Nathan Louis Gibson Assistant Professor Department of Mathematics Kidder Hall 368 Oregon State University Corvallis, Oregon 97331-4605 USA (541) 737-4894 (Voice) (541) 737-0517 (Fax)

Background

Professor Gibson received his Ph.D. in Computational Mathematics from North Carolina State University in 2004 under the direction of Professor H. T. Banks. Previously, he obtained a Master's Degree in Applied Mathematics with Concentrations in Numerical Analysis and Mathematical Modeling at the University of Tennessee, Knoxville, in August of 2001, and a Bachelor's Degree in Mathematics with a Concentration in Computational and Applied Analysis and a minor in Computer Science from Worcester Polytechnic Institute in Worcester, MA, in August of 1998. Before coming to Oregon State University, he was an NIA (National Institute for Aerospace) postdoctoral research fellow at the CRSC (Center for Research in Scientific Computation) working with engineers from NASA Langley. More information can be seen on his curriculum vitae.

Research

Currently, Professor Gibson investigating electromagnetic interrogation of dispersive and scattering media, including biological tissue, foam, powders, and wet soil. Recently, he has worked with NASA Langley Research Center on inverse problem techniques related to non-destructive evaluation (NDE) of space shuttle foam. His primary research interests are

• computational electromagnetics
• finite element and finite difference methods
• inverse problems

• direct and indirect (sparse) linear solvers
• high performance and parallel computing
• parameter identification and sensitivity analysis
• optimization and regularization techniques
• modeling uncertainty in coefficients of PDE's
• homogenization involving Maxwell's equations

• modeling dielectric heterogeneities
• electromagnetic detection of gaps or voids in space shuttle foam
• generating synthetic data involving complicated geometries for crack detection techniques
• cancer/defect detection
• material (e.g., explosives) identification
• cave/tunnel locating for defense applications

Teaching

MTH 452/552-001 Winter 10

MTH 451/551-001 Fall 09

MTH 351-020 Fall 09

MTH 323-001 Spring 09

MTH 351-001 Winter 09

MTH 654-001 Fall 08

MTH 256-010 Fall 08

MTH 256-010 Spring 08

MTH 341-020 Spring 08

MTH 256-020 Winter 08

MTH 341-020 Fall 07

MTH 451-001 Fall 07

MTH 351-001 Spring 07

MTH 351-002 Spring 07

MTH 256-030 Winter 07

MTH 351-010 Fall 06

MTH 351-020 Fall 06

MA 141-008 Fall 05 (NCSU)

Service

• Math Club: Advisor
• Pi Mu Epsilon Student Chapter Oregon Beta: Advisor
• SIAM Student Chapter: Advisor
• Association for Women in Mathematics Chapter: Co-advisor
• Mathematical Contests: Organizer
• Oregon Space Grant Consortium: Affliated Faculty

Communications

• H.T. Banks, V.A. Bokil, and N.L.Gibson, "Analysis of stability and dispersion in a finite element method for Debye and Lorentz dispersive media", accepted into Numerical Methods for Partial Differential Equations, 2008, PDF Online.

• H.T. Banks, V.A. Bokil, and N.L. Gibson, "Parameter estimation versus homogenization techniques in time-domain characterization of composite dielectrics", Journal of Inverse and Ill-Posed Problems, 15, no. 2, 117-135, 2007, PDF Online.

• H. T. Banks and N. L. Gibson, "Void detection in foam with knit lines using THz pulse interrogation", Mathematical and Computer Modelling 44, nos. 9-10, 807- 815, 2006, PDF Online.

• H. T. Banks and N. L. Gibson, "Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters", Quarterly of Applied Mathematics, 64, no. 4, 749-795, 2006, PDF Online.

• H. T. Banks, N. L. Gibson, and W. P. Winfree, "Gap detection with electromagnetic terahertz signals", Nonlinear Analysis: Real World Applications 6, no. 2, 381-416, 2005, PDF Online.

• H. T. Banks, V. A. Bokil, D. Cioranescu, N. L. Gibson, G. Griso, and B. Miara, "Homogenization of periodically varying coefficients in electromagnetic materials", Journal of Scientific Computing, 28, no. 2, 191-221, 2006, PDF Online.

• H. T. Banks and N. L. Gibson, "Well-posedness in Maxwell systems with distributions of polarization relaxation parameters", Applied Mathematics Letters 18, 423-430, 2005, PDF Online.

• S. Gavrilets and N. L. Gibson, "Fixation probabilities in a spatially heterogeneous environment", Population Ecology 44, no. 2, 51-58, 2002 PDF Online.

• Solid-state and Optics Seminar, Oregon State University, Corvallis, OR. "Approximating Dispersive Mechanisms Using the Debye Model with Distributions of Dielectric Parameters", October, 2008.

• Applied Mathematics and Computation Seminar, Oregon State University, Corvallis, OR. "Gradient-based Methods for Optimization": Part 1 Part 2, November, 2007.

• Conference on Applied Inverse Problems 2007: Theoretical and Computational Aspects, University of British Columbia Campus Vancouver, Canada. " Electromagnetic Characterization of Damage in Complex Dielectrics", Identification of Defects and Cracks Minisymposium organized by Shiro Kubo, June 2007.

• Mathematics REU, Oregon State University, Corvallis, OR. "Finding damage in Space Shuttle foam", July, 2007.

• Mathematics Colloquium, Oregon State University, Corvallis, OR. "Electromagnetic characterization of damage in Space Shuttle foam", March, 2007.

• Applied Mathematics and Computation Seminar, Oregon State University, Corvallis, OR. "Inverse Problem for Distributions of Dielectric Parameters", November, 2006.

• Review of Progress in Quantitative NDE, Portland, OR. "2D Modeling of Pulsed THz Interrogation of SOFI with Knit Lines", Terahertz Imaging Session, chaired by H. Ringermacher, August, 2006.

• Third International Conference "Inverse Problems : Modeling and Simulation", Oldeniz-Fethiye, TURKEY. "Parameter Identification using Electromagnetic Interrogation of Heterogeneous Dielectrics", Inverse Problems Related to Scattering in Complex Structures Session, organized by Dr. J. A. Burns and Dr. H. T. Banks, May, 2006.

• Colloquium Talk, Sandia National Laboratories, Albuquerque, NM. "On Various Inverse Problems in Electromagnetics Involving Distributions of Dielectric Parameters", February, 2006.

• Sixth SIAM Conference on Control and its Applications, New Orleans, LA. "Electromagnetic Inverse Problem Involving Distributions of Dielectric Parameters", Inverse Problems in Electromagnetics and Biology Minisymposium, organized by H. T. Banks and A. S. Ackleh, July 2005.

• 29th Annual SIAM Southeast Atlantic Section Meeting, Charleston, SC. "Gap Detection with Electromagnetic Terahertz Signals", Inverse Problems in Electromagnetics and Biology Minisymposium, organized by H. T. Banks and N. L. Gibson, March 2005.

• SAMSI Multiscale Working Group Closing Workshop, RTP, NC. "Multiscale and Polarization in Dielectric Materials: A Probabilistic Approach", invited by R. C. Smith, September 2004.

• "Journees Jeunes" at Laboratoire J.-L. Lions/Paris VI, Paris, France. "Pulsed Terahertz Electromagnetic Inverse Problems", invited by D. Cioranescu, March 2004.

• Applied Math Graduate Student Seminar, North Carolina State University. "Electromagnetic Crack Detection Inverse Problems Using Terahertz Interrogating Signals", October 2003.