Symmetry, Nonlinear Bifurcation Analysis, and Parallel Computation

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In the natural and engineering sciences the equations which model physical systems with symmetry often exhibit an invariance with respect to a particular group "G" of linear transformations. "G" is typically a linear representation of a symmetry group "g" which characterizes the symmetry of the physical system. In this work, we will discuss the natural parallelism which arises while seeking families of solutions to a specific class of nonlinear vector equations which display a special type of group invariance, referred to as equivariance. The inherent parallelism stems for a global de-coupling, due to symmetry, of the full nonlinear equations which effectively splits the original problem into a set of smaller problems. Numerical results from asymmetry-adapted numerical procedure, (MMcontcm.m), written in MultiMATLAB are discussed.

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1996-10
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Cornell University
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theory center
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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.tc/96-264
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technical report
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