Variable-order modeling of nonlocal emergence in many-body systems: Application to radiative dispersion

J. Orosco and C. F. M. Coimbra
Phys. Rev. E 98, 032208 – Published 13 September 2018

Abstract

We describe a physical framework for analyzing the spectral dynamics of a broad range of media. The framework is built on a variable-order calculus formalism that permits the description of temporally nonlocal behavior. Such emergent behavior is observed in the response of assorted complex media. The analytical features of the formalism are discussed and it is demonstrated how they correspond to the generalization of other well known theories for the description of nonlocal many-body effects. The framework is employed to analyze a set of spectroscopic data for the high-frequency dielectric response of a nanofluidic graphene dispersion and the midinfrared optical response of amorphous quartz silica. A practical application of the analysis is facilitated by a model definition that generalizes the semiclassical Lorentz theory to allow for nonlocal damping effects. The model is derived from a fractional order differential equation of motion. From the analysis, an estimated parametrization for the model structure is obtained. The fidelity of the analysis methodology is validated against optimized parametrizations in a multiobjective (optical and radiative) setting. The results demonstrate the utility of the analysis and indicate a specific well-defined region of nonlocality having a distinct fidelity that encompasses the entire Pareto front. This region is shown to be inaccessible to integer order descriptions of the mean field dynamics.

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  • Received 12 July 2018

DOI:https://doi.org/10.1103/PhysRevE.98.032208

©2018 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

J. Orosco and C. F. M. Coimbra*

  • Department of Mechanical and Aerospace Engineering, Center for Energy Research, University of California San Diego, La Jolla, California 92093-0411, USA

  • *ccoimbra@ucsd.edu

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Issue

Vol. 98, Iss. 3 — September 2018

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