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This dissertation covers the two major parts of my PhD research on statistical physics and complex networks: i) modeling a new type of attack – localized attack, and investigating robustness of complex networks under this type of attack; ii) discovering the clustering structure in complex networks and its influence on the robustness of coupled networks. Complex networks appear in every aspect of our daily life and are widely studied in Physics, Mathematics, Biology, and Computer Science. One important property of complex networks is their robustness under attacks, which depends crucially on the nature of attacks and the structure of the networks themselves. Previous studies have focused on two types of attack: random attack and targeted attack, which, however, are insufficient to describe many real-world damages. Here we propose a new type of attack – localized attack, and study the robustness of complex networks under this type of attack, both analytically and via simulation. On the other hand, we also study the clustering structure in the network, and its influence on the robustness of a complex network system. In the first part, we propose a theoretical framework to study the robustness of complex networks under localized attack based on percolation theory and generating function method. We investigate the percolation properties, including the critical threshold of the phase transition pc and the size of the giant component P∞. We compare localized attack with random attack and find that while random regular (RR) networks are more robust against localized attack, Erd ̋os-R ́enyi (ER) networks are equally robust under both types of attacks. As for scale-free (SF) networks, their robustness depends crucially on the degree exponent λ. The simulation results show perfect agreement with theoretical predictions. We also test our model on two real-world networks: a peer-to-peer computer network and an airline network, and find that the real-world networks are much more vulnerable to localized attack compared with random attack. In the second part, we extend the tree-like generating function method to incorporating clustering structure in complex networks. We study the robustness of a complex network system, especially a network of networks (NON) with clustering structure in each network. We find that the system becomes less robust as we increase the clustering coefficient of each network. For a partially dependent network system, we also find that the influence of the clustering coefficient on network robustness decreases as we decrease the coupling strength, and the critical coupling strength qc, at which the first-order phase transition changes to second-order, increases as we increase the clustering coefficient.

Thesis (Ph. D.)--Boston University, 2003. / In this thesis, studies which concern two different subjects related to phase transitions in fluids and crystalline solids are presented. Condensed matter formation, structure, and phase transitions are modeled using molecular dynamics simulations of simple discontinuous potentials with attractive and repulsive interactions. Novel phase diagrams are proposed for quasicrystals, crystals, and liquids. In the first part of the thesis, the formation of a quasicrystal in a two dimensional monodisperse system is investigated using molecular dynamics simulations of hard sphere particles interacting via a two-dimensional square-well potential. It is found that for certain values of the square-well parameters more than one stable crystalline phase can form. By quenching the liquid phase at a very low temperature, an amorphous phase is obtained. When this the amorphous phase is heated, a quasicrystalline structure with five-fold symmetry forms. From estimations of the Helmholtz potentials of the stable crystalline phases and of the quasicrystal, it is concluded that within a specific temperature range, the observed quasicrystal phase can be the stable phase. The second part of the thesis concerns a study of the liquid-liquid phase transition for a single-component system in three dimensions, interacting via an isotropic potential with a repulsive soft-core shoulder at short distance and an attractive well at an intermediate distance. The potential is similar to potentials used to describe [TRUNCATED}

This thesis studies three models: Multi-type TASEP in discrete time, long-range last- passage percolation on the line and convoy formation in a travelling servers model. All three models are relatively easy to state but they show a very rich and interesting behaviour. The TASEP is a basic model for a one-dimensional interacting particle system with non-reversible dynamics. We study some aspects of the TASEP in discrete time and compare the results to recently obtained results for the TASEP in continuous time. In particular we focus on stationary distributions for multi-type models, speeds of second- class particles, collision probabilities and the speed process. We consider various natural update rules.

