Neumann nodal domains

As an alternative to nodal domains in the usual sense, we propose a partition of the domain of a real-valued eigenfunction in ℝ2 by trajectories of the gradient, linking saddle points to extrema. Its most elementary properties are listed and exemplified. The main point is that the problem of avoided...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2014-01, Vol.372 (2007), p.1-6
Main Authors: McDonald, Ross B., Fulling, Stephen A.
Format: Article
Language:English
Subjects:
Boundary conditions
Critical points
Eigenfunctions
Eigenvalues
Extrema
Laplacians
Mathematical functions
Property partitioning
Saddle points
Trajectories
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Summary:As an alternative to nodal domains in the usual sense, we propose a partition of the domain of a real-valued eigenfunction in ℝ2 by trajectories of the gradient, linking saddle points to extrema. Its most elementary properties are listed and exemplified. The main point is that the problem of avoided crossings is largely eliminated.
ISSN:1364-503X