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Partial Differential Equations Commons

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Articles 1 - 5 of 5

Full-Text Articles in Partial Differential Equations

A Review Of Selected Works On Crack Indentification, Kurt M. Bryan Oct 2002

A Review Of Selected Works On Crack Indentification, Kurt M. Bryan

Mathematical Sciences Technical Reports (MSTR)

We give a short survey of some of the results obtained within the last 10 years or so concerning crack identification using impedance imaging techniques. We touch upon uniqueness results, continuous dependence results, and computational algorithms.


Characterizing A Defect In A One-Dimensional Bar, Cynthia Gangi, Sameer Shah Sep 2002

Characterizing A Defect In A One-Dimensional Bar, Cynthia Gangi, Sameer Shah

Mathematical Sciences Technical Reports (MSTR)

We examine the inverse problem of locating and describing an internal point defect in a one­ dimensional rod W by controlling the heat inputs and measuring the subsequent temperatures at the boundary of W. We use a variation of the forward heat equation to model heat flow through W, then propose algorithms for locating an internal defect and quantifying the effect the defect has on the heat flow. We implement these algorithms, analyze the stability of the procedures, and provide several computational examples.


Reconstruction Of Cracks With Unknown Transmission Condition From Boundary Data, F Ronald Ogborne Iii, Melissa E. Vellela Sep 2002

Reconstruction Of Cracks With Unknown Transmission Condition From Boundary Data, F Ronald Ogborne Iii, Melissa E. Vellela

Mathematical Sciences Technical Reports (MSTR)

We examine the problem of Identifying both the location and constitutive law governing electrical current flow across a one-dimensional linear crack in a two dimensional region when the crack only partially blocks the flow of current. We develop a a constructive numerical procedure for solving the inverse problem and provide computational examples.


Fast Reconstruction Of Cracks Using Boundary Measurements, Nicholas A. Trainor, Rachel M. Krieger Jul 2002

Fast Reconstruction Of Cracks Using Boundary Measurements, Nicholas A. Trainor, Rachel M. Krieger

Mathematical Sciences Technical Reports (MSTR)

This paper develops a fast algorithm for locating one or more perfectly insulating, pair-wise disjoint, linear cracks in a homogeneous two-dimensional electrical conductor, using boundary measurements.


Nonlinear Dynamics Of Mode-Locking Optical Fiber Ring Lasers, Kristin M. Spaulding, Darryl H. Yong, Arnold D. Kim, J Nathan Kutz May 2002

Nonlinear Dynamics Of Mode-Locking Optical Fiber Ring Lasers, Kristin M. Spaulding, Darryl H. Yong, Arnold D. Kim, J Nathan Kutz

All HMC Faculty Publications and Research

We consider a model of a mode-locked fiber ring laser for which the evolution of a propagating pulse in a birefringent optical fiber is periodically perturbed by rotation of the polarization state owing to the presence of a passive polarizer. The stable modes of operation of this laser that correspond to pulse trains with uniform amplitudes are fully classified. Four parameters, i.e., polarization, phase, amplitude, and chirp, are essential for an understanding of the resultant pulse-train uniformity. A reduced set of four coupled nonlinear differential equations that describe the leading-order pulse dynamics is found by use of the variational nature …