Predictions of first passage times in sparse discrete fracture networks using graphbased reductions
Abstract
Here, we present a graphbased methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We also derive graph representations of generic threedimensional discrete fracture networks (DFNs) using the DFN topology and flow boundary conditions. Subgraphs corresponding to the union of the k shortest paths between the inflow and outflow boundaries are identified and transport on their equivalent subnetworks is compared to transport through the full network. The number of paths included in the subgraphs is based on the scaling behavior of the number of edges in the graph with the number of shortest paths. First passage times through the subnetworks are in good agreement with those obtained in the full network, both for individual realizations and in distribution. We obtain accurate estimates of first passage times with an order of magnitude reduction of CPU time and mesh size using the proposed method.
 Authors:
 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
 OSTI Identifier:
 1374351
 Report Number(s):
 LAUR1722022
Journal ID: ISSN 24700045; PLEEE8
 Grant/Contract Number:
 AC5206NA25396; 20150763PRD4; 20170103DR
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review E
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 24700045
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 54 ENVIRONMENTAL SCIENCES; Earth Sciences; discrete fracture networks, graph theory, shortest paths, flow and transport
Citation Formats
Hyman, Jeffrey De'Haven, Hagberg, Aric Arild, MohdYusof, Jamaludin, Srinivasan, Gowri, and Viswanathan, Hari S. Predictions of first passage times in sparse discrete fracture networks using graphbased reductions. United States: N. p., 2017.
Web. doi:10.1103/PhysRevE.96.013304.
Hyman, Jeffrey De'Haven, Hagberg, Aric Arild, MohdYusof, Jamaludin, Srinivasan, Gowri, & Viswanathan, Hari S. Predictions of first passage times in sparse discrete fracture networks using graphbased reductions. United States. doi:10.1103/PhysRevE.96.013304.
Hyman, Jeffrey De'Haven, Hagberg, Aric Arild, MohdYusof, Jamaludin, Srinivasan, Gowri, and Viswanathan, Hari S. 2017.
"Predictions of first passage times in sparse discrete fracture networks using graphbased reductions". United States.
doi:10.1103/PhysRevE.96.013304.
@article{osti_1374351,
title = {Predictions of first passage times in sparse discrete fracture networks using graphbased reductions},
author = {Hyman, Jeffrey De'Haven and Hagberg, Aric Arild and MohdYusof, Jamaludin and Srinivasan, Gowri and Viswanathan, Hari S.},
abstractNote = {Here, we present a graphbased methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We also derive graph representations of generic threedimensional discrete fracture networks (DFNs) using the DFN topology and flow boundary conditions. Subgraphs corresponding to the union of the k shortest paths between the inflow and outflow boundaries are identified and transport on their equivalent subnetworks is compared to transport through the full network. The number of paths included in the subgraphs is based on the scaling behavior of the number of edges in the graph with the number of shortest paths. First passage times through the subnetworks are in good agreement with those obtained in the full network, both for individual realizations and in distribution. We obtain accurate estimates of first passage times with an order of magnitude reduction of CPU time and mesh size using the proposed method.},
doi = {10.1103/PhysRevE.96.013304},
journal = {Physical Review E},
number = 1,
volume = 96,
place = {United States},
year = 2017,
month = 7
}

Fracture size and transmissivity correlations: Implications for transport simulations in sparse threedimensional discrete fracture networks following a truncated power law distribution of fracture size
We characterize how different fracture sizetransmissivity relationships influence flow and transport simulations through sparse threedimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semicorrelation, and noncorrelation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected somore »Cited by 1 
Discrete dynamics and metastability: mean first passage times and escape rates
The problem of escape from a domain of attraction is applied to the case of discrete dynamical systems possessing stable and unstable fixed points. In the presence of noise, the otherwise stable fixed point of a nonlinear map becomes metastable, due to the noiseinduced hopping events, which eventually pass the unstable fixed point. Exact integral equations for the moments of the first passage time variable are derived, as well as an upper bound for the first moment. In the limit of weak noise, the integral equation for the first moment, i.e., the mean first passage time (MFPT), is treated, bothmore » 
Parameters estimation using the first passage times method in a jumpdiffusion model
The main purposes of this paper are two contributions: (1) it presents a new method, which is the first passage time (FPT method) generalized for all passage times (GPT method), in order to estimate the parameters of stochastic JumpDiffusion process. (2) it compares in a time series model, share price of gold, the empirical results of the estimation and forecasts obtained with the GPT method and those obtained by the moments method and the FPT method applied to the Merton JumpDiffusion (MJD) model. 
Regenerative simulation of networks of queues with general service times: passage through subnetworks
A linear job stack, an enumeration by service center and job class of all the jobs, is an appropriate state vector for simulation of closed networks of queues with priorities among job classes. Using a representation of the job stack process as an irreducible generalized semiMarkov process, the authors develop a regenerative simulation method for passage times in networks with general service times. The estimation procedure avoids coxphase representation of general service time distributions and is applicable to networks with single states for passage times. Based on a single simulation run, the procedure provides point estimates and confidence intervals formore »