Collaborative Research: Long-Term Chaotic Transport in Volume-Preserving Flows

合作研究：保体积流中的长期混沌传输

• 批准号: 0900018
• 负责人: Roman Grigoriev
• 金额: $ 13.5万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0900018&HistoricalAwards=false
• 关键词: Collaborative; Research; Long; Term; Chaotic

0900177/0900018 Vainchtein/Grigoriev The goal of this research program is to construct a general quantitative theory of long-time resonance-driven chaotic transport and mixing in near-integrable autonomous and non-autonomous volume-preserving flows. Specific examples of microscale flows will be used to illustrate the general approach and develop specific tools that can be naturally generalized to a wide class of volume-preserving and Hamiltonian systems. The deterministic theory of resonance processes will be combined with the theory of random walks and theory of stability islands to develop a statistical long-term description of the Lagrangian transport in systems with separatrices and/or resonances. A unique feature of the planned approach is that it will apply both when chaotic advection is the only transport mechanism as well as when chaotic advection competes with thermal or molecular diffusion. This work includes integration of often disconnected methods and techniques used to describe resonant interactions and regular transport into a general transport theory for near-integrable systems, and development of a novel technique to quantify mixing rate, thoroughness, and uniformity for incompressible fluid flows. The PIs' research has direct applications to a wide range of problems in science and engineering, such as the transport of comets and asteroids through the solar system, energy exchange between excitation modes in condensed matter, and motion of charged particles in electromagnetic fields with applications to atmospheric science and magnetic confinement fusion devices. The key application is in the field of microfluidics which promises major advances in drug discovery, medical diagnostics, and national security through its impact on chemical processing and sensor technology. The research program will be tightly integrated with teaching and learning at the undergraduate and graduate levels and will include activities aimed at increased participation of underrepresented groups in research and integration of research advances into the curriculum. The PIs will also seek to extend and establish microfluidics collaborations with the plasma physics community.

0900177/0900018 Vainchtein/Grigoriev 该研究项目的目标是构建近可积自主和非自主体积保持流中长期共振驱动的混沌输运和混合的通用定量理论。将使用微尺度流动的具体示例来说明一般方法并开发可以自然推广到各种体积保持和哈密顿系统的特定工具。共振过程的确定性理论将与随机游走理论和稳定性岛理论相结合，以开发具有分离和/或共振的系统中拉格朗日输运的统计长期描述。该计划方法的一个独特之处在于，它既适用于混沌平流是唯一传输机制的情况，也适用于混沌平流与热或分子扩散竞争的情况。这项工作包括将用于描述共振相互作用和规则传输的经常分离的方法和技术集成到近可积系统的一般传输理论中，并开发一种量化不可压缩流体流动的混合速率、彻底性和均匀性的新技术。 PI 的研究可直接应用于科学和工程中的广泛问题，例如彗星和小行星在太阳系中的传输、凝聚态物质中激发模式之间的能量交换，以及电磁场中带电粒子的运动以及在大气科学和磁约束聚变装置中的应用。其关键应用是微流体领域，通过其对化学加工和传感器技术的影响，有望在药物发现、医疗诊断和国家安全方面取得重大进展。该研究计划将与本科生和研究生的教学紧密结合，并将包括旨在增加代表性不足群体参与研究以及将研究进展纳入课程的活动。 PI 还将寻求扩大和建立与等离子体物理学界的微流体合作。