Index Catalog // ScholarsArchive@OSU

Creator:: Gibson, Nathan L.
Abstract:: Electromagnetic wave propagation in complex dispersive media is governed by the time dependent Maxwell’s equations coupled to equations that describe the evolution of the induced macroscopic polarization. We consider “polydispersive” materials represented by distributions of dielectric parameters in a polarization model. The work focuses on a novel computational framework for...
Resource Type:: Article
Full Text:: ). Thus we first consider the system ∂B ∂t +∇×E = 0, in (0, T ) ×D, (1a) ∂D ∂t + J−∇×H = 0, in (0, T

Creator:: Bokil, Vrushali A. and Gibson, Nathan L.
Abstract:: We study the stability properties of, and the phase error present in, several higher order (in space) staggered finite difference schemes for Maxwell's equations coupled with a Debye or Lorentz polarization model. We present a novel expansion of the symbol of finite difference approximations, of arbitrary (even) order, of the...
Resource Type:: Technical Report
Full Text:: ∂t = J along with the constitutive law (2.10b) as Lorentz Model 3: ∂P ∂t = J, (2.12a) ∂J ∂t + νJ

Creator:: Rajbhandari, Evan, Gibson, Nathan L., and Woodside, C. Rigel
Abstract:: We explore one numerical method for dealing with uncertainty quantification, stochastic collocation. We adapt this method for the uncertain kinematic magnetohydrodynamic system. We then demonstrate well-posedness of the uncertain forward problem. We also describe the method in detail, and perform an error analysis of the method, describing the necessary assumptions...
Resource Type:: Preprint
Full Text:: Magnetohydrodynamics Framework Evan Rajbhandari1,2, Nathan Gibson1, and C. Rigel Woodside2 1Department of Mathematics

Creator:: Rajbhandari, Evan, Gibson, Nathan L., and Woodside, C. Rigel
Abstract:: We discuss the well-posedness of the forward problem for the magnetohydrodynamic system with the inclusion of the ion-slip parameter. We also demonstrate the convergence of a parameter estimation scheme. Focusing on power-generation, we implement and the validate a numerical model with an engineering multi-physics software, COMSOL, using ideal-power equations. We...
Resource Type:: Preprint
Full Text:: Magnetohydrodynamics Framework Evan Rajbhandari1, Nathan Gibson2, and C. Rigel Woodside3 1Department of Mathematics

Creator:: Chen, Duan, Leon, Arturo S., Gibson, Nathan L., and Hosseini, Parnian
Abstract:: Optimizing the operation of a multireservoir system is challenging due to the high dimension of the decision variables that lead to a large and complex search space. A spectral optimization model (SOM), which transforms the decision variables from time domain to frequency domain, is proposed to reduce the dimensionality. The...
Resource Type:: Article
Full Text:: . Leon1, Nathan L. Gibson3, and Parnian Hosseini1 1School of Civil and Construction Engineering, Oregon

Creator:: Rajbhandari, Evan, Gibson, Nathan L., and Woodside, C. Rigel
Abstract:: We discuss an efficient numerical method for the uncertain kinematic magnetohydrodynamic system. We include aleatoric uncertainty in the parameters, and then describe a stochastic collocation method to handle this randomness. Numerical demonstrations of this method are discussed. We find that the shape of the parameter distributions affect not only the...
Resource Type:: Preprint
Full Text:: [∫ D σ−1J · φ ] − E [∫ D ∇V · φ ] = 0 ∀φ ∈ V , (1a) − E [∫ D Ji · ∇ψ ] = E [∫ D ( σ(u×B

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