2023_programme: Stochastic models for pulse propagation : transport equations and random matrix models

• Session: 02. Advances in acoustic measurement systems: Technologies and applications
  Organiser(s): Alessandra Tesei and Purnima Ratilal-Makris
• Lecture: Stochastic models for pulse propagation : transport equations and random matrix models [invited]
  Paper ID: 1976
  Author(s): Chandrayadula Tarun
  Presenter: Chandrayadula Tarun
  Abstract: Scattering models which predict intensities, loss of coherence, and scintillation for signals at a single frequency form an extensive area called wave propagation through random media. In comparison, models to predict predict temporal spread, and peak-intensities of broadband pulses are a recent development. This talk presents two types of broadband models that describe the scattering effects on pulses that propagate through internal waves spread across long-ranges. Both the models use the modes derived from the acoustic wave equation. The first broadband model (Periyasamy and Chandrayadula JASA 2023) uses the modes in a set of diffusion equations called the transport method to predict the cross-frequency coherences. The model then applies the Fourier integral to transform the frequency coherences into time-domain statistics. The second method describes mode propagation through the waveguide using a set of random matrices at the different frequencies across the bandwidth. The method initially defines a reference matrix at the center frequency, and then perturbs the reference to model the other frequencies. In order to fix the amount of perturbation, a parameter is defined to account for the magnitude and scale of perturbations. These parametric ensembles of random matrices are then used to simulate pulses, from which the statistics are estimated. The results from both the methods are compared with each other. While the transport equations provide only second order statistics, the random matrix simulations also yield high order statistics such as scintillation indices.
• Corresponding author: Prof Tarun Chandrayadula
  Affiliation: Indian Institute of Technology Madras
  Country: India
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