A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

NASA Astrophysics Data System (ADS)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

A Sensitivity Analysis of Circular Error Probable Approximation Techniques

DTIC Science & Technology

1992-03-01

SENSITIVITY ANALYSIS OF CIRCULAR ERROR PROBABLE APPROXIMATION TECHNIQUES THESIS Presented to the Faculty of the School of Engineering of the Air Force...programming skills. Major Paul Auclair patiently advised me in this endeavor, and Major Andy Howell added numerous insightful contributions. I thank my...techniques. The two ret(st accuratec techniiques require numerical integration and can take several hours to run ov a personal comlputer [2:1-2,4-6]. Some

An integral formulation for wave propagation on weakly non-uniform potential flows

NASA Astrophysics Data System (ADS)

Mancini, Simone; Astley, R. Jeremy; Sinayoko, Samuel; Gabard, Gwénaël; Tournour, Michel

2016-12-01

An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels for wave propagation on non-uniform flow. The integral solution is formulated using a Green's function obtained by combining the Taylor and Lorentz transformations. Although most conventional approaches based on either transform solve the Helmholtz problem in a transformed domain, the current Green's function and associated integral equation are derived in the physical space. A dimensional error analysis is developed to identify the limitations of the current formulation. Numerical applications are performed to assess the accuracy of the integral solution. It is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field, and as a means of solving scattering problems by rigid surfaces in non-uniform flows. The results show that the error associated with the physical model deteriorates with increasing frequency and mean flow Mach number. However, the error is generated only in the domain where mean flow non-uniformities are significant and is constant in regions where the flow is uniform.

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

NASA Technical Reports Server (NTRS)

Rummel, R.; Sjoeberg, L.; Rapp, R. H.

1978-01-01

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.

Analysis of all-optical temporal integrator employing phased-shifted DFB-SOA.

PubMed

Jia, Xin-Hong; Ji, Xiao-Ling; Xu, Cong; Wang, Zi-Nan; Zhang, Wei-Li

2014-11-17

All-optical temporal integrator using phase-shifted distributed-feedback semiconductor optical amplifier (DFB-SOA) is investigated. The influences of system parameters on its energy transmittance and integration error are explored in detail. The numerical analysis shows that, enhanced energy transmittance and integration time window can be simultaneously achieved by increased injected current in the vicinity of lasing threshold. We find that the range of input pulse-width with lower integration error is highly sensitive to the injected optical power, due to gain saturation and induced detuning deviation mechanism. The initial frequency detuning should also be carefully chosen to suppress the integration deviation with ideal waveform output.

A novel approach to evaluation of pest insect abundance in the presence of noise.

PubMed

Embleton, Nina; Petrovskaya, Natalia

2014-03-01

Evaluation of pest abundance is an important task of integrated pest management. It has recently been shown that evaluation of pest population size from discrete sampling data can be done by using the ideas of numerical integration. Numerical integration of the pest population density function is a computational technique that readily gives us an estimate of the pest population size, where the accuracy of the estimate depends on the number of traps installed in the agricultural field to collect the data. However, in a standard mathematical problem of numerical integration, it is assumed that the data are precise, so that the random error is zero when the data are collected. This assumption does not hold in ecological applications. An inherent random error is often present in field measurements, and therefore it may strongly affect the accuracy of evaluation. In our paper, we offer a novel approach to evaluate the pest insect population size under the assumption that the data about the pest population include a random error. The evaluation is not based on statistical methods but is done using a spatially discrete method of numerical integration where the data obtained by trapping as in pest insect monitoring are converted to values of the population density. It will be discussed in the paper how the accuracy of evaluation differs from the case where the same evaluation method is employed to handle precise data. We also consider how the accuracy of the pest insect abundance evaluation can be affected by noise when the data available from trapping are sparse. In particular, we show that, contrary to intuitive expectations, noise does not have any considerable impact on the accuracy of evaluation when the number of traps is small as is conventional in ecological applications.

On the Calculation of Uncertainty Statistics with Error Bounds for CFD Calculations Containing Random Parameters and Fields

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2016-01-01

This chapter discusses the ongoing development of combined uncertainty and error bound estimates for computational fluid dynamics (CFD) calculations subject to imposed random parameters and random fields. An objective of this work is the construction of computable error bound formulas for output uncertainty statistics that guide CFD practitioners in systematically determining how accurately CFD realizations should be approximated and how accurately uncertainty statistics should be approximated for output quantities of interest. Formal error bounds formulas for moment statistics that properly account for the presence of numerical errors in CFD calculations and numerical quadrature errors in the calculation of moment statistics have been previously presented in [8]. In this past work, hierarchical node-nested dense and sparse tensor product quadratures are used to calculate moment statistics integrals. In the present work, a framework has been developed that exploits the hierarchical structure of these quadratures in order to simplify the calculation of an estimate of the quadrature error needed in error bound formulas. When signed estimates of realization error are available, this signed error may also be used to estimate output quantity of interest probability densities as a means to assess the impact of realization error on these density estimates. Numerical results are presented for CFD problems with uncertainty to demonstrate the capabilities of this framework.

QUANTIFYING UNCERTAINTY DUE TO RANDOM ERRORS FOR MOMENT ANALYSES OF BREAKTHROUGH CURVES

EPA Science Inventory

The uncertainty in moments calculated from breakthrough curves (BTCs) is investigated as a function of random measurement errors in the data used to define the BTCs. The method presented assumes moments are calculated by numerical integration using the trapezoidal rule, and is t...

Fast maximum likelihood estimation using continuous-time neural point process models.

PubMed

Lepage, Kyle Q; MacDonald, Christopher J

2015-06-01

A recent report estimates that the number of simultaneously recorded neurons is growing exponentially. A commonly employed statistical paradigm using discrete-time point process models of neural activity involves the computation of a maximum-likelihood estimate. The time to computate this estimate, per neuron, is proportional to the number of bins in a finely spaced discretization of time. By using continuous-time models of neural activity and the optimally efficient Gaussian quadrature, memory requirements and computation times are dramatically decreased in the commonly encountered situation where the number of parameters p is much less than the number of time-bins n. In this regime, with q equal to the quadrature order, memory requirements are decreased from O(np) to O(qp), and the number of floating-point operations are decreased from O(np(2)) to O(qp(2)). Accuracy of the proposed estimates is assessed based upon physiological consideration, error bounds, and mathematical results describing the relation between numerical integration error and numerical error affecting both parameter estimates and the observed Fisher information. A check is provided which is used to adapt the order of numerical integration. The procedure is verified in simulation and for hippocampal recordings. It is found that in 95 % of hippocampal recordings a q of 60 yields numerical error negligible with respect to parameter estimate standard error. Statistical inference using the proposed methodology is a fast and convenient alternative to statistical inference performed using a discrete-time point process model of neural activity. It enables the employment of the statistical methodology available with discrete-time inference, but is faster, uses less memory, and avoids any error due to discretization.

Molecular radiotherapy: the NUKFIT software for calculating the time-integrated activity coefficient.

PubMed

Kletting, P; Schimmel, S; Kestler, H A; Hänscheid, H; Luster, M; Fernández, M; Bröer, J H; Nosske, D; Lassmann, M; Glatting, G

2013-10-01

Calculation of the time-integrated activity coefficient (residence time) is a crucial step in dosimetry for molecular radiotherapy. However, available software is deficient in that it is either not tailored for the use in molecular radiotherapy and/or does not include all required estimation methods. The aim of this work was therefore the development and programming of an algorithm which allows for an objective and reproducible determination of the time-integrated activity coefficient and its standard error. The algorithm includes the selection of a set of fitting functions from predefined sums of exponentials and the choice of an error model for the used data. To estimate the values of the adjustable parameters an objective function, depending on the data, the parameters of the error model, the fitting function and (if required and available) Bayesian information, is minimized. To increase reproducibility and user-friendliness the starting values are automatically determined using a combination of curve stripping and random search. Visual inspection, the coefficient of determination, the standard error of the fitted parameters, and the correlation matrix are provided to evaluate the quality of the fit. The functions which are most supported by the data are determined using the corrected Akaike information criterion. The time-integrated activity coefficient is estimated by analytically integrating the fitted functions. Its standard error is determined assuming Gaussian error propagation. The software was implemented using MATLAB. To validate the proper implementation of the objective function and the fit functions, the results of NUKFIT and SAAM numerical, a commercially available software tool, were compared. The automatic search for starting values was successfully tested for reproducibility. The quality criteria applied in conjunction with the Akaike information criterion allowed the selection of suitable functions. Function fit parameters and their standard error estimated by using SAAM numerical and NUKFIT showed differences of <1%. The differences for the time-integrated activity coefficients were also <1% (standard error between 0.4% and 3%). In general, the application of the software is user-friendly and the results are mathematically correct and reproducible. An application of NUKFIT is presented for three different clinical examples. The software tool with its underlying methodology can be employed to objectively and reproducibly estimate the time integrated activity coefficient and its standard error for most time activity data in molecular radiotherapy.

