| 1. Introduction 2. Self-Similarity 2.1 Self-Similarity in Lattices and Networks 2.1.1 The concept of self-similarity: a few examples 2.1.2 Self-similarity and scale 2.2 Mathematical Description of Self-Similar Growth 2.3 One-Sided Growth by Agglomeration 2.3.1 Probabilistic description of agglomeration process 2.3.2 Energy barriers and Boltzmann factors 3. Topological and Statistical Properties of Networks 3.1 General Considerations 3.2 Topology and Geometry of Tilings and Networks 3.3 Statistical Properties of Networks, Configurational Entropy and Local Order 3.4 Topological Defects and Curvature 4: Bonds and Interactions in Networks 4.1 Preamble: A Historical Reminder 4.2 Properties of Chemical Bonds 4.2.1 Generalities 4.2.2 The four types of bonds 4.3 Dendritic and Ring-Forming Tendencies in Covalent Networks 4.4 A Lagrangean Approach to Network Interactions 4.4.1 A model in two dimensions 4.4.2 Generalization to three dimensions 5. Stochastic Agglomeration Model 5.1 General Considerations 5.2 A Two-Component Model in One Dimension 5.3 Dendritic Agglomeration of Star-Like Entities 5.4 Agglomeration of Rings in Two Dimensions 5.4.1 Second agglomeration step: chains and cells 5.5 Markov Chains and Random Walks 5.5.1 Basic definitions 5.5.2 Detailed balancing 5.6 The Stochastic Matrix Method 5.6.1 Bond saturation 5.6.2 Rim saturation 6. Model of Quasi-Crystalline Growth 6.1 Preamble: Aperiodic Structures and Quasicrystals 6.1.1 The discovery of quasicrystals 6.1.2 A few generalities on aperiodic structures 6.2 Mathematical Properties of Penrose Tilings 6.3 Agglomeration Model for a 2-dimensional Quasicrystal 6.3.1 The first agglomeration step: creating the doublets 6.3.2 The second step: creating chains and cells 6.4 Other Models of Quasi-Crystalline growth 7. Nucleation and Growth of Fullerenes 7.1 Preamble: A Short History of Fullerenes' Discovery 7.1.1 Other carbon nanostructures 7.2 Dynamical Model of Fullerene Growth 7.2.1 Statistical model based on self-similarity 7.2.2 Kinetic and energetic considerations 7.3 Geometry of Onion Fullerenes 8. Icosahedral Virus Capsid Growth 8.1 Preamble:Capsid Viruses 8.2 Probabilistic Analysis of Capsid Agglomeration …… 9. Glasses and their Properties 10. Kinetics of Crystallization in Liquids 11. Stochastic Agglomeration Model of Glass Transition 12. Ternary and Multicomponent Glasses.Immiscibility 13. Glass Transition and the Cooling Rate 14. Rigidity,Connectivity and Homogeneity in Glasses Appendix A Mathematical Complement Bibliography Index |
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