SECOND-ORDER CROSS TERMS IN MONTE CARLO DIFFERENTIAL OPERATOR PERTURBATION ESTIMATES

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Given some initial, unperturbed problem and a desired perturbation, a second-order accurate Taylor series perturbation estimate for a Monte Carlo tally that is a function of two or more perturbed variables can be obtained using an implementation of the differential operator method that ignores cross terms, such as in MCNP4C{trademark}. This requires running a base case defined to be halfway between the perturbed and unperturbed states of all of the perturbed variables and doubling the first-order estimate of the effect of perturbing from the ''midpoint'' base case to the desired perturbed case. The difference between such a midpoint perturbation estimate ... continued below

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FAVORITE, J. A. & PARSONS, D. K. March 1, 2001.

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Given some initial, unperturbed problem and a desired perturbation, a second-order accurate Taylor series perturbation estimate for a Monte Carlo tally that is a function of two or more perturbed variables can be obtained using an implementation of the differential operator method that ignores cross terms, such as in MCNP4C{trademark}. This requires running a base case defined to be halfway between the perturbed and unperturbed states of all of the perturbed variables and doubling the first-order estimate of the effect of perturbing from the ''midpoint'' base case to the desired perturbed case. The difference between such a midpoint perturbation estimate and the standard perturbation estimate (using the endpoints) is a second-order estimate of the sum of the second-order cross terms of the Taylor series expansion. This technique is demonstrated on an analytic fixed-source problem, a Godiva k{sub eff} eigenvalue problem, and a concrete shielding problem. The effect of ignoring the cross terms in all three problems is significant.

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167 Kilobytes pages

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  • Report No.: LA-UR-01-1640
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 776530
  • Archival Resource Key: ark:/67531/metadc724009

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  • March 1, 2001

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  • Sept. 29, 2015, 5:31 a.m.

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  • March 23, 2016, 4:24 p.m.

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FAVORITE, J. A. & PARSONS, D. K. SECOND-ORDER CROSS TERMS IN MONTE CARLO DIFFERENTIAL OPERATOR PERTURBATION ESTIMATES, article, March 1, 2001; New Mexico. (digital.library.unt.edu/ark:/67531/metadc724009/: accessed August 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.