research was to gain fundamental knowledge of the drag and lift forces on ellipsoidal air bubbles in tap water in the above turbulent flow. The cinematic PIV allowed for high resolution of the unsteady liquid velocity vector field, in conjunction with measurements of bubble size, velocity, acceleration. A bubble dynamic equation was then applied to allow determination of the time-evolving drag and lift forces acting upon bubbles within the shear layer. The results indicate that for a fixed bubble diameter (and fixed Bond and Morton numbers), the drag coefficient decreases for increasing Reynolds number (opposite of the conventional trend for bubbles rising in quiescent baths of increasing diameter). In addition, the side (lift) forces measured in this study were dominated by the inherent deformation-induced vortex-shedding of the bubble wake rather than the conventional inviscid lift force based on the background fluid vorticity.
Brown Analysis Seminar
LEMS and Electrical Science Seminar
Abstract: This talk presents a method that uses the level sets of volumes to reconstruct the shapes of 3D objects from range data. The strategy is to formulate 3D reconstruction as a statistical problem: find that surface which is mostly likely, given the data and some prior knowlege about the application domain. The resulting optimization problem is solved by an incremental process of deformation. We represent a deformable surface as the level set of a discretely sampled scalar function of 3 dimensions, i.e. a volume. Such level-set models have been shown to mimic conventional deformable surface models by encoding surface movements as changes in the greyscale values of the volume. The result is a voxel-based modeling technology that offers several advantages over conventional parametric models, including flexible topology, no need for reparameterization, concise descriptions of differential structure, and a natural scale space for hierarchical representations. This work builds on previous work in both 3D reconstruction and level-set modeling. It presents a fundamental result in surface estimation from range data: an analytical characterization of the surface that maximizes the posterior probability. It also presents a novel computational technique for level-set modeling, called the sparse-field algorithm, which combines the advantages of a level-set approach with the computational efficiency and accuracy of a parametric representation. The sparse-field algorithm is more efficient than other approaches, and because it assigns the level set to a specific set of grid points, it positions the level-set model more accurately than the grid itself. These properties, computational efficiency and sub-cell accuracy, are essential when trying to reconstruct the shapes of 3D objects. Results are shown for the reconstruction objects from sets of noisy and overlapping range maps.
PDE Seminar
Department of Mathematics Colloquium
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