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Title: Locality of interactions for planar memristive circuits

Abstract

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.

Authors:
ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1410621
Alternate Identifier(s):
OSTI ID: 1408058
Report Number(s):
[LA-UR-17-23533]
[Journal ID: ISSN 2470-0045; PLEEE8; TRN: US1800141]
Grant/Contract Number:  
[AC52-06NA25396]
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
[ Journal Volume: 96; Journal Issue: 5]; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 30 DIRECT ENERGY CONVERSION; memristors, interaction, locality

Citation Formats

Caravelli, Francesco. Locality of interactions for planar memristive circuits. United States: N. p., 2017. Web. doi:10.1103/PhysRevE.96.052206.
Caravelli, Francesco. Locality of interactions for planar memristive circuits. United States. doi:10.1103/PhysRevE.96.052206.
Caravelli, Francesco. Wed . "Locality of interactions for planar memristive circuits". United States. doi:10.1103/PhysRevE.96.052206. https://www.osti.gov/servlets/purl/1410621.
@article{osti_1410621,
title = {Locality of interactions for planar memristive circuits},
author = {Caravelli, Francesco},
abstractNote = {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.},
doi = {10.1103/PhysRevE.96.052206},
journal = {Physical Review E},
number = [5],
volume = [96],
place = {United States},
year = {2017},
month = {11}
}

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