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NetMOD Version 2.0 Mathematical Framework

NetMOD ( Net work M onitoring for O ptimal D etection) is a Java-based software package for conducting simulation of seismic, hydroacoustic and infrasonic networks. Network simulations have long been used to study network resilience to station outages and to determine where additional stations are needed to reduce monitoring thresholds. NetMOD makes use of geophysical models to determine the source characteristics, signal attenuation along the path between the source and station, and the performance and noise properties of the station. These geophysical models are combined to simulate the relative amplitudes of signal and noise that are observed at each of the stations. From these signal-to-noise ratios (SNR), the probabilities of signal detection at each station and event detection across the network of stations can be computed given a detection threshold. The purpose of this document is to clearly and comprehensively present the mathematical framework used by NetMOD, the software package developed by Sandia National Laboratories to assess the monitoring capability of ground-based sensor networks. Many of the NetMOD equations used for simulations are inherited from the NetSim network capability assessment package developed in the late 1980s by SAIC (Sereno et al., 1990).

58 GEOSCIENCES↗

FNCS: A Framework for Power System and Communication Networks Co-Simulation

This paper describes the Fenix framework that uses a federated approach for integrating power grid and communication network simulators. Compared existing approaches, Fenix al- lows co-simulation of both transmission and distribution level power grid simulators with the communication network sim- ulator. To reduce the performance overhead of time synchro- nization, Fenix utilizes optimistic synchronization strategies that make speculative decisions about when the simulators are going to exchange messages. GridLAB-D (a distribution simulator), PowerFlow (a transmission simulator), and ns-3 (a telecommunication simulator) are integrated with the frame- work and are used to illustrate the enhanced performance pro- vided by speculative multi-threading on a smart grid applica- tion. Our speculative multi-threading approach achieved on average 20% improvement over the existing synchronization methods

Co-simulation↗

NetMOD Version 2.0 Parameters

NetMOD ( Net work M onitoring for O ptimal D etection) is a Java-based software package for conducting simulation of seismic, hydroacoustic and infrasonic networks. Network simulations have long been used to study network resilience to station outages and to determine where additional stations are needed to reduce monitoring thresholds. NetMOD makes use of geophysical models to determine the source characteristics, signal attenuation along the path between the source and station, and the performance and noise properties of the station. These geophysical models are combined to simulate the relative amplitudes of signal and noise that are observed at each of the stations. From these signal-to-noise ratios (SNR), the probability of detection can be computed given a detection threshold. This document describes the parameters that are used to configure the NetMOD tool and the input and output parameters that make up the simulation definitions.

58 GEOSCIENCES↗

PYSIMFRAC: A Python library for synthetic fracture generation and analysis

In this paper, we introduce PYSIMFRAC, an open-source python library for generating 3-D synthetic fracture realizations, integrating with fluid simulators, and performing analysis. PYSIMFRAC allows the user to specify one of three fracture generation techniques (Box, Gaussian, or Spectral) and perform statistical analysis including the autocorrelation, moments, and probability density functions of the fracture surfaces and aperture. This analysis and accessibility of a python library allows the user to create realistic fracture realizations and vary properties of interest. In addition, PYSIMFRAC includes integration examples to two different pore-scale simulators and the discrete fracture network simulator, dfnWorks. The capabilities developed in this work provides opportunity for quick and smooth adoption and implementation by the wider scientific community for accurate characterization of fluid transport in geologic media. We present PYSIMFRAC along with integration examples and discuss the ability to extend PYSIMFRAC from a single complex fracture to complex fracture networks.