Trajectory errors of different numerical integration schemes diagnosed with the MPTRAC advection module driven by ECMWF operational analyses

NASA Astrophysics Data System (ADS)

Rößler, Thomas; Stein, Olaf; Heng, Yi; Baumeister, Paul; Hoffmann, Lars

2018-02-01

The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration scheme and the appropriate time step should possibly take into account the typical altitude ranges as well as the total length of the simulations to achieve the most efficient simulations. However, trying to summarize, we recommend the third-order Runge-Kutta method with a time step of 170 s or the midpoint scheme with a time step of 100 s for efficient simulations of up to 10 days of simulation time for the specific ECMWF high-resolution data set considered in this study. Purely stratospheric simulations can use significantly larger time steps of 800 and 1100 s for the midpoint scheme and the third-order Runge-Kutta method, respectively.

Effect of atmospheric turbulence on the bit error probability of a space to ground near infrared laser communications link using binary pulse position modulation and an avalanche photodiode detector

NASA Technical Reports Server (NTRS)

Safren, H. G.

1987-01-01

The effect of atmospheric turbulence on the bit error rate of a space-to-ground near infrared laser communications link is investigated, for a link using binary pulse position modulation and an avalanche photodiode detector. Formulas are presented for the mean and variance of the bit error rate as a function of signal strength. Because these formulas require numerical integration, they are of limited practical use. Approximate formulas are derived which are easy to compute and sufficiently accurate for system feasibility studies, as shown by numerical comparison with the exact formulas. A very simple formula is derived for the bit error rate as a function of signal strength, which requires only the evaluation of an error function. It is shown by numerical calculations that, for realistic values of the system parameters, the increase in the bit error rate due to turbulence does not exceed about thirty percent for signal strengths of four hundred photons per bit or less. The increase in signal strength required to maintain an error rate of one in 10 million is about one or two tenths of a db.

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

NASA Technical Reports Server (NTRS)

Felici, Helene M.; Drela, Mark

1993-01-01

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields.

PubMed

Steffen, Michael; Curtis, Sean; Kirby, Robert M; Ryan, Jennifer K

2008-01-01

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

Goal-oriented explicit residual-type error estimates in XFEM

NASA Astrophysics Data System (ADS)

Rüter, Marcus; Gerasimov, Tymofiy; Stein, Erwin

2013-08-01

A goal-oriented a posteriori error estimator is derived to control the error obtained while approximately evaluating a quantity of engineering interest, represented in terms of a given linear or nonlinear functional, using extended finite elements of Q1 type. The same approximation method is used to solve the dual problem as required for the a posteriori error analysis. It is shown that for both problems to be solved numerically the same singular enrichment functions can be used. The goal-oriented error estimator presented can be classified as explicit residual type, i.e. the residuals of the approximations are used directly to compute upper bounds on the error of the quantity of interest. This approach therefore extends the explicit residual-type error estimator for classical energy norm error control as recently presented in Gerasimov et al. (Int J Numer Meth Eng 90:1118-1155, 2012a). Without loss of generality, the a posteriori error estimator is applied to the model problem of linear elastic fracture mechanics. Thus, emphasis is placed on the fracture criterion, here the J-integral, as the chosen quantity of interest. Finally, various illustrative numerical examples are presented where, on the one hand, the error estimator is compared to its finite element counterpart and, on the other hand, improved enrichment functions, as introduced in Gerasimov et al. (2012b), are discussed.

Improving the numerical integration solution of satellite orbits in the presence of solar radiation pressure using modified back differences

NASA Technical Reports Server (NTRS)

Lundberg, J. B.; Feulner, M. R.; Abusali, P. A. M.; Ho, C. S.

1991-01-01

The method of modified back differences, a technique that significantly reduces the numerical integration errors associated with crossing shadow boundaries using a fixed-mesh multistep integrator without a significant increase in computer run time, is presented. While Hubbard's integral approach can produce significant improvements to the trajectory solution, the interpolation method provides the best overall results. It is demonstrated that iterating on the point mass term correction is also important for achieving the best overall results. It is also shown that the method of modified back differences can be implemented with only a small increase in execution time.

FEWZ 2.0: A code for hadronic Z production at next-to-next-to-leading order

NASA Astrophysics Data System (ADS)

Gavin, Ryan; Li, Ye; Petriello, Frank; Quackenbush, Seth

2011-11-01

We introduce an improved version of the simulation code FEWZ ( Fully Exclusive W and Z Production) for hadron collider production of lepton pairs through the Drell-Yan process at next-to-next-to-leading order (NNLO) in the strong coupling constant. The program is fully differential in the phase space of leptons and additional hadronic radiation. The new version offers users significantly more options for customization. FEWZ now bins multiple, user-selectable histograms during a single run, and produces parton distribution function (PDF) errors automatically. It also features a significantly improved integration routine, and can take advantage of multiple processor cores locally or on the Condor distributed computing system. We illustrate the new features of FEWZ by presenting numerous phenomenological results for LHC physics. We compare NNLO QCD with initial ATLAS and CMS results, and discuss in detail the effects of detector acceptance on the measurement of angular quantities associated with Z-boson production. We address the issue of technical precision in the presence of severe phase-space cuts. Program summaryProgram title: FEWZ Catalogue identifier: AEJP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 6 280 771 No. of bytes in distributed program, including test data, etc.: 173 027 645 Distribution format: tar.gz Programming language: Fortran 77, C++, Python Computer: Mac, PC Operating system: Mac OSX, Unix/Linux Has the code been vectorized or parallelized?: Yes. User-selectable, 1 to 219 RAM: 200 Mbytes for common parton distribution functions Classification: 11.1 External routines: CUBA numerical integration library, numerous parton distribution sets (see text); these are provided with the code. Nature of problem: Determination of the Drell-Yan Z/photon production cross section and decay into leptons, with kinematic distributions of leptons and jets including full spin correlations, at next-to-next-to-leading order in the strong coupling constant. Solution method: Virtual loop integrals are decomposed into master integrals using automated techniques. Singularities are extracted from real radiation terms via sector decomposition, which separates singularities and maps onto suitable phase space variables. Result is convoluted with parton distribution functions. Each piece is numerically integrated over phase space, which allows arbitrary cuts on the observed particles. Each sample point may be binned during numerical integration, providing histograms, and reweighted by parton distribution function error eigenvectors, which provides PDF errors. Restrictions: Output does not correspond to unweighted events, and cannot be interfaced with a shower Monte Carlo. Additional comments: !!!!! The distribution file for this program is over 170 Mbytes and therefore is not delivered directly when download or E-mail is requested. Instead a html file giving details of how the program can be obtained is sent. Running time: One day for total cross sections with 0.1% integration errors assuming typical cuts, up to 1 week for smooth kinematic distributions with sub-percent integration errors for each bin.

An Improved Neutron Transport Algorithm for HZETRN

NASA Technical Reports Server (NTRS)

Slaba, Tony C.; Blattnig, Steve R.; Clowdsley, Martha S.; Walker, Steven A.; Badavi, Francis F.

2010-01-01

Long term human presence in space requires the inclusion of radiation constraints in mission planning and the design of shielding materials, structures, and vehicles. In this paper, the numerical error associated with energy discretization in HZETRN is addressed. An inadequate numerical integration scheme in the transport algorithm is shown to produce large errors in the low energy portion of the neutron and light ion fluence spectra. It is further shown that the errors result from the narrow energy domain of the neutron elastic cross section spectral distributions, and that an extremely fine energy grid is required to resolve the problem under the current formulation. Two numerical methods are developed to provide adequate resolution in the energy domain and more accurately resolve the neutron elastic interactions. Convergence testing is completed by running the code for various environments and shielding materials with various energy grids to ensure stability of the newly implemented method.

Lateral charge transport from heavy-ion tracks in integrated circuit chips

NASA Technical Reports Server (NTRS)

Zoutendyk, J. A.; Schwartz, H. R.; Nevill, L. R.

