Controllability for swimming phenomena

该项目的目标是开发一种方法，用于研究模拟游泳现象的偏微分和常微分（或积分微分）方程的复杂耦合非线性系统的可控性。这些系统包括流体方程（例如，斯托克斯或纳维尔-斯托克斯方程）和描述游泳装置（或活有机体）在流体中的位置的方程。后者的游泳运动是由装置产生的“内部”力的作用的结果，该“内部”力也用作周围流体的“外部”力。在典型的游泳模型中，上述内力是保持手头装置的结构的力或使其游泳的“推进”力（例如，旋转或划船性质的）。后者的力量的大小被建模为系数，并作为非传统的（在数学可控性理论的框架）乘法或双线性controls.In这个项目中，我们将调查的数学性质的游泳运动的机械设备（如机器鱼或机器鳗鱼）或活的有机体在流体中。是什么让后者以这种方式游泳？或者更确切地说，需要使用什么样的力来实现理想的游泳运动？我们怎样才能设计出一个机械装置来做同样的事情呢？这些问题的答案是非常感兴趣的生物和医学应用和工程应用处理推进系统的流体。

The goal of this project is to develop a methodology for the study of controllability properties of complex coupled nonlinear systems of partial and ordinary differential (or integro-differential) equations modeling the swimming phenomena. These systems include the fluid equations (for example, Stokes or Navier-Stokes equations) and the equations describing the position of a swimming device (or a living organism) in the fluid. The swimming motion of the latter is the result of the action of "internal" forces generated by the device, which also serve as the "external" forces for the surrounding fluid. In a typical swimming model the aforementioned internal forces are either the forces, preserving the structure of the device at hand or the "propulsion" forces (for example, of rotation or rowing nature), which make it swim. The magnitudes of the latter forces are modeled as coefficients and serve as nontraditional (in the framework of the mathematical controllability theory) multiplicative or bilinear controls.In this project we will investigate the mathematical nature of the swimming motion of a mechanical device (such as a robotic fish or a robotic eel) or a living organism in a fluid. What makes the latter to swim the way it does? Or more precisely, what kind forces are necessary to employ to achieve the desirable swimming motion? How can we design a mechanical device that can do the same? Answers to these questions are of great interest in biological and medical applications and in engineering applications dealing with propulsion systems in fluids.