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

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 in view that its formal improvement within the Nineteen Forties. every one of these educational 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 laptop codes to be had for acting Monte Carlo shipping 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. hence, 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 functional radiation delivery difficulties. this is often performed through the use of the computer because the simple instructing instrument. This ebook assumes the reader has an information of necessary calculus, neutron delivery conception, and Fortran programming. It additionally assumes the reader has on hand a laptop with a Fortran compiler. Any notebook of average measurement may be enough to breed the examples or remedy the routines contained herein. The authors think it is vital for the reader to execute those examples and workouts, and through doing so that you can turn into finished at getting ready applicable software program for fixing radiation shipping difficulties utilizing Monte Carlo. The step from the software program defined during this e-book to using creation Monte Carlo codes could be uncomplicated.

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One commonly used distribution for which an inverse can be easily calculated is the exponential distribution. 11 ) where 'Y) is a constant. 11 may be the fraction of particles removed from a parallel beam of particles by scattering or absorption after passing a distance x through a uniform material, or it may be the fraction of a population of radioactive nuclei that have decayed after C If the set {x:f(x)=O}, where f(x) is a pdf, is a Lebesque measurable set with measure greater than zero, for x in the range of interest, then F') does not exist for x in that range.

X2, ... 22) Finally, the standard deviation, cr, of the set of numbers is the positive square root of the variance. 23) -00 This is also referred to as the first moment of V. 25) -00 The variance of a continuous random variable V is the second central moment of V, which is the expected value of [V - E(V)f, or 33 2. 26) -00 Again, the standard deviation cr of a continuous random variable V is the positive square root of the variance of V. 29 is useful for calculating or estimating the variance of a random variable.

Since the points are selected from a uniform distribution over the space S, the distribution of the accepted points is also uniform over the enclosed space S'. For the rejection technique to be efficient, it is necessary to ensure that the fraction of points that are rejected is small. This means that the volume of S should not be much larger than the volume of S', since the ratio of the volumes S'/S will determine the expected fraction of all the points chosen that will be accepted. It is also important that the process for choosing the randomly selected points within S be as simple as possible so that a minimum amount of time is spent in accepting or rejecting the points.

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