Academic Communication

Piecewise smooth solutions to the Burgers-Hilbert equation 2015-06-29

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Presenter: Prof. Weizhu Bao (Department of Mathematics, National University of Singapore) 
Time: At 3:00 p.m. on July 2, 2015
Location:Room 517, Teaching Building, 56 West Third Ring Road North, Haidian District, Beijing.
Organizer: College of Marxism Education
Introduction:Quantized vortices have been experimentally observed in type-II superconductors,superfluids, nonlinear optics, etc. In this talk, I will review different mathematical equations for modeling quantized vortices in superfluidity and superconductivity, including the nonlinear Schrodinger/Gross-Pitaevskii equation, Ginzburg-Landau equation,nonlinear wave equation, etc. Asymptotic approximations on single quantized vortex state and the reduced dynamic laws for quantized vortex interaction are reviewed and solved analytically in several cases. Efficient and accurate numerical methods will be presented for computing quantized vortex lattices and ther dynamics. Direct numerical simulation results from different PDE models are reported for quantized vortex dynamics and they are compared with those from the reduced dynamics laws. Some open problems and emerging applications will be discussed.