skip to main content


This content will become publicly available on November 8, 2018

Title: Locality of interactions for planar memristive circuits

The dynamics of purely memristive circuits has been shown to depend on a projection operator which expresses the Kirchhoff constraints, is naturally non-local in nature, and does represent the interaction between memristors. In the present paper we show that for the case of planar circuits, for which a meaningful Hamming distance can be defined, the elements of such projector can be bounded by exponentially decreasing functions of the distance. We provide a geometrical interpretation of the projector elements in terms of determinants of Dirichlet Laplacian of the dual circuit. For the case of linearized dynamics of the circuit for which a solution is known, this can be shown to provide a light cone bound for the interaction between memristors. Furthermore, this result establishes a finite speed of propagation of signals across the network, despite the non-local nature of the system.
ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 2470-0045; PLEEE8; TRN: US1800141
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2470-0045
American Physical Society (APS)
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
36 MATERIALS SCIENCE; 30 DIRECT ENERGY CONVERSION; memristors, interaction, locality
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1408058