Denigrating E. L. Godkin

Hoogenboom, Ari; Hoogenboom, Olive; Armstrong, William D.

doi:10.2307/2701098

Cited by 1 publication

(2 citation statements)

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“…Both types of importance functions are necessary to construct a Monte Carlo zero-variance sampling scheme (Dwivedi, 1982;Hoogenboom, 2003) by applying it as biasing functions for the collision kernel and transition kernel, respectively.…”

Section: Adjoint Functions and Equations In The Two-direction Modelmentioning

confidence: 99%

“…As the two-direction model is a simplified but true transport model, it can easily be incorporated in a Monte Carlo code, which is not Downloaded by [University of California Santa Cruz] at 13:58 28 November 2014 possible for the normal diffusion model. The author used this model before (Hoogenboom, 1981(Hoogenboom, , 2003 to demonstrate a zerovariance Monte Carlo sampling scheme.…”

Section: Introductionmentioning

confidence: 99%

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The Two-Direction Neutral-Particle Transport Model: A Useful Tool for Research and Education

Hoogenboom

2008

Transport Theory and Statistical Physics

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The two-direction transport model limits the transport of neutrons and photons to the +X and -X directions, resulting in a diffusion-type differential equation for the total flux. Anisotropic scattering can easily be incorporated. Analytical solutions of this equation can easily be obtained, as well as for the flux in either direction. This may help students to better understand transport and diffusion theory and the continuity or discontinuity of transport quantities and their derivatives at internal medium boundaries. As the two-direction transport model is a simplified but true transport model, it can easily be incorporated in a Monte Carlo code, and can then be used to test the operation and performance of the Monte Carlo code-especially to test methods for variance reduction, including zero-variance schemes.The adjoint equations for two different types of importance functions are derived, for which analytical solutions are possible. The less well-known importance function for particles entering a collision is essential in constructing Monte Carlo zero-variance sampling schemes.Several examples are worked out with analytical and numerical solutions, which demonstrate the use of the two-direction model; the application of the various boundary, interface, and source conditions; and the application of the adjoint functions. It also shows the unusual solution of an eigenfunction problem with anisotropic fission. The numerical results from analytical solutions are confirmed by Monte Carlo and discrete ordinates calculations.

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Section: Adjoint Functions and Equations In The Two-direction Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%