Residence and First Passage Time Functionals in Heterogeneous Ecological Dispersion

异质生态分散中的停留时间和首次通过时间泛函

• 批准号: 1122699
• 负责人: Edward Waymire
• 金额: $ 25万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1122699&HistoricalAwards=false
• 关键词: Residence; First; Passage; Time; Functionals

Residence and First Passage Time Functionals in Heterogeneous Ecological Dispersion Multiscale problems continue to motivate important mathematical modeling and research. This proposal aims to develop and analyze models relevant to several examples from biology, ecology, oceanography and epidemiology, that involve interfacial effects defined by discontinuities in values of coefficients in the models. These phenomena occur on highly heterogeneous domains in which sharp or abrupt discontinuities in certain physical, chemical, or biological properties of the landscape occur in the coefficients of the basic equations. The Pis will analyze functionals of the associated processes, both for fragmented or patchy domains and for discrete graphical structures, to quantify the effects that smaller scale interfacial discontinuities have on macro scale variables, such as resident and occupation time functionals. In the first part of the proposal, the PIs will develop stochastic approaches to the advection-dispersion-reaction equations with discontinuous coefficients that model different biological processes. Unlike more classical physical models where the micro-scale interface conditions can be determined by macro-scale conservation laws, data on biological responses to interfacial boundaries can be quite different. The determination of the appropriate models requires the development of new micro-scale methods of analysis involving local time and the Ito-Tanaka stochastic calculus to uncover the appropriate macro-scale equations governing population densities and characteristic functionals of dispersion. In the second part of the proposal the Pis will develop numerical methods, Monte-Carlo stochastic particle schemes, and new methods of statistical parameter estimation for advection-dispersion equations involving discontinuous coefficients with special interface geometries relevant to key biological field data.Natural physical processes, as well as certain anthropogenic activities, result in fragmented habitats to which species (animal, plants and bacteria) adapt or modify their behavior. Changes in the habitat configuration and/or its conditions, present new challenges and pose important broad new questions to scientists, policy makers and resource managers concerned with natural resources. Several contemporary problems in the biological and environmental sciences and engineering where such effects are reported to occur include: Bio-remediation of contaminated sediments in heterogeneous landscapes; Spread of infectious disease over fragmented habitats causing shifts in community structures possibly leading to invasion by exotic species; Species dispersal and sustainability in a heterogeneous environment affecting persistence of endangered species; Spatial localization of oceanic chlorophyll blooms impacting the fisheries industry. The specific mathematical issues common to these examples involve appropriate modeling of interfacial processes,i.e., mathematical discontinuities in the coefficients of the model equations, that affect the large scale behavior of species movement. The mathematical framework to be developed in this research is particularly aimed at assessing and quantifying interfacial effects on the large scale caused by these abrupt small -scale changes. This research will provide a mathematical framework and tools to support field and laboratory efforts to quantify and resolve fundamental questions about species dispersal through a combination of numerical and statistical algorithms, together with a theoretical mathematical analysis involving tools from deterministic and stochastic calculus.

非均匀生态扩散中的停留时间和首次通过时间泛函多尺度问题继续激发重要的数学建模和研究。该提案旨在开发和分析与生物学、生态学、海洋学和流行病学的几个例子相关的模型，这些例子涉及由模型中系数值的不连续性定义的界面效应。这些现象发生在高度异质性的领域，在这些领域中，景观的某些物理、化学或生物特性在基本方程的系数中出现尖锐或突然的不连续性。Pis将分析相关过程的泛函，无论是碎片或斑块域还是离散的图形结构，以量化较小尺度的界面不连续性对宏观尺度变量的影响，例如驻留和占用时间泛函。在提案的第一部分，PI将开发随机方法来模拟不同生物过程的不连续系数的对流-弥散-反应方程。与更经典的物理模型不同，其中微观尺度的界面条件可以由宏观尺度的守恒定律来确定，界面边界的生物反应数据可能会有很大的不同。确定适当的模型需要开发新的微观尺度的分析方法，包括当地时间和伊藤田中随机微积分，以揭示适当的宏观尺度方程的人口密度和分散的特征泛函。在提案的第二部分，Pis将开发数值方法、蒙特-卡罗随机粒子方案和对流-弥散方程统计参数估计的新方法，该方程涉及与关键生物场数据相关的特殊界面几何形状的不连续系数。（动物、植物和细菌）适应或改变它们的行为。生境结构和（或）其条件的变化，对与自然资源有关的科学家、决策者和资源管理者提出了新的挑战和重要的广泛的新问题。据报告，在生物和环境科学及工程领域出现的几个当代问题包括：对异质景观中受污染沉积物的生物补救;传染病在支离破碎的生境中的传播，造成群落结构的变化，可能导致外来物种的入侵;异质环境中的物种扩散和可持续性影响到濒危物种的持久性;影响渔业的海洋叶绿素水华的空间定位。这些例子共同的具体数学问题涉及界面过程的适当建模，即，模型方程系数的数学不连续性，影响物种运动的大尺度行为。在这项研究中开发的数学框架特别旨在评估和量化这些突然的小尺度变化所引起的大尺度界面效应。这项研究将提供一个数学框架和工具，以支持现场和实验室的努力，量化和解决有关物种扩散的基本问题，通过结合数值和统计算法，以及涉及工具的理论数学分析从确定性和随机微积分。