逾渗（第2版）（英文版） [Percolation] 下载 mobi epub pdf 电子书 2024

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内容简介

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.

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目录

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

逾渗（第2版）（英文版） [Percolation] 下载 mobi epub pdf txt 电子书 格式

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表5-1的下部列出了逾渗理论对非晶态固体的应用。请注意逾渗现象与电子定域问题（非晶态固体的迁移率或安德森转变）以及原子定域问题（玻璃化转变）的联系，二者均属于凝聚态物理现象，其特征长度的典型值为10-8—10-2cm。非晶态固体是逾渗理论概念的一个富有成果的应用领域，它提供了一个具有丰富的无规结构的自然对象。在这里，拓朴无序起着至关重要的作用。对聚合物科学而言，逾渗理论可用于阐明玻璃化转变、溶胶-凝胶转变（见图5-11，它是一种特殊类型的玻璃化转变）等相变过程，也可用于说明聚合物功能化和高性能化改性研究中（如导电、导磁、发光、阻燃、组装、共聚、共混、复合、增韧、交联、碳黑增强、凝胶化、IPN等）各式各样的临界现象及其中最重要的物理概念。导电粒子填充的聚合中,当填充粒子达到一定的浓度时,体系的电导率发生突变,称为逾渗现象。这和贯穿于体系的导电网络形成直接相关，并依赖于基体的自身特性、加工条件等因素。解释逾渗现象的理论模型主要有基于几何学的唯象理论和基于热力学的理论模型导电逾渗阀值:就是能够起到导电作用所需要添加的最低导电材料的量，开展烟气的脱硫脱硝及固体废弃物（垃圾、污泥）的焚烧处理的研究，并对""理论变技术、技术变产品""的科研模式进行探索。

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帮别人买得，还没来得及看，说是不错。

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表1中约一半属宏观现象，一半属微观过程。宏观和微观的分界线在表的中间。这儿特意把两种极端情形并列以便于区别，请注意不同例子的特征长度相差可达1035。银河系的特征尺度量级为1022cm，而核子的尺度量级为10-13cm，用以说明逾渗理论广阔的适用范围。

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评分☆☆☆☆☆

帮别人买得，还没来得及看，说是不错。

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评分☆☆☆☆☆

表1中约一半属宏观现象，一半属微观过程。宏观和微观的分界线在表的中间。这儿特意把两种极端情形并列以便于区别，请注意不同例子的特征长度相差可达1035。银河系的特征尺度量级为1022cm，而核子的尺度量级为10-13cm，用以说明逾渗理论广阔的适用范围。

评分☆☆☆☆☆

表1中约一半属宏观现象，一半属微观过程。宏观和微观的分界线在表的中间。这儿特意把两种极端情形并列以便于区别，请注意不同例子的特征长度相差可达1035。银河系的特征尺度量级为1022cm，而核子的尺度量级为10-13cm，用以说明逾渗理论广阔的适用范围。

评分☆☆☆☆☆

表1中约一半属宏观现象，一半属微观过程。宏观和微观的分界线在表的中间。这儿特意把两种极端情形并列以便于区别，请注意不同例子的特征长度相差可达1035。银河系的特征尺度量级为1022cm，而核子的尺度量级为10-13cm，用以说明逾渗理论广阔的适用范围。

类似图书 点击查看全场最低价