Electromagnetic Fields and Waves in Fractional Dimensional Space
This book presents the concept of fractional dimensional space applied to the use of electromagnetic fields and waves. It demonstrates the advantages in studying the behavior of electromagnetic fields and waves in fractal media. The book
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Muhammad Zubair Muhammad Junaid Mughal Qaisar Abbas Naqvi •
Electromagnetic Fields and Waves in Fractional Dimensional Space
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Muhammad Zubair Faculty of Electronic Engineering GIK Institute of Engineering Sciences and Technology Topi Pakistan e-mail: [email protected]
Qaisar Abbas Naqvi Department of Electronics Quaid-e-Azam University Islamabad Pakistan e-mail: [email protected]
Muhammad Junaid Mughal Faculty of Electronic Engineering GIK Institute of Engineering Sciences and Technology Topi Pakistan e-mail: [email protected]
ISSN 2191-530X ISBN 978-3-642-25357-7 DOI 10.1007/978-3-642-25358-4
e-ISSN 2191-5318 e-ISBN 978-3-642-25358-4
Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011942412 Ó The Author(s) 2012 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
It’s ironic that fractals, many of which were invented as examples of pathological behavior, turn out to be pathological at all. In fact they are the rule in the universe. Shapes, which are not fractal, are the exception. I love Euclidean geometry, but it is quite clear that it does not give a reasonable presentation of the world. Mountains are not cones, clouds are not spheres, trees are not cylinders, neither does lightning travel in a straight line. Almost everything around us is non-Euclidean. Benoit Mandelbrot, 1924
To my beloved father Mr. Hafiz Muhammad Makhdoom whose utmost efforts since my childhood make me what I am today M. Zubair To my father Mr. Abdul Ghafoor Mughal for his love and kindness when he was alive and his beautiful memories when he is no longer with us M. J. Mughal To my parents Q. A. Naqvi
Preface
The concept of fractional dimensional space is being effectively used in many areas of physics to describe the effective parameters of physical systems. Although the space, embedding things, in real world is three dimensional Euclidean space, the material objects are not always moving in three dimensional space. The dimensionality depends upon the restraint conditions. The phenomenon of electromagnetic wave propagation, radiation and s
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