Heterogeneous Materials I

Linear Transport and Optical Properties

Muhammad Sahimi

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English

Springer Verlag
01 June 2007

Mathematics & Sciences; Maths for engineers; Materials science

Series: Interdisciplinary Applied Mathematics

8. Rigidity and Elastic Properties: The Discrete Approach 8. 0 Introduction 8. 1 Elastic Networks in Biological Materials 8. 2 Number of Elastic Moduli of a Lattice 8. 3 Numerical Simulation and Finite-Size Scaling 8. 4 Derivation of Elastic Networks from Continuum Elasticity 8. 4. 1 The Born model 8. 4. 2 Shortcomings of the Born model 8. 5 The Central-Force Network 8. 6 Rigidity Percolation 8. 6. 1 Static and dynamic rigidity and ?oppiness of networks 8. 6. 2 The correlation length of rigidity percolation 8. 6. 3 The force distribution 8. 6. 4 Determination of the percolation threshold 8. 6. 4. 1 Moments of the force distribution 8. 6. 4. 2 The pebble game 8. 6. 4. 3 Constraint-counting method 8. 6. 5 Mapping between rigidity percolation and resistor networks 8. 6. 6 Nature of phase transition in rigidity percolation 8. 6. 7 Scaling properties of the elastic moduli 8. 7 Green Function Formulation and Perturbation Expansion 8. 7. 1 E?ective-medium approximation 8. 7. 2 The Born model 8. 7. 3 Rigidity percolation 8. 8 The Critical Path Method 8. 9 Central-Force Networks at Non-zero Temperature and under Stress 8. 10 Shortcomings of the Central-Force Networks 8. 11 Elastic Percolation Networks with Bond-Bending Forces 8. 11. 1 The Kirkwood-Keating model xiv 8. 11. 2 The bond-bending model 8. 11. 3 The percolation thresholds 8. 11. 4 The force distribution 8. 11. 5 Comparison of the central-force and bond-bending networks 8. 11.

By: Muhammad Sahimi
Imprint: Springer Verlag
Country of Publication: United States
Volume: v.22
Dimensions: Height: 235mm, Width: 155mm, Spine: 36mm
Weight: 1.232kg
ISBN: 9780387001678
ISBN 10: 0387001670
Series: Interdisciplinary Applied Mathematics
Pages: 710
Publication Date: 01 June 2007
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Reviews for Heterogeneous Materials I: Linear Transport and Optical Properties

From the reviews: </p> This work represents the first part of an impressive two-volume book that describes various theoretical and computational approaches related to effective macroscopic properties of heterogeneous materials. A main goal is to compare two fundamental directions used to study the heterogeneous materials properties, namely the continuum mechanics approach and the discrete model approach. This multidisciplinary book is recommended to materials scientists, chemical and mechanical engineers, and applied physicists and mathematicians. (Olivian Simionescu, Zentralblatt MATH, Vol. 1028, 2004)</p>