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Technical Note

Polynomial Chaos Functions and Neutron Diffusion

Pages 109-118 | Published online: 10 Apr 2017

REFERENCES

  • G. C. POMRANING, Linear Kinetic Theory and Particle Transport in Stochastic Mixtures, World Scientific Press Publishing, Singapore (1991).
  • M. M.R. WILLIAMS, “Some Aspects of Neutron Transport in Spatially Random Media,” Nucl. Sci. Eng., 136, 34 (2000).
  • R. G. GHANEM and P. D. SPANOS, Stochastic Finite Elements: A Spectral Approach, Dover Publications (2003).
  • A. F. EMERY, “Some Thoughts on Solving the Radiative Transfer Equation in Stochastic Media Using Polynomial Chaos and Wick Products as Applied to Radiative Equilibrium,” J. Quant. Spectrosc. Radiat. Transfer, 93, 61 (2005).
  • N. WIENER, “The Homogeneous Chaos,” Am. J. Math., 60, 897 (1938).
  • R. CAMERON and W. MARTIN, “The Orthogonal Development of Nonlinear Functionals in Series of Fourier-Hermite Polynomials,” Ann. Math., 48, 385 (1947).
  • R. ASKEY and J. WILSON, “Some Basic Hypergeometric Polynomials that Generalize Jacobi Polynomials,” Mem. Am. Math. Soc., 319 (1985).
  • D. XIU and G. E. M. KARNIADAKIS, “The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations,” SIAM J. Sci. Comput., 24, 619 (2002).
  • A. PAPOULIS, Probability, Random Variables and Stochastic Processes, McGraw Hill Book Co., New York (2000).
  • G. I. BELL and S. GLASSTONE, Nuclear Reactor Theory, Van Nostrand and Reinhold, New York (1970).
  • M. M. R. WILLIAMS, “The Effect of Random Geometry on the Criticality of a Multiplying System,” Ann. Nucl. Energy, 27, 143 (2000).
  • A. Z. AKCASU and M. M.R. WILLIAMS, “An Analytical Study of Particle Transport in Spatially Random Media in One Dimension: Mean and Variance Calculations,” Nucl. Sci. Eng., 148, 403 (2004).

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