By F. Richard Moore
It is a normal advent to the speculation of computing device tune, giving info on sound, electronic sign processing, math, and C programming. It assumes a robust wisdom of track and arithmetic.
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Extra info for Elements of Computer Music
Note that the percolation phenomenon as deﬁned above is a static process. That is, once a percolation network with a given value of p is generated, its conﬁguration does not change with time. Such static networks sufﬁce for modeling certain ﬂow phenomena in porous media. For other problems, for example, displacement of one ﬂuid by another immiscible ﬂuid in a porous medium, the conﬁguration of the network in terms of the open and closed bonds and/or sites is dynamic. We will consider such dynamic percolation networks later in this book, although, it must be emphasized that many concepts described here are equally applicable to both static and dynamic percolation networks.
Finite-size scaling theory has been successfully used for obtaining accurate estimates of the critical exponents and even the percolation thresholds from simulation of ﬁnite systems. , 1976): pc p c (L) L 1 ν . 19) In this equation, p c is the percolation threshold of the inﬁnite system and p c (L) is an effective p c for a ﬁnite system of linear dimension L. However, we should point out that Eqs. 19) are valid for very large network size L, whereas in practice, very large systems cannot be easily simulated.
We will come back to this very important point later in this book. 9 Finite-Size Effects All the percolation properties described so far, including the percolation thresholds and the critical exponents, are deﬁned for those that are of inﬁnite extent. However, percolation in ﬁnite systems is important since, both in practical applications and in computer simulations, one usually works with systems of ﬁnite extent. In such systems, as p c is approached, the correlation length ξp eventually exceeds the system’s linear size L, in which case, as pointed out above, L becomes the dominant length scale.
Elements of Computer Music by F. Richard Moore