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Reduction and Reconstruction for Self-Similar Dynamical Systems Clancy Rowley, Department of Mechanical and Aerospace Engineering, Princeton University Wednesday, January 8, 20032:00 PM to 3:00 PM Steele 125 We present a general method for analyzing and numerically solving partial differential equations with self-similar solutions. The method employs ideas from symmetry reduction in geometric mechanics, and involves separating the dynamics on the shape space (which determines the overall shape of the solution) from those on the group space (which determines the size and scale of the solution). The method is computationally tractable as well, allowing one to compute self-similar solutions by evolving a dynamical system to a steady state, in a scaled reference frame where the self similarity has been factored out. More generally, bifurcation techniques can be used to find self-similar solutions, and determine their behavior as parameters in the equations are varied. |
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