Department of Mathematical Sciences

School of Natural Sciences and Mathematics

Faculty and research

M. Ali Hooshyar, PhD

Education

Ph.D., Indiana, 1970

Overview

Scattering theory, inverse scattering theory with geophysical and optical applications, fission.

Research Interests

My research interests have been primarily in the areas of integral and differential equations and their applications to problems in physical sciences and engineering. More specifically, I work in the areas of scattering theory, inverse scattering theory, and wave propagation.

The problem of interest is the recovery of the property of the inhomogeneous medium from the far field wave propagation data. Such a problem appears in may applied fields, such as quantum mechanics, geophysical exploration, medical imaging and electromagnetic soundings, where the direct measurement of the property under consideration is not achievable. Therefore an indirect (inverse) method is used to deduce information about the problem.

Because of its wide reaching applications, exact and approximate mathematical methods to study such inverse problems and their numerical implementations have been of special interest to me. A problem of great interest has been the development of a practical non iterative inversion method for the three dimensional acoustic medium.This problem has been an ongoing research endeavor for me and some of my Ph.D. students.

My recent interests have also included application of inverse scattering theory and wavelets to science and engineering problems and also to investigate the possibility of applications of these theories in human perception such as hearing and / or image recognition.

The other very important area which I have always found to be very challenging and rewarding is developing effective and innovative methods to teach and present new and / or standard educational materials to students in such a way as to motivate and excite their imaginations, induce creative thinking and help them reach their potentials.

In order to further facilitate the realization of such goals, more effective use of computers, other technical tools, and innovative educational methods in presenting course materials are also planned to be explored and implemented.

Selected Publications:

  1. On the Inverse Scattering Problem at Fixed Energy for the Tensor and Spin-Orbit Potentials. J. Math. Phys. 12, 2243-2258 (1971).
  2. On the Inverse Scattering Problem for a Class of Spin-Orbit and Central Potentials. J. Math. Phys. 19, 253-263 (1978).
  3. Determination of the Radial Variations of the Density and Shear Modulus of a flaw from the Angular Dependence of the Scattering Amplitude. Co-author: M. Razavy, Wave Motion 6, 591-600 (1984).
  4. Inversion of the Two Dimensional SH Elastic Wave Equation for the Density and Shear Modulus. Co-author A.B. Weglein, J. Acous. Soc. Am. 79, 1280-1283 (1986).
  5. Construction of Spin-Orbit and Central Potentials. Co-author: P. Richardson, J. Math. Phys. 32, 1310-1317 (1991).
  6. The Inverse Problem of Transversely Isotropic Media. Co-author: S.M. Kelly, Wave Motion, 14, 233-242 (1991).
  7. Inverse Scattering Theory and the Design of Planar Optical Waveguides with Same Propagation Constant for Different Frequencies. Co-author: L.S. Tamil, Inverse Problems, 9, 69-80 (1993).
  8. Variational principles and the One-dimensional profile reconstruction. J. Optical Soc. Am. 15, 1867-1876 (1998).
  9. Inverse problem of the wave equation and the Schwinger approximation. Co-authors: T.H. Lam and M. Razavy, J. Acous. Soc. Am. 107, 404-423 (2000).
  10. An inverse problem of electromagnetic scattering and the method of lines. Microwave and Optical Technology Letters, 29, 420-426 (2001).
  11. The Method of Lines and Electromagnetic Scattering for Line Sources. Co-author: L.V. Lasater, Microwave and Optical Technology Letters, 41, 286-290 (2004)
  12. Nuclear Fission and Cluster Radioactivity; An Energy-Density Functional Approach. Co-authors: I. Reichstein & F.B. Malik, Springer-Verlag, Berlin Heidelberg (2005).
  • Updated: February 6, 2006