Anomalous diffusion in disordered media, scaling theory and renormalization of group analysis.

• Other Authors: Cheung, Kei Wai.
• Format: Others
• Language: English
• Published: Chinese University of Hong Kong 1992
• Subjects: Diffusion processes > Mathematical models; Order-disorder models
• Online Access: http://library.cuhk.edu.hk/record=b5886968; http://repository.lib.cuhk.edu.hk/en/item/cuhk-318991

by Cheung Kei Wai. === Parallel title in Chinese. === Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. === Includes bibliographical references (leaves 119-123). === Acknowledgement --- p.ii === Abstract --- p.iii === List of Abbreviations --- p.vii === List of Figure and Table Captions --- p.viii === List of Publication --- p.xiii === Chapter 1. --- Introduction --- p.1 === Chapter 1.1 --- Normal Diffusion --- p.4 === Chapter 1.2 --- Statistical Origin of Anomalous Diffusion --- p.10 === Chapter 1.3 --- Various Models of Diffusion --- p.15 === Chapter 2. --- Scaling Theory of Hopping Transport in One Dimension --- p.21 === Chapter 2.1 --- "Scaling Exponents, the Models and their Solutions" --- p.22 === Chapter 2.2 --- Numerical Simulations --- p.32 === Chapter 2.3 --- Relations to Diffusion on Fractals and Hierarchical Structures --- p.37 === Chapter 2.4 --- Non-Markovian Nature of Results and Quasi-localization Effect --- p.42 === Chapter 3. --- Renormalization Group (RG) Analysis of the Problem --- p.43 === Chapter 3.1 --- The Length Scale Renormalization (LSR) --- p.45 === Chapter 3.2 --- Application of the LSR to Random Barrier Model --- p.52 === Chapter 3.2.1 --- The distribution of the renormalized coupling constants === Chapter 3.2.2 --- Behaviour of W and V under the LSR transformation === Chapter 3.3.3 --- The scaling exponents from LSR === Chapter 3.3 --- Scaling Form of Diffusion Front --- p.66 === Chapter 4. --- Diffusion in Hierarchical Systems --- p.72 === Chapter 4.1 --- Scaling and Probability Densities --- p.75 === Chapter 4.2 --- Exact Renormalization and Lattice Green Function --- p.82 === Chapter 4.3 --- The Range of Diffusion --- p.89 === Chapter 5. --- Biased Diffusion --- p.95 === Chapter 5.1 --- Scaling Theory --- p.98 === Chapter 5.1.1 --- Linear Response === Chapter 5.1.2 --- Diffusion-Drift Crossover === Chapter 5.2 --- Crossover Behaviour under an Additional Bias --- p.103 === Chapter 6. --- Physical Realizations and Related Problems --- p.108 === Chapter 6.1 --- Physical Realizations --- p.109 === Chapter 6.2 --- Equivalence with Random Resistor Network (RRN) Problems --- p.113 === Chapter 7. --- Discussion and Conclusion --- p.116 === References --- p.119 === Chapter Appendix A --- Derivation of Eq. (1.3.8) --- p.124 === Chapter Appendix B --- Derivation of Eq. (1.3.10) --- p.126 === Chapter Appendix C --- Sampling from a Distribution --- p.129 === Chapter Appendix D --- Scaling Form of P (s) in Ordered System --- p.130 === Chapter Appendix E --- Explicit Form of the Lattice Green Function --- p.132