By Stephen A. Dupree, Stanley K. Fraley

ISBN-10: 1441984917

ISBN-13: 9781441984913

The mathematical means of Monte Carlo, as utilized to the shipping of sub-atomic debris, has been defined in different studies and books due to the fact its formal improvement within the Forties. each one of these tutorial efforts were directed both on the mathematical foundation of the approach or at its sensible software as embodied within the a number of huge, formal desktop codes to be had for appearing Monte Carlo shipping calculations. This booklet makes an attempt to fill what seems to be a spot during this Monte Carlo literature among the math and the software program. hence, whereas the mathematical foundation for Monte Carlo shipping is roofed in a few element, emphasis is put on the appliance of the strategy to the answer of functional radiation delivery difficulties. this can be performed by utilizing the computer because the simple instructing instrument. This booklet assumes the reader has a data of necessary calculus, neutron delivery conception, and Fortran programming. It additionally assumes the reader has to be had a laptop with a Fortran compiler. Any computing device of moderate dimension can be sufficient to breed the examples or clear up the workouts contained herein. The authors think it is necessary for the reader to execute those examples and workouts, and through doing to be able to turn into complete at getting ready acceptable software program for fixing radiation delivery difficulties utilizing Monte Carlo. The step from the software program defined during this e-book to using creation Monte Carlo codes will be user-friendly.

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**Additional info for A Monte Carlo Primer: A Practical Approach to Radiation Transport**

**Sample text**

44 it is apparent that improvement in the accuracy of an estimate of the mean of a random variable can be made by increasing the number of samples calculated. However, improvements are typically expensive to obtain using this "brute force" method. For example, obtaining a factor of ten improvement in the accuracy of the result requires increasing the number of samples by a factor of 100. Other methods to reduce the variance are usually preferred in order to obtain accurate results with reasonable computation times.

The proof did not, however, depend upon this assumption. As long as the fraction of samples used for solving the problem was the same in each stratum for both the stratified and unstratified schemes, the above proof, suitably modified, would follow. Based on the preceding proof we can consider first an optimal scheme for selecting the fraction of the number of samples that should be used in each stratum of a stratified sampling process. 86) made with n total samples, with m samples used for the first stratum and n-m samples used for the second stratum.

The unbiased result is closer to the true answer than the biased result in this case because of the particular random number sequence used. 06507. This is approximately the reduction expected if the sample size were increased by a factor of 50. The reduction in the standard deviation indicates that the 54 Chapter 2 biased result is more reliable than the unbiased result. The modified pdf chosen here is not an optimal scheme in any normal sense of the word. It was chosen because it was easy to define and easy to implement.

### A Monte Carlo Primer: A Practical Approach to Radiation Transport by Stephen A. Dupree, Stanley K. Fraley

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