University of Illinois Urbana-Champaign

Stochastic green’s function method for the statistical analysis of wave chaotic systems

Lin, Shen

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https://hdl.handle.net/2142/115665

Description

Title
Stochastic green’s function method for the statistical analysis of wave chaotic systems
Author(s)
Lin, Shen
Issue Date
2022-03-02
Director of Research (if dissertation) or Advisor (if thesis)
Peng, Zhen
Doctoral Committee Chair(s)
Peng, Zhen
Committee Member(s)
  • Jin, Jianming
  • Bernhard, Jennifer Truman
  • Zhao, Yang
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Wave chaos
  • Electromagnetic coupling
  • Stochastic Green's function
  • Scalar
  • Vector
  • Stochastic integral equation
  • Statistics
  • Intentional electromagnetic interfere
  • MIMO
Abstract
There is a long-standing need for the statistical description of complex wave systems displaying ray chaotic dynamics. This thesis presents a stochastic Green’s function (SGF) method for wave interaction within wave-chaotic media, which quantitatively describes generic statistical properties of wave scattering dynamics rather than detailed specifics inside the system. The statistically fluctuating (random) portion of the Green’s function is characterized by random wave model and random matrix theory. The formulation rigorously characterizes coherent and incoherent propagation within a comprehensive form. Built upon the stochastic Green’s function, we have derived a stochastic integral equation method, and a hybrid formulation to incorporate the component-specific attributes. The extensions of the SGF method are discussed next: The vector dyadic SGF approach is proposed to study the correlations of the boundary fields and predict the statistics of vector EM fields; the Broadband SGF approach is developed to investigate spectral-spatial correlations of wave propagation. Finally, we extend the theory of SGF from the spatial domain to the spatio-temporal domain to characterize both spatial and temporal variations and correlations of EM fields in the fully developed wave-chaotic dynamics. The model enables a spatio-temporal statistical analysis of chaotic wave dynamics without the need for detailed knowledge of the complex environment. The proposed models are evaluated and validated through representative experiments.
Graduation Semester
2022-05
Type of Resource
Thesis
Copyright and License Information
Copyright 2022 Shen Lin

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