NL Gibson, C Gifford-Miears, AS Leon, VS Vasylkivska, "Efficient computation of unsteady flow in complex river systems with uncertain inputs", International Journal of Computer Mathematics 91 (4), 781-797, 2014. (pre-print).
N. L. Gibson, P. Medina, M. Peszynska, and R. E. Showalter, "Evolution of phase transitions in methane hydrate", Journal of Mathematical Analysis and Applications, Volume 409, Issue 2, Pages 816–833, January 2014. PDF
Online.
M. G. McIntire , V. Vasylkivska, C. Hoyle, and N. L. Gibson, "Applying Robust
Design Optimization to Large Systems", ASME 2014 International Design Engineering
Technical Conferences and Computers and Information in Engineering Conference,
2014. (pre-print).
V. A. Bokil and N. L. Gibson, "Convergence Analysis of Yee Schemes for Maxwell's Equations in Debye and Lorentz Dispersive Media", 11(4), 657-687, International Journal of Numerical Analysis and Modeling (IJNAM), 2014. (pre-print). OSU Technical Report version, 2013 (formerly http://hdl.handle.net/1957/38475).
V. A. Bokil and N. L. Gibson, "Stability and Dispersion Analysis of High Order FDTD Methods for Maxwell's Equations in Dispersive Media", Contemporary Mathematics, Volume 586, 2013 PDF
Online.
A. S. Leon, N. L. Gibson, and C. H. Gifford-Miears, “Toward reduction of uncertainty in complex multi-reservoir river systems”, Proceedings, XIX Intl Conference on Water Resources,
2012. (pre-print).
M. J. Armentrout and N. L. Gibson, "Time Domain Parameter Distribution
Estimation in Dispersive Media", Proceedings of the 10th International
Conference on Mathematical and Numerical Aspects of Waves (Waves 2011), published by PIMS, 2011
, PDF
Online.
V. A. Bokil and N. L. Gibson, "Analysis of Spatial
High-Order Finite Difference Methods for Maxwell's Equations in Dispersive
Media", IMA Journal of Numerical Analysis, 32(3), 926-956, 2012, (first published online doi:10.1093/imanum/drr001, 2011), PDF
Online. (pre-print).
Proceedings version: "Analysis of High Order FDTD Methods For
Maxwell's Equations in Dispersive Media", Proceedings of the 10th International
Conference on Mathematical and Numerical Aspects of Waves (Waves 2011), published by PIMS, 2011
, PDF
Online. OSU Technical Report version, 2013 (formerly http://hdl.handle.net/1957/13786).
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", Numerical Methods for
Partial Differential Equations, 25(4), pp 885-917, July 2009, 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, N. L. Gibson, and W. P. Winfree,
"2D Modeling
of Pulsed THz Interrogation of SOFI with Knit Lines", Proceedings of Review of Progress in Quantitative NDE,
2007. (pre-print).
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.
Applied and Computational Math Seminar, Portland State University, virtual.
"Uncertainty Quantification Methods for Multiscale Modeling and Dimension Reduction"
April, 2022.
"Numerical Methods for Dispersive Electromagnetics with Distributions of Parameters", in Recent Advances in Numerical Methods for Maxwell's Equations in Complex Media minisymposium, SIAM Annual Meeting, Portland, OR, July 2018.
Polynomial Chaos for Dispersive Electromagnetics, in Topical Workshop on Computational Aspects of Time Dependent Electromagnetic Wave Problems in Complex Materials, ICERM, Providence, RI, June, 2018.
"Numerical Modeling Methane Hydrate Evolution", in Recent Developments in Numerical Methods for PDEs minisymposium, invited by Yekaterina Epshteyn and Fengyan Li, SIAM Annual Meeting, San Diego, CA, July 2013.
2011 Joint Mathematics Meeting, New Orleans, LA. MAA Panel
Discussion: The benefits of hosting a regional undergraduate
mathematics conference. "Northwest Undergraduate
Mathematics Symposium", January, 2011.
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.