Swimming Phenomenon from the Viewpoint of Controllability Theory for Partial Differential Equations

从偏微分方程可控性理论角度看游泳现象

• 批准号: 1007981
• 负责人: Alexander Khapalov
• 金额: $ 24万
• 依托单位: Washington State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2014-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007981&HistoricalAwards=false
• 关键词: Swimming; Phenomenon; Viewpoint; Controllability; Theory

This project develops new methodology to study controllability properties of swimming locomotion. Unlike other approaches available in this area, which reduce the analytical study of swimming phenomena to finite dimensional models, in this study, the problem is attacked in its original intrinsic realm of highly nonlinear infinite dimensional distributed parameter systems. A particular feature of the approach is that it links the swimmer?s motion to an explicit analysis of its internal forces and shape-changing strategy. The former is determined by the choice of respective scalar multiplicative controls, while the latter is regarded as a geometric control. These types of controls are novel in the context of mathematical controllability theory for partial differential equations.This field is of great interest in biological and engineering applications, especially when dealing with propulsion systems in fluids. Of particular importance are three-dimensional models of bio-mimetic devices, which employ the change of their geometry, inflicted by internal forces, as the means for self-propulsion in a fluid. A specific focus of this project is the development of methodology as to how one can recalculate the swimmer?s internal forces into the forces that act upon the surrounding fluid as determined by the swimmer?s shape. This is a key issue for understanding the nature of swimming phenomena and these models are critical for better understanding of the mechanics of swimming and flying motions of biological organisms.

本课题为研究游泳运动的可控性特性提供了新的方法。与该领域现有的将游泳现象的分析研究简化为有限维模型的方法不同，在本研究中，该问题在其原始的高度非线性无限维分布参数系统的固有领域中受到攻击。这种方法的一个特别之处在于，它将游泳者？对S运动进行了明确的内力分析和变形策略。前者由各自标量乘法控制的选择决定，而后者被视为几何控制。在偏微分方程的数学可控性理论背景下，这些类型的控制是新颖的。该领域在生物和工程应用中具有重要意义，特别是在处理流体推进系统时。特别重要的是仿生装置的三维模型，它利用内力造成的几何变化作为在流体中自我推进的手段。这个项目的一个重点是方法论的发展，即如何重新计算游泳者？S内力转化为作用在周围流体上的力，由游泳者决定？s形状。这是理解游泳现象本质的关键问题，这些模型对于更好地理解生物有机体游泳和飞行运动的力学至关重要。