CAREER: Physics-Oriented Statistical Wave Analysis Integrating Order and Chaos

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Wireless communications, electronics, and sensor systems are expected to take place in increasingly congested, contested, and competitive environments. The evolving complexity of wireless communications demands fundamental changes to existing electromagnetic wave analysis and modeling methodologies. Often at times, there is no precise knowledge of the wave system, the radiating noise source, and the propagation environment. Furthermore, in the short-wavelength regime, the electromagnetic wave scattering process can be very sensitive to details. It results in a very high variability of wave distributions, and makes the deterministic solution relevant only to the specific configuration. This project proposes new physics-oriented statistical electromagnetic wave models to resolve environmental uncertainties. The proposed research opens up new pathways to exploit the complexity of propagation environments when designing wireless devices and antennas. The outcomes will establish a configurable virtual testbed for communications in complex environments not confined by the laboratory measurements. The research advancements will be integrated with the education to develop unconventional educational tools. The project will create a virtual reality electromagnetic laboratory at University of New Mexico (UNM), which offers a multifaceted teaching and learning environment through innovative data visualization and interactive simulation. Other educational components include developing online courses and advanced cross-disciplinary courses, mentoring high school students through UNMTemps Youth Summer program, and broadening participation of underrepresented groups by working with UNM's state-funded Multicultural Engineering Program and the New Mexico Alliance for Minority Participation. The objective of this research is to investigate fundamental mathematical models and computational algorithms for the statistical wave analysis in complex electromagnetic environments. The project will study an innovative theoretical solution to Maxwell's Equations in the wave-chaotic media (domains exhibiting ray-chaotic dynamics). The fundamental solution (stochastic Green's function) rigorously integrates the coherent and incoherent propagations within a compact form. A new stochastic integral equation method is proposed for the statistical wave propagation through the chaotic environment. It quantitatively interprets the universal statistical properties of wave chaos through the random matrix theory. Since real-world electromagnetic systems often exhibit mixed chaotic and regular wave dynamics, the second part of the work investigates the first-principles theoretical framework of combing the integrable (regular) and non-integrable (chaotic) wave dynamics. By incorporating the component-, site-, and system-specific information with the universal chaotic dynamics, the work accomplishes a comprehensive framework for the statistical analysis and uncertainty quantification of complex wave systems. The advancements will establish an imperative simulation-driven, design-under-chaos capability, which is expected to have a big impact in the engineering discipline. Knowledge from this project will bring forth a new generation of computer-aided design (CAD) tools that will revolutionize electromagnetic simulation, prediction, design and optimization in complex environments. While the proposed research primarily focuses on electrodynamics, the methodology can be applied to other fields including acoustics and vibrations, quantum mesoscopic transport, and nuclear physics.