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About 1,474 papers for “Isospectral”

Isospectral Systems

G. M. L. Gladwell · 2016

Two vibrating systems are said to be isospectral if they have the same natural frequencies. The paper examines how families of isospectral sys-tems may be constructed. The examples which are considered include rods, beams and simple finite element models. 1.

Cited by 0

isospectral flows

M. P. Calvo, England Cb Ew, A. Iserles et al. · 1996

Orthogonal and isospectral flows occur in many applications and they possess important invariants. However, a naive application of Runge--Kutta methods is bound to render these invariants incorrectly. In this paper we describe how to retain relevant invariants with Runge--Kutta methods or, alternatively, incur an error in the rendition of the invariants which is significantly smaller than the overall numerical error.

Cited by 0

Isospectral measures

Dorin Ervin Dutkay, Palle E. T. Jørgensen · Rocky Mountain Journal of Mathematics · 2013

In recent papers a number of authors have considered Borel probability measures in R d such that the Hilbert space L 2 () has a Fourier basis (orthogonal) of complex exponentials. If satisfies this property, the set of frequencies in this set is called a spectrum for . Here we fix a spectrum, say , and we study the possibilities for measures having as spectrum.

Cited by 6Open access

Isospectral Operators

Mu-Fa Chen, Xu Zhang · Communications in Mathematics and Statistics · 2014

Cited by 13Open access

Isospectral flows

S. Watkins, David S. Watkinst · 1984

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Society for Industrial and Applied Mathematics is collaborating with JSTOR to digitize, preserve and extend

Cited by 0

Isospectral Deformations

Carlo Cercignani, D. H. Sattinger · Birkhäuser Basel eBooks · 1998

The Korteweg-de Vries (KdV) equation, $$ {u_t} + {u_{xxx}} + u{u_x} = 0 $$ (4.1.1) has smooth solutions for all positive and negative time given initial data which is sufficiently smooth, say C3. We won't go into the existence theory of the KdV equation here since the existence and uniqueness issues are ultimately resolved very simply by the method of inverse scattering, and since the algebraic/ geometric structure of this simple nonlinear equation is far more interesting.

Cited by 0

Isospectral circular membranes

H.P.W. Gottlieb · Inverse Problems · 2003

A prescription for finding the densities of circular membranes which are isospectral to a uniform circular membrane is extended to cover isospectrality to any circular membrane density, thereby also revealing the underlying grouptheoretical structure which is further elucidated. Membranes isospectral to radial-density membranes no longer possess the radial symmetry, and some examples are discussed.

Cited by 14Open access

Quasi-isospectral systems

Antonino Morassi · 2016

We show that if we start from one longitudinally vibrating rod we may construct one-parameter t-families of rods which have the same spectrum as the original rod, with the exception of a single eigenvalue which is free to move under some conditions on the parameter t. We call these rods quasi-isospectral rods. The analysis uses the results obtained in [1] and [2], and it is essentially based on a double application of a Darboux Lemma [3] after reducing the equation to normal form by the Liouville transformation. The new rods and their normal modes can be constructed explicitly by means of closed-form expressions. We also show how to use the above results to construct a rod under given end conditions with prescribed values of a finite set of eigenvalues. The reconstruction procedure needs the specification of an initial rod whose eigenvalues must be close to the assigned eigenvalues. The analysis can be adapted to construct quasi-isospectral strings and some special classes of quasi-isospectral beams in bending vibration [4].

Cited by 0

ISOSPECTRAL MULTITREES t

Milan Randić · 1988

We examined trees with onc multiple edge (of multiplicity k) and report all isospectral graphs found when the number of vertices was n ~< 9. The search I~r isospectral multitrees was carried out systematically by constructing the character- istic polynomials of all trees having one weighted edge. For all multitrees having n -<, 7 vertices, we tabulated the coefficients of the characteristic polynomial. We restricted the analysis to trees with the maximal valency d = 4. The number of graphs considered exceeds 300. The smallest pair of isospectral multitrees (i.e. trees with a multiple edge) has n = 6 vertices. There is a pair of trees \~hen n = 7, three pairs when n = 8, and five pairs when n = 9. In all cases, when k = 1 is assumed, isospectral multitreesreduce to the same tree. When k = 0 isassumed, isospectral

Cited by 0

Isospectral Submersion Metrics

Alexander Engel · arXiv (Cornell University) · 2011

We construct continuous families of pairwise isospectral metrics on various Riemannian manifolds (e.g., Lie groups, projective spaces and products of these with tori) which arise as quotients of other manifolds. This is done by developing a general principle which guarantees that the torus method can be used to simultaneously construct isospectral metrics on a manifold and a quotient of it. Furthermore, a suffient condition will be given such that the constructed metrics are submersion metrics.

