# Eliciting harmonics on strings

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 14, Issue: 4, page 657-677
- ISSN: 1292-8119

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topCox, Steven J., and Henrot, Antoine. "Eliciting harmonics on strings." ESAIM: Control, Optimisation and Calculus of Variations 14.4 (2008): 657-677. <http://eudml.org/doc/250319>.

@article{Cox2008,

abstract = {
One may produce the qth harmonic of a string of length π by
applying the 'correct touch' at the node $\pi/q$
during a simultaneous pluck or bow. This notion was
made precise by a model of Bamberger, Rauch and Taylor. Their 'touch' is
a damper of magnitude b concentrated at $\pi/q$.
The 'correct touch' is that b for which the modes, that do not vanish
at $\pi/q$, are maximally damped. We here examine the associated spectral
problem. We find the spectrum to be periodic and determined by a polynomial
of degree $q-1$. We establish lower and upper bounds on the spectral abscissa
and show that the set of associated root vectors constitutes a Riesz basis
and so identify 'correct touch' with the b that minimizes the spectral
abscissa.
},

author = {Cox, Steven J., Henrot, Antoine},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Point-wise damping; spectral abscissa; Riesz basis; pointwise damping},

language = {eng},

month = {1},

number = {4},

pages = {657-677},

publisher = {EDP Sciences},

title = {Eliciting harmonics on strings},

url = {http://eudml.org/doc/250319},

volume = {14},

year = {2008},

}

TY - JOUR

AU - Cox, Steven J.

AU - Henrot, Antoine

TI - Eliciting harmonics on strings

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/1//

PB - EDP Sciences

VL - 14

IS - 4

SP - 657

EP - 677

AB -
One may produce the qth harmonic of a string of length π by
applying the 'correct touch' at the node $\pi/q$
during a simultaneous pluck or bow. This notion was
made precise by a model of Bamberger, Rauch and Taylor. Their 'touch' is
a damper of magnitude b concentrated at $\pi/q$.
The 'correct touch' is that b for which the modes, that do not vanish
at $\pi/q$, are maximally damped. We here examine the associated spectral
problem. We find the spectrum to be periodic and determined by a polynomial
of degree $q-1$. We establish lower and upper bounds on the spectral abscissa
and show that the set of associated root vectors constitutes a Riesz basis
and so identify 'correct touch' with the b that minimizes the spectral
abscissa.

LA - eng

KW - Point-wise damping; spectral abscissa; Riesz basis; pointwise damping

UR - http://eudml.org/doc/250319

ER -

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