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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Electrothermal Imaging In One And Two Dimensions, Michael Janus, David Kibbling
Electrothermal Imaging In One And Two Dimensions, Michael Janus, David Kibbling
Mathematical Sciences Technical Reports (MSTR)
Developing methods for the nondestructive testing of materials is an important area of research for industry. Situations often arise in which the integrity of an object is questioned, but testing it is very difficult. For example, a support bar may be embedded in a larger structure so that testing the bar’s integrity directly would require the impractical task of breaking down the larger structure. Instead, the ends of the bar might be accessible without dismantling the enclosing structure. The goal of nondestructive testing is to use methods that require taking measurements at the ends of the bar alone to give …
Thermal Imaging To Recover A Defect In Three Dimensional Objects, Breanne Baker
Thermal Imaging To Recover A Defect In Three Dimensional Objects, Breanne Baker
Mathematical Sciences Technical Reports (MSTR)
This paper focuses on the inverse problem of identifying an internal void in a bounded two- or three-dimensional region. Information, in form of a heat flux and temperature, is assumed to be obtainable only on the external boundary of the region. The reciprocity gap approach with a suitable test functions is used in both the two- and three-dimensional cases.
Non-Destructive Recovery Of Voids Within A Three Dimensional Domain Using Thermal Imaging, Victor B. Oyeyemi
Non-Destructive Recovery Of Voids Within A Three Dimensional Domain Using Thermal Imaging, Victor B. Oyeyemi
Mathematical Sciences Technical Reports (MSTR)
We develop an algorithm capable of detecting the presence of spherical voids in a thermally conducting object. In addition, the process recovers both the radii and locations of each void. Our method involves the application of a known steady state heat flux to the object's boundary and measurement of the induced steady state temperature on the boundary.
Non-Destructive Testing Of Thermal Resistances For A Single Inclusion In A 2-Dimensional Domain, Nicholas Christian, Mathew A. Johnson
Non-Destructive Testing Of Thermal Resistances For A Single Inclusion In A 2-Dimensional Domain, Nicholas Christian, Mathew A. Johnson
Mathematical Sciences Technical Reports (MSTR)
In this paper we examine the inverse problem of determining the amount of corrosion/disbonding which has occurred on the boundary of a single circular (or nearly circular) inclusion D in a two dimensional domain W using Cauchy data for the steady-state heat equation. We develop an algorithm for reconsructing a function which qunatifies the level of corrosion/disbonding at each point in ¶W. We also address the issue of well-posedness and develop a simple regularization scheme. Then we provide several numerical examples. We shall show a simple procedure for recovering the center of D assuming that the boundary of W and …
A Review Of Selected Works On Crack Indentification, Kurt M. Bryan
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.
Stability And Reconstruction For An Inverse Problem For The Heat Equations, Kurt M. Bryan, Lester Caudill
Stability And Reconstruction For An Inverse Problem For The Heat Equations, Kurt M. Bryan, Lester Caudill
Mathematical Sciences Technical Reports (MSTR)
We examine the inverse problem of determining the shape of some unknown portion of the boundary of a region W from measurements of the Cauchy data for solutions to the heat equation on W. By suitably linearizing the inverse problem we obtain uniqueness and continuous dependence results. We propose an algorithm for recovering estimates of the unknown portion of the surface and use the insight gained from a detailed analysis of the inverse problem to regularize the inversion. Several computational examples are presented.
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.