Dr. Peter Massopust, senior research scientist at Tuboscope Vetco International Inc. in Houston, Texas, will speak at a math colloquium sponsored by the Center for Applied Mathematics.

The talk, “On Magnetic Fields Generated by Classes of Defects in Hard Ferromagnets,” will be held at 3 p.m. (refreshments at 2:45 p.m.) Wednesday, Dec. 1, in the 3M Auditorium, Owens Science Hall.

One of the main tasks of the pipeline integrity industry is the detection and classification of defects in pipelines. The detection process uses a coil or a Hall sensor to measure the voltage induced by the magnetic field that “leaks out” of the pipe when encountering a defect.

In the classification process, the exact nature of the defect needs to be inferred from the magnetic flux leakage (MFL) signal and relevant geometric parameters, such as length, width and depth, must be computed.

The problem of inferring the exact geometry of a defect in a hard ferromagnet from its MFL signal is highly ill posed; different defects may induce the same MFL signal. In order to obtain a viable solution of this problem, a better understanding of the form and structure of an MFL signal needs to be achieved.

As an MFL signal is — up to a proportionality constant — equal to the magnetic flux leakage field B generated around a defect, it is natural to try to obtain exact analytical expressions for such fields based on rigorous mathematical models. The knowledge of the precise nature of the magnetic flux leakage field around a defect provides an exact relationship between the different parameters describing the geometry of a defect. This exact relationship needs to be used for the solution of the inverse problem.

In this expository talk, a first order model with analytical solutions for magnetic flux leakage problems is presented and discussed in the context of the inverse problem mentioned above. Several other issues surrounding this problem, such as wavelet denoising techniques for MFL signals, also are examined.

About the speaker:

Massopust studied at the University of Munich, receiving B.S. degrees in mathematics and physics in 1980. He was a Fulbright scholar studying theoretical physics at Georgia Tech and was awarded an MS in physics in 1981. He completed his doctoral dissertation in applied mathematics at Georgia Tech in 1986 under the supervision of Michael Barnsley. He taught at several universities and was a researcher at Sandia National Laboratories.

Massopust’s research interests are in fractal geometry and analysis, wavelet theory and applied harmonic analysis, the theory and numerics of partial differential equations.