U.S.-Polish Collaborative Research: Multidimensional Nonlinear Fractal Dynamics in Continuous Media

美波合作研究：连续介质中的多维非线性分形动力​​学

• 批准号: 0310055
• 负责人: Wojbor Woyczynski
• 金额: --
• 依托单位: Case Western Reserve University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0310055&HistoricalAwards=false
• 关键词: U.S.; Polish; Collaborative; Research; Multidimensional

This is a U.S.-Polish cooperative research project that will investigate analytical and computational tools for multidimensional nonlinear fractal dynamics in continuous media. Nonlinear and nonlocal advection-dispersion equations involving generators of continuous-time random walks will also be studied. The tools from both probability theory and the theory of nonlinear partial differential equations will be utilized, including theoretical results on critical nonlinearities for Levy conservations laws obtained under prior NSF support. The principal investigators are Dr. Wojbor Woyczynski from Case Western Reserve University and Professor Grzegorz Karch from the University of Wroclaw. The broader impact resulting from the proposed activity is assured by the fact that the dynamics to be studied reflect behavior of a variety of complex systems of a large number of nonlinearly interacting components which operate in uncertain environments and with imperfect information about their initial states. Examples of such systems are networks of servers on the internet, power grids distributing electric power, environmental systems in the presence of turbulent atmosphere and complex oceanic flows, and chemical vapor deposition systems for manufacturing thin semiconductor films.This project in mathematics research fulfills the program objectives of bringing together leading experts in the U.S. and Central/Eastern Europe to combine complementary efforts and capabilities in areas of strong mutual interest and competence on the basis of equality, reciprocity, and mutuality of benefit.

这是一个美国-波兰合作研究项目，将研究连续介质中多维非线性分形动力学的分析和计算工具。还将研究包含连续时间随机游动的生成元的非线性和非局部对流-弥散方程。将利用概率论和非线性偏微分方程理论的工具，包括在先前的NSF支持下得到的关于Levy守恒律的临界非线性的理论结果。主要研究人员是凯斯西储大学的沃伊博尔·沃伊琴斯基博士和弗罗茨瓦夫大学的格泽戈尔茨·卡奇教授。要研究的动力学反映了各种复杂系统的行为，这些复杂系统由大量在不确定环境中运行且具有关于其初始状态的不完全信息的非线性相互作用的组件组成，这一事实确保了所提议的活动所产生的更广泛的影响。这类系统的例子包括互联网上的服务器网络、分配电力的电网、在湍流大气和复杂海洋流动中存在的环境系统，以及用于制造半导体薄膜的化学气相沉积系统。这个数学研究项目实现了将美国和中东欧的顶尖专家聚集在一起，在平等互利和互惠互利的基础上，在共同利益和能力强的领域结合互补努力和能力的计划目标。