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.

该项目的重点是理解三种环境中的随机空间模型：化学反应，与多发性硬化症的病变形成的病毒噬菌体以及合作的病变形成。传统的建模方法通常会忽略随机性和异质性。这样的假设产生了可拖动的方程，但牺牲了正在建模的过程的显着特征。随机空间模型提供了更细微的观点。探索理论前沿将使我们能够更好地利用其未开发的潜力。该项目协同纳入了被监禁的本科生，初级研究人员和学生的研究培训。对以不对称扩散率的歼灭和融合粒子系统的了解有限。客观的人设计新方法，例如耦合和多尺度渗透结构，以描述这些系统中的相位转换。目标两个涉及空间易感感染模型中的合作感染动态。将研究这些模型中大规模感染在稀疏随机图和整数晶格上的出现。目标三提出了由于多发性硬化而引起的新型轴突脱髓鞘范式。将利用随机生长模型的变体，例如内部扩散限制聚合和伊甸园模型。目的是通过研究这些模型中的增长与抑制之间的相互作用来捕获炎症过程的各个方面。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子和更广泛影响的评估来审查标准的评估值得支持的。