Division of Applied Mathematics

Seminars for Sep 4 - Sep 8, 2000

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• Tuesday, September 5, 2000
  
  

  Stochastic Systems Seminar

  Speaker:	Harold J. Kushner, Brown University, Division of Applied Mathematics
  Title:	Analysis and Control of Mobile Communications with Time Varying Channels: A Heavy Traffic Approach
  Time/Place:	4:00 p.m., 182 George Street, Room 110 **PLEASE NOTE CHANGE OF ROOM FOR THIS WEEK ONLY **

• Friday, September 8, 2000
  
  

  Scientific Computing Seminar

  Speaker:	Mitchell Luskin, University of Minnesota, School of Mathematics
  Title:	A Sharp Interface Model for Martensitic Single Crystal Thin Films
  Time/Place:	11:00 a.m., 182 George Street, Room 110

  Abstract:   Martinsitic thin films are being used as the active element in actuators, sensors, and micromachines. Single-crystal martinsitic thin films have recently been grown in the laboratory by Palmstrom and theoretically offer even larger displacements during the solid-solid phase transformation.

  Bhattacharya and James have derived a thin film variational principle from the three-dimensional elastic energy for martinsitic crystals with the surface energy density modeled by the square of the strain gradient. We give a derivation of an alternative thin film variational principle in which the interfacial energy is modeled by the total variation of the strain gradient. Deformations of finite energy can have sharp interfaces with our model,and simpler finate element approximations can be used for the deformation.

  We will present numerical methods and computational results for the simulation of the deformation of a martensitic single crystal thin film during thermally activated and stress induced phase changes.

  Joint work with Pavel Belik.

  Joint Seminar, Division of Engineering and The Center for Fluid Mechanics

  Speaker:	Masaharu Matsubara, Department of Mechanical Systems Engineering, Shinshu University, Japan
  Title:	Streaky Structure in Natural Transition
  Time/Place:	3:00 p.m., 37 Manning Street, Room 104

  Abstract:   Investigation of a new transition process has been done in a boundary layer subjected to high levels of free stream turbulence in the range of 1 to 6%. In a series of experiments in a wind tunnel and a water channel it was shown that the boundary layer develops unsteady streaky structures with high and low streamwise velocity. This leads to large amplitude low frequency fluctuations inside the boundary layer although the mean flow is still close to the laminar profile. Visualization using the hydrogen bubble method directly shows the lift-up mechanism that causes low and high velocity streaks in a boundary layer. Breakdown to turbulence occurs through an instability of the streaks which leads to the formation of turbulent spots. The new transition scenario can also be explained by a recent theory of non-modal growth and the experimental results will compared with the theory.

  Department of Mathematics Colloquium

  Speaker:	Richard Hamilton, Columbia University and U.C. San Diego
  Title:	Positive Solutions on The One-Dimensional Burgers Equation $ u_{t} + uu_{x} = u_{xx} $
  Time/Place:	4:30 p.m., Kassar 105 *** LATE NOTICE ***

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