By Alireza Haghighat
The Monte Carlo procedure has turn into the de facto average in radiation delivery. even supposing robust, if no longer understood and used thoroughly, the strategy may give deceptive effects.
Monte Carlo equipment for Particle Transport
teaches acceptable use of the Monte Carlo technique, explaining the method’s basic techniques in addition to its obstacles. Concise but complete, this well-organized text:
- Introduces the particle significance equation and its use for variance reduction
- Describes common and particle-transport-specific variance relief techniques
- Presents particle shipping eigenvalue concerns and methodologies to handle those issues
- Explores complicated formulations in accordance with the author’s learn activities
- Discusses parallel processing ideas and elements affecting parallel performance
Featuring illustrative examples, mathematical derivations, computing device algorithms, and homework difficulties, Monte Carlo equipment for Particle delivery provides nuclear engineers and scientists with a pragmatic consultant to the appliance of the Monte Carlo method.
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E. , and M. E. Muller. 1958. A note on the generation of random normal deviates. The Annals of Mathematical Statistics 29: 610–611. Ca s h w e l l , E. , C. J. Everett, and G. D. Turner. 1973. A method of sampling certain probability densities without inversion of their distribution functions. Report LA-5407+4S. Los Alamos, NM: Los Alamos Scientific Laboratory. E v e r e t t, C. , and E. D. Cashwell. 1983. A third Monte Carlo sampler. Report LA-9721-MS. Los Alamos, NM: Los Alamos Scientific Laboratory.
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).
Then sampling is performed by generating a random number, which is compared with the cdf to determine the random variable. , continuous versus discrete, somewhat different procedures are used as follows. 5 should be applied. indb 23 1. A random variable η is generated. A search for i is conducted such that the Pi − 1 < η ≤ Pi inequality is satisfied. 10/24/14 12:16 PM 24 Monte C arlo Me thods for Particle Tr ansport Note that a linear or binary search algorithm, as discussed in the previous section, should be employed in step 2.