Quantifying Volume Changing Perturbations in a Wave Chaotic System

Abstract

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.

13 pages, 13 figures

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