by Tong Pak Yee. / Parallel title in Chinese characters. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 12-16). / Acknowledgement --- p.i / List of Publications --- p.ii / Abstract --- p.iii / Chapter 1. --- Introduction / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Outline of the article --- p.5 / Chapter 1.2.1 --- Multifractal Scaling in Fractal Lattice --- p.6 / Chapter 1.2.2 --- Anomalous Multifractality in Percolation Model --- p.7 / Chapter 1.2.3 --- Anomalous Crossover Behavior in Two-Component Random Resistor Network --- p.8 / Chapter 1.2.4 --- Current Distribution in Two-Component Random Resistor Network --- p.10 / Chapter 1.2.5 --- Multif ractality in Wide Distribution Fractal Models --- p.11 / References --- p.12 / Chapter 2. --- Multifractal Analysis of Percolation Backbone and Fractal Lattices / Chapter 2.1 --- Multifractal Scaling in Fractal Lattice --- p.17 / Chapter 2.1.1 --- Multifractal Scaling in a Sierpinski Gasket --- p.18 / Chapter 2.1.2 --- Hierarchy of Critical Exponents on a Sierpinski Honeycomb --- p.38 / Chapter 2.2 --- Anomalous Multifractality in Percolation Model --- p.51 / Chapter 2.2.1 --- Anomalous Multifractality of Conductance Jumps in a Hierarchical Percolation Model --- p.52 / Chapter 2.3 --- Anomalous Crossover Behavior in Two-Component Random Resistor Network --- p.74 / Chapter 2.3.1 --- Anomalous Crossover Behaviors in the Two- Component Deterministic Percolation Model --- p.75 / Chapter 2.3.2 --- Minimum Current in the Two-Component Random Resistor Network --- p.90 / Chapter 2.4 --- Current Distribution in Two-Component Random Resistor Network --- p.105 / Chapter 2.4.1 --- Current Distribution in the Two-Component Hierarchical Percolation Model --- p.106 / Chapter 2.4.2 --- Current Distribution and Local Power Dissipation in the Two-Component Deterministic Percolation Model --- p.136 / Chapter 2.5 --- Multifractality in Wide Distribution Fractal Models --- p.174 / Chapter 2.5.1 --- Fractal Networks with a Wide Distribution of Conductivities --- p.175 / Chapter 2.5.2 --- Power Dissipation in an Exactly Solvable Wide Distribution Model --- p.193 / Chapter 3. --- Conclusion --- p.210

Lee Kuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 123-128). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Minority Game: A Review --- p.3 / Chapter 2.1 --- The basic MG --- p.9 / Chapter 2.2 --- The basic features of MG --- p.11 / Chapter 2.3 --- Crowd-Anticrowd Theory --- p.15 / Chapter 2.4 --- Some variation on the Minority Game --- p.20 / Chapter 2.4.1 --- The Thermal Minority Game (TMG) --- p.20 / Chapter 2.4.2 --- The Evolutionary Minority Game (EMG) --- p.21 / Chapter 3 --- The Minority Game with different payoff functions --- p.23 / Chapter 3.1 --- Review --- p.24 / Chapter 3.1.1 --- Models of Savit et al [48] --- p.24 / Chapter 3.1.2 --- Results --- p.25 / Chapter 3.2 --- Applying Crowd-anticrowd theory to the models --- p.27 / Chapter 4 --- The Minority Game with k-sided imitation in regular net- works --- p.33 / Chapter 4.1 --- Review --- p.34 / Chapter 4.1.1 --- 1-sided follow-action model --- p.34 / Chapter 4.1.2 --- Results --- p.36 / Chapter 4.2 --- Follow-action model --- p.37 / Chapter 4.2.1 --- 2-sided model --- p.37 / Chapter 4.2.2 --- Results --- p.38 / Chapter 4.2.3 --- k-sided model and results --- p.40 / Chapter 4.3 --- Follow-strategy model --- p.43 / Chapter 4.3.1 --- 1-sided and 2-sided models --- p.43 / Chapter 4.3.2 --- Results --- p.45 / Chapter 4.3.3 --- k-sided model and results --- p.47 / Chapter 4.4 --- Summary --- p.51 / Chapter 5 --- One-lane traffic flow models --- p.53 / Chapter 5.1 --- Introduction --- p.54 / Chapter 5.2 --- NS dynamics --- p.56 / Chapter 5.3 --- FI dynamics --- p.60 / Chapter 6 --- One-lane traffic flow models with anticipation effects --- p.63 / Chapter 6.1 --- Review --- p.64 / Chapter 6.1.1 --- Model using NS dynamics --- p.64 / Chapter 6.1.2 --- Results --- p.65 / Chapter 6.2 --- Models using FI dynamics --- p.65 / Chapter 6.2.1 --- Models --- p.65 / Chapter 6.2.2 --- Results and Discussion --- p.68 / Chapter 6.2.3 --- Mean Field Theory --- p.76 / Chapter 6.3 --- Summary --- p.89 / Chapter 7 --- Two-route Models with Global Information --- p.91 / Chapter 7.1 --- Review: Two-route model with global information using NS dynamics --- p.92 / Chapter 7.1.1 --- Announcing transit time as global information --- p.92 / Chapter 7.1.2 --- Results --- p.93 / Chapter 7.2 --- Announcing instantaneous average speed model using NS dy- namics [87] --- p.95 / Chapter 7.2.1 --- Model --- p.95 / Chapter 7.2.2 --- Results --- p.95 / Chapter 7.2.3 --- Discussion --- p.99 / Chapter 7.3 --- Two-route models with global information using FI dynamics --- p.103 / Chapter 7.3.1 --- Models --- p.103 / Chapter 7.3.2 --- Results --- p.105 / Chapter 7.3.3 --- Discussion --- p.110 / Chapter 7.4 --- Summary --- p.120 / Chapter 8 --- Conclusion --- p.121 / Bibliography --- p.123

