A Hamilton-Jacobi Equation for Evaluating EEMI Propagation in a Computing System
MetadataShow full item record
CitationValbuena, L., Heileman, G. L., Hemmady, S., & Schamiloglu, E. (2019, September). A Hamilton-Jacobi Equation for Evaluating EEMI Propagation in a Computing System. In 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA) (pp. 0851-0856). IEEE.
JournalPROCEEDINGS OF THE 2019 INTERNATIONAL CONFERENCE ON ELECTROMAGNETICS IN ADVANCED APPLICATIONS (ICEAA)
RightsCopyright © 2019 IEEE
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractIn 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 , 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(x,...) and some constant 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.
VersionFinal accepted manuscript