结构对液体表面波传播特性的调制研究
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摘要
本论文研究的是结构对液体表面波传播特性的调制研究,内容安排如下：
第一章概述了周期性结构中液体表面波的研究背景。从海洋能以及海啸出发,阐述了该课题研究意义,然后着重介绍了液体表面波国内外的研究现状以及我们组在液体表面波研究中所做的工作。
第二章阐述了液体表面波的波动理论以及我们的理论计算方法,重点介绍了传输矩阵方法、平面波方法、多重散射方法和有限元方法,理论结果和先前的实验的对比。
第三章介绍了我们实验研究手段：定性展示和定量测量。介绍了我们设计的实验装置,着重讨论了波源的设计和振幅测量的设计方案及测量原理。
第四章讨论了液体表面波混沌现象的研究。主要介绍了我们通过液体表面波的双缝实验说明了在一个不规则体系中,双缝干涉的相干峰消失,其多次测量平均之后的强度是两单缝强度之和。
第五章介绍了液体表面波的聚焦,给出了理论解释并给出了相应的实验结果,这样的设计可以用于提高海浪发电的效率。
第六章着重阐述了变换光学,通过设计可以实现完美隐身衣,旋转衣,并且介绍了隐身相关的实验以及我们做的液体表面波的旋转衣实验。
第七章论述了实验装置的改进以及一些水波可能实现的新现象。
In this thesis, the propagation of liquid surface waves in structures are studied both experimentally and theoretically. This thesis consists of seven chapters.
In the first chapter, the backgrounds of liquid surface waves propagating in periodic structures are introduced, including wave power, tsunami, recent progresses and our previous research works.
In the second chapter, basic theories for liquid surface waves are briefly discussed. Several theoretical methods are introduced to study the propagation of liquid surface waves in periodic structures, including transfer matrix method, multiple scattering method, plane wave method and finite element method. Based on these methods, band structures, transmission and field distributions can be calculated.
In the third chapter, the experimental methods of qualitative observation and quantitative measurement and the experimental setup are introduced.
In the fourth chapter, chaos in water waves is studied. With a double slit experiment, we find that the interference fringes disappear from the screen and the intensity obeys the addition rule after averaging if the source is placed in a billiard whose classical ray dynamics is chaotic.
In the fifth chapter, the focusing of a plane wave in the 2D cylinder arrays is studied experimentally and theoretically. This design could be used to increase the harvest efficiency of wave power.
In the sixth chapter, transformation optics is discussed, including perfect cloaking and rotation cloaking. Latest experiments are also introduced. Results of rotating cloaking and our experiment in liquid surface waves are presented.
In the seventh chapter, further study of liquid surface waves is discussed, including improvements of experimental setups and new phenomena that could be realized in water waves.
第一章概述了周期性结构中液体表面波的研究背景。从海洋能以及海啸出发,阐述了该课题研究意义,然后着重介绍了液体表面波国内外的研究现状以及我们组在液体表面波研究中所做的工作。
第二章阐述了液体表面波的波动理论以及我们的理论计算方法,重点介绍了传输矩阵方法、平面波方法、多重散射方法和有限元方法,理论结果和先前的实验的对比。
第三章介绍了我们实验研究手段：定性展示和定量测量。介绍了我们设计的实验装置,着重讨论了波源的设计和振幅测量的设计方案及测量原理。
第四章讨论了液体表面波混沌现象的研究。主要介绍了我们通过液体表面波的双缝实验说明了在一个不规则体系中,双缝干涉的相干峰消失,其多次测量平均之后的强度是两单缝强度之和。
第五章介绍了液体表面波的聚焦,给出了理论解释并给出了相应的实验结果,这样的设计可以用于提高海浪发电的效率。
第六章着重阐述了变换光学,通过设计可以实现完美隐身衣,旋转衣,并且介绍了隐身相关的实验以及我们做的液体表面波的旋转衣实验。
第七章论述了实验装置的改进以及一些水波可能实现的新现象。
In this thesis, the propagation of liquid surface waves in structures are studied both experimentally and theoretically. This thesis consists of seven chapters.
