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	The form-invariance of wave equations without requiring a priori relations between field variables
	XIANG Zhi Hai ; XIANG Zhi Hai
	2016-03-30 ; 2016-03-30
关键词	wave equations transformation methods inhomogeneity metamaterials O441 O412.1
其他题名	The form-invariance of wave equations without requiring a priori relations between field variables
中文摘要	According to the principle of relativity,the equations describing the laws of physics should have the same forms in all admissible frames of reference,i.e.,form-invariance is an intrinsic property of correct wave equations.However,so far in the design of metamaterials by transformation methods,the form-invariance is always proved by using certain relations between field variables before and after coordinate transformation.The main contribution of this paper is to give general proofs of form-invariance of electromagnetic,sound and elastic wave equations in the global Cartesian coordinate system without using any assumption of the relation between field variables.The results show that electromagnetic wave equations and sound wave equations are intrinsically form-invariant,but traditional elastodynamic equations are not.As a by-product,one can naturally obtain new elastodynamic equations in the time domain that are locally accurate to describe the elastic wave propagation in inhomogeneous media.The validity of these new equations is demonstrated by some numerical simulations of a perfect elastic wave rotator and an approximate elastic wave cloak.These findings are important for solving inverse scattering problems in many fields such as seismology,nondestructive evaluation and metamaterials.; According to the principle of relativity,the equations describing the laws of physics should have the same forms in all admissible frames of reference,i.e.,form-invariance is an intrinsic property of correct wave equations.However,so far in the design of metamaterials by transformation methods,the form-invariance is always proved by using certain relations between field variables before and after coordinate transformation.The main contribution of this paper is to give general proofs of form-invariance of electromagnetic,sound and elastic wave equations in the global Cartesian coordinate system without using any assumption of the relation between field variables.The results show that electromagnetic wave equations and sound wave equations are intrinsically form-invariant,but traditional elastodynamic equations are not.As a by-product,one can naturally obtain new elastodynamic equations in the time domain that are locally accurate to describe the elastic wave propagation in inhomogeneous media.The validity of these new equations is demonstrated by some numerical simulations of a perfect elastic wave rotator and an approximate elastic wave cloak.These findings are important for solving inverse scattering problems in many fields such as seismology,nondestructive evaluation and metamaterials.
语种	英语 ; 英语
内容类型	期刊论文
源URL	[http://ir.lib.tsinghua.edu.cn/ir/item.do?handle=123456789/143814]
专题	清华大学
推荐引用方式 GB/T 7714	XIANG Zhi Hai,XIANG Zhi Hai. The form-invariance of wave equations without requiring a priori relations between field variables[J],2016, 2016.
APA	XIANG Zhi Hai,&XIANG Zhi Hai.(2016).The form-invariance of wave equations without requiring a priori relations between field variables..
MLA	XIANG Zhi Hai,et al."The form-invariance of wave equations without requiring a priori relations between field variables".(2016).

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