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Neumann nodal domains

Published:2014-01-28 Issue:2007 Volume:372 Page:20120505
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

McDonald Ross B.¹,Fulling Stephen A.¹²

Affiliation:

1. Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-3368, USA

2. Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA

Abstract

As an alternative to nodal domains in the usual sense, we propose a partition of the domain of a real-valued eigenfunction in

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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2012.0505

Reference7 articles.

1. McDonald RB. 2008 Neumann bounded partitions of eigenfunctions. Research Scholar thesis Texas A&M University. See http://repository.tamu.edu/handle/1969.1/85733.

2. Asymptotic equipartition of energy by nodal points of an eigenfunction

3. Generic Properties of Eigenfunctions

4. Avoided intersections of nodal lines

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