The Experts below are selected from a list of 19296 Experts worldwide ranked by ideXlab platform
Philip H. Stauffer - One of the best experts on this subject based on the ideXlab platform.
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On estimating functional Average breakthrough curve using time‐warping technique and perturbation approach
Water Resources Research, 2012Co-Authors: Zhiming Lu, Philip H. StaufferAbstract:[1] Simulated contaminant breakthrough curves (BTC) are often used to predict mass arrival at compliance boundaries at waste storage sites. In numerical simulations that involve uncertainties on input parameters such as randomly heterogeneous rock properties, Monte Carlo simulations are commonly utilized and the mean breakthrough curve is often calculated from the Arithmetic Average of all realizations. The Arithmetic mean breakthrough curve in general overestimates the mass flow rate at early and late time but underestimates the peak mass flow rate. The Averaged breakthrough curve usually does not resemble any of individual breakthrough curves. The reason is that BTCs vary not only on amplitude but also on dynamics (time) and therefore it is not appropriate to take the Arithmetic Average directly. In this study, we consider each BTC as a random curve, and use time-warping techniques to align all curves in a time-warped space, compute the sample mean of the curves in the time-warped space, and transform the means back to the original time space. We show that all BTCs are aligned based on the percentile of mass reaching the compliance boundary, and the functional Average is the percentile Average of all BTCs. The confidence interval of the sample mean curve is estimated using the perturbation approach. The functional Average provides an additional metric that can be used to characterize the breakthrough behavior in addition to more traditional median and Arithmetic Average curves. The method is illustrated using transport simulations at the Material Disposal Area G, Los Alamos National Laboratory (LANL) in New Mexico.
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on estimating functional Average breakthrough curve using time warping technique and perturbation approach
Water Resources Research, 2012Co-Authors: Zhiming Lu, Philip H. StaufferAbstract:[1] Simulated contaminant breakthrough curves (BTC) are often used to predict mass arrival at compliance boundaries at waste storage sites. In numerical simulations that involve uncertainties on input parameters such as randomly heterogeneous rock properties, Monte Carlo simulations are commonly utilized and the mean breakthrough curve is often calculated from the Arithmetic Average of all realizations. The Arithmetic mean breakthrough curve in general overestimates the mass flow rate at early and late time but underestimates the peak mass flow rate. The Averaged breakthrough curve usually does not resemble any of individual breakthrough curves. The reason is that BTCs vary not only on amplitude but also on dynamics (time) and therefore it is not appropriate to take the Arithmetic Average directly. In this study, we consider each BTC as a random curve, and use time-warping techniques to align all curves in a time-warped space, compute the sample mean of the curves in the time-warped space, and transform the means back to the original time space. We show that all BTCs are aligned based on the percentile of mass reaching the compliance boundary, and the functional Average is the percentile Average of all BTCs. The confidence interval of the sample mean curve is estimated using the perturbation approach. The functional Average provides an additional metric that can be used to characterize the breakthrough behavior in addition to more traditional median and Arithmetic Average curves. The method is illustrated using transport simulations at the Material Disposal Area G, Los Alamos National Laboratory (LANL) in New Mexico.
Zhiming Lu - One of the best experts on this subject based on the ideXlab platform.
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On estimating functional Average breakthrough curve using time‐warping technique and perturbation approach
Water Resources Research, 2012Co-Authors: Zhiming Lu, Philip H. StaufferAbstract:[1] Simulated contaminant breakthrough curves (BTC) are often used to predict mass arrival at compliance boundaries at waste storage sites. In numerical simulations that involve uncertainties on input parameters such as randomly heterogeneous rock properties, Monte Carlo simulations are commonly utilized and the mean breakthrough curve is often calculated from the Arithmetic Average of all realizations. The Arithmetic mean breakthrough curve in general overestimates the mass flow rate at early and late time but underestimates the peak mass flow rate. The Averaged breakthrough curve usually does not resemble any of individual breakthrough curves. The reason is that BTCs vary not only on amplitude but also on dynamics (time) and therefore it is not appropriate to take the Arithmetic Average directly. In this study, we consider each BTC as a random curve, and use time-warping techniques to align all curves in a time-warped space, compute the sample mean of the curves in the time-warped space, and transform the means back to the original time space. We show that all BTCs are aligned based on the percentile of mass reaching the compliance boundary, and the functional Average is the percentile Average of all BTCs. The confidence interval of the sample mean curve is estimated using the perturbation approach. The functional Average provides an additional metric that can be used to characterize the breakthrough behavior in addition to more traditional median and Arithmetic Average curves. The method is illustrated using transport simulations at the Material Disposal Area G, Los Alamos National Laboratory (LANL) in New Mexico.
