New Journal of Physics Material parameters and vector scaling in transformation acoustics
New Journal of Physics Material parameters and vector scaling in transformation acoustics
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发表时间：
2008
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通讯作者：
Steven A. Cummer;Marco Rahm;David Schurig
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作者：
Steven A. Cummer;Marco Rahm;David Schurig
最先证明的电磁波的坐标变换概念在多大程度上可以应用于其他类型的波仍然是一个悬而未决的问题。在这项工作中，我们深入研究了声波的坐标变换不变性。我们用一个纯粹的物理论证来说明声速矢量必须与麦克斯韦方程中的E场和H场不同的变换，这解释了为什么在以前的一些分析中没有发现声坐标变换的不变性。对声学方程在任意坐标变换下的第一性原理分析证实，只有当速度以这种物理正确的方式变换时，散度算符才能保持不变。这种分析还给出了在声场上实现任意坐标变换所需的材料的体弹模张量和质量密度张量的闭合形式，我们证明了它与其他地方的形式是等价的。我们演示了在两种具体情况下这些材料参数的计算，并证明了在非正交坐标变换下速度和压力梯度矢量的变化正是这些矢量必须如何从纯粹的物理论证变化的过程。这一分析证实，使用坐标变换方法构思的所有电磁装置和材料原则上也可以由声学作者实现，任何通信都应该寄给他。新物理杂志10(2008年)115025 1367-2630/08/115025+12$30
The degree to which the coordinate transformation concept first demonstrated for electromagnetic waves can be applied to other classes of waves remains an open question. In this work, we thoroughly examine the coordinate transformation invariance of acoustic waves. We employ a purely physical argument to show how the acoustic velocity vector must transform differently than the E and H fields in Maxwell’s equations, which explains why acoustic coordinate transformation invariance was not found in some previous analyses. A first principles analysis of the acoustic equations under arbitrary coordinate transformations confirms that the divergence operator is preserved only if velocity transforms in this physically correct way. This analysis also yields closed-form expressions for the bulk modulus and mass density tensor of the material required to realize an arbitrary coordinate transformation on the acoustic fields, which we show are equivalent to forms presented elsewhere. We demonstrate the computation of these material parameters in two specific cases and show that the change in velocity and pressure gradient vectors under a nonorthogonal coordinate transformation is precisely how these vectors must change from purely physical arguments. This analysis confirms that all of the electromagnetic devices and materials that have been conceived using the coordinate transformation approach are also in principle realizable for acoustic 3 Author to whom any correspondence should be addressed. New Journal of Physics 10 (2008) 115025 1367-2630/08/115025+12$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft