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| post | Physics-Oriented Statistical Wave Analysis Integrating Order and Chaos | /research/physics-oriented-statistical-wave-analysis |
Physics-Oriented Statistical Wave Analysis Integrating Order and Chaos
Collaborators: Thomas Antonsen@UMD, Edl Schamiloglu@UNM, Sameer Hemmady@UNM)
Even though we are seeking the highest possible fidelity, the computer representation will not be exactly the samecompared to the real world. These uncertainties may arise from imprecise knowledge of the system, small differencesin manufacturing, or numerical errors in the simulations. In integrable, regular wave systems, these small differencescan be considered as local perturbations of the entire system. Hence, the numerical solution is still a very goodapproximation to the exact solution of the physical problem. However, the situation can be completely different innon-integrable, wave-chaotic systems. The wave solutions can be extremely sensitive to details and initial conditions.It makes the traditional first-principles deterministic approaches relevant only to a specific realization.
This project investigates an innovative theoretical solution to Maxwell’s Equations in the wave chaotic (random,diffuse) media. The fundamental solution, named stochastic Green’s function, rigorously integrates the coherent andincoherent contributions within a unified compact form. Furthermore, by incorporating the component-, site-, system-specific information with the universal chaotic dynamics, the work accomplishes a comprehensive framework for thestatistical analysis and uncertainty quantification of complex wave systems. The advancements will achieve first-ever an imperative simulation-driven, design-under-chaos capability, and a virtual experimental facility statisticallyreplicating real-world wave propagation environments.
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