Journal ArticleDOI
Drums That Sound the Same
Reads0
Chats0
TLDR
In this paper, the authors discuss the drums that sound the same and propose the Drums That Sound the Same (DST) method. The American Mathematical Monthly: Vol. 102, No. 2, pp. 124-138.Abstract:
(1995). Drums That Sound the Same. The American Mathematical Monthly: Vol. 102, No. 2, pp. 124-138.read more
Citations
More filters
Journal ArticleDOI
Time-dependent diffusion coefficient as a probe of geometry
TL;DR: In this paper, the authors describe how the time-dependent diffusion coefficient D(t) of mobile molecules confined in pore or cells carries information about the confining geometry, and the geometrical parameter “tortuosity” α plays an important role in various transport processes in porous media, such as the electrical conductivity.
Journal ArticleDOI
Acoustic echoes reveal room shape
TL;DR: This work shows how to compute the shape of a convex polyhedral room from its response to a known sound, recorded by a few microphones, and reconstructs the full 3D geometry of the room from a single sound emission, and with an arbitrary geometry ofThe microphone array.
Journal ArticleDOI
Geometrical structure of Laplacian eigenfunctions
TL;DR: The main focus is put onto multiple intricate relations between the shape of a domain and the geometrical structure of eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition.
Journal ArticleDOI
Can one hear the shape of a graph
Boris Gutkin,Uzy Smilansky +1 more
TL;DR: In this article, the spectrum of the Schroperator on a finite, metric graph was shown to determine uniquely the connectivity matrix and the bond lengths, provided that the lengths are not commensurate and the connectivity is simple (no parallel bonds between vertices and no loops connecting a vertex to itself).
Journal ArticleDOI
Eigenmodes of Isospectral Drums
TL;DR: An algorithm due to Descloux and Tolley is described that blends singular finite elements with domain decomposition and it is shown that, with a modification that doubles its accuracy, this algorithm can be used to compute efficiently the eigenvalues for polygonal regions.
References
More filters
Journal ArticleDOI
Can One Hear the Shape of a Drum
TL;DR: Can one hear the shape of a drum? as discussed by the authors, 1966; The American Mathematical Monthly: Vol. 73, No. 4P2, pp. 1-23.
Journal ArticleDOI
One cannot hear the shape of a drum
TL;DR: In this paper, Sunada's theorem was used to construct a pair of isospectral simply connected domains in the Euclidean plane, thus answering negatively Kac's question, can one hear the shape of a drum?
Journal ArticleDOI
Isospectral plane domains and surfaces via Riemannian orbifolds.
Journal ArticleDOI
Transplantation et isospectralité. I
TL;DR: In this paper, the Séminaire de Théorie spectrale et géométrie implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
Journal ArticleDOI
Some planar isospectral domains
TL;DR: In this paper, the authors give a number of examples of two noncongruent isospectral domains in the plane and a particularly simple method of proof that they sound the same.