342,694 research outputs found

    Methods for Large Scale Hydraulic Fracture Monitoring

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    In this paper we propose computationally efficient and robust methods for estimating the moment tensor and location of micro-seismic event(s) for large search volumes. Our contribution is two-fold. First, we propose a novel joint-complexity measure, namely the sum of nuclear norms which while imposing sparsity on the number of fractures (locations) over a large spatial volume, also captures the rank-1 nature of the induced wavefield pattern. This wavefield pattern is modeled as the outer-product of the source signature with the amplitude pattern across the receivers from a seismic source. A rank-1 factorization of the estimated wavefield pattern at each location can therefore be used to estimate the seismic moment tensor using the knowledge of the array geometry. In contrast to existing work this approach allows us to drop any other assumption on the source signature. Second, we exploit the recently proposed first-order incremental projection algorithms for a fast and efficient implementation of the resulting optimization problem and develop a hybrid stochastic & deterministic algorithm which results in significant computational savings.Comment: arXiv admin note: text overlap with arXiv:1305.006

    Online Multivariate Changepoint Detection: Leveraging Links With Computational Geometry

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    The increasing volume of data streams poses significant computational challenges for detecting changepoints online. Likelihood-based methods are effective, but their straightforward implementation becomes impractical online. We develop two online algorithms that exactly calculate the likelihood ratio test for a single changepoint in p-dimensional data streams by leveraging fascinating connections with computational geometry. Our first algorithm is straightforward and empirically quasi-linear. The second is more complex but provably quasi-linear: O(nlog(n)p+1)\mathcal{O}(n\log(n)^{p+1}) for nn data points. Through simulations, we illustrate, that they are fast and allow us to process millions of points within a matter of minutes up to p=5p=5.Comment: 31 pages,15 figure

    Two-step percolation in aggregating systems

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    The two-step percolation behavior in aggregating systems was studied both experimentally and by means of Monte Carlo (MC) simulations. In experimental studies, the electrical conductivity, σ\sigma, of colloidal suspension of multiwalled carbon nanotubes (CNTs) in decane was measured. The suspension was submitted to mechanical de-liquoring in a planar filtration-compression conductometric cell. During de-liquoring, the distance between the measuring electrodes continuously decreased and the CNT volume fraction φ\varphi continuously increased (from 10310^{-3} up to 0.3\approx 0.3% v/v). The two percolation thresholds at φ1103\varphi_{1}\lesssim 10^{-3} and φ2102\varphi_{2}\approx 10^{-2} can reflect the interpenetration of loose CNT aggregates and percolation across the compact conducting aggregates, respectively. The MC computational model accounted for the core-shell structure of conducting particles or their aggregates, the tendency of a particle for aggregation, the formation of solvation shells, and the elongated geometry of the conductometric cell. The MC studies revealed two smoothed percolation transitions in σ(φ)\sigma(\varphi) dependencies that correspond to the percolation through the shells and cores, respectively. The data demonstrated a noticeable impact of particle aggregation on anisotropy in electrical conductivity σ(φ)\sigma(\varphi) measured along different directions in the conductometric cell.Comment: 10 pages, 6 figure

    Development of High-Order P\u3cem\u3e\u3csub\u3eN\u3c/sub\u3e\u3c/em\u3e Models for Radiative Heat Transfer in Special Geometries and Boundary Conditions

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    The high-order spherical harmonics () method for 2-D Cartesian domains is extracted from the 3-D formulation. The number of equations and intensity coefficients reduces to (N+1)2/4 in the 2-D Cartesian formulation compared with N(N+1)/2 for the general 3-D formulation. The Marshak boundary conditions are extended to solve problems with nonblack and mixed diffuse-specular surfaces. Additional boundary conditions for specified radiative wall flux, for symmetry/specular reflection boundaries have also been developed. The mathematical details of the formulations and their implementation in the OpenFOAM finite volume based CFD software platform are presented. The accuracy and computational cost of the 2-D Cartesian are compared with that of the 3-D solver and a Photon Monte Carlo solver for a square enclosure, as well as a 45° wedge geometry with variable radiative properties. The new boundary conditions have been applied for both test cases, and the boundary condition for mixed diffuse-specular surfaces is further illustrated by numerical examples of a rectangular geometry enclosed by walls with different surface characteristics

    A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting

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    An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of standard fluxes from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Comment: 30 pages, 27 figures, 3 table
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