1988-01-01

A 256K DRAM has been used to study the lateral transport of charge (electron-hole pairs) induced by direct ionization from heavy-ion tracks in an IC. The qualitative charge transport has been simulated using a two-dimensional numerical code in cylindrical coordinates. The experimental bit-map data clearly show the manifestation of lateral charge transport in the creation of adjacent multiple-bit errors from a single heavy-ion track. The heavy-ion data further demonstrate the occurrence of multiple-bit errors from single ion tracks with sufficient stopping power. The qualitative numerical simulation results suggest that electric-field-funnel-aided (drift) collection accounts for single error generated by an ion passing through a charge-collecting junction, while multiple errors from a single ion track are due to lateral diffusion of ion-generated charge.

A multiphysical ensemble system of numerical snow modelling

NASA Astrophysics Data System (ADS)

Lafaysse, Matthieu; Cluzet, Bertrand; Dumont, Marie; Lejeune, Yves; Vionnet, Vincent; Morin, Samuel

2017-05-01

Physically based multilayer snowpack models suffer from various modelling errors. To represent these errors, we built the new multiphysical ensemble system ESCROC (Ensemble System Crocus) by implementing new representations of different physical processes in the deterministic coupled multilayer ground/snowpack model SURFEX/ISBA/Crocus. This ensemble was driven and evaluated at Col de Porte (1325 m a.s.l., French alps) over 18 years with a high-quality meteorological and snow data set. A total number of 7776 simulations were evaluated separately, accounting for the uncertainties of evaluation data. The ability of the ensemble to capture the uncertainty associated to modelling errors is assessed for snow depth, snow water equivalent, bulk density, albedo and surface temperature. Different sub-ensembles of the ESCROC system were studied with probabilistic tools to compare their performance. Results show that optimal members of the ESCROC system are able to explain more than half of the total simulation errors. Integrating members with biases exceeding the range corresponding to observational uncertainty is necessary to obtain an optimal dispersion, but this issue can also be a consequence of the fact that meteorological forcing uncertainties were not accounted for. The ESCROC system promises the integration of numerical snow-modelling errors in ensemble forecasting and ensemble assimilation systems in support of avalanche hazard forecasting and other snowpack-modelling applications.

hp-Adaptive time integration based on the BDF for viscous flows

NASA Astrophysics Data System (ADS)

Hay, A.; Etienne, S.; Pelletier, D.; Garon, A.

2015-06-01

This paper presents a procedure based on the Backward Differentiation Formulas of order 1 to 5 to obtain efficient time integration of the incompressible Navier-Stokes equations. The adaptive algorithm performs both stepsize and order selections to control respectively the solution accuracy and the computational efficiency of the time integration process. The stepsize selection (h-adaptivity) is based on a local error estimate and an error controller to guarantee that the numerical solution accuracy is within a user prescribed tolerance. The order selection (p-adaptivity) relies on the idea that low-accuracy solutions can be computed efficiently by low order time integrators while accurate solutions require high order time integrators to keep computational time low. The selection is based on a stability test that detects growing numerical noise and deems a method of order p stable if there is no method of lower order that delivers the same solution accuracy for a larger stepsize. Hence, it guarantees both that (1) the used method of integration operates inside of its stability region and (2) the time integration procedure is computationally efficient. The proposed time integration procedure also features a time-step rejection and quarantine mechanisms, a modified Newton method with a predictor and dense output techniques to compute solution at off-step points.

Emissivity correction for interpreting thermal radiation from a terrestrial surface

NASA Technical Reports Server (NTRS)

Sutherland, R. A.; Bartholic, J. F.; Gerber, J. F.

1979-01-01

A general method of accounting for emissivity in making temperature determinations of graybody surfaces from radiometric data is presented. The method differs from previous treatments in that a simple blackbody calibration and graphical approach is used rather than numerical integrations which require detailed knowledge of an instrument's spectral characteristics. Also, errors caused by approximating instrumental response with the Stephan-Boltzman law rather than with an appropriately weighted Planck integral are examined. In the 8-14 micron wavelength interval, it is shown that errors are at most on the order of 3 C for the extremes of the earth's temperature and emissivity. For more practical limits, however, errors are less than 0.5 C.

Zdeněk Kopal: Numerical Analyst

NASA Astrophysics Data System (ADS)

Křížek, M.

2015-07-01

We give a brief overview of Zdeněk Kopal's life, his activities in the Czech Astronomical Society, his collaboration with Vladimír Vand, and his studies at Charles University, Cambridge, Harvard, and MIT. Then we survey Kopal's professional life. He published 26 monographs and 20 conference proceedings. We will concentrate on Kopal's extensive monograph Numerical Analysis (1955, 1961) that is widely accepted to be the first comprehensive textbook on numerical methods. It describes, for instance, methods for polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations with initial or boundary conditions, and numerical solution of integral and integro-differential equations. Special emphasis will be laid on error analysis. Kopal himself applied numerical methods to celestial mechanics, in particular to the N-body problem. He also used Fourier analysis to investigate light curves of close binaries to discover their properties. This is, in fact, a problem from mathematical analysis.

ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve☆

PubMed Central

Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk

2014-01-01

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments. PMID:24748725

A multilevel finite element method for Fredholm integral eigenvalue problems

NASA Astrophysics Data System (ADS)

Xie, Hehu; Zhou, Tao

2015-12-01

In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.

Assessment of numerical techniques for unsteady flow calculations

NASA Technical Reports Server (NTRS)

Hsieh, Kwang-Chung

1989-01-01

The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.

Stable Numerical Approach for Fractional Delay Differential Equations

NASA Astrophysics Data System (ADS)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

Model reference tracking control of an aircraft: a robust adaptive approach

NASA Astrophysics Data System (ADS)

Tanyer, Ilker; Tatlicioglu, Enver; Zergeroglu, Erkan

2017-05-01

This work presents the design and the corresponding analysis of a nonlinear robust adaptive controller for model reference tracking of an aircraft that has parametric uncertainties in its system matrices and additive state- and/or time-dependent nonlinear disturbance-like terms in its dynamics. Specifically, robust integral of the sign of the error feedback term and an adaptive term is fused with a proportional integral controller. Lyapunov-based stability analysis techniques are utilised to prove global asymptotic convergence of the output tracking error. Extensive numerical simulations are presented to illustrate the performance of the proposed robust adaptive controller.

Finite element implementation of state variable-based viscoplasticity models

NASA Technical Reports Server (NTRS)

Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.

1991-01-01

The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.

Numerical experiment for ultrasonic-measurement-integrated simulation of three-dimensional unsteady blood flow.

PubMed

Funamoto, Kenichi; Hayase, Toshiyuki; Saijo, Yoshifumi; Yambe, Tomoyuki

2008-08-01

Integration of ultrasonic measurement and numerical simulation is a possible way to break through limitations of existing methods for obtaining complete information on hemodynamics. We herein propose Ultrasonic-Measurement-Integrated (UMI) simulation, in which feedback signals based on the optimal estimation of errors in the velocity vector determined by measured and computed Doppler velocities at feedback points are added to the governing equations. With an eye towards practical implementation of UMI simulation with real measurement data, its efficiency for three-dimensional unsteady blood flow analysis and a method for treating low time resolution of ultrasonic measurement were investigated by a numerical experiment dealing with complicated blood flow in an aneurysm. Even when simplified boundary conditions were applied, the UMI simulation reduced the errors of velocity and pressure to 31% and 53% in the feedback domain which covered the aneurysm, respectively. Local maximum wall shear stress was estimated, showing both the proper position and the value with 1% deviance. A properly designed intermittent feedback applied only at the time when measurement data were obtained had the same computational accuracy as feedback applied at every computational time step. Hence, this feedback method is a possible solution to overcome the insufficient time resolution of ultrasonic measurement.

Efficiency analysis of numerical integrations for finite element substructure in real-time hybrid simulation

NASA Astrophysics Data System (ADS)

Wang, Jinting; Lu, Liqiao; Zhu, Fei

2018-01-01

Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.

Cubic spline numerical solution of an ablation problem with convective backface cooling

NASA Astrophysics Data System (ADS)

Lin, S.; Wang, P.; Kahawita, R.

1984-08-01

An implicit numerical technique using cubic splines is presented for solving an ablation problem on a thin wall with convective cooling. A non-uniform computational mesh with 6 grid points has been used for the numerical integration. The method has been found to be computationally efficient, providing for the care under consideration of an overall error of about 1 percent. The results obtained indicate that the convective cooling is an important factor in reducing the ablation thickness.

