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Physical Sciences and Mathematics Commons™
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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Uniqueness For A Boundary Identification Problem In Thermal Imaging, Kurt M. Bryan, Lester F. Caudill
Uniqueness For A Boundary Identification Problem In Thermal Imaging, Kurt M. Bryan, Lester F. Caudill
Mathematical Sciences Technical Reports (MSTR)
An inverse problem for a parabolic initial-boundary value problem is considered. The goal is to determine an unknown portion of the boundary of a region in Rn from measurements of Dirichlet data on a known portion of the boundary. It is shown that under reasonable hypotheses uniqueness results hold.
An Inverse Problem In Thermal Imaging, Kurt Bryan, Lester Caudill
An Inverse Problem In Thermal Imaging, Kurt Bryan, Lester Caudill
Department of Math & Statistics Faculty Publications
This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample. The problem is studied in both the case in which one has data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.
Effective Behavior Of Clusters Of Microscopic Cracks Inside A Homogeneous Conductor, Kurt M. Bryan, Michael Vogelius
Effective Behavior Of Clusters Of Microscopic Cracks Inside A Homogeneous Conductor, Kurt M. Bryan, Michael Vogelius
Mathematical Sciences Technical Reports (MSTR)
We study the effective behaviour of a periodic array of microscopic cracks inside a homogeneous conductor. Special emphasis is placed on a rigorous study of the case in which the corresponding effective conductivity becomes nearly singular, due to the fact that adjacent cracks nearly touch. It is heuristically shown how thin clusters of such extremely close cracks may macroscopically appear as a single crack. The results have implications for our earlier work on impedance imaging.