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.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1410621
- Alternate ID(s):
- OSTI ID: 1408058
- Report Number(s):
- LA-UR-17-23533; PLEEE8; TRN: US1800141
- Journal Information:
- Physical Review E, Vol. 96, Issue 5; ISSN 2470-0045
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Scalable Method to Find the Shortest Path in a Graph with Circuits of Memristors
|
journal | December 2018 |
Memristors for the Curious Outsiders
|
journal | December 2018 |
| A scalable method to find the shortest path in a graph with circuits of memristors | text | January 2018 |
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