By Krauth W.
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Example text
There has been a lot of discussion about how big the little squares have to be taken, and there is no clear-cut answer. Some people prefer a box of size approximately √ 2 times the radius of the spheres. In this case you are sure that at most 1 sphere per square is present, but the number of boxes which need to be scrutinized is quite large. Others have adopted larger boxes which have the advantage that only the contents of 9 boxes have to be checked. In any case, one gains an important factor N with respect to the naive implementation.
If you want to know more about random deposition, notice that there is a vast research literature, and an algorithm has been presented in [10]. Notice that in our algorithm it was very important for the spheres to be monodisperse, ie for them all to have the same 1 There is no help in turning to the literature. the Question is neither treated in “Le Petit Prince” by A. de St. Exupery, nor in any other book I know. 9: The ultimate algorithm for random sequential adsorption needs a program to calculate the area of a star (straightforward), and a method to sample a random point within it.
Imagine a large two-dimensional square on which you deposit one coin per second - but attention: we only put the coin if it does not overlap with any of the coins already deposited. 6 will immediately be taken away. Random sequential adsorp- 35 tion is a particularly simple dynamical system because of its irreversibility. We are interested in two questions: • The game will stop at the moment at which it is impossible to deposit a new coin. What is the time after which this “jamming” state is reached and what are its properties?