CAREER: Research and training in stochastic dynamics
职业:随机动力学研究和培训
基本信息
- 批准号:1351653
- 负责人:
- 金额:$ 45.19万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2014
- 资助国家:美国
- 起止时间:2014-07-01 至 2020-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The project involves analysis of two types of stochastic dynamics. First, the PI will study solutions to stochastic differential equations which undergo rare, random transitions between two or more regions of the state space. The goal of this work is to understand the statistics of these transitions, especially in the small-noise regime: what are the typical pathways by which the transitions occur? what is the typical time required for a transition? These issues are very relevant to problems in chemistry and molecular dynamics, as well as many other physical systems exhibiting metastable behavior. The second type of stochastic dynamics which the PI will study has to do with stochastic interacting particle systems. Specific systems to be studied involve random motion, growth, and selection, as in models of evolution, population genetics, adaptive dynamics. The PI will study continuum limits and large-time limits for such systems. In particular, this will illuminate new relations between interacting particle systems and continuum free boundary problems.When viewed at a certain scale, many physical and biological systems seem to behave randomly or are influenced by small random fluctuations. Mathematical models of such systems involve probability theory. Nevertheless, it is very difficult to use these mathematical models to efficiently predict the system behavior over a long period of time or over a large spatial region. Therefore, a fundamental scientific and mathematical problem is to understand how random dynamics or interactions at one spatial or temporal scale influence a system at another spatial or temporal scale. This research project develops mathematical tools for predicting and describing the macroscopic behavior of certain systems which behave randomly at a microscopic level. The specific systems to be studied are motivated by problems in chemistry and by models of biological evolution. One common feature in these systems is the appearance of random, perhaps rare, transitions: a chemical reaction occurs or a cell produces a mutation. The educational component of the project includes the training of graduate and undergraduate students at the intersection of probability, analysis, and applications, preparing them for careers in STEM-related disciplines.
该项目涉及两种类型的随机动力学分析。首先,PI将研究随机微分方程的解,这些方程在状态空间的两个或多个区域之间进行罕见的随机转换。 这项工作的目标是了解这些过渡的统计,特别是在小噪声制度:什么是典型的途径,过渡发生?过渡一般需要多长时间? 这些问题与化学和分子动力学以及许多其他表现出亚稳态行为的物理系统中的问题非常相关。PI将研究的第二种类型的随机动力学与随机相互作用粒子系统有关。 要研究的特定系统涉及随机运动、生长和选择,如进化模型、群体遗传学和适应动力学。PI将研究此类系统的连续极限和大时间极限。特别是,这将阐明相互作用粒子系统和连续介质自由边界问题之间的新关系。当在一定尺度上观察时,许多物理和生物系统似乎表现为随机或受小的随机波动的影响。这种系统的数学模型涉及概率论。 然而,很难使用这些数学模型来有效地预测长时间或大空间区域内的系统行为。 因此,一个基本的科学和数学问题是理解一个空间或时间尺度上的随机动力学或相互作用如何影响另一个空间或时间尺度上的系统。该研究项目开发了数学工具,用于预测和描述某些系统的宏观行为,这些系统在微观水平上表现随机。 要研究的特定系统的动机是化学问题和生物进化模型。这些系统的一个共同特征是随机的,也许是罕见的,转变的出现:化学反应发生或细胞产生突变。该项目的教育部分包括在概率,分析和应用的交叉点培训研究生和本科生,为他们在STEM相关学科的职业生涯做好准备。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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James Nolen其他文献
A Variational Principle for KPP Front Speeds in Temporally Random Shear Flows
- DOI:
10.1007/s00220-006-0144-8 - 发表时间:
2006-11-04 - 期刊:
- 影响因子:2.600
- 作者:
James Nolen;Jack Xin - 通讯作者:
Jack Xin
Multiscale modelling and inverse problems
多尺度建模和反问题
- DOI:
10.1007/978-3-642-22061-6_1 - 发表时间:
2010 - 期刊:
- 影响因子:0
- 作者:
James Nolen;G. Pavliotis;Andrew M. Stuart - 通讯作者:
Andrew M. Stuart
Normal approximation for the net flux through a random conductor
- DOI:
10.1007/s40072-015-0068-4 - 发表时间:
2015-12-16 - 期刊:
- 影响因子:1.400
- 作者:
James Nolen - 通讯作者:
James Nolen
Erratum to: Reactive trajectories and the transition path process
- DOI:
10.1007/s00440-014-0558-8 - 发表时间:
2014-04-09 - 期刊:
- 影响因子:1.600
- 作者:
Jianfeng Lu;James Nolen - 通讯作者:
James Nolen
James Nolen的其他文献
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{{ truncateString('James Nolen', 18)}}的其他基金
AMC-SS: Analysis of Fluctuations for PDEs with Random Coefficients
AMC-SS:具有随机系数的偏微分方程的波动分析
- 批准号:
1007572 - 财政年份:2010
- 资助金额:
$ 45.19万 - 项目类别:
Standard Grant
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