Stochastic investigation of graphene structures with efficient polynomial models

Abstract

Purpose

The extraordinary properties of graphene render it ideal for diverse contemporary and future applications. Aiming at the investigation of certain aspects commonly overlooked in pertinent works, the authors study wave-propagation phenomena supported by graphene layers within a stochastic framework, i.e. when uncertainty in various factors affects the graphene’s surface conductivity. Given that the consideration of an increasing number of graphene sheets may increase the stochastic dimensionality of the corresponding problem, efficient surrogates with reasonable computational cost need to be developed.

Design/methodology/approach

The authors exploit the potential of generalized Polynomial Chaos (PC) expansions and develop low-cost surrogates that enable the efficient extraction of the necessary statistical properties displayed by stochastic graphene-related quantities of interest (QoI). A key step is the incorporation of an initial variance estimation, which unveils the significance of each input parameter and facilitates the selection of the most appropriate basis functions, by favoring anisotropic formulae. In addition, the impact of controlling the allowable input interactions in the expansion terms is investigated, aiming at further PC-basis elimination.

Findings

The proposed stochastic methodology is assessed via comparisons with reference Monte-Carlo results, and the developed reduced basis models are shown to be sufficiently reliable, being at the same time computationally cheaper than standard PC expansions. In this context, different graphene configurations with varying numbers of random inputs are modeled, and interesting conclusions are drawn regarding their stochastic responses.

Originality/value

The statistical properties of surface-plasmon polaritons and other QoIs are predicted reliably in diverse graphene configurations, when the surface conductivity displays non-trivial uncertainty levels. The suggested PC methodology features simple implementation and low complexity, yet its performance is not compromised, compared to other standard approaches, and it is shown to be capable of delivering valid results.

Citation

Zygiridis, T., Amanatiadis, S.A., Karamanos, T. and Kantartzis, N.V. (2020), "Stochastic investigation of graphene structures with efficient polynomial models", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 39 No. 3, pp. 611-622. https://doi.org/10.1108/COMPEL-10-2019-0376