Fundamentals of the Monte Carlo Method for Neutral and Charged Particle Transport

By Bielajew, Alex F.

Book Id: WPLBN0000659732
Format Type: PDF eBook:
File Size: 2.88 MB
Reproduction Date: 2005

Title:	Fundamentals of the Monte Carlo Method for Neutral and Charged Particle Transport
Author:	Bielajew, Alex F.
Volume:
Language:	English
Subject:	Science., Physics, Physics--Research
Collections:	Physics Literature Collection
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Citation APA MLA Chicago F. Bielaje, B. A. (n.d.). Fundamentals of the Monte Carlo Method for Neutral and Charged Particle Transport. Retrieved from http://gutenberg.cc/

Description
Physics Literature

Excerpt
Preface: This book arises out of a course I am teaching for a two-credit (26 hour) graduate-level course Monte Carlo Methods being taught at the Department of Nuclear Engineering and Radiological Sciences at the University of Michigan.

Table of Contents
Contents 1 What is the Monte Carlo method? 1 1.1 Why isMonte Carlo? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Some history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Elementary probability theory 15 2.1 Continuous randomvariables . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.1 One-dimensional probability distributions . . . . . . . . . . . . . . . 15 2.1.2 Two-dimensional probability distributions . . . . . . . . . . . . . . . 17 2.1.3 Cumulative probability distributions . . . . . . . . . . . . . . . . . . 20 2.2 Discrete randomvariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3 Random Number Generation 25 3.1 Linear congruential randomnumber generators . . . . . . . . . . . . . . . . . 26 3.2 Long sequence randomnumber generators . . . . . . . . . . . . . . . . . . . 30 4 Sampling Theory 35 4.1 Invertible cumulative distribution functions (direct method) . . . . . . . . . 36 4.2 Rejectionmethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.3 Mixed methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.4 Examples of sampling techniques . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4.1 Circularly collimated parallel beam . . . . . . . . . . . . . . . . . . . 44 4.4.2 Point source collimated to a planar circle . . . . . . . . . . . . . . . . 46 4.4.3 Mixed method example . . . . . . . . . . . . . . . . . . . . . . . . . . 47