逾滲（第2版）（英文版） [Percolation] 下載 mobi epub pdf 電子書 2024

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內容簡介

This book is about the mathematics of percolation theory，with the emphasis upon presenting the shortest rigorous proofs of the main facts.I have made certain sacrifices in order to maximize the accessibility of the theory，and the major one has been to restrict myself almost entirely to the special case of bond percolation on the cubic lattice Zd.Thus there is only little discussion of such processes as continuum，mixed，inhomogeneous，long-range， first-passage，and oriented percolation.Nor have I spent much time or space on the relationship of percolation to statistical physics，infinite particle systems，disordered media，reliability theory，and so on.With the exception of the two final chapters，I have tried to stay reasonably close to core material of the sort which most graduate students in the area might aspire to know.No critical reader will agree entirely with my selection，and physicists may sometimes feel that my intuition is crooked.

內頁插圖

目錄

1 What is Percolation？
1.1 Modelling a Random Medium
1.2 Why Percolation？
1.3 Bond Percolation
1.4 The Critical Phenomenon
1.5 The Main Questions
1.6 Site Percolation
1.7 Notes

2 Some Basic Techniques
2.1 Increasing Events
2.2 The FKG Inequality
2.3 The BK Inequality
2.4 Russo's Formula
2.5 Inequalities of Reliability Theory
2.6 Another Inequality
2.7 Notes

3 Critical Probabilities
3.1 Equalities and Inequalities
3.2 Strict Inequalities
3.3 Enhancements
3.4 Bond and Site Critical Probabilities
3.5 Notes

4 The Number of Open Clusters per Vertex
4.1 Definition
4.2 Lattice Animals and Large Deviations
4.3 Differentiability of K
4.4 Notes

5 Exponential Decay
5.1 Mean Cluster Size
5.2 Exponential Decay of the Radius Distribution beneath Pe
5.3 Using Differential Inequalities
5.4 Notes

6 The Subcritical Phase
6.1 The Radius of an Open Cluster
6.2 Connectivity Functions and Correlation Length
6.3 Exponential Decay of the Cluster Size Distribution
6.4 Analyticity of K and X
6.5 Notes

7 Dynamic and Static Renormalization
7.1 Percolation in Slabs
7.2 Percolation of Blocks
7.3 Percolation in Half-Spaces
7.4 Static Renormalization
7.5 Notes

8 The Supercritical Phase
8.1 Introduction
8.2 Uniqueness of the Infinite Open Cluster
8.3 Continuity of the Percolation Probability
8.4 The Radius of a Finite Open Cluster
8.5 Truncated Connectivity Functions and Correlation Length
8.6 Sub-Exponential Decay of the Cluster Size Distribution
8.7 Differentiability of
8.8 Geometry of the Infinite Open Cluster
8.9 Notes

9 Near the Critical Point： Scaling Theory
9.1 Power Laws and Critical Exponents
9.2 Scaling Theory
9.3 Renormalization
9.4 The Incipient Infinite Cluster
9.5 Notes

10 Near the Critical Point：Rigorous Results
10.1 Percolation on a Tree
10.2 Inequalities for Critical Exponents
10.3 Mean Field Theory
10.4 Notes

11 Bond Percolation in Two Dimensions
12 Extensions of Percolation
13 Pereolative Systems
Appendix Ⅰ The Infinite-Volume Limit for Percolation
Appendix Ⅱ The Subadditive Inequality
List of Notation
References
Index of Names
Subject Index

前言/序言

逾滲（第2版）（英文版） [Percolation] 下載 mobi epub pdf txt 電子書 格式

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給彆人買的，他說還行吧

評分☆☆☆☆☆

給彆人買的，他說還行吧

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給彆人買的，他說還行吧

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錶1中約一半屬宏觀現象，一半屬微觀過程。宏觀和微觀的分界綫在錶的中間。這兒特意把兩種極端情形並列以便於區彆，請注意不同例子的特徵長度相差可達1035。銀河係的特徵尺度量級為1022cm，而核子的尺度量級為10-13cm，用以說明逾滲理論廣闊的適用範圍。

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這類書並不多見，很值得看一看。所謂逾滲就是指在一元或多元體係中，體係以外的一種介質通過一定的路徑進入體係內的過程。它是一種廣泛存在的物理現象，既存在於微觀世界，又存在於客觀世界，如液體可以擴散及逾滲過程穿過無序的介質。

評分☆☆☆☆☆

錶5-1的下部列齣瞭逾滲理論對非晶態固體的應用。請注意逾滲現象與電子定域問題（非晶態固體的遷移率或安德森轉變）以及原子定域問題（玻璃化轉變）的聯係，二者均屬於凝聚態物理現象，其特徵長度的典型值為10-8—10-2cm。非晶態固體是逾滲理論概念的一個富有成果的應用領域，它提供瞭一個具有豐富的無規結構的自然對象。在這裏，拓樸無序起著至關重要的作用。對聚閤物科學而言，逾滲理論可用於闡明玻璃化轉變、溶膠-凝膠轉變（見圖5-11，它是一種特殊類型的玻璃化轉變）等相變過程，也可用於說明聚閤物功能化和高性能化改性研究中（如導電、導磁、發光、阻燃、組裝、共聚、共混、復閤、增韌、交聯、碳黑增強、凝膠化、IPN等）各式各樣的臨界現象及其中最重要的物理概念。導電粒子填充的聚閤中,當填充粒子達到一定的濃度時,體係的電導率發生突變,稱為逾滲現象。這和貫穿於體係的導電網絡形成直接相關，並依賴於基體的自身特性、加工條件等因素。解釋逾滲現象的理論模型主要有基於幾何學的唯象理論和基於熱力學的理論模型導電逾滲閥值:就是能夠起到導電作用所需要添加的最低導電材料的量，開展煙氣的脫硫脫硝及固體廢棄物（垃圾、汙泥）的焚燒處理的研究，並對""理論變技術、技術變産品""的科研模式進行探索。

評分☆☆☆☆☆

錶1中約一半屬宏觀現象，一半屬微觀過程。宏觀和微觀的分界綫在錶的中間。這兒特意把兩種極端情形並列以便於區彆，請注意不同例子的特徵長度相差可達1035。銀河係的特徵尺度量級為1022cm，而核子的尺度量級為10-13cm，用以說明逾滲理論廣闊的適用範圍。

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