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Download e-book for iPad: Elements of Computer Music by F. Richard Moore

By F. Richard Moore

ISBN-10: 0132525526

ISBN-13: 9780132525527

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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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.

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Elements of Computer Music by F. Richard Moore

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