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on estimating functional Average breakthrough curve using time warping technique and perturbation approach
Water Resources Research, 2012Co-Authors: Zhiming Lu, Philip H. StaufferAbstract:[1] Simulated contaminant breakthrough curves (BTC) are often used to predict mass arrival at compliance boundaries at waste storage sites. In numerical simulations that involve uncertainties on input parameters such as randomly heterogeneous rock properties, Monte Carlo simulations are commonly utilized and the mean breakthrough curve is often calculated from the Arithmetic Average of all realizations. The Arithmetic mean breakthrough curve in general overestimates the mass flow rate at early and late time but underestimates the peak mass flow rate. The Averaged breakthrough curve usually does not resemble any of individual breakthrough curves. The reason is that BTCs vary not only on amplitude but also on dynamics (time) and therefore it is not appropriate to take the Arithmetic Average directly. In this study, we consider each BTC as a random curve, and use time-warping techniques to align all curves in a time-warped space, compute the sample mean of the curves in the time-warped space, and transform the means back to the original time space. We show that all BTCs are aligned based on the percentile of mass reaching the compliance boundary, and the functional Average is the percentile Average of all BTCs. The confidence interval of the sample mean curve is estimated using the perturbation approach. The functional Average provides an additional metric that can be used to characterize the breakthrough behavior in addition to more traditional median and Arithmetic Average curves. The method is illustrated using transport simulations at the Material Disposal Area G, Los Alamos National Laboratory (LANL) in New Mexico.
R. K. Mohanty - One of the best experts on this subject based on the ideXlab platform.
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A Combined Arithmetic Average Discretization and TAGE Iterative Method for Non-linear Two Point Boundary Value Problems with a Source Function in Integral Form
Differential Equations and Dynamical Systems, 2012Co-Authors: R. K. MohantyAbstract:In this article, we report the derivation of high accuracy numerical method based on Arithmetic Average discretization for the solution of $${u^{\prime\prime} = F(x, u, {u}^{\prime})+\int_0^1 {K(x, s)ds}, 0 < x < 1, 0 < s < 1}$$ subject to natural boundary conditions and the application of two parameter alternating group explicit (TAGE) iterative method on a non-uniform mesh. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compare to the method discussed in Mohanty and Dhall (Appl Math Comput 215:2024–2034, 2009). The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of the method is briefly discussed. The advantage of using this new variable mesh strategy is highlighted computationally.
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high accuracy Arithmetic Average type discretization for the solution of two space dimensional nonlinear wave equations
International Journal of Modeling Simulation and Scientific Computing, 2012Co-Authors: R. K. Mohanty, Venu GopalAbstract:In this paper, we propose a new high accuracy discretization based on the ideas given by Chawla and Shivakumar for the solution of two-space dimensional nonlinear hyperbolic partial differential equation of the form utt = A(x, y, t)uxx + B(x, y, t)uyy + g(x, y, t, u, ux, uy, ut), 0 0 subject to appropriate initial and Dirichlet boundary conditions. We use only five evaluations of the function g and do not require any fictitious points to discretize the differential equation. The proposed method is directly applicable to wave equation in polar coordinates and when applied to a linear telegraphic hyperbolic equation is shown to be unconditionally stable. Numerical results are provided to illustrate the usefulness of the proposed method.
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High Accuracy Arithmetic Average Discretization for Non-Linear Two Point Boundary Value Problems with a Source Function in Integral Form
Applied Mathematics-a Journal of Chinese Universities Series B, 2011Co-Authors: R. K. Mohanty, Deepika DhallAbstract:In this article, we report the derivation of high accuracy finite difference method based on Arithmetic Average discretization for the solution of Un=F(x,u,u´)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.
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Application of AGE Method to High Accuracy Variable Mesh Arithmetic Average Type Discretization for 1D Non-linear Parabolic Initial Boundary Value Problems
International Journal for Computational Methods in Engineering Science and Mechanics, 2010Co-Authors: R. K. MohantyAbstract:In this article, we discuss the application of Arithmetic Average discretization alternating group explicit (A-AGE) method to a new two-level implicit variable mesh formula of O(k2hl − 1+ khl + hl 3) for the solution of non-linear parabolic equation uxx = F(x,t,u,ux, ut) subject to appropriate initial and Dirichlet boundary conditions, where k > 0 and hl > 0 are the variable step lengths in time and space directions, respectively. The proposed technique is also useful to solve parabolic singular problems. Our discretization procedure requires only 3-spatial grid points. A-AGE and Newton-A-AGE algorithms are discussed in detail. Comparison of numerical results of these methods with the corresponding successive over relaxation (SOR) and Newton-SOR methods is also included.
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An O(k2 + kh2 + h4) Arithmetic Average discretization for the solution of 1-D nonlinear parabolic equations
Numerical Methods for Partial Differential Equations, 2007Co-Authors: R. K. Mohanty, Samir Karaa, Urvashi AroraAbstract:This article develops a new two-level three-point implicit finite difference scheme of order 2 in time and 4 in space based on Arithmetic Average discretization for the solution of nonlinear parabolic equation e uxx = f(x, t, u, ux, ut), 0 0 subject to appropriate initial and Dirichlet boundary conditions, where e > 0 is a small positive constant. We also propose a new explicit difference scheme of order 2 in time and 4 in space for the estimates of (∂u/∂x). The main objective is the proposed formulas are directly applicable to both singular and nonsingular problems. We do not require any fictitious points outside the solution region and any special technique to handle the singular problems. Stability analysis of a model problem is discussed. Numerical results are provided to validate the usefulness of the proposed formulas. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007
