Magnetic damping of an elastic conductor

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dc.contributor.advisorEmbree, Mark
dc.contributor.advisorCox, Steven J.
dc.creatorHokanson, Jeffrey M.
dc.date.accessioned2011-07-25T01:39:13Z
dc.date.available2011-07-25T01:39:13Z
dc.date.issued2009
dc.description.abstractMany applications call for a design that maximizes the rate of energy decay. Typical problems of this class include one dimensional damped wave operators, where energy dissipation is caused by a damping operator acting on the velocity. Two damping operators are well understood: a multiplication operator (known as viscous damping) and a scaled Laplacian (known as Kelvin---Voigt damping). Paralleling the analysis of viscous damping, this thesis investigates energy decay for a novel third operator known as magnetic damping, where the damping is expressed via a rank-one self-adjoint operator, dependent on a function a. This operator describes a conductive monochord embedded in a spatially varying magnetic field perpendicular to the monochord and proportional to a. Through an analysis of the spectrum, this thesis suggests that unless a has a singularity at one boundary for any finite time, there exist initial conditions that give arbitrarily small energy decay at any time.
dc.format.mimetypeapplication/pdf
dc.identifier.callnoTHESIS MATH.SCI. 2009 HOKANSON
dc.identifier.citationHokanson, Jeffrey M.. "Magnetic damping of an elastic conductor." (2009) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/61897">https://hdl.handle.net/1911/61897</a>.
dc.identifier.urihttps://hdl.handle.net/1911/61897
dc.language.isoeng
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.
dc.subjectMathematics
dc.titleMagnetic damping of an elastic conductor
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematical Sciences
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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