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Introduction

  • Stephen A. Dupree
  • Stanley K. Fraley

Abstract

The Monte Carlo method can be used to solve a wide range of physical and mathematical problems. Its utility has increased with the general availability of fast computing machines, and new applications are continually forthcoming. However, the basic concepts of Monte Carlo are both simple and straightforward, and can be learned by using a personal computer. In this book we will use such a computer as the basis for developing and explaining the fundamental concepts of Monte Carlo as applied to neutral particle transport. As each topic is addressed a corresponding set of software instructions will be developed. The software that results will be assembled into a program configuration that is representative of a full-scale Monte Carlo radiation transport program. The components of the program will be explained and combined in a fashion that will allow the reader to understand the function and contribution of each to the final, and sometimes daunting, whole.

Keywords

Monte Carlo Method Random Number Unit Circle Random Number Generator Monte Carlo Calculation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    G. Comte de Buffon, “Essai d’arithmétique morale,” Supplément à I’Histoire Naturelle 4, 1777. Buffon’s method is described in numerous texts. See, for example, Y. A. Shreider, ed., The Monte Carlo Method, Pergamon Press, Oxford, 1966, pp. 4–5. The variance in the estimate of π using Buffon’s method is given by Hammersley and Handscomb, Monte Carlo Methods, Chapman and Hall, London, 1964, pp. 74–75. See also B. C. Kahan, “A Practical Demonstration of a Needle Experiment Designed to Give a Number of Concurrent Estimates of π.” J. Roy. Statist. Soc. A, 124, 1961, pp. 227–239.Google Scholar
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    W. S. Gosset, “Probable Error ofa Correlation Coefficient,”Biometrika 6, 1908, p. 302.Google Scholar
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    A. S. Householder, G. E. Forsythe, and H. H. Germond, eds.,Monte Carlo Method, U.S. Department of Commerce, National Bureau of Standards Applied Mathematics Series 12, U.S. Government Printing Office, Washington, D.C., 1951.Google Scholar
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    The Rand Corporation, A Million Random Digits with 100,000 Normal Deviates, Free Press Publishers, Glencoe, IL, 1955.Google Scholar
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    Herman Kahn, “Applications of Monte Carlo,” U.S. Atomic Energy Commission Report AECU-3259, Rand Corporation, Santa Monica, CA, 1954. Revised 1956.Google Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Stephen A. Dupree
    • 1
  • Stanley K. Fraley
    • 1
  1. 1.Sandia National LaboratoriesAlbuquerqueUSA

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