S. J. Lee - One of the best experts on this subject based on the ideXlab platform.
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soft data space time mapping of coarse particulate matter annual Arithmetic Average over the u s
2004Co-Authors: Marc L. Serre, George Christakos, S. J. LeeAbstract:In the U.S., particulate matter (PM10) is considered an important criteria air pollutant and it is monitored throughout the country by means of a considerably dense network of stations. Because of the health risks associated with PM10, it is important to study carefully the spatiotemporal distribution of the air pollutant. In the last decade, the modern BME approach has emerged as an advanced function of temporal GIS (TGIS). The BME approach has certain powerful features and has been used for mapping PM10 and PM2.5 distributions in the U.S. and abroad. In this work we propose an approach to use available information to develop probabilistic soft data about the annual Arithmetic Average of PM10, and we use the BME framework to rigorously process that information and produce realistic spatiotemporal maps of PM10 distribution over the US. We apply the approach presented on a large PM10 dataset from the USEPA AIRS database covering the 1984 to 2000 period.
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Soft Data Space/Time Mapping of Coarse Particulate Matter Annual Arithmetic Average Over the U.S
Quantitative Geology and Geostatistics, 1Co-Authors: Marc L. Serre, George Christakos, S. J. LeeAbstract:In the U.S., particulate matter (PM10) is considered an important criteria air pollutant and it is monitored throughout the country by means of a considerably dense network of stations. Because of the health risks associated with PM10, it is important to study carefully the spatiotemporal distribution of the air pollutant. In the last decade, the modern BME approach has emerged as an advanced function of temporal GIS (TGIS). The BME approach has certain powerful features and has been used for mapping PM10 and PM2.5 distributions in the U.S. and abroad. In this work we propose an approach to use available information to develop probabilistic soft data about the annual Arithmetic Average of PM10, and we use the BME framework to rigorously process that information and produce realistic spatiotemporal maps of PM10 distribution over the US. We apply the approach presented on a large PM10 dataset from the USEPA AIRS database covering the 1984 to 2000 period.
Jinfa Cai - One of the best experts on this subject based on the ideXlab platform.
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teachers conceptions and constructions of pedagogical representations in teaching Arithmetic Average
2002Co-Authors: Jinfa Cai, Christine Carrino GorowaraAbstract:This study examined twelve inexperienced and eleven experienced teachers’ constructions of and conceptions about pedagogical representations for teaching Arithmetic Average. The teachers were asked to generate appropriate pedagogical representations as well as predict and evaluate the uses of different representations for solving problems involving the Arithmetic Average. The experienced teachers were able to predict a variety of representations as well as errors that are recognized as common among middle-school students, while the inexperienced teachers used algebraic representations almost exclusively. Additionally, the inexperienced teachers tended to value algebraic solutions over guess-and-check or visual drawing solutions, more so than did the experienced teachers. However, the differences in the experienced and inexperienced teachers’ abilities to predict and evaluate the use of different representations were not clearly evident in their generation of pedagogical representations in a lesson plan context.
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TEACHERS' CONCEPTIONS AND CONSTRUCTIONS OF PEDAGOGICAL REPRESENTATIONS IN TEACHING Arithmetic Average ®
2002Co-Authors: Jinfa Cai, Christine Carrino GorowaraAbstract:This study examined twelve inexperienced and eleven experienced teachers’ constructions of and conceptions about pedagogical representations for teaching Arithmetic Average. The teachers were asked to generate appropriate pedagogical representations as well as predict and evaluate the uses of different representations for solving problems involving the Arithmetic Average. The experienced teachers were able to predict a variety of representations as well as errors that are recognized as common among middle-school students, while the inexperienced teachers used algebraic representations almost exclusively. Additionally, the inexperienced teachers tended to value algebraic solutions over guess-and-check or visual drawing solutions, more so than did the experienced teachers. However, the differences in the experienced and inexperienced teachers’ abilities to predict and evaluate the use of different representations were not clearly evident in their generation of pedagogical representations in a lesson plan context.
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Intended Treatments of Arithmetic Average in U.S. and Asian School Mathematics Textbooks.
School Science and Mathematics, 2002Co-Authors: Jinfa Cai, Tad WatanabeAbstract:This study examined how selected U.S. and Asian mathematics curricula are designed to facilitate students' understanding of the Arithmetic Average. There is a consistency regarding the learning goals among these curriculum series, but the focuses are different between the Asian series and the U.S. reform series. The Asian series and the U.S. commercial series focus the Arithmetic Average more on conceptual and procedural understanding of the concept as a computational algorithm than on understanding the concept as a representative of a data set; however, the two U.S. reform series focus the concept more on the latter. Because of the different focuses, the Asian and the U.S. curriculum series treat the concept differently. In the Asian series, the concept is first introduced in the context of “equal-sharing” or “per-unit-quantity,” and the averaging formula is formally introduced at a very early stage. In the U.S. reform series, the concept is discussed as a measure of central tendency, and after students have some intuitive ideas of the statistical aspect of the concept, the averaging algorithm is briefly introduced.