Mixing by Resonances in Multi-Scale Systems

该项目的目标是在有限惯性、随机波动和分子扩散等现象存在的情况下，发展多尺度系统中的共振混合理论。所构建的理论将提供一个有效和准确的方法来计算在一个给定的系统中的混合域的大小，估计的速度，彻底性，和混合的均匀性，并描述在一个混乱的海洋相干结构的外观。共振表面上的过程理论将与这些表面之间的绝热传输模型相结合，以开发一个统计的长期描述与共振系统中的传输。将对来自微流控实验室和空间等离子体实验的实验数据进行数值模拟和研究，以确定引起粒子输运的共振机制，并描述附加随机过程对输运稳定性的影响，如果成功，这项工作将导致将经常不连贯的方法和技术整合到一个适用于各种流、离散映射、和共振的哈密顿系统其中一个主要组成部分将是一种新的技术，在各种多尺度系统存在不确定性和波动的情况下，量化混合的不同方面和量化特征的持久性。所获得的结果将直接应用于科学和工程中的广泛问题，例如微流体或其他低雷诺数（微尺度）流动，彗星和小行星通过太阳系的运输，凝聚态物质中激发模式之间的能量交换，以及带电粒子在地球磁层或磁约束聚变装置的各种电磁场中的运动。

The goal of this project is to develop the theory of mixing by resonances in multi-scale systems in the presence of such phenomena as finite inertia, random fluctuations, and molecular diffusion. The constructed theory will provide an effective and accurate method to compute the size of the mixing domain in a given system, to estimate the rate, thoroughness, and uniformity of mixing, and to describe the appearance of coherent structures in a chaotic sea. The theory of processes on resonance surfaces will be combined with the adiabatic model of transport between those surfaces to develop a statistical long-term description of transport in systems with resonances. Numerical simulations and study of experimental data from microfluidics laboratory and space plasma experiments will be performed to identify the resonance mechanisms causing the transport of particles and describe the impact of additional stochastic processes on the stability of transport.If successful, this work will result in the integration of often disconnected methods and techniques into a general transport theory for a wide class of flows, discrete maps, and Hamiltonian systems with resonances. One of the main components will be a novel technique to quantify different aspects of mixing and the persistence of quantitative characteristics in the presence of uncertainties and fluctuations in various multi-scale systems. The obtained results will have direct applications to a wide range of problems in science and engineering, such as microfluidics or other low Reynolds-number (microscale) flows, the transport of comets and asteroids through the solar system, energy exchange between excitation modes in condensed matter, and motion of charged particles in various electromagnetic fields of the Earth's magnetosphere or magnetic confinement fusion devices.