We consider the M → 0 limit for tagged particle diffusion in a 1-dimensional Rayleigh-gas, studied originaly by Sinai and Soloveichik [14], respectively by Szász and Tóth [19]. In this limit we derive a new type of model for tagged paricle diffusion, with Calogero-Moser-Sutherland (i.e. inverse quadratic) interaction potential between the two central particles. Computer simulations on this new model reproduce exactly the numerical value of the limiting variance obtained by Boldrighini, Frigio and Tognetti in [4].
This paper summarizes a case study example on the methodology used for phased array microphone measurements in a realistic acoustic environment. A ducted fan rotor is measured in an environment, where structure born noise and aerodynamically generated noise cannot be separated using conventional single microphone acoustic analysis. The conditions of the measurement are similar to an industrial acoustic measurement scenario, where no acoustics treatment can be implemented for aiding in the source localization. The acoustics propagation paths are complex and combined with the high level of wind noise which the microphones exposed to, the interpretation of the results is difficult. The paper presents the processing and analyses of the many microphone worth of data of the phased array microphone system. The wind noise dominated cross spectral matrix is analyzed and source positions are obtained with beamforming procedures for both stationary and rotating sources.
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