By Stephen A. Dupree, Stanley K. Fraley
The mathematical means of Monte Carlo, as utilized to the delivery of sub-atomic debris, has been defined in several studies and books due to the fact its formal improvement within the Forties. almost all these educational efforts were directed both on the mathematical foundation of the approach or at its sensible software as embodied within the numerous huge, formal laptop codes to be had for appearing Monte Carlo shipping calculations. This ebook makes an attempt to fill what seems to be a niche during this Monte Carlo literature among the maths and the software program. hence, whereas the mathematical foundation for Monte Carlo delivery is roofed in a few aspect, emphasis is put on the appliance of the strategy to the answer of sensible radiation delivery difficulties. this is often performed through the use of the computer because the uncomplicated instructing software. This publication assumes the reader has an information of vital calculus, neutron delivery conception, and Fortran programming. It additionally assumes the reader has on hand a computer with a Fortran compiler. Any workstation of average measurement may be sufficient to breed the examples or remedy the routines contained herein. The authors think it is necessary for the reader to execute those examples and routines, and by way of doing so that you can develop into comprehensive at getting ready acceptable software program for fixing radiation delivery difficulties utilizing Monte Carlo. The step from the software program defined during this publication to using construction Monte Carlo codes will be straight forward.
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Additional resources for A Monte Carlo Primer: A Practical Approach to Radiation Transport
A brief description of the terminology that will be used in the remainder of this book is also necessary. The intent of this chapter is to introduce the mathematical concepts that underlie the Monte Carlo method and provide a basis for further development of selected topics. To obtain a broader and more rigorous development of the underlying mathematical concepts than is presented here the interested reader may consult any of a number of standard textbooks and references on statistics and probability.!
The sampling of events uses the following information: • The sample space from which a particular event or sample is to be selected, • The value of the random variables associated with every event in the sample space (this is required so that the Monte Carlo model can deal with real numbers), • The cumulative distribution and/or the pdf for the random variables involved in the problem, and • A method of obtaining a sequence of random numbers. These four elements are used in a Monte Carlo calculation in the following manner: • One or more random numbers are selected.
In order to calculate the statistical uncertainty in estimates of random variables, a few rules regarding the sums and products of variances and standard deviations are needed. 1 Stratified Sampling One effective technique for reducing the variance of a Monte Carlo estimate of a random variable is stratified sampling. With this technique the range over which the independent variable is sampled is divided into strata, and each stratum is sampled separately. 30. We wish to select subranges of the independent variable x to serve as strata for a demonstration of stratified sampling.
A Monte Carlo Primer: A Practical Approach to Radiation Transport by Stephen A. Dupree, Stanley K. Fraley