Numerical Error Estimation with UQ

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Korn, Peter; Marotzke, Jochem

2014-05-01

Ocean models are still in need of means to quantify model errors, which are inevitably made when running numerical experiments. The total model error can formally be decomposed into two parts, the formulation error and the discretization error. The formulation error arises from the continuous formulation of the model not fully describing the studied physical process. The discretization error arises from having to solve a discretized model instead of the continuously formulated model. Our work on error estimation is concerned with the discretization error. Given a solution of a discretized model, our general problem statement is to find a way to quantify the uncertainties due to discretization in physical quantities of interest (diagnostics), which are frequently used in Geophysical Fluid Dynamics. The approach we use to tackle this problem is called the "Goal Error Ensemble method". The basic idea of the Goal Error Ensemble method is that errors in diagnostics can be translated into a weighted sum of local model errors, which makes it conceptually based on the Dual Weighted Residual method from Computational Fluid Dynamics. In contrast to the Dual Weighted Residual method these local model errors are not considered deterministically but interpreted as local model uncertainty and described stochastically by a random process. The parameters for the random process are tuned with high-resolution near-initial model information. However, the original Goal Error Ensemble method, introduced in [1], was successfully evaluated only in the case of inviscid flows without lateral boundaries in a shallow-water framework and is hence only of limited use in a numerical ocean model. Our work consists in extending the method to bounded, viscous flows in a shallow-water framework. As our numerical model, we use the ICON-Shallow-Water model. In viscous flows our high-resolution information is dependent on the viscosity parameter, making our uncertainty measures viscosity-dependent. We will show that we can choose a sensible parameter by using the Reynolds-number as a criteria. Another topic, we will discuss is the choice of the underlying distribution of the random process. This is especially of importance in the scope of lateral boundaries. We will present resulting error estimates for different height- and velocity-based diagnostics applied to the Munk gyre experiment. References [1] F. RAUSER: Error Estimation in Geophysical Fluid Dynamics through Learning; PhD Thesis, IMPRS-ESM, Hamburg, 2010 [2] F. RAUSER, J. MAROTZKE, P. KORN: Ensemble-type numerical uncertainty quantification from single model integrations; SIAM/ASA Journal on Uncertainty Quantification, submitted

The Role of Model and Initial Condition Error in Numerical Weather Forecasting Investigated with an Observing System Simulation Experiment

NASA Technical Reports Server (NTRS)

Prive, Nikki C.; Errico, Ronald M.

2013-01-01

A series of experiments that explore the roles of model and initial condition error in numerical weather prediction are performed using an observing system simulation experiment (OSSE) framework developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASA/GMAO). The use of an OSSE allows the analysis and forecast errors to be explicitly calculated, and different hypothetical observing networks can be tested with ease. In these experiments, both a full global OSSE framework and an 'identical twin' OSSE setup are utilized to compare the behavior of the data assimilation system and evolution of forecast skill with and without model error. The initial condition error is manipulated by varying the distribution and quality of the observing network and the magnitude of observation errors. The results show that model error has a strong impact on both the quality of the analysis field and the evolution of forecast skill, including both systematic and unsystematic model error components. With a realistic observing network, the analysis state retains a significant quantity of error due to systematic model error. If errors of the analysis state are minimized, model error acts to rapidly degrade forecast skill during the first 24-48 hours of forward integration. In the presence of model error, the impact of observation errors on forecast skill is small, but in the absence of model error, observation errors cause a substantial degradation of the skill of medium range forecasts.

Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

NASA Astrophysics Data System (ADS)

Wu, Jiang; Liao, Fucheng; Tomizuka, Masayoshi

2017-01-01

This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.

QIKAIM, a fast seminumerical algorithm for the generation of minute-of-arc accuracy satellite predictions

NASA Astrophysics Data System (ADS)

Vermeer, M.

1981-07-01

A program was designed to replace AIMLASER for the generation of aiming predictions, to achieve a major saving in computing time, and to keep the program small enough for use even on small systems. An approach was adopted that incorporated the numerical integration of the orbit through a pass, limiting the computation of osculating elements to only one point per pass. The numerical integration method which is fourth order in delta t in the cumulative error after a given time lapse is presented. Algorithms are explained and a flowchart and listing of the program are provided.

On the Minimal Accuracy Required for Simulating Self-gravitating Systems by Means of Direct N-body Methods

NASA Astrophysics Data System (ADS)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-01

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-body interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.

A study of the displacement of a Wankel rotary engine

NASA Astrophysics Data System (ADS)

Beard, J. E.; Pennock, G. R.

1993-03-01

The volumetric displacement of a Wankel rotary engine is a function of the trochoid ratio and the pin size ratio, assuming the engine has a unit depth and the number of lobes is specified. The mathematical expression which defines the displacement contains a function which can be evaluated directly and a normal elliptic integral of the second type which does not have an explicit solution. This paper focuses on the contribution of the elliptic integral to the total displacement of the engine. The influence of the elliptic integral is shown to account for as much as 20 percent of the total displacement, depending on the trochoid ratio and the pin size ratio. Two numerical integration techniques are compared in the paper, namely, the trapezoidal rule and Simpson's 1/3 rule. The bounds on the error, associated with each numerical method, are analyzed. The results indicate that the numerical method has a minimal effect on the accuracy of the calculated displacement for a practical number of integration steps. The paper also evaluates the influence of manufacturing tolerances on the calculated displacement and the actual displacement. Finally. a numerical example of the common three-lobed Wankel rotary engine is included for illustrative purposes.

Evaluation of SMART sensor displays for multidimensional precision control of Space Shuttle remote manipulator

NASA Technical Reports Server (NTRS)

Bejczy, A. K.; Brown, J. W.; Lewis, J. L.

1982-01-01

An enhanced proximity sensor and display system was developed at the Jet Propulsion Laboratory (JPL) and tested on the full scale Space Shuttle Remote Manipulator at the Johnson Space Center (JSC) Manipulator Development Facility (MDF). The sensor system, integrated with a four-claw end effector, measures range error up to 6 inches, and pitch and yaw alignment errors within + or 15 deg., and displays error data on both graphic and numeric displays. The errors are referenced to the end effector control axes through appropriate data processing by a dedicated microcomputer acting on the sensor data in real time. Both display boxes contain a green lamp which indicates whether the combination of range, pitch and yaw errors will assure a successful grapple. More than 200 test runs were completed in early 1980 by three operators at JSC for grasping static and capturing slowly moving targets. The tests have indicated that the use of graphic/numeric displays of proximity sensor information improves precision control of grasp/capture range by more than a factor of two for both static and dynamic grapple conditions.

Analytic Method for Computing Instrument Pointing Jitter

NASA Technical Reports Server (NTRS)

Bayard, David

2003-01-01

A new method of calculating the root-mean-square (rms) pointing jitter of a scientific instrument (e.g., a camera, radar antenna, or telescope) is introduced based on a state-space concept. In comparison with the prior method of calculating the rms pointing jitter, the present method involves significantly less computation. The rms pointing jitter of an instrument (the square root of the jitter variance shown in the figure) is an important physical quantity which impacts the design of the instrument, its actuators, controls, sensory components, and sensor- output-sampling circuitry. Using the Sirlin, San Martin, and Lucke definition of pointing jitter, the prior method of computing the rms pointing jitter involves a frequency-domain integral of a rational polynomial multiplied by a transcendental weighting function, necessitating the use of numerical-integration techniques. In practice, numerical integration complicates the problem of calculating the rms pointing error. In contrast, the state-space method provides exact analytic expressions that can be evaluated without numerical integration.

New Langevin and gradient thermostats for rigid body dynamics.

PubMed

Davidchack, R L; Ouldridge, T E; Tretyakov, M V

2015-04-14

We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.

Measurement system and model for simultaneously measuring 6DOF geometric errors.

PubMed

Zhao, Yuqiong; Zhang, Bin; Feng, Qibo

2017-09-04

A measurement system to simultaneously measure six degree-of-freedom (6DOF) geometric errors is proposed. The measurement method is based on a combination of mono-frequency laser interferometry and laser fiber collimation. A simpler and more integrated optical configuration is designed. To compensate for the measurement errors introduced by error crosstalk, element fabrication error, laser beam drift, and nonparallelism of two measurement beam, a unified measurement model, which can improve the measurement accuracy, is deduced and established using the ray-tracing method. A numerical simulation using the optical design software Zemax is conducted, and the results verify the correctness of the model. Several experiments are performed to demonstrate the feasibility and effectiveness of the proposed system and measurement model.

