Division of Applied Mathematics

Seminars for Apr 22 - Apr 26, 2002

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• Monday, April 22, 2002
  
  

  Lefschetz Center for Dynamical Systems Seminar

  Speaker:	Joseph Biello, Rensselaer Polytechnic Institute
  Title:	Hamiltonian Moment Reduction for Incompressible Fluids: The Riemann Ellipsoids
  Time/Place:	3:30 p.m., B&H 161

  Abstract:   I shall begin by describing the Riemann ellipsoids, which are an exact, self-graviting solution of the incompressible Euler equations with free boundary. This problem has a rich history and I shall outline some of the main participants - from Newton to Riemann - and their contributions.

  The non-canonical (Lie-Poisson) formulation of the compressible ideal fluid equations was presented by Morrison and Greene (1980). This work shows how to extend that description to the case of incompressible fluids (with free boundary) by careful application of a Hodge-Weyl decomposition of functional variations.

  Using the Hamiltonian formulation and a moment description of incompressible flow, an exact reduction of the full partial differential equations to a 15-dimensional, non-canonical Hamiltonian system is afforded. This dynamical system has 3 Casimirs corresponding to circulation, volume and divergence of the velocity field, respectively. I shall discuss the bracket structure of the non-canonical symplectic structure and its consequences for equilibria and dynamics.

  In conclusion, I will show how the Dirac bracket formulation - essentially a projection approach for symplectic structures - yields the same non-canonical structure. This is the first example I have seen of the Dirac Bracket formalism used to generate additional Casimirs of a non-canonical symplectic structure resulting in an exact, finite dimensional reduction of an infinite dimensional problem.

• Wednesday, April 24, 2002
  
  

  Brown Analysis Seminar

  Speaker:	Jill Pipher, Brown University
  Title:	To Be Announced
  Time/Place:	4:00 p.m., Kassar 105

• Thursday, April 25, 2002
  
  

  Brown University Graduate School Dissertation Defense

  Speaker:	Jamison T. Moeser, Brown University Division of Applied Mathematics
  Title:	Stable Pulse Propagation in Optical Fibers with Varying Dispersion
  Time/Place:	2:30 p.m./182 George Street, Room 110

• Friday, April 26, 2002
  
  

  Scientific Computing Seminar

  Speaker:	Z. J. Wang, Michigan State University
  Title:	A New High-Order Finite Volume Method for Conservation Laws on Unstructured Grids
  Time/Place:	11:00 a.m., 182 George Street, Room 110

  Abstract:   A high-order finite volume method - the spectral volume (SV) method - will be presented for conservation laws on unstructured grids. We will show why the SV method is much more efficient than the k-exact and WENO methods on unstructured grids. The SV method shares some advantages with the discontinuous Galerkin method, such as compactness and geometric flexibility. However, the SV method seems to allow larger time steps, higher resolution for discontinuities and avoidance of volume integrals. Numerical examples for scalar conservation laws and the Euler equations will be presented.

  Brown University Graduate School Dissertation Defense

  Speaker:	Brian Lucena, Brown University Division of Applied Mathematics
  Title:	Dynamic Programming, Tree-Width and Computation on Graphic Models
  Time/Place:	1:00 p.m., 182 George Street, Room 110

  PDE Seminar

  Speaker:	Charles Doering, University of Michigan
  Title:	Bounds on Turbulent Transport
  Time/Place:	3:00 p.m., Kassar 105

  Department of Mathematics Colloquium

  Speaker:	Bob Zimmer, University of Chicago
  Title:	Group Actions and Geometric Structures
  Time/Place:	4:30 p.m., Kassar 105

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