In the first chapter, the backgrounds of liquid surface waves propagating in periodic structures are introduced, including wave power, tsunami, recent progresses and our previous research works.
In the second chapter, basic theories for liquid surface waves are briefly discussed. Several theoretical methods are introduced to study the propagation of liquid surface waves in periodic structures, including transfer matrix method, multiple scattering method, plane wave method and finite element method. Based on these methods, band structures, transmission and field distributions can be calculated.
In the third chapter, the experimental methods of qualitative observation and quantitative measurement and the experimental setup are introduced.
In the fourth chapter, chaos in water waves is studied. With a double slit experiment, we find that the interference fringes disappear from the screen and the intensity obeys the addition rule after averaging if the source is placed in a billiard whose classical ray dynamics is chaotic.
In the fifth chapter, the focusing of a plane wave in the 2D cylinder arrays is studied experimentally and theoretically. This design could be used to increase the harvest efficiency of wave power.
In the sixth chapter, transformation optics is discussed, including perfect cloaking and rotation cloaking. Latest experiments are also introduced. Results of rotating cloaking and our experiment in liquid surface waves are presented.
In the seventh chapter, further study of liquid surface waves is discussed, including improvements of experimental setups and new phenomena that could be realized in water waves.
引文
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[22]Xinhua Hu, Yifeng Shen, Xiaohan Liu, Rongtang Fu, and Jian Zi. Superlensing effect in liquid surface waves [J]. Physical Review E,2004,69(3):030201(R).
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[24]沈义峰.液体表面波在周期结构调制下传播行为的研究[D].上海：复旦大学,2005：
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[9]Tom Chou. Band structure of surface flexural-gravity waves along periodic interfaces [J]. The Journal of Fluid Mechanics,1998,369:333-350.
[10]M. Torres, J. P. Adrados, F. R. Montero de Espinosa. Visualization of Bloch waves and domain walls [J]. Nature,1999,398:114-115.
[11]M. Torres, J. P. Adrados, F. R. Montero de Espinosa, D. Garcia-Pablos, and J. Fayos. Parametric Bragg resonances in waves on a shallow fluid over a periodically drilled bottom [J]. Physical Review E,2000,63(1):011204
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[14]Eric Falcon, Claude Laroche, and Stephan Fauve. Observation of Depression Solitary Surface Waves on a Thin Fluid Layer [J]. Physical Review Letters,2002, 89(20):204501.
[15]I. V. Barashenkov, S. R. Woodford, and E. V. Zemlyanaya. Parametrically Driven Dark Solitons [J]. Physical Review Letters,2003,90(5):054103.
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[17]Doug Binks, Mark-Tiele Westra, and Willem van de Water. Effect of Depth on the Pattern Formation of Faraday Waves [J]. Physical Review Letters,1997,79(25): 5010-5013.
[18]Eli Yablonovitch. Inhibited Spontaneous Emission in Solid-State Physics and Electronics [J]. Physical Review Letters,1987,58(20):2059-2062.
[19]Sajeev John. Strong localization of photons in certain disordered dielectric superlattices [J]. Physical Review Letters,1987,58(23):2486-2489.
[20]汤云飞.液体表面波在周期结构中的传播及水波的混沌现象研究[D].上海：复旦大学,2007：
[21]Yifeng Shen, Xiaohan Liu, Yunfei Tang, Yanfei Chen and Jian Zi. Observation of a complete band gap for liquid surface waves propagating over a periodically drilled bottom [J]. Journal of Physics:Condensed Matter,2005,17(26):L287.
[22]Xinhua Hu, Yifeng Shen, Xiaohan Liu, Rongtang Fu, and Jian Zi. Superlensing effect in liquid surface waves [J]. Physical Review E,2004,69(3):030201(R).
[23]Yifeng Shen, Kaixuan Chen, Yanfei Chen, Xiaohan Liu, and Jian Zi. Self-collimation in liquid surface waves propagating over a bottom with periodically drilled holes [J]. Physical Review E,2005,71(3):036301.
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