Energy bounds on point-wise damped wave operators

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dc.contributor.advisorEmbree, Marken_US
dc.creatorHardesty, Sean S.en_US
dc.date.accessioned2009-06-04T07:56:05Zen_US
dc.date.available2009-06-04T07:56:05Zen_US
dc.date.issued2006en_US
dc.description.abstractOne plays a harmonic by gently touching a finger to a vibrating string so as to divide it into two segments whose lengths form the ratio of small integers. The only prominent frequencies in the sound thereby produced correspond to those modes of the undamped string that have nodes at the contact point; the others are damped by the action of the finger. Bamberger, Rauch, and Taylor [1] modeled the phenomenon with point-wise damping and suggested that the "correct touch" (force applied by the finger) is that which causes the damped modes to decay most rapidly. Cox and Henrot [3] investigated the spectral properties of the associated operator, and identified the correct touch as that which minimizes its spectral abscissa. We give bounds on the total energy associated with the damped modes, and assess their utility in helping us understand the correct touch.en_US
dc.format.extent53 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 2006 HARDESTYen_US
dc.identifier.citationHardesty, Sean S.. "Energy bounds on point-wise damped wave operators." (2006) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/17881">https://hdl.handle.net/1911/17881</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/17881en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.titleEnergy bounds on point-wise damped wave operatorsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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