RUI: Transport of inertial particles in time-dependent and stochastic flows

流动的流体中的物体很少随波逐流。相反，它们可能会下沉、游泳或转向以到达目的地，或者它们可能会对其他影响做出反应，包括它们自己的大小和形状。利用真实对象与流交互的方式可以实现广泛的重要技术。在小范围内，微型机器人可以在人体内进行手术。在最大的范围内，海洋漂流者可以有效地监测洋流、海洋生物或全球天气模式。每个例子都提出了挑战，这些挑战源于复杂的流体流动模式和规划最有效的导航策略的困难。该项目专注于在海洋中定位自动驾驶车辆的挑战，在海洋中，不可预测和可变的水流、季节性变化、天气事件和其他随机影响也必须考虑在内。流体流动的计算机模型和控制的数学模型将结合在一起，以找到定位自主海洋航行器的最佳策略。实验室实验将使用精确调节的流体流动和遥控颗粒来捕捉飞行器质量、大小和形状的重要影响。该项目的回报是显著的，因为更好的海洋监测有利于渔业和航运、军事和环境监测。该项目将涉及并支持本科生和研究生的前沿研究。值得注意的是，蒙特克莱尔州立大学，尤其是数学科学系的学生中，有相当一部分是在STEM学科中代表性不足的群体(包括女性和少数族裔)，研究计划将利用针对这些学生的现有计划。研究成果将通过研讨会、在会议上的陈述以及在同行评议期刊上发表的文章来传播。在这个项目中，流体流动的计算机模型与运输和控制的数学模型将结合在一起，以找到自主海洋航行器的最优控制策略，这些航行器将被建模为惯性和非惯性对象。对精确调谐的流动和磁控颗粒的实验室实验将用于验证和指导调查。其目标是使用实验和计算的流场来识别关键的传输特征，并将这些特征集成到控制算法中，以优化颗粒的位置。该项目将通过开发受时间依赖和随机扰动的规范流中惯性物体的运输和控制模型来提高运输控制能力。流动数据将通过对旋涡流动、射流和边界流的数值模拟来产生。惯性粒子将使用最先进的界面多相数值代码直接建模。已经设计了实验室实验，通过重新配置几何强迫装置可以产生类似的流动。通过高分辨率粒子成像测速(PIV)和粒子跟踪，实验流场及其输运特性将与相关的模型流相关联。此外，将使用铁磁性示踪剂颗粒和磁脉冲来实施控制策略。为了深入了解流动的输运特性，流动和示踪剂数据将使用各种几何和概率方法进行分析，包括有限时间Lyapunov指数、惯性粒子模型、几乎不变集和有限时间相干集。这些技术将直接导致识别游荡区域及其边界和确定最大传输速率的能力。这些信息将被用来开发简单的运输和轨迹控制预测模型，这些模型可以有效地适应紧急应用。

Objects in moving fluids rarely go with the flow. Instead they may sink, swim or steer in order to reach a destination, or they may respond to other influences, including their own sizes and shapes. Taking advantage of the ways that real objects interact with flows enables a wide range of important technologies. On small scales, micro robots may be steered inside the human body to perform surgery. On the largest scales, ocean drifters may efficiently monitor currents, marine life or global weather patterns. Each example presents challenges originating from the complex fluid flow patterns and from the difficulty in planning the most efficient navigation strategy. This project concentrates on the challenges of positioning autonomous vehicles in the ocean, where unpredictable and variable currents, seasonal variability, weather events, and other random influences must also be accounted for. Computer models of fluid flows and mathematical models of control will be combined to find optimal strategies to position autonomous ocean vehicles. Laboratory experiments will use precisely tuned fluid flows and remotely controlled particles to capture the important effects of the vehicles' mass, size, and shape. The project payoff is significant in that a better monitored ocean is advantageous to fishing and shipping, the military, and environmental monitoring. The project will involve and support undergraduate and graduate students in leading-edge research. Significantly, the student population at Montclair State University, and in particular, the Department of Mathematical Sciences, includes a substantial proportion who are members of groups underrepresented in STEM disciplines (including women and minorities) and the research program will leverage existing programs directed to these students. The outcome of the research will be disseminated through seminars, presentations at meetings, and publications in peer-reviewed journals. In this project computer models of fluid flows and mathematical models of transport and control will be combined to find optimal control strategies for autonomous ocean vehicles, which will be modeled both as inertial and non-inertial objects. Laboratory experiments on precisely tuned flows and magnetically controlled particles will be used both to validate and guide the investigations. The goal is to use experimental and computed flow fields to identify critical transport features and integrate these features into control algorithms that optimally position particles. This project will improve transport control capabilities by developing models for transport and control of inertial objects in canonical flows subject to time-dependent and stochastic perturbations. Flow data will be generated by the numerical simulation of gyre flows, jets, and boundary currents. Inertial particles will be modeled directly using a state-of-the-art interfacial multi-phase numerical code. Laboratory experiments have been designed so that similar flows can be generated by reconfiguring the geometric forcing devices. Through high resolution particle imaging velocimetry (PIV) and particle tracking, experimental flow fields and their transport properties will be correlated with those of the associated model flows. Additionally, control strategies will be implemented using ferromagnetic tracer particles and magnetic pulses. To gain insight into the flow transport properties, flow and tracer data will be analyzed using a variety of geometric and probabilistic methods including finite-time Lyapunov exponents, inertial particle models, almost invariant sets, and finite-time coherent sets. These techniques will directly result in the ability to identify loitering regions and their boundaries and to determine maximal transport rates. This information will be leveraged to develop simple predictive models of transport and trajectory control that can be efficiently adapted to emergent applications.