On the inversion of geodetic integrals defined over the sphere using 1-D FFT

NASA Astrophysics Data System (ADS)

García, R. V.; Alejo, C. A.

2005-08-01

An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine’s integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.

Implicit time accurate simulation of unsteady flow

NASA Astrophysics Data System (ADS)

van Buuren, René; Kuerten, Hans; Geurts, Bernard J.

2001-03-01

Implicit time integration was studied in the context of unsteady shock-boundary layer interaction flow. With an explicit second-order Runge-Kutta scheme, a reference solution to compare with the implicit second-order Crank-Nicolson scheme was determined. The time step in the explicit scheme is restricted by both temporal accuracy as well as stability requirements, whereas in the A-stable implicit scheme, the time step has to obey temporal resolution requirements and numerical convergence conditions. The non-linear discrete equations for each time step are solved iteratively by adding a pseudo-time derivative. The quasi-Newton approach is adopted and the linear systems that arise are approximately solved with a symmetric block Gauss-Seidel solver. As a guiding principle for properly setting numerical time integration parameters that yield an efficient time accurate capturing of the solution, the global error caused by the temporal integration is compared with the error resulting from the spatial discretization. Focus is on the sensitivity of properties of the solution in relation to the time step. Numerical simulations show that the time step needed for acceptable accuracy can be considerably larger than the explicit stability time step; typical ratios range from 20 to 80. At large time steps, convergence problems that are closely related to a highly complex structure of the basins of attraction of the iterative method may occur. Copyright

Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations

PubMed Central

Feischl, Michael; Gantner, Gregor; Praetorius, Dirk

2015-01-01

We consider the Galerkin boundary element method (BEM) for weakly-singular integral equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the unknown Galerkin BEM error. The required assumptions are weak and allow for piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. In particular, our analysis gives a first contribution to adaptive BEM in the frame of isogeometric analysis (IGABEM), for which we formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments underline the theoretical findings and show that the proposed adaptive strategy leads to optimal convergence. PMID:26085698

Kalman Filter Estimation of Spinning Spacecraft Attitude using Markley Variables

NASA Technical Reports Server (NTRS)

Sedlak, Joseph E.; Harman, Richard

2004-01-01

There are several different ways to represent spacecraft attitude and its time rate of change. For spinning or momentum-biased spacecraft, one particular representation has been put forward as a superior parameterization for numerical integration. Markley has demonstrated that these new variables have fewer rapidly varying elements for spinning spacecraft than other commonly used representations and provide advantages when integrating the equations of motion. The current work demonstrates how a Kalman filter can be devised to estimate the attitude using these new variables. The seven Markley variables are subject to one constraint condition, making the error covariance matrix singular. The filter design presented here explicitly accounts for this constraint by using a six-component error state in the filter update step. The reduced dimension error state is unconstrained and its covariance matrix is nonsingular.

Numerical Solution of Optimal Control Problem under SPDE Constraints

DTIC Science & Technology

2011-10-14

Faure and Sobol sequences are used to evaluate high dimensional integrals, and the errors in the numerical results for over 30 dimensions become quite...sequence; right: 1000 points of dimension 26 and 27 projection for optimal Kronecker sequence. benchmark Faure and Sobol methods. 2.2 High order...J. Goodman and J. O’Rourke, Handbook of discrete and computational geome- try, CRC Press, Inc., (2004). [5] S. Joe and F. Kuo, Constructing Sobol

A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations

NASA Technical Reports Server (NTRS)

Womble, M. E.; Potter, J. E.

1975-01-01

A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.

The integration of the motion equations of low-orbiting earth satellites using Taylor's method

NASA Astrophysics Data System (ADS)

Krivov, A. V.; Chernysheva, N. A.

1990-04-01

A method for the numerical integration of the equations of motion for a satellite is proposed, taking the earth's oblateness and atmospheric drag into account. The method is based on Taylor's representation of the solution to the corresponding polynomial system. The algorithm for choosing the integration step and error estimation is constructed. The method is realized as a subrouting package. The method is applied to a low-orbiting earth satellite and the results are compared with those obtained using Everhart's method.

Numerical Algorithms for Acoustic Integrals - The Devil is in the Details

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.

1996-01-01

The accurate prediction of the aeroacoustic field generated by aerospace vehicles or nonaerospace machinery is necessary for designers to control and reduce source noise. Powerful computational aeroacoustic methods, based on various acoustic analogies (primarily the Lighthill acoustic analogy) and Kirchhoff methods, have been developed for prediction of noise from complicated sources, such as rotating blades. Both methods ultimately predict the noise through a numerical evaluation of an integral formulation. In this paper, we consider three generic acoustic formulations and several numerical algorithms that have been used to compute the solutions to these formulations. Algorithms for retarded-time formulations are the most efficient and robust, but they are difficult to implement for supersonic-source motion. Collapsing-sphere and emission-surface formulations are good alternatives when supersonic-source motion is present, but the numerical implementations of these formulations are more computationally demanding. New algorithms - which utilize solution adaptation to provide a specified error level - are needed.

Integrity modelling of tropospheric delay models

NASA Astrophysics Data System (ADS)

Rózsa, Szabolcs; Bastiaan Ober, Pieter; Mile, Máté; Ambrus, Bence; Juni, Ildikó

2017-04-01

The effect of the neutral atmosphere on signal propagation is routinely estimated by various tropospheric delay models in satellite navigation. Although numerous studies can be found in the literature investigating the accuracy of these models, for safety-of-life applications it is crucial to study and model the worst case performance of these models using very low recurrence frequencies. The main objective of the INTegrity of TROpospheric models (INTRO) project funded by the ESA PECS programme is to establish a model (or models) of the residual error of existing tropospheric delay models for safety-of-life applications. Such models are required to overbound rare tropospheric delays and should thus include the tails of the error distributions. Their use should lead to safe error bounds on the user position and should allow computation of protection levels for the horizontal and vertical position errors. The current tropospheric model from the RTCA SBAS Minimal Operational Standards has an associated residual error that equals 0.12 meters in the vertical direction. This value is derived by simply extrapolating the observed distribution of the residuals into the tail (where no data is present) and then taking the point where the cumulative distribution has an exceedance level would be 10-7.While the resulting standard deviation is much higher than the estimated standard variance that best fits the data (0.05 meters), it surely is conservative for most applications. In the context of the INTRO project some widely used and newly developed tropospheric delay models (e.g. RTCA MOPS, ESA GALTROPO and GPT2W) were tested using 16 years of daily ERA-INTERIM Reanalysis numerical weather model data and the raytracing technique. The results showed that the performance of some of the widely applied models have a clear seasonal dependency and it is also affected by a geographical position. In order to provide a more realistic, but still conservative estimation of the residual error of tropospheric delays, the mathematical formulation of the overbounding models are currently under development. This study introduces the main findings of the residual error analysis of the studied tropospheric delay models, and discusses the preliminary analysis of the integrity model development for safety-of-life applications.

Numerical Optimization of Density Functional Tight Binding Models: Application to Molecules Containing Carbon, Hydrogen, Nitrogen, and Oxygen

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krishnapriyan, A.; Yang, P.; Niklasson, A. M. N.

New parametrizations for semiempirical density functional tight binding (DFTB) theory have been developed by the numerical optimization of adjustable parameters to minimize errors in the atomization energy and interatomic forces with respect to ab initio calculated data. Initial guesses for the radial dependences of the Slater- Koster bond integrals and overlap integrals were obtained from minimum basis density functional theory calculations. The radial dependences of the pair potentials and the bond and overlap integrals were represented by simple analytic functions. The adjustable parameters in these functions were optimized by simulated annealing and steepest descent algorithms to minimize the value ofmore » an objective function that quantifies the error between the DFTB model and ab initio calculated data. The accuracy and transferability of the resulting DFTB models for the C, H, N, and O system were assessed by comparing the predicted atomization energies and equilibrium molecular geometries of small molecules that were not included in the training data from DFTB to ab initio data. The DFTB models provide accurate predictions of the properties of hydrocarbons and more complex molecules containing C, H, N, and O.« less

Numerical Optimization of Density Functional Tight Binding Models: Application to Molecules Containing Carbon, Hydrogen, Nitrogen, and Oxygen

DOE PAGES

Krishnapriyan, A.; Yang, P.; Niklasson, A. M. N.; ...

