By Alireza Haghighat
The Monte Carlo approach has turn into the de facto common in radiation delivery. even supposing strong, if now not understood and used effectively, the tactic can provide deceptive effects.
Monte Carlo equipment for Particle Transport teaches applicable use of the Monte Carlo approach, explaining the method’s basic recommendations in addition to its obstacles. Concise but finished, this well-organized text:
- Introduces the particle significance equation and its use for variance reduction
- Describes normal and particle-transport-specific variance relief techniques
- Presents particle delivery eigenvalue concerns and methodologies to handle those issues
- Explores complicated formulations in line with the author’s learn activities
- Discusses parallel processing options and elements affecting parallel performance
Featuring illustrative examples, mathematical derivations, computing device algorithms, and homework difficulties, Monte Carlo tools for Particle shipping provides nuclear engineers and scientists with a pragmatic advisor to the applying of the Monte Carlo method.
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Additional info for Monte Carlo Methods for Particle Transport
Set ∆ x = bN− a . b. xi = xi − 1 + ∆ x. 18). If p( xi − 1 ) ≤ pi ≤ p( xi ) , then xi is accepted, otherwise divide Δx by 2, and repeat steps b through d. This process of determining the xi’s is a one-time calculation for a given pdf. Generate two random numbers (η1 and η2). Sample an interval (area) using i = INT( N ⋅ η1 ) + 1. Sample x within the ith interval using x = xi − 1 + η2 ( xi − xi − 1 ). 22) where αi is a constant to normalize fi. Hence, the p(x) formulation reduces to n p( x ) = ∑ α1 p (x).
The quality of any Monte Carlo simulation depends on the quality (or randomness) of the random numbers used. A high degree of randomness is achieved if the random numbers follow a uniform distribution. Therefore, we need to devise approaches that yield sequences of numbers that are random, have a long period before repeating, and do not require significant resources to obtain. Early implementation of random number generators on computers can be traced back to John von Neumann who used them for Monte Carlo simulation related to the Manhattan project (1941–1945).
A third Monte Carlo sampler. Report LA-9721-MS. Los Alamos, NM: Los Alamos Scientific Laboratory. Fo d e r a r o, A. H. 1986. A Monte Carlo primer. (Unpublished notes) University Park, PA: Pennsylvania State University. K a l o s , M. , and P. A. Whitlock. 1986. Monte Carlo methods, Volume I: Basics. New York: John Wiley & Sons. , and E. M. Gelbard. 2008. Monte Carlo principles and neutron transport problems. Mineola, NY: Dover. Vo n N e u m a n n, J. 1951. Various techniques used in connection with random digits.