A Hamilton-jacobi equation for evaluating eemi propagation in a computing system

Luis Valbuena, Gregory L. Heileman, Sameer Hemmady, Edl Schamiloglu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we present a theoretical framework for modeling the empirically observed cascading of software failures on a complicated computing system exposed to extreme electromagnetic interference (EEMI). Our approach is to treat the temporal evolution of the electromagnetic coupling and the resultant cascading series of electromagnetic-induced faults as the 'flow' in a dynamic fluid-mechanical system and thereby utilize aspects of the Navier Stokes and Hamilton-Jacobi equations to predict the rate of this flow. Therefore, inspired by the concepts of fluid dynamics [1], we include a diffusion term in the Hamilton-Jacobi-Isaacs (HJI) equation. We have considered two approaches. In one we apply a Taylor expansion to the optimality principle and consider additional terms; in the other scenario, we simply add a diffusion term in the form of a Laplacian applied to the cost function H(mathbf{x},ldots) and some constant mathbf{c}, as it is present in the Navier-Stokes equation for incompressible flow. We provide numerical comparisons for both approaches with respect to the original HJI equation where the dynamical vector field corresponds to analytical models of a NOR logic gate. This model is a second-order differential equation that describes the behavior of the gate that incorporates a new term accounting for EEMI injection.

Original languageEnglish (US)
Title of host publicationProceedings of the 2019 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages851-856
Number of pages6
ISBN (Electronic)9781728105635
DOIs
StatePublished - Sep 2019
Externally publishedYes
Event21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019 - Granada, Spain
Duration: Sep 9 2019Sep 13 2019

Publication series

NameProceedings of the 2019 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

Conference

Conference21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019
Country/TerritorySpain
CityGranada
Period9/9/199/13/19

Keywords

  • EEMI
  • Electromagnetics
  • Hamilton-Jacobi-Isaacs

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Geophysics
  • Radiation
  • Modeling and Simulation
  • Statistics and Probability
  • Instrumentation

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