Emergence of Stable Laws for First Passage Times in Three-Dimensional Random Fracture Networks

We study first passage behaviors in the flow through three-dimensional random fracture networks. Network and flow heterogeneity lead to the emergence of heavy-tailed first passage time distributions that evolve with increasing distance between the start and target planes, and transition toward stabl...

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Bibliographic Details
Published in:Physical review letters 2019-12, Vol.123 (24), p.248501-248501, Article 248501
Main Authors: Hyman, Jeffrey D, Dentz, Marco, Hagberg, Aric, Kang, Peter K
Format: Article
Language:English
Subjects:
bipartite graphs
diffusion & random walks
Dimensional stability
earth sciences
Emergence
energy storage
environmental research
fossil fuels
geophysical networks
geophysics
information science
mathematical physics
mathematics
MATHEMATICS AND COMPUTING
Memory tasks
Particle motion
Planes
Random walk
Random walk theory
real world networks
scaling laws of complex systems
Spatial analysis
stochastic networks
Three dimensional flow
Tortuosity
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Summary:We study first passage behaviors in the flow through three-dimensional random fracture networks. Network and flow heterogeneity lead to the emergence of heavy-tailed first passage time distributions that evolve with increasing distance between the start and target planes, and transition toward stable laws. Analysis of the spatial memory of the first passage process shows that particle motion can be quantified stochastically by a time domain random walk conditioned on the initial velocity data. This approach identifies advective tortuosity, the velocity point distribution and the average fracture link length as key quantities for the prediction of first passage times. Using this approach, we develop a theory for the evolution of first passage times with increasing distance between the start and target planes and the convergence towards stable laws.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.123.248501