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E-book Percolation Theory Using Python

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Penilaian

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n this chapter we motivate the study of disordered media through the example of a porous system. The basic terms in percolation theory are introduced, and you learn how to generate, visualize and measure on percolation systems in Python. We demonstrate how to find exact results for small systems in two dimensions by addressing all configurations of the system, and show that this approach becomes unfeasible for large system sizes. Percolation is the study of connectivity of random media and of other properties of connected subsets of random media [8, 30, 37]. Figure 1.1 illustrates a porous material—a material with holes, pores, of various sizes. This is an example of a random material with built-in disorder. In this book, we will address the physical properties of such media, develop the underlying mathematical theory and the computational and statistical methods needed to discuss the physical properties of random media. In order to do that, we will develop a simplified model system, a model porous medium, for which we can develop a well-founded mathematical theory, and then afterwards we can apply this model to realistic random systems. he porous medium illustrated in the figure serves as a useful, fundamental model for random media in general. What characterizes the porous material in Fig.1.1? The porous material consists of regions with and without material. It is therefore an extreme, binary version of a random medium. An actual physical porous material will be generated by some physical process, which will affect the properties of the porous medium in some way. For example, if the material is generated by sedimentary deposition, details of the deposition process may affect the shape and connectivity of the pores, or later fracturing may generate straight, open cracks in addition to more round pores. These features are always present in the complex geometries found in nature, and they will generate correlations in the randomness of the material. While these correlations can be addressed in detailed, specific studies of random materials, we will here instead start with a simpler class of materials—uncorrelated random, porous materials.

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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

530.072 MAL p

Penerbit

Switzerland : Springer Nature., 2024

Deskripsi Fisik

221 hlm

Bahasa

English

ISBN/ISSN

9783031599002

Klasifikasi

530.072

Tipe Isi

text

Tipe Media

computer

Tipe Pembawa

online resource

Edisi

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Subjek

Research and Statistical Methods of Physics

Info Detail Spesifik

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Pernyataan Tanggungjawab

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Versi lain/terkait

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