By R. Byron Bird, Warren E. Stewart, Edwin N. Lightfoot
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Extra resources for Transport Phenomena: Solutions to the Class 1 and Class 2 Problems
Example text
Another benefit of this is that it avoids an exact zero which can cause problems in certain sampling algorithms. We will see more on this later. Although the endpoints of the distribution are truncated, it usually has no effect. Moreover, if you are depending upon good uniformity at the endpoints of the random number distribution, then you probably have to resort to special techniques to obtain them. 2 Long sequence random number generators For many practical applications, cycle lengths of one or four billion are just simply inadequate.
23283064e-09 Some computers will generate one exact floating-point zero with this algorithm, others may generate 2! 2328306e-09. This makes the range to be approximately 10−7 ≤ rn < 1 − 10−7 and appears 30 CHAPTER 3. RANDOM NUMBER GENERATION to work on all computers. Another benefit of this is that it avoids an exact zero which can cause problems in certain sampling algorithms. We will see more on this later. Although the endpoints of the distribution are truncated, it usually has no effect. Moreover, if you are depending upon good uniformity at the endpoints of the random number distribution, then you probably have to resort to special techniques to obtain them.
For example, if a cumulative probability distribution function is represented by a set of linear splines, differentiation will lead to a step-wise continuous probability distribution function. 1. 2. 40 CHAPTER 4. SAMPLING THEORY This is exactly the form used to calculate a particle’s distance to an interaction in all Monte Carlo codes. 7 will cause a floating-point error. 2 Rejection method While the invertible cumulative probability distribution function method is always possible, at least in principle, it is often impractical to calculate c()−1 because it may be exceedingly complicated mathematically or contain mathematical structure that is difficult to control.