Cited by 0Open access

Isospectral SUSY potentials

C Chaun · Journal of Physics A Mathematical and General · 1991

The authors introduce a new linear transformation in order to construct isospectral potentials within the framework of supersymmetric quantum mechanics. Under this transformation, the adjoint character of the 'ladder operator' is destroyed but with preservation of the energy spectrum leading to some interesting consequences such as the concept of pseudo-partnership of the two components. Connection with the Darboux Theorem as well as with some other recent methods of construction is analysed.

Cited by 8

Isospectral Riemann surfaces

Peter Buser · Annales de l’institut Fourier · 1986

We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> and for all <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:math> . In a second part we give examples of isospectral non isometric surfaces in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi mathvariant="bold">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> which are realizable by paper models.

Cited by 109Open access

Constructing Isospectral Manifolds

Robert Brooks · American Mathematical Monthly · 1988

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsRobert BrooksRobert Brooks is an Associate Professor of Mathematics at the University of Southern California. He received his Ph.D. from Raoul Bott at Harvard, and was awarded an Alfred P. Sloan fellowship in 1984. His research interests include differential geometry and topology and the geometry of the Laplace operator.

Cited by 32

Isospectral Network Transformations

Webb, Ben · ScholarsArchive (Brigham Young University) · 2014

Areas of Interest: Dynamical Systems & Applications; Dynamics of Networks; Particle Dynamics on Lattices; and, Spectral Estimates & Dynamics

Cited by 0

Rotating Isospectral Drums

Anton Lebedev · ArXiv.org · 2025

In this thesis I demonstrate that isospectral domains, that is domains of differing geometric shapes that possess identical spectra, do not remain isospectral when subject to uniform rotation. One thus *can* hear the shape of a rotating drum. It is shown that the spectra diverge as $\propto\left(\fracω{c}\right)^2$ similarly to a square but different from a circle, whose degenerate eigenfrequencies split $\propto \left(\fracω{c}\right)$. The latter two cases are studied analytically and used as test cases for the selection of numerical solution methods. I demonstrate that the presence of a simple medium attenuates the effects of rotation on the spectrum differences. Further I show that the common but linearised augmented wave equation yields eigenmodes with sensible structure for non-physical parameters, whereas a full equation destroys the structure as intended. The full equation is obtained from first principles using Maxwell equations formulated as differential forms and a careful application of the 3+1 foliation of space-time. The differences of the result from literature arXiv:physics/0607016 are highlighted and their effects studied. The equation is treated analytically on simple domains to obtain reference data for numerical analysis. Nodal and modal discretisations of the PDE are tested and a self-written FEM implementation is chosen due to higher precision of the results. As part of the validation process I demonstrate that results of arXiv:physics/0607016 are reproducible. The resulting gyroscopic quadratic eigenvalue problem is linearised into a Hamiltonian/skew-Hamiltonian pencil and a suitable shift operator for the Arnoldi iteration is determined. The resulting formulation is solved using ARPACK.

Cited by 0Open access

Isospectral Compression and Other Useful Isospectral Transformations of Dynamical Networks

Bunimovich, Leonid, Webb, Benjamin · arXiv (Cornell University) · 2012

It is common knowledge that a key dynamical characteristic of a network is its spectrum (the collection of all eigenvalues of the network's weighted adjacency matrix). In \cite{BW10} we demonstrated that it is possible to reduce a network, considered as a graph, to a smaller network with fewer vertices and edges while preserving the spectrum (or spectral information) of the original network. This procedure allows for the introduction of new equivalence relations between networks, where two networks are spectrally equivalent if they can be reduced to the same network. Additionally, using this theory it is possible to establish whether a network, modeled as a dynamical system, has a globally attracting fixed point (is strongly synchronizing). In this paper we further develop this theory of isospectral network transformations and demonstrate that our procedures are applicable to families of parameterized networks and networks of arbitrary size.

Cited by 0Open access