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- W44344089 abstract "The intent of the present chapter is to derive and discuss some basic results and specific developments in continuum percolation theory. We will begin with a discussion of exact results for cluster statistics and other percolation descriptors for a prototypical model of continuum percolation, namely, identical overlapping spheres in d dimensions. Subsequently, we will describe an Ornstein-Zernike formalism to find the pair-connectedness function P 2(r) for general isotropic models of continuum percolation. The reader should note the beautiful correspondence of this theory to the Ornstein-Zernike formalism for the total correlation function h(r) of equilibrium (or thermal) systems discussed in Chapter 3. This will be followed by a discussion of various approximation schemes to close the resulting integral equation, including the Percus-Yevick approximation. The next topic will be the two-point cluster function C 2(r). First we will present an exact series representation of C 2(r) for dispersions and then discuss its analytical evaluation for certain models. The chapter will conclude with a presentation of percolation thresholds for overlapping sphere systems, overlapping particles of nonspherical shape, and interacting particle systems. The reader is referred to Meester and Roy (1996) for a more mathematical treatment of continuum percolation." @default.
- W44344089 created "2016-06-24" @default.
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- W44344089 date "2002-01-01" @default.
- W44344089 modified "2023-09-23" @default.
- W44344089 title "Some Continuum Percolation Results" @default.
- W44344089 doi "https://doi.org/10.1007/978-1-4757-6355-3_10" @default.
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