2017-10-17

New parametrizations for semiempirical density functional tight binding (DFTB) theory have been developed by the numerical optimization of adjustable parameters to minimize errors in the atomization energy and interatomic forces with respect to ab initio calculated data. Initial guesses for the radial dependences of the Slater- Koster bond integrals and overlap integrals were obtained from minimum basis density functional theory calculations. The radial dependences of the pair potentials and the bond and overlap integrals were represented by simple analytic functions. The adjustable parameters in these functions were optimized by simulated annealing and steepest descent algorithms to minimize the value ofmore » an objective function that quantifies the error between the DFTB model and ab initio calculated data. The accuracy and transferability of the resulting DFTB models for the C, H, N, and O system were assessed by comparing the predicted atomization energies and equilibrium molecular geometries of small molecules that were not included in the training data from DFTB to ab initio data. The DFTB models provide accurate predictions of the properties of hydrocarbons and more complex molecules containing C, H, N, and O.« less

Bounds of the error of Gauss-Turan-type quadratures

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2005-06-01

We consider the remainder term of the Gauss-Turan quadrature formulaefor analytic functions in some region of the complex plane containing the interval [-1,1] in its interior. The remainder term is presented in the form of a contour integral over confocal ellipses or circles. A strong error analysis is given for the case with a generalized class of weight functions, introduced recently by Gori and Micchelli. Also, we discuss a general case with an even weight function defined on [-1,1]. Numerical results are included.

ON THE MINIMAL ACCURACY REQUIRED FOR SIMULATING SELF-GRAVITATING SYSTEMS BY MEANS OF DIRECT N-BODY METHODS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-10

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-bodymore » interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.« less

Integrated model reference adaptive control and time-varying angular rate estimation for micro-machined gyroscopes

NASA Astrophysics Data System (ADS)

Tsai, Nan-Chyuan; Sue, Chung-Yang

2010-02-01

Owing to the imposed but undesired accelerations such as quadrature error and cross-axis perturbation, the micro-machined gyroscope would not be unconditionally retained at resonant mode. Once the preset resonance is not sustained, the performance of the micro-gyroscope is accordingly degraded. In this article, a direct model reference adaptive control loop which is integrated with a modified disturbance estimating observer (MDEO) is proposed to guarantee the resonant oscillations at drive mode and counterbalance the undesired disturbance mainly caused by quadrature error and cross-axis perturbation. The parameters of controller are on-line innovated by the dynamic error between the MDEO output and expected response. In addition, Lyapunov stability theory is employed to examine the stability of the closed-loop control system. Finally, the efficacy of numerical evaluation on the exerted time-varying angular rate, which is to be detected and measured by the gyroscope, is verified by intensive simulations.

An arbitrary-order staggered time integrator for the linear acoustic wave equation

NASA Astrophysics Data System (ADS)

Lee, Jaejoon; Park, Hyunseo; Park, Yoonseo; Shin, Changsoo

2018-02-01

We suggest a staggered time integrator whose order of accuracy can arbitrarily be extended to solve the linear acoustic wave equation. A strategy to select the appropriate order of accuracy is also proposed based on the error analysis that quantitatively predicts the truncation error of the numerical solution. This strategy not only reduces the computational cost several times, but also allows us to flexibly set the modelling parameters such as the time step length, grid interval and P-wave speed. It is demonstrated that the proposed method can almost eliminate temporal dispersive errors during long term simulations regardless of the heterogeneity of the media and time step lengths. The method can also be successfully applied to the source problem with an absorbing boundary condition, which is frequently encountered in the practical usage for the imaging algorithms or the inverse problems.

Sources of error in the retracted scientific literature.

PubMed

Casadevall, Arturo; Steen, R Grant; Fang, Ferric C

2014-09-01

Retraction of flawed articles is an important mechanism for correction of the scientific literature. We recently reported that the majority of retractions are associated with scientific misconduct. In the current study, we focused on the subset of retractions for which no misconduct was identified, in order to identify the major causes of error. Analysis of the retraction notices for 423 articles indexed in PubMed revealed that the most common causes of error-related retraction are laboratory errors, analytical errors, and irreproducible results. The most common laboratory errors are contamination and problems relating to molecular biology procedures (e.g., sequencing, cloning). Retractions due to contamination were more common in the past, whereas analytical errors are now increasing in frequency. A number of publications that have not been retracted despite being shown to contain significant errors suggest that barriers to retraction may impede correction of the literature. In particular, few cases of retraction due to cell line contamination were found despite recognition that this problem has affected numerous publications. An understanding of the errors leading to retraction can guide practices to improve laboratory research and the integrity of the scientific literature. Perhaps most important, our analysis has identified major problems in the mechanisms used to rectify the scientific literature and suggests a need for action by the scientific community to adopt protocols that ensure the integrity of the publication process. © FASEB.

compuGUT: An in silico platform for simulating intestinal fermentation

NASA Astrophysics Data System (ADS)

Moorthy, Arun S.; Eberl, Hermann J.

The microbiota inhabiting the colon and its effect on health is a topic of significant interest. In this paper, we describe the compuGUT - a simulation tool developed to assist in exploring interactions between intestinal microbiota and their environment. The primary numerical machinery is implemented in C, and the accessory scripts for loading and visualization are prepared in bash (LINUX) and R. SUNDIALS libraries are employed for numerical integration, and googleVis API for interactive visualization. Supplementary material includes a concise description of the underlying mathematical model, and detailed characterization of numerical errors and computing times associated with implementation parameters.

Analysis of thin plates with holes by using exact geometrical representation within XFEM.

PubMed

Perumal, Logah; Tso, C P; Leng, Lim Thong

2016-05-01

This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.

Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system.

PubMed

Sun, Dong; Zhao, Daomu

2005-08-01

By introducing the hard-aperture function into a finite sum of complex Gaussian functions, the approximate analytical expressions of the Wigner distribution function for Hermite-cosine-Gaussian beams passing through an apertured paraxial ABCD optical system are obtained. The analytical results are compared with the numerically integrated ones, and the absolute errors are also given. It is shown that the analytical results are proper and that the calculation speed for them is much faster than for the numerical results.

Statistical Mechanics and Dynamics of the Outer Solar System.I. The Jupiter/Saturn Zone

NASA Technical Reports Server (NTRS)

Grazier, K. R.; Newman, W. I.; Kaula, W. M.; Hyman, J. M.

1996-01-01

We report on numerical simulations designed to understand how the solar system evolved through a winnowing of planetesimals accreeted from the early solar nebula. This sorting process is driven by the energy and angular momentum and continues to the present day. We reconsider the existence and importance of stable niches in the Jupiter/Saturn Zone using greatly improved numerical techniques based on high-order optimized multi-step integration schemes coupled to roundoff error minimizing methods.

Surface albedo from bidirectional reflectance

NASA Technical Reports Server (NTRS)

Ranson, K. J.; Irons, J. R.; Daughtry, C. S. T.

1991-01-01

The validity of integrating over discrete wavelength bands is examined to estimate total shortwave bidirectional reflectance of vegetated and bare soil surfaces. Methods for estimating albedo from multiple angle, discrete wavelength band radiometer measurements are studied. These methods include a numerical integration technique and the integration of an empirically derived equation for bidirectional reflectance. It is concluded that shortwave albedos estimated through both techniques agree favorably with the independent pyranometer measurements. Absolute rms errors are found to be 0.5 percent or less for both grass sod and bare soil surfaces.

Impact of numerical choices on water conservation in the E3SM Atmosphere Model Version 1 (EAM V1)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Kai; Rasch, Philip J.; Taylor, Mark A.

