'Can one hear the shape of a drum?'

Revisited

Y. Okada, A. Shudo, S. Tasaki, Takahisa Harayama

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

A famous inverse problem posed by M Kac 'Can one hear the shape of a drum?' is concerned with isospectrality of drums or planer billiards, and the first counter example was constructed by Gordon, Webb and Wolpert (1992 Invent. Math. 110 1). Here we present pieces of numerical evidence showing that 'One can distinguish isospectral drums by measuring the scattering poles of exterior Neumann problems'. This is based on the observation that the Fredholm determinant appearing in the boundary element method admits a factorization into interior and exterior parts.

Original languageEnglish
JournalJournal of Physics A: Mathematical and General
Volume38
Issue number9
DOIs
Publication statusPublished - 2005 Mar 4
Externally publishedYes

Fingerprint

Fredholm Determinant
Exterior Problem
drums
Billiards
Neumann Problem
Boundary element method
Factorization
Inverse problems
Boundary Elements
Counterexample
Pole
Poles
Inverse Problem
Interior
Scattering
Neumann problem
boundary element method
factorization
determinants
counters

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

'Can one hear the shape of a drum?' : Revisited. / Okada, Y.; Shudo, A.; Tasaki, S.; Harayama, Takahisa.

In: Journal of Physics A: Mathematical and General, Vol. 38, No. 9, 04.03.2005.

Research output: Contribution to journalArticle

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