Deterministic and Stochastic Growth Models

确定性和随机增长模型

• 批准号: 0204376
• 负责人: Janko Gravner
• 金额: $ 11.57万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0204376&HistoricalAwards=false
• 关键词: Deterministic; Stochastic; Growth; Models

0204367Gravner Professor Gravner will pursue further research in cellular automata. The research will continue in several new directions. The growth models featured in this project range from simple threshold rules and competition dynamics, to interacting systems of random walks and percolation models in low- and high-dimensional spaces. Among the principle topics are: effects of random perturbations in the environment and in the rule, fluctuations of random interfaces, generation of fractal patterns, behavior of large--neighborhood systems, large scale limits of systems of random walks, and relationship between structure of genotype space and genetic diversity. The aim of this project is to understand microscopic and macroscopic principles by which various physical systems propagate disturbances far from the equilibrium. Among instances of such growth dynamics are crystal growth, spread of epidemics, propagation of waves, competition between species, and genetic diversification. Such research can contribute to understanding of such natural phenomena as: threshold density for survival and growth vs. the range of interaction for species in an unfriendly environment, transition between sharp geometric crystal shapes and rough random ones, effects of noisy environments on spread of infections, validity of approximation based on large range of interaction or fast diffusion, and role of neutral mutations in genetic drift.

[20436 . 67] Gravner教授将进一步研究元胞自动机。这项研究将在几个新的方向上继续进行。该项目采用的生长模型包括从简单的阈值规则和竞争动态，到低维和高维空间中随机游走和渗透模型的相互作用系统。主要主题包括：环境和规则中随机扰动的影响、随机界面的波动、分形模式的产生、大邻域系统的行为、随机行走系统的大规模限制、基因型空间结构与遗传多样性之间的关系。这个项目的目的是了解微观和宏观的原理，通过这些原理，各种物理系统传播远离平衡的干扰。这种生长动力学的实例包括晶体生长、流行病的传播、波浪的传播、物种之间的竞争和遗传多样化。这些研究有助于理解以下自然现象：生存和生长的阈值密度与物种在不友好环境中的相互作用范围，尖锐几何晶体形状与粗糙随机晶体形状之间的过渡，嘈杂环境对感染传播的影响，基于大范围相互作用或快速扩散的近似有效性，以及中性突变在遗传漂变中的作用。