波动混沌系统中体积变化扰动的量化
Quantifying Volume Changing Perturbations in a Wave Chaotic System
摘要：
研制了一种能定量测量扰动的传感器，该扰动改变了波混沌腔的体积，而保持其形状不变。传感器通过使用传输信号的散射保真度或时间反转镜在时域中工作。通过对一立方米的混沌和规则台球混合系统施加体积变化扰动，对传感器进行了实验测试。定量测量了引起百万分之五十四的体积变化的扰动。这些结果是通过使用波长约为5 cm的电磁波获得的，因此，传感器对腔体边界的极端亚波长变化敏感。将实验结果与时域有限差分（FDTD）仿真结果进行了比较，发现两者吻合较好。此外，采用频域方法对具有代表性的波动混沌系统--星图的数值模型进行了测试。这些结果开辟了有趣的应用，如：监测加热/冷却过程中的均匀腔的温度的空间均匀性，验证一个流体的均匀位移波混沌腔中的另一种流体，等等。
英文摘要：
A sensor was developed to quantitatively measure perturbations which change the volume of a wave chaotic cavity while leaving its shape intact. The sensors work in the time domain by using either scattering fidelity of the transmitted signals or time reversal mirrors. The sensors were tested experimentally by inducing volume changing perturbations to a one cubic meter mixed chaotic and regular billiard system. Perturbations which caused a volume change that is as small as 54 parts in a million were quantitatively measured. These results were obtained by using electromagnetic waves with a wavelength of about 5cm, therefore, the sensor is sensitive to extreme sub-wavelength changes of the boundaries of a cavity. The experimental results were compared with Finite Difference Time Domain (FDTD) simulation results, and good agreement was found. Furthermore, the sensor was tested using a frequency domain approach on a numerical model of the star graph, which is a representative wave chaotic system. These results open up interesting applications such as: monitoring the spatial uniformity of the temperature of a homogeneous cavity during heating up / cooling down procedures, verifying the uniform displacement of a fluid inside a wave chaotic cavity by another fluid, etc.
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