CAREER: Stochastic Spatial Systems

职业：随机空间系统

• 批准号: 2238272
• 负责人: Matthew Junge
• 金额: $ 45.11万
• 依托单位: CUNY Baruch College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2028-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2238272&HistoricalAwards=false
• 关键词: CAREER; Stochastic; Spatial; Systems

This project focuses on understanding stochastic spatial models in three settings: chemical reactions, viral phages cooperating to attack bacteria, and lesion formation from multiple sclerosis. Traditional modeling approaches often omit randomness and heterogeneity. Such assumptions yield tractable equations but sacrifice salient features of the processes being modeled. Stochastic spatial models provide a more nuanced perspective. Exploring the theoretical frontier will allow us to better harness their untapped potential. This project synergistically incorporates research training for undergraduates, junior researchers, and students who are incarcerated.There is limited understanding of annihilating and coalescing particle systems with asymmetric diffusion rates. Objective One devises new methods, such as couplings and multi-scale percolation constructions, to describe phase-transitions in these systems. Objective Two involves cooperative infection dynamics in spatial Susceptible-Infected models. The emergence of large-scale infections in these models on sparse random graphs and integer lattices will be studied. Objective Three proposes a new modeling paradigm for axon demyelination due to multiple sclerosis. Variants of stochastic growth models such as internal diffusion-limited aggregation and the Eden model will be utilized. The goal is to capture aspects of inflammatory processes that damage the central nervous system by studying the interplay between growth and suppression in these models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目的重点是了解三种环境下的随机空间模型：化学反应、病毒噬菌体协同攻击细菌以及多发性硬化症的病变形成。传统的建模方法常常忽略随机性和异质性。这种假设产生了易于处理的方程，但牺牲了所建模过程的显着特征。随机空间模型提供了更细致的视角。探索理论前沿将使我们能够更好地利用它们尚未开发的潜力。该项目协同整合了针对本科生、初级研究人员和被监禁学生的研究培训。人们对具有不对称扩散率的湮灭和合并粒子系统的了解有限。目标一设计了新的方法，例如耦合和多尺度渗流结构，来描述这些系统中的相变。目标二涉及空间易感感染模型中的协作感染动态。将研究这些模型在稀疏随机图和整数格上出现的大规模感染。目标三提出了多发性硬化症导致的轴突脱髓鞘的新建模范例。将使用随机增长模型的变体，例如内部扩散限制聚合和伊甸园模型。目标是通过研究这些模型中生长和抑制之间的相互作用来捕获损害中枢神经系统的炎症过程的各个方面。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。