Electromagnetic.Fields.and.Waves.in.Fractional.Dimensional.Space,.Zubair,..Mugha.pdf

Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Fractional Dimensional Space . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Axiomatic Basis for Fractional Dimensional Space . . . . . . . . . . 3
1.3 Differential Geometry of Fractional Dimensional Space . . . . . . . 4
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Differential Electromagnetic Equations in Fractional Space. . . . . . 7
2.1 Fractional Space Generalization of Laplacian Operator . . . . . . . 7
2.2 Fractional Space Generalization of Del Operator
and Related Differential Operators. . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Del Operator in Fractional Space . . . . . . . . . . . . . . . . . 8
2.2.2 Gradient Operator in Fractional Space . . . . . . . . . . . . . . 10
2.2.3 Divergence Operator in Fractional Space . . . . . . . . . . . . 10
2.2.4 Curl Operator in Fractional Space . . . . . . . . . . . . . . . . . 10
2.3 Fractional Space Generalization of Differential
Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Fractional Space Generalization of Potentials for Static Fields,
Poisson’s and Laplace’s Equations. . . . . . . . . . . . . . . . . . . . . . 12
2.5 Fractional Space Generalization of Potentials
for Time-Varying Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Fractional Space Generalization of the Helmholtz’s Equation . . . 15
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Potentials for Static and Time-Varying Fields
in Fractional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1 Electrostatic Potential in Fractional Space . . . . . . . . . . . . . . . . 17
3.1.1 An Exact Solution of the Laplace’s Equation
in D-dimensional Fractional Space . . . . . . . . . . . . . . . . 17
xiii
3.1.2 Electrostatic Potential Inside a Rectangular Box
in Fractional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Time-Varying Potentials in Fractional Space. . . . . . . . . . . . . . . 21
3.2.1 Inhomogeneous Vector Potential Wave Equation
in D-dimensional Fractional Space . . . . . . . . . . . . . . . . 21
3.2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4 Electromagnetic Wave Propagation in Fractional Space . . . . . . . . 27
4.1 General Plane Wave Solutions in Fractional Space:
Lossless Medium Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.1 General Plane Wave Solutions in Fractional Space . . . . . 27
4.1.2 Discussion on Fractional Space Solution . . . . . . . . . . . . 30
4.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 General Plane Wave Solutions in Fractional Space:
Lossy Medium Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.1 General Plane Wave Solutions in Lossy Medium
in Fractional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.2 Discussion on Fractional Space Solution
in Lossy Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.3 Example: Current Sheet as Source of Plane Waves
in Fractional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Cylindrical Wave Propagation in Fractional Space . . . . . . . . . . 42
4.3.1 An Exact Solution of Cylindrical Wave Equation
in Fractional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.2 Discussion on Cylindrical Wave Solution
in Fractional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Spherical Wave Propagation in Fractional Space . . . . . . . . . . . . 51
4.4.1 Spherical Wave Equation in D-dimensional
Fractional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4.2 Discussion on Fractional Space Solution . . . . . . . . . . . . 55
4.4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5 Electromagnetic Radiations from Sources in Fractional Space. . . . 61
5.1 Solution Procedure for Radiation Problems
in Fractional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.1.1 The Vector Potential AD for Electric Current Source J . . 61
5.1.2 The Vector Potential FD for Magnetic
Current Source M. . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
xiv Contents
5.1.3 Radiated Electric and Magnetic Fields in Far Zone
for Electric J and Magnetic Current Source M. . . . . . . . 63
5.2 Elementary Hertzian Dipole in Fractional Space . . . . . . . . . . . . 64
5.2.1 Fields Radiated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2.2 Directivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

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曾经上MEMS的时候有老师就提出过在MEMS里电路应该用场还是路分析，看书的标题貌似对解答这个问题有帮助

想了解一下这个是讲什么的。

{:7_1234:}

我对这方面的问题很感兴趣啊，谢谢楼主老大了

分型？空间？

。。。。。。。。。。。。。。

好，。。。。。。。

看看

怎么都是英文啊  不怎么看的懂的呢

绝对的好东西，看看

这个是讲什么的。

看了半天目录，好像还是有点不太清楚！

看看

感谢

下来看看看

好像很复杂呀 ：）

kankan

新东西好

thanks

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来电来函..欢迎洽购...

wow this one is new

感谢了

不错的书，收藏

很感兴趣

看看，应该不错的资料，收藏了，谢谢分享

楼主真给力，谢谢

好，。。。。。。。

Thanks a lot

Good luck

thanks

good,thank you!!!!!!!!!!!!!!{:7_1234:}

好书，好人品！

谢谢分享！！！！！！！！！！

谢谢分享！！！！！！！！！！

分形最近比较火，下来看看

下载下来看看，谢谢

额外哥特人23而二人让 23人