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 different reviews and books on the grounds that its formal improvement within the Forties. every one of these tutorial efforts were directed both on the mathematical foundation of the strategy or at its functional software as embodied within the a number of huge, formal desktop codes on hand for appearing Monte Carlo delivery calculations. This publication makes an attempt to fill what seems to be a niche during this Monte Carlo literature among the math and the software program. therefore, whereas the mathematical foundation for Monte Carlo delivery is roofed in a few aspect, emphasis is put on the applying of the strategy to the answer of sensible radiation delivery difficulties. this can be performed by utilizing the computer because the simple educating instrument. This e-book assumes the reader has an information of critical calculus, neutron shipping concept, and Fortran programming. It additionally assumes the reader has to be had a laptop with a Fortran compiler. Any workstation of average dimension will be enough to breed the examples or resolve the workouts contained herein. The authors think it is vital for the reader to execute those examples and routines, and by means of doing in an effort to develop into comprehensive at getting ready applicable software program for fixing radiation delivery difficulties utilizing Monte Carlo. The step from the software program defined during this e-book to using construction Monte Carlo codes could be trouble-free.
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Extra info for A Monte Carlo Primer: A Practical Approach to Radiation Transport
00 200 i=l,nstrata ! Get sums for integral and standard deviatioo var=O. l)var = (sumsq(i)/dj - (sumf(i)/dj)**2) totals=totals+sumf (i) /dj; tvarl=tvar1+var; tvar2=tvar2+var/dj 200 CCNI'INUE WRITE (8, 16)totals,DSQRT(tvarl),DSQRT(tvar2) 16 ~T(' sum:', flO . 6,' stdevof distr:', flO. 6) var=O . OdO ! 6,' stdev of distr: ',fl0 . 7,' stdevof sum:',eI4 . 6) REIURN END For many random variables of interest, the range over which a Monte Carlo estimate varies within a stratum can be less than that for the total sample space.
73% of the time the estimate will be within three standard deviations of the correct value. 5 Introduction to Variance Reduction Techniques As indicated above, the purpose of a Monte Carlo calculation is usually to obtain an estimate of the expected value of a random variable. The usual measure of the accuracy of the result is the standard deviation of the 2. Monte Carlo Sampling Techniques 39 estimate obtained. 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.
4 provides the set of all samples of two numbers taken from V. A typical Monte Carlo sampling scheme does not remove the numbers selected during the sampling process and thus values previously selected are available for subsequent selection. Hence a number can be repeated in a single sample. This is referred to as sampling with replacement. 4. 9195 The expected value of the mean, m, of the samples can be evaluated by averaging the means of all possible samples, since all samples have equal likelihood of occurring.
A Monte Carlo Primer: A Practical Approach to Radiation Transport by Stephen A. Dupree, Stanley K. Fraley