Random walks on jammed networks: Spectral properties

Journal Article · 15 July 2019 · Physical Review E

DOI: https://doi.org/10.1103/PhysRevE.100.012905 · OSTI ID:1559545

Lechman, Jeremy B. ^[1]; Bond, Stephen D. ^[1]; Bolintineanu, Dan S. ^[1]; Grest, Gary S. ^[1]; Yarrington, Cole D. ^[1]; Silbert, Leonardo E. ^[2]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2. Central New Mexico Community College, Albuquerque, NM (United States)

Using random walk analyses we explore diffusive transport on networks obtained from contacts between isotropically compressed, monodisperse, frictionless sphere packings generated over a range of pressures in the vicinity of the jamming transition p → 0 . For conductive particles in an insulating medium, conduction is determined by the particle contact network with nodes representing particle centers and edges contacts between particles. The transition rate is not homogeneous, but is distributed inhomogeneously due to the randomness of packing and concomitant disorder of the contact network, e.g., the distribution of the coordination number. A narrow escape time scale is used to write a Markov process for random walks on the particle contact network. This stochastic process is analyzed in terms of spectral density of the random, sparse, Euclidean and real, symmetric, positive, semidefinite transition rate matrix. Findings reveal network structures derived from jammed particles have properties similar to ordered, euclidean lattices but also some unique properties that distinguish them from other structures that are in some sense more homogeneous. Specifically, the distribution of eigenvalues of the transition rate matrix follow a power law with spectral dimension 3. Yet, quantitative details of the statistics of the eigenvectors show subtle differences with homogeneous lattices and allow us to distinguish between topological and geometric sources of disorder in the network.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division
• Grant/Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1559545
• Alternate ID(s): OSTI ID: 1542529
• Report Number(s): SAND-2018-9709J; PLEEE8; 667602; TRN: US2000364
• Journal Information: Physical Review E, Vol. 100, Issue 1; ISSN 2470-0045
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English