The conservation of total water is an important numerical feature for global Earth system models. Even small conservation problems in the water budget can lead to systematic errors in century-long simulations for sea level rise projection. This study quantifies and reduces various sources of water conservation error in the atmosphere component of the Energy Exascale Earth System Model. Several sources of water conservation error have been identified during the development of the version 1 (V1) model. The largest errors result from the numerical coupling between the resolved dynamics and the parameterized sub-grid physics. A hybrid coupling using different methods formore » fluid dynamics and tracer transport provides a reduction of water conservation error by a factor of 50 at 1° horizontal resolution as well as consistent improvements at other resolutions. The second largest error source is the use of an overly simplified relationship between the surface moisture flux and latent heat flux at the interface between the host model and the turbulence parameterization. This error can be prevented by applying the same (correct) relationship throughout the entire model. Two additional types of conservation error that result from correcting the surface moisture flux and clipping negative water concentrations can be avoided by using mass-conserving fixers. With all four error sources addressed, the water conservation error in the V1 model is negligible and insensitive to the horizontal resolution. The associated changes in the long-term statistics of the main atmospheric features are small. A sensitivity analysis is carried out to show that the magnitudes of the conservation errors decrease strongly with temporal resolution but increase with horizontal resolution. The increased vertical resolution in the new model results in a very thin model layer at the Earth’s surface, which amplifies the conservation error associated with the surface moisture flux correction. We note that for some of the identified error sources, the proposed fixers are remedies rather than solutions to the problems at their roots. Future improvements in time integration would be beneficial for this model.« less

Impact of numerical choices on water conservation in the E3SM Atmosphere Model version 1 (EAMv1)

NASA Astrophysics Data System (ADS)

Zhang, Kai; Rasch, Philip J.; Taylor, Mark A.; Wan, Hui; Leung, Ruby; Ma, Po-Lun; Golaz, Jean-Christophe; Wolfe, Jon; Lin, Wuyin; Singh, Balwinder; Burrows, Susannah; Yoon, Jin-Ho; Wang, Hailong; Qian, Yun; Tang, Qi; Caldwell, Peter; Xie, Shaocheng

2018-06-01

The conservation of total water is an important numerical feature for global Earth system models. Even small conservation problems in the water budget can lead to systematic errors in century-long simulations. This study quantifies and reduces various sources of water conservation error in the atmosphere component of the Energy Exascale Earth System Model. Several sources of water conservation error have been identified during the development of the version 1 (V1) model. The largest errors result from the numerical coupling between the resolved dynamics and the parameterized sub-grid physics. A hybrid coupling using different methods for fluid dynamics and tracer transport provides a reduction of water conservation error by a factor of 50 at 1° horizontal resolution as well as consistent improvements at other resolutions. The second largest error source is the use of an overly simplified relationship between the surface moisture flux and latent heat flux at the interface between the host model and the turbulence parameterization. This error can be prevented by applying the same (correct) relationship throughout the entire model. Two additional types of conservation error that result from correcting the surface moisture flux and clipping negative water concentrations can be avoided by using mass-conserving fixers. With all four error sources addressed, the water conservation error in the V1 model becomes negligible and insensitive to the horizontal resolution. The associated changes in the long-term statistics of the main atmospheric features are small. A sensitivity analysis is carried out to show that the magnitudes of the conservation errors in early V1 versions decrease strongly with temporal resolution but increase with horizontal resolution. The increased vertical resolution in V1 results in a very thin model layer at the Earth's surface, which amplifies the conservation error associated with the surface moisture flux correction. We note that for some of the identified error sources, the proposed fixers are remedies rather than solutions to the problems at their roots. Future improvements in time integration would be beneficial for V1.

On Accuracy of Adaptive Grid Methods for Captured Shocks

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2002-01-01

The accuracy of two grid adaptation strategies, grid redistribution and local grid refinement, is examined by solving the 2-D Euler equations for the supersonic steady flow around a cylinder. Second- and fourth-order linear finite difference shock-capturing schemes, based on the Lax-Friedrichs flux splitting, are used to discretize the governing equations. The grid refinement study shows that for the second-order scheme, neither grid adaptation strategy improves the numerical solution accuracy compared to that calculated on a uniform grid with the same number of grid points. For the fourth-order scheme, the dominant first-order error component is reduced by the grid adaptation, while the design-order error component drastically increases because of the grid nonuniformity. As a result, both grid adaptation techniques improve the numerical solution accuracy only on the coarsest mesh or on very fine grids that are seldom found in practical applications because of the computational cost involved. Similar error behavior has been obtained for the pressure integral across the shock. A simple analysis shows that both grid adaptation strategies are not without penalties in the numerical solution accuracy. Based on these results, a new grid adaptation criterion for captured shocks is proposed.

Integrated fiducial sample mount and software for correlated microscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Timothy R McJunkin; Jill R. Scott; Tammy L. Trowbridge

2014-02-01

A novel design sample mount with integrated fiducials and software for assisting operators in easily and efficiently locating points of interest established in previous analytical sessions is described. The sample holder and software were evaluated with experiments to demonstrate the utility and ease of finding the same points of interest in two different microscopy instruments. Also, numerical analysis of expected errors in determining the same position with errors unbiased by a human operator was performed. Based on the results, issues related to acquiring reproducibility and best practices for using the sample mount and software were identified. Overall, the sample mountmore » methodology allows data to be efficiently and easily collected on different instruments for the same sample location.« less

Multiscale Modeling and Uncertainty Quantification for Nuclear Fuel Performance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Estep, Donald; El-Azab, Anter; Pernice, Michael

2017-03-23

In this project, we will address the challenges associated with constructing high fidelity multiscale models of nuclear fuel performance. We (*) propose a novel approach for coupling mesoscale and macroscale models, (*) devise efficient numerical methods for simulating the coupled system, and (*) devise and analyze effective numerical approaches for error and uncertainty quantification for the coupled multiscale system. As an integral part of the project, we will carry out analysis of the effects of upscaling and downscaling, investigate efficient methods for stochastic sensitivity analysis of the individual macroscale and mesoscale models, and carry out a posteriori error analysis formore » computed results. We will pursue development and implementation of solutions in software used at Idaho National Laboratories on models of interest to the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program.« less

Predictive Lateral Logic for Numerical Entry Guidance Algorithms

NASA Technical Reports Server (NTRS)

Smith, Kelly M.

2016-01-01

Recent entry guidance algorithm development123 has tended to focus on numerical integration of trajectories onboard in order to evaluate candidate bank profiles. Such methods enjoy benefits such as flexibility to varying mission profiles and improved robustness to large dispersions. A common element across many of these modern entry guidance algorithms is a reliance upon the concept of Apollo heritage lateral error (or azimuth error) deadbands in which the number of bank reversals to be performed is non-deterministic. This paper presents a closed-loop bank reversal method that operates with a fixed number of bank reversals defined prior to flight. However, this number of bank reversals can be modified at any point, including in flight, based on contingencies such as fuel leaks where propellant usage must be minimized.

Symbolic-numeric interface: A review

NASA Technical Reports Server (NTRS)

Ng, E. W.

1980-01-01

A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach.

A time-efficient implementation of Extended Kalman Filter for sequential orbit determination and a case study for onboard application

NASA Astrophysics Data System (ADS)

Tang, Jingshi; Wang, Haihong; Chen, Qiuli; Chen, Zhonggui; Zheng, Jinjun; Cheng, Haowen; Liu, Lin

2018-07-01

Onboard orbit determination (OD) is often used in space missions, with which mission support can be partially accomplished autonomously, with less dependency on ground stations. In major Global Navigation Satellite Systems (GNSS), inter-satellite link is also an essential upgrade in the future generations. To serve for autonomous operation, sequential OD method is crucial to provide real-time or near real-time solutions. The Extended Kalman Filter (EKF) is an effective and convenient sequential estimator that is widely used in onboard application. The filter requires the solutions of state transition matrix (STM) and the process noise transition matrix, which are always obtained by numerical integration. However, numerically integrating the differential equations is a CPU intensive process and consumes a large portion of the time in EKF procedures. In this paper, we present an implementation that uses the analytical solutions of these transition matrices to replace the numerical calculations. This analytical implementation is demonstrated and verified using a fictitious constellation based on selected medium Earth orbit (MEO) and inclined Geosynchronous orbit (IGSO) satellites. We show that this implementation performs effectively and converges quickly, steadily and accurately in the presence of considerable errors in the initial values, measurements and force models. The filter is able to converge within 2-4 h of flight time in our simulation. The observation residual is consistent with simulated measurement error, which is about a few centimeters in our scenarios. Compared to results implemented with numerically integrated STM, the analytical implementation shows results with consistent accuracy, while it takes only about half the CPU time to filter a 10-day measurement series. The future possible extensions are also discussed to fit in various missions.

On the limits of numerical astronomical solutions used in paleoclimate studies

NASA Astrophysics Data System (ADS)

Zeebe, Richard E.

