Eletrodinâmica by David J. Griffiths

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5. Reflection-diffusion This is a generalization of the reverse approach, inspired by the movement of a particle in a closed space. The particle bounces of the walls, not like a billiard ball, but in a more or less random manner and with variable elasticity. 46 Guided Randomness in Optimization The first step in this method is to find the intersection X2 of segment X (t) , X (t + 1) with the closest edge. Sometimes, this can be carried out analytically, but in practice, it is better to carry out reversal by dichotomy; this requires a longer calculation period, but can be used to satisfy constraints which are more complex than a simple interval of acceptable values (where the border is no longer linear).

Using Linux, for example, two files permanently collate these noises (the C and Scilab source codes for these files are included in the appendix). The second file facilitates faster generation, but the numbers are less “truly” random, as, if there is too little noise, a program is used to complete the generation process. The first file contains only material noise, which can result in delays before modification occurs. In both cases, the process is relatively slow in comparison with softwarebased generation.

Marsaglia method. Histogram of 50,000 values, split into 100 classes. 2. Additive All congruential linear generators are periodic, and cannot, therefore, produce dense sequences across a given interval: there will always be “gaps”, intervals of unattainable values. From a theoretical perspective, this is a drawback, though minimal in cases where the period is large; the issue can also be overcome easily. 1] where {u} is the fractional part of u. This is known as modulo 1 generation. If α is irrational or, better, transcendental, such as π, e, or sin (1), then it is easy to prove that the generated sequence is distributed evenly across ]0, 1[ (and is therefore dense) for this interval.