Mixing by Resonances in Multi-Scale Systems

Drexel University, Philadelphia PA

Investigators

Abstract

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.