58 GEOSCIENCES↗

XML Network Description Language (XNDL) for ns-3: ns-3 XSD v0.9

This document is the “XML Network Description Language (XNDL) for ns-3 ns-3 XSD v0.9” addressing the Statement of Work for the Proposed Research in Network Simulation under contract L145271. This work performed by Lawrence Livermore National Laboratory (LLNL) is specifically for the Army Research Laboratory. There exists a dichotomy between a desire to create generic network models that are framework-agnostic and models that are tailored to specific simulation implementations. Both methods have advantages and disadvantages. A generic approach would yield models that can be used and shared among many implementations and thus potentially gain support of a larger user community. However, there would remain a gap between concepts in a generic model and the corresponding representation needed for specific implementations. An approach that targets a specific implementation allows models to take full advantage of tighter integration and have a more explicit representation of simulation concepts and relationships. But locking into a specific implementation removes the portability aspect of the model. See Barnes, et al, for a more complete discussion. XNDL is a XML-based architecture being developed at LLNL for the purpose modeling networks at a high level of abstraction while using a hierarchical structure of targeted grammars to interface with a broader base of network simulation frameworks and their associated tools (see Figure 1).

97 MATHEMATICS AND COMPUTING↗

Incorporating social impact on new product adoption in choice modeing: A case study in green vehicles

While discrete choice analysis is prevalent in capturing consumer preferences and describing their choice behaviors in product design, the traditional choice modeling approach assumes that each individual makes independent decisions, without considering the social impact. However, empirical studies show that choice is social - influenced by many factors beyond engineering performance of a product and consumer attributes. To alleviate this limitation, we propose a new choice modeling framework to capture the dynamic influence from social networks on consumer adoption of new products. By introducing social influence attributes into a choice utility function, social network simulation is integrated with the traditional discrete choice analysis in a three-stage process. Our study shows the need for considering social impact in forecasting new product adoption. Using hybrid electric vehicles as an example, our work illustrates the procedure of social network construction, social influence evaluation, and choice model estimation based on data from the National Household Travel Survey. Our study also demonstrates several interesting findings on the dynamic nature of new technology adoption and how social networks may influence hybrid electric vehicle adoption. (C) 2014 Elsevier Ltd. All rights reserved

Discrete choice analysis↗

Simulators for quantum network modeling: A comprehensive review

Quantum network research is exploring new networking protocols, physics-based hardware and novel experiments to demonstrate how quantum distribution will work over large distances. Current work explores much of these concepts in simulations, that are developed to understand how quantum networking will be set up and researchers can experiment virtually. Exposing flaws in network designs, like unsustainable topologies, or develop protocols that efficiently utilize network resources, simulators can also help assess whether workloads are balanced across virtual machines in the network. However, much of these simulation models come without reliable verification methods, for testing performance in real deployments. Here, in this paper, we present a review of, to the best of our knowledge, currently used toolkits for modeling quantum networks. With these toolkits and standardized validation techniques, we can lay down the foundations for more accurate and reliable quantum network simulators.

97 MATHEMATICS AND COMPUTING↗

Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

Here, we develop a theoretical model for power law tailing behavior of transport in fractured rock based on the relative dominance of the decay rate of the advective travel time distribution, modeled using a Pareto distribution (with tail decaying as ~ time -(1+α) ), versus matrix diffusion, modeled using a Lévy distribution. The theory predicts that when the advective travel time distribution decays sufficiently slowly (α<1), the late-time decay rate of the breakthrough curve is -(1+α/2) rather than the classical -3/2. Yet, if α>1, the -3/2 decay rate is recovered. For weak matrix diffusion or short advective first breakthrough times, we identify an early-time regime where the breakthrough curve follows the Pareto distribution, before transitioning to the late-time decay rate. The theoretical predictions are validated against particle tracking simulations in the three-dimensional discrete fracture network simulator dfnWorks, where matrix diffusion is incorporated using a time domain random walk.

58 GEOSCIENCES↗

Simulating lossy Gaussian boson sampling with matrix-product operators

Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. Here, to understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the N out ∝ √N scaling of the number of surviving photons N out in the number of input photons N. We numerically verify this result using a tensor network algorithm with U⁡(1) symmetry, and we overcome previous challenges due to the large local Hilbert-space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