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Theoretical Study of Applications of Fractional Calculus in Electromagnetism

分数阶微积分在电磁学中应用的理论研究

基本信息

批准号：
9612634
负责人：
Nader Engheta
金额：
$ 8.5万
依托单位：
University of Pennsylvania
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1997
资助国家：
美国
起止时间：
1997-09-01 至 1999-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9612634&HistoricalAwards=false
关键词：
Theoretical Study Applications Fractional Calculus

项目摘要

Proposal Number: ECS-9612634 Principal Investigator: Nader Engheta Title: Theoretical study of applications of fractional calculus in electromagnetism In this research, a theoretical investigation using the fractional calculus approach to waves and geometries of interest will be developed. The fractional calculus approach enables the study of waves and structures with an intermediate character. It is an area which has been developed with major contributions from the PI. Under the present study, the following topics will be investigated: (1) "fractional" intermediate sources and (2) applications of fractional calculus in electromagnetic scattering. Dual investigations of geometries and boundaries for which an incident plane waves generates scattered waves with fractional characteristics, and, conversely the scattering of incident waves with fractional characteristics from various geometries will be carried out. In each of these areas, a new corresponding development of the theory itself will be investigated (1') extension of the concept of fractional order multipoles for complex sources involving electric and magnetic fractional-order multipoles and/or aperture fields and (2') the development of a "fractional" curl operator, both for analysis of the electromagnetic scattering interactions as stated in (2) and for investigation the basic concepts involved in the duality of the fractional character of the waves and the geometries.

提案编号：ECS-9612634 主要研究者：Nader Engheta 标题：分数阶微积分在电磁学中应用的理论研究在这项研究中，使用分数阶微积分方法的波和感兴趣的几何形状的理论研究将被开发。分数阶微积分方法使研究波和结构的中间字符。这是一个在PI的重大贡献下发展起来的领域。本研究将探讨下列主题：（1）分数阶中间源及（2）分数阶微积分在电磁散射中的应用。几何形状和边界的双重调查，入射平面波产生的散射波与分数的特性，相反，从各种几何形状的分数特性的入射波的散射将进行。在这些领域中的每一个中，将研究理论本身的新的相应发展：（1）对于涉及电和磁分数阶多极子和/或孔径场的复杂源的分数阶多极子概念的扩展，以及（2）“分数”旋度算子的发展，既用于分析（2）中所述的电磁散射相互作用，又用于研究波的分数特征和几何的对偶性中所涉及的基本概念。