Topics in Percolationand Particle Models

渗流和粒子模型主题

基本信息

  • 批准号:
    9803267
  • 负责人:
  • 金额:
    $ 10万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    1998
  • 资助国家:
    美国
  • 起止时间:
    1998-07-01 至 2002-06-30
  • 项目状态:
    已结题

项目摘要

9803267 Newman This research is in the general area of Probability Theory with special emphasis on a number of stochastic models with interesting spatial structure. One specific topic is first- passage percolation based on d-dimensional Poisson point processes, with particular emphasis on results related to the existence and nonexistence of semi-infinite and doubly infinite geodesics. A second major part of the work concerns a class of voter models in random environments which exhibit the intriguing phenomenon of "chaotic time dependence." This is when the model (which is a Markov process in time) has multiple invariant distributions and the distribution at time t (starting from a randomly selected initial state) does not converge as t tends to infinity. A smaller, but significant, part of the research involves continuum scaling limits of minimal spanning trees in the plane. In the general area of probability theory, an increasingly important role has been played in recent years by systems in which random effects are observed in the spatial structure rather than in (or in addition to) the behavior as a function of time (as in models of equity prices). Some of these models, such as first-passage percolation, have arisen separately in multiple contexts, such as fluid flow in porous media (which is relevant for example to modeling of pollutant dispersion in aquifers), polymer structure, and other parts of materials science. There are also connections to combinatorial optimization (as in the minimal spanning tree problem, which is a variant of the classical traveling salesman problem of designing optimal routings) and thus to various parts of theoretical computer science. The research under this grant concerns the mathematical phenomena that occur in several representative examples of such stochastic systems with interesting spatial structure. One particular issue of study is the connection between randomness in the spatial environment and chaotic depe ndence in time.
9803267纽曼 本研究属于概率论的一般领域,特别强调 一些具有有趣空间结构的随机模型。一个具体的主题是基于d维泊松点过程的首次通过渗流,特别是 重点讨论了半无限和双无限的存在性和不存在性 无限测地线第二个主要部分的工作涉及一类选民模型, 随机环境,表现出有趣的现象"混沌时间 依赖"这是当模型(时间上的马尔可夫过程)具有多个 不变分布和时间t处的分布(从随机选择的 初始状态)不收敛,因为t趋于无穷大。一个较小但重要的部分, 研究涉及平面中最小生成树的连续体缩放极限。 在概率论的一般领域, 近年来,在空间上观察到随机效应的系统发挥了作用, 结构,而不是在(或除了)作为时间函数的行为(如在模型中 股票价格)。其中一些模型,如首次通过渗流,已经出现 分别在多种情况下,如多孔介质中的流体流动(这与 含水层中污染物扩散模型的实例)、聚合物结构和其他 部分材料科学。也有连接到组合优化(如在 最小生成树问题,这是一个经典的旅行推销员的变种 设计最佳路线的问题),从而应用于理论计算机的各个部分 科学这项研究涉及的数学现象,发生在 几个有代表性的例子,这种随机系统与有趣的空间 结构研究的一个特殊问题是, 空间环境和时间上的混沌依赖。

项目成果

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Charles Newman其他文献

Cleaning and Sterilization of Used Cardiac Implantable Electronic Devices With Process Validation
通过流程验证对用过的心脏植入电子设备进行清洁和灭菌
  • DOI:
  • 发表时间:
    2017
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Thomas C. Crawford;Craig Allmendinger;Jay Snell;Kevin Weatherwax;Balasundaram Lavan;T. Baman;Patricia Sovitch;Daniel Alyesh;Thomas Carrigan;Noah Klugman;Denis Kune;Andrew B Hughey;Daniel Lautenbach;Nathan Sovitch;Karman Tandon;George Samson;Charles Newman;Sheldon Davis;Archie Brown;Brad Wasserman;Edward B Goldman;S. Arlinghaus;Hakan Oral;Kim A. Eagle
  • 通讯作者:
    Kim A. Eagle
What can the Defence Medical Services learn from the COVID-19 pandemic in order to be ready for the future?
国防医疗服务部门可以从 COVID-19 大流行中学到什么,以便为未来做好准备?
  • DOI:
    10.1136/military-2022-002205
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    1.5
  • 作者:
    Charles Newman
  • 通讯作者:
    Charles Newman

Charles Newman的其他文献

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{{ truncateString('Charles Newman', 18)}}的其他基金

Particle Systems, Percolation, and Scaling Limits
粒子系统、渗透和缩放限制
  • 批准号:
    1507019
  • 财政年份:
    2015
  • 资助金额:
    $ 10万
  • 项目类别:
    Continuing Grant
Pan American Advanced Studies Institute on Topics in Percolative and Disordered Systems; Argentina and Chile; January 1-15, 2012
泛美渗透和无序系统高级研究所;
  • 批准号:
    1036424
  • 财政年份:
    2011
  • 资助金额:
    $ 10万
  • 项目类别:
    Standard Grant
Particle Systems and Scaling Limits in Two (and More) Dimensions
二维(及更多)维度的粒子系统和缩放限制
  • 批准号:
    1007524
  • 财政年份:
    2010
  • 资助金额:
    $ 10万
  • 项目类别:
    Continuing Grant
Near-critical two-dimensional random systems
近临界二维随机系统
  • 批准号:
    1007626
  • 财政年份:
    2010
  • 资助金额:
    $ 10万
  • 项目类别:
    Standard Grant
PIRE: Percolative and Disordered Systems: A U.S.- Brazil-Netherlands Based International Collaboration
PIRE:渗透和无序系统:美国-巴西-荷兰的国际合作
  • 批准号:
    0730136
  • 财政年份:
    2008
  • 资助金额:
    $ 10万
  • 项目类别:
    Continuing Grant
Topics in Percolation & Particle Models
渗透主题
  • 批准号:
    0606696
  • 财政年份:
    2006
  • 资助金额:
    $ 10万
  • 项目类别:
    Continuing Grant
Mathematical Studies of Short-Ranged Spin Glasses
短程自旋玻璃的数学研究
  • 批准号:
    0604869
  • 财政年份:
    2006
  • 资助金额:
    $ 10万
  • 项目类别:
    Continuing Grant
Establishing a Chemical Laboratory Technician Program at Mt. San Antonio College
在圣安东尼奥山学院建立化学实验室技术员计划
  • 批准号:
    0302944
  • 财政年份:
    2003
  • 资助金额:
    $ 10万
  • 项目类别:
    Continuing grant
Collaborative Research: Mathematical Studies of Short-Ranged Spin Glasses
合作研究:短程自旋玻璃的数学研究
  • 批准号:
    0102587
  • 财政年份:
    2001
  • 资助金额:
    $ 10万
  • 项目类别:
    Continuing Grant
Topics in Percolation and Particle Models
渗流和粒子模型主题
  • 批准号:
    0104278
  • 财政年份:
    2001
  • 资助金额:
    $ 10万
  • 项目类别:
    Continuing Grant
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