Brown University Joint Seminar, Department of Neuroscience, Division of Biology and Medicine and
Division of Applied Mathematics
Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
Joint Seminar - Lefschetz Center for Dynamical Systems and Center for Fluid Mechanics
Abstract: The accuracy of drifter paths calculated from the surface velocity field from the Princeton Ocean Model of the Gulf of Mexico is assessed with observed drifter data. The approach is to project the model results onto geometric orthogonal functions. The projection is further constrained to exactly match the observed drifter velocities. In a Eularian reference the model velocity field and the reconstructed field are quite similar. In a Lagrangian reference, however, the paths integrated from the two fields differ appreciably. This difference is quantified by two Lagrangian metrics. The Lagrangian metrics for the constrained projections are about an order of magnitude better than the unconstrained projections. Some speculations on assimilation of Lagrangian data directly into predictive models are offered.
Brown University Joint Seminar, Department of Neuroscience, Division of Biology and Medicine and
Division of Applied Mathematics
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: Ideas from differential geometry have been rather successful in analysis and control of nonlinear systems. In this talk we will present some model problems and characteristic phenomenon arising in the area of nonlinear control with applications to robotics and locomotion systems. We will then treat is some detail, the control of nuclear spins in NMR spectroscopy as a problem in geometric control.
Scientific Computing Seminar
Abstract: Fluid mixing, as with turbulence modeling, acquires its difficulty from the very large number of active length scales and degrees of freedom to be understood. A survey of recent work of the speaker, colleagues, and other workers will be presented, showing that progress has been made on some of the long standing problems in this area.
Direct numerical simulation results will be presented, as well as results from simple physical models and from formal averaging and closure models. We will present a closed form solution for a mathematically and physically consistent multiphase flow model, and we apply formal asymptotics to extend the scope of this closed form solution.
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PDE Seminar
Abstract: Nineteenth century hydrodynamics saw a long discussion before a set of partial differential equations and appropriate boundary conditions were settled upon, somewhat uneasily, as the proper mathematical description of the behavior of everyday fluids such as water and air. Though existence proofs are still lacking, a wide consensus exists that the Navier-Stokes description serves about as well as can be done. With somewhat less focus, an equally important discussion is in progress now on the subject of electrically conducting fluids in strong magnetic fields: magnetohydrodynamics, or "MHD." One central problem in MHD consists of finding, and studying the stability of, electrically-driven MHD steady states inside a toroid. Rather surprisingly, one feature of the nineteenth century hydrodynamic debate repeats itself: ideal, or "conservative," dynamics vs. the inclusion of dissipative terms such as those involving viscosity, electrical resistivity, and thermal conductivity; these render the MHD equations even more difficult but may be necessary to achieve real-world status for the solutions obtained [1]. The subject could use the scrutiny of mathematicians whose attention to fine points in the analysis will go beyond those of the physicists and astronomers who have developed the subject up to now. One purpose of this talk is to invite such mathematical participation.
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