Wang, Xiaohui. / "November 1999." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Yu Wei-jian. / Thesis submitted in: November 2000. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 70-71). / Text in English; abstracts in English and Chinese. / Yu Wei-jian. / TITLE PAGE --- p.i / THESIS COMMITTEE --- p.ii / ABSTRACT (English) --- p.iii / ABSTRACT (Chinese) --- p.iv / ACKNOWLEDGEMENTS --- p.v / TABLE OF CONTENTS --- p.vi / LIST OF FIGURES --- p.viii / LIST OF TABLES --- p.ix / Chapter CHAPTER 1 --- INTRUDUCTION --- p.1 / Chapter Section 1.1 --- Background of the BN System --- p.1 / Chapter 1.1.1 --- Desirable Properties of c-BN --- p.1 / Chapter 1.1.2 --- Phases in the BN System --- p.2 / Chapter 1.1.3 --- Phase Diagram of BN --- p.4 / Chapter 1.1.4 --- Synthesis Techniques for c-BN Films --- p.5 / Chapter 1.1.5 --- Characterization of BN Films --- p.6 / Chapter Section 1.2 --- Background of Theory --- p.7 / Chapter Section 1.3 --- Objectives --- p.9 / Chapter 1.3.1 --- Determination of Stable State of BN --- p.9 / Chapter 1.3.2 --- Phonon-dispersion Relations of BN --- p.9 / Chapter 1.3.3 --- "Phase (p, T) Diagram" --- p.10 / Chapter 1.3.4 --- Transformation Paths in Direct Compressions --- p.10 / Chapter Section 1.4 --- Roadmap --- p.11 / Chapter CHAPTER 2 --- METHODS --- p.12 / Chapter Section 2.1 --- Density Functional Theory (DFT) for E0 Calculation --- p.12 / Chapter Section 2.2 --- Direct Force-constant Method --- p.16 / Chapter Section 2.2 --- Quasi-harmonic Approximation --- p.26 / Chapter CHAPTER 3 --- RESULTS --- p.27 / Chapter Section 3.1 --- Stable State of BN --- p.27 / Chapter Section 3.2 --- Phonon-dispersion Relations --- p.29 / Chapter Section 3.3 --- "Phase (p, T) Diagram of BN" --- p.36 / Chapter Section 3.4 --- Transformation Paths via Direct Compression --- p.44 / Chapter 3.4.1 --- Direct Compression of h-BN and r-BN --- p.46 / Chapter 3.4.2 --- Direct Compression of t-BN --- p.50 / Chapter Section 3.5 --- Energy Barriers in the Transformation of h-BN to c-BN --- p.52 / Chapter CHAPTER 4 --- DISCUSSION --- p.58 / Chapter Section 4.1 --- Transition States in the Transformation of h-BN to c-BN --- p.58 / Chapter Section 4.2 --- Phonon-dispersion Relations --- p.60 / Chapter Section 4.3 --- Phase Diagrams --- p.62 / Chapter Section 4.4 --- Future Studies --- p.63 / Chapter 4.4.1 --- Cubic BN Films Formation --- p.63 / Chapter 4.4.1.1 --- Nanoarches Nucleation --- p.64 / Chapter 4.4.1.2 --- Growth: Interfaces Between h-BN {0001} and c-BN Planes --- p.64 / Chapter 4.4.2 --- Transformation Paths of w-BN to c-BN and h-BN to r-BN --- p.65 / Chapter CHAPTER 5 --- CONCLUSION --- p.66 / APPENDIX: Mechanistic Models in c-BN Films Formation --- p.67 / REFERENCES --- p.70

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE / Vita. / Includes bibliographical references. / by Lawrence Maxwell Krauss. / Ph.D.