Nonlinear Waves Seminar
Special LCDS/PDE Seminar
Brown Analysis Seminar
Special Stochastic Systems Seminar
CINVESTAV - IPN, Mexico
We prove the large deviations principle for a certain class of
random walks, where the evolution
of the noise process depends on the state of the random walk. This type of model has important applications
in queueing and communication theory, and in the area of stochastic approximation.
Scientific Computing Seminar
A particle method is presented for computing vortex sheet motion
in three-dimensional flow.
The particles representing the sheet are advected using the Rosenhead-Moore form of regularized
Biot-Savart kernel and new particles are inserted during the simulation to maintain resolution as the
sheet rolls up. The particle velocities are computed using a treecode based on Taylor approximation in
Cartesian coordinates. The necessary coefficients are computed using a recurrence relation and several
adaptive techniques are employed to gain efficiency including nonuniform rectangular cells, variable order approximation, and a run-time choice between approximation and direct summation. Tests show that the
treecode is significantly faster than direct summation for systems having a large number of particles. The
algorithm is applied to simulate flows in which a vortex sheet rolls up to form a vortex ring. Two examples
are presented: (1) azimuthal waves on a vortex ring, and (2) merger of two vortex rings.
(This is a joint work with Keith Lindsay, NCAR.)
Department of Mathematics Colloquium
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