Numerical Analysis of Nodal Sets for Eigenvalues of Aharonov–Bohm Hamiltonians on the Square with Application to Minimal Partitions

DOI10.1080/10586458.2011.565240zbMath1270.35025OpenAlexW2078788770MaRDI QIDQ4915394

Bernard Helffer, Virginie Bonnaillie-Noël

Publication date: 10 April 2013

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1317924423

zbMATH Keywords

numerical simulationsnodal domainsAharonov-Bohm Hamiltonian

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Estimates of eigenvalues in context of PDEs (35P15) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items

Spectral flow for pair compatible equipartitions ⋮ Multiple Aharonov–Bohm eigenvalues: The case of the first eigenvalue on the disk ⋮ A minimal surface criterion for graph partitioning ⋮ Sharp boundary behavior of eigenvalues for Aharonov-Bohm operators with varying poles ⋮ On a magnetic characterization of spectral minimal partitions ⋮ Spectral minimal partitions of a sector ⋮ Introduction to some conjectures for spectral minimal partitions ⋮ On the Aharonov-Bohm operators with varying poles: the boundary behavior of eigenvalues ⋮ On multiple eigenvalues for Aharonov-Bohm operators in planar domains ⋮ On Aharonov-Bohm operators with two colliding poles ⋮ On spectral minimal partitions: a survey ⋮ Sharp asymptotic estimates for eigenvalues of Aharonov-Bohm operators with varying poles ⋮ On the Leading Term of the Eigenvalue Variation for Aharonov--Bohm Operators with a Moving Pole ⋮ Eigenvalues variations for Aharonov-Bohm operators

Uses Software

• Triangle

Cites Work

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• A variational problem for the spatial segregation of reaction-diffusion systems