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Statistical mechanics of transport in disordered lattices and reaction-diffusion systems.

机译：在无序晶格和反应扩散系统中的传输统计力学。

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摘要

This thesis is the report of a study of several different problems in statistical physics. The first two are about random walks in a disordered lattice, with applications to a biological system, the third is about reaction-diffusion systems, particularly the phenomena of front propagation and pattern formation, and the last is about a special kind of evolving complex networks, the addition-deletion network. The motivation for the first of the two random walk investigations is provided by the diffusion of molecules in cell membranes. A mathematical model is constructed in order to predict molecular diffusion phenomena relating to the so-called compartmentalized view of the cell membrane. The theoretical results are compared with experimental observations available in the literature. The second random walk part in the thesis contains contributions to the analysis of transport in disordered systems via effective medium theory. Calculation of time-dependent transport quantities are presented along with discussion of effects of finite system size, significance of long-range memory functions, and consequences of correlated disorder. The investigation of reaction-diffusion systems that deals with front propagation is concerned with providing a method of studying transient dynamics in such systems whereas the study of pattern formation focuses on determining necessary conditions for such patterns to arise in situations wherein sub- and super-diffusion are present in addition to simple diffusion. In the network study, results are reported on cluster size distribution in addition-deletion networks, on the basis of both numerical and analytic investigations.
机译：本文是对统计物理学中几个不同问题的研究报告。前两个是关于无序晶格中的随机游走，并应用于生物系统；第三个是关于反应扩散系统，特别是前传播和图案形成的现象；最后一个是关于一种特殊的演化的复杂网络。 ，即添加删除网络。分子在细胞膜中的扩散提供了两个随机行走研究中第一个的动机。构建数学模型以便预测与所谓的细胞膜分隔图有关的分子扩散现象。将理论结果与文献中的实验观察结果进行比较。本文的第二个随机游走部分包含了通过有效介质理论对无序系统中运输的分析的贡献。提出了随时间变化的运输量的计算，并讨论了有限系统大小的影响，远程记忆功能的重要性以及相关疾病的后果。研究涉及前沿传播的反应扩散系统的目的是提供一种研究此类系统中瞬态动力学的方法，而模式形成的研究则侧重于确定在亚扩散和超扩散情况下此类模式出现的必要条件。除了简单的扩散外，还存在。在网络研究中，在数值和分析研究的基础上，报告了删除网络中簇大小分布的结果。

著录项

  • 作者

    Kalay, Ziya.;

  • 作者单位

    The University of New Mexico.;

  • 授予单位 The University of New Mexico.;
  • 学科 Physics Condensed Matter.;Physics Theory.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 207 p.
  • 总页数 207
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 O49;
  • 关键词

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