2017-04-01

Numerical solutions of the equations of the Solar System estimate Earth's orbital parameters in the past and represent the backbone of cyclostratigraphy and astrochronology, now widely applied in geology and paleoclimatology. Given one numerical realization of a Solar System model (i.e., obtained using one code or integrator package), various parameters determine the properties of the solution and usually limit its validity to a certain time period. Such limitations are denoted here as "internal" and include limitations due to (i) the underlying physics/physical model and (ii) numerics. The physics include initial coordinates and velocities of Solar System bodies, treatment of the Moon and asteroids, the Sun's quadrupole moment, and the intrinsic dynamics of the Solar System itself, i.e., its chaotic nature. Numerical issues include solver algorithm, numerical accuracy (e.g., time step), and round-off errors. At present, internal limitations seem to restrict the validity of astronomical solutions to perhaps the past 50 or 60 myr. However, little is currently known about "external" limitations, that is, how do different numerical realizations compare, say, between different investigators using different codes and integrators? Hitherto only two solutions for Earth's eccentricity appear to be used in paleoclimate studies, provided by two different groups that integrated the full Solar System equations over the past >100 myr (Laskar and coworkers and Varadi et al. 2003). In this contribution, I will present results from new Solar System integrations for Earth's eccentricity obtained using the integrator package HNBody (Rauch and Hamilton 2002). I will discuss the various internal limitations listed above within the framework of the present simulations. I will also compare the results to the existing solutions, the details of which are still being sorted out as several simulations are still running at the time of writing.

Numerical study of time domain analogy applied to noise prediction from rotating blades

NASA Astrophysics Data System (ADS)

Fedala, D.; Kouidri, S.; Rey, R.

2009-04-01

Aeroacoustic formulations in time domain are frequently used to model the aerodynamic sound of airfoils, the time data being more accessible. The formulation 1A developed by Farassat, an integral solution of the Ffowcs Williams and Hawkings equation, holds great interest because of its ability to handle surfaces in arbitrary motion. The aim of this work is to study the numerical sensitivity of this model to specified parameters used in the calculation. The numerical algorithms, spatial and time discretizations, and approximations used for far-field acoustic simulation are presented. An approach of quantifying of the numerical errors resulting from implementation of formulation 1A is carried out based on Isom's and Tam's test cases. A helicopter blade airfoil, as defined by Farassat to investigate Isom's case, is used in this work. According to Isom, the acoustic response of a dipole source with a constant aerodynamic load, ρ0c02, is equal to the thickness noise contribution. Discrepancies are observed when the two contributions are computed numerically. In this work, variations of these errors, which depend on the temporal resolution, Mach number, source-observer distance, and interpolation algorithm type, are investigated. The results show that the spline interpolating algorithm gives the minimum error. The analysis is then extended to Tam's test case. Tam's test case has the advantage of providing an analytical solution for the first harmonic of the noise produced by a specific force distribution.

Multiclass Bayes error estimation by a feature space sampling technique

NASA Technical Reports Server (NTRS)

Mobasseri, B. G.; Mcgillem, C. D.

1979-01-01

A general Gaussian M-class N-feature classification problem is defined. An algorithm is developed that requires the class statistics as its only input and computes the minimum probability of error through use of a combined analytical and numerical integration over a sequence simplifying transformations of the feature space. The results are compared with those obtained by conventional techniques applied to a 2-class 4-feature discrimination problem with results previously reported and 4-class 4-feature multispectral scanner Landsat data classified by training and testing of the available data.

A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics

NASA Astrophysics Data System (ADS)

Brovont, Aaron D.

The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.

Adaptive integral robust control and application to electromechanical servo systems.

PubMed

Deng, Wenxiang; Yao, Jianyong

2017-03-01

This paper proposes a continuous adaptive integral robust control with robust integral of the sign of the error (RISE) feedback for a class of uncertain nonlinear systems, in which the RISE feedback gain is adapted online to ensure the robustness against disturbances without the prior bound knowledge of the additive disturbances. In addition, an adaptive compensation integrated with the proposed adaptive RISE feedback term is also constructed to further reduce design conservatism when the system also exists parametric uncertainties. Lyapunov analysis reveals the proposed controllers could guarantee the tracking errors are asymptotically converging to zero with continuous control efforts. To illustrate the high performance nature of the developed controllers, numerical simulations are provided. At the end, an application case of an actual electromechanical servo system driven by motor is also studied, with some specific design consideration, and comparative experimental results are obtained to verify the effectiveness of the proposed controllers. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Tropical cyclones over the North Indian Ocean: experiments with the high-resolution global icosahedral grid point model GME

NASA Astrophysics Data System (ADS)

Kumkar, Yogesh V.; Sen, P. N.; Chaudhari, Hemankumar S.; Oh, Jai-Ho

2018-02-01

In this paper, an attempt has been made to conduct a numerical experiment with the high-resolution global model GME to predict the tropical storms in the North Indian Ocean during the year 2007. Numerical integrations using the icosahedral hexagonal grid point global model GME were performed to study the evolution of tropical cyclones, viz., Akash, Gonu, Yemyin and Sidr over North Indian Ocean during 2007. It has been seen that the GME model forecast underestimates cyclone's intensity, but the model can capture the evolution of cyclone's intensity especially its weakening during landfall, which is primarily due to the cutoff of the water vapor supply in the boundary layer as cyclones approach the coastal region. A series of numerical simulation of tropical cyclones have been performed with GME to examine model capability in prediction of intensity and track of the cyclones. The model performance is evaluated by calculating the root mean square errors as cyclone track errors.

Enabling Predictive Simulation and UQ of Complex Multiphysics PDE Systems by the Development of Goal-Oriented Variational Sensitivity Analysis and a-Posteriori Error Estimation Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Estep, Donald

2015-11-30

This project addressed the challenge of predictive computational analysis of strongly coupled, highly nonlinear multiphysics systems characterized by multiple physical phenomena that span a large range of length- and time-scales. Specifically, the project was focused on computational estimation of numerical error and sensitivity analysis of computational solutions with respect to variations in parameters and data. In addition, the project investigated the use of accurate computational estimates to guide efficient adaptive discretization. The project developed, analyzed and evaluated new variational adjoint-based techniques for integration, model, and data error estimation/control and sensitivity analysis, in evolutionary multiphysics multiscale simulations.

Simulating and quantifying legacy topographic data uncertainty: an initial step to advancing topographic change analyses

NASA Astrophysics Data System (ADS)

Wasklewicz, Thad; Zhu, Zhen; Gares, Paul

2017-12-01

Rapid technological advances, sustained funding, and a greater recognition of the value of topographic data have helped develop an increasing archive of topographic data sources. Advances in basic and applied research related to Earth surface changes require researchers to integrate recent high-resolution topography (HRT) data with the legacy datasets. Several technical challenges and data uncertainty issues persist to date when integrating legacy datasets with more recent HRT data. The disparate data sources required to extend the topographic record back in time are often stored in formats that are not readily compatible with more recent HRT data. Legacy data may also contain unknown error or unreported error that make accounting for data uncertainty difficult. There are also cases of known deficiencies in legacy datasets, which can significantly bias results. Finally, scientists are faced with the daunting challenge of definitively deriving the extent to which a landform or landscape has or will continue to change in response natural and/or anthropogenic processes. Here, we examine the question: how do we evaluate and portray data uncertainty from the varied topographic legacy sources and combine this uncertainty with current spatial data collection techniques to detect meaningful topographic changes? We view topographic uncertainty as a stochastic process that takes into consideration spatial and temporal variations from a numerical simulation and physical modeling experiment. The numerical simulation incorporates numerous topographic data sources typically found across a range of legacy data to present high-resolution data, while the physical model focuses on more recent HRT data acquisition techniques. Elevation uncertainties observed from anchor points in the digital terrain models are modeled using "states" in a stochastic estimator. Stochastic estimators trace the temporal evolution of the uncertainties and are natively capable of incorporating sensor measurements observed at various times in history. The geometric relationship between the anchor point and the sensor measurement can be approximated via spatial correlation even when a sensor does not directly observe an anchor point. Findings from a numerical simulation indicate the estimated error coincides with the actual error using certain sensors (Kinematic GNSS, ALS, TLS, and SfM-MVS). Data from 2D imagery and static GNSS did not perform as well at the time the sensor is integrated into estimator largely as a result of the low density of data added from these sources. The estimator provides a history of DEM estimation as well as the uncertainties and cross correlations observed on anchor points. Our work provides preliminary evidence that our approach is valid for integrating legacy data with HRT and warrants further exploration and field validation. [Figure not available: see fulltext.

Numerical convergence of the self-diffusion coefficient and viscosity obtained with Thomas-Fermi-Dirac molecular dynamics.

PubMed

Danel, J-F; Kazandjian, L; Zérah, G

2012-06-01

Computations of the self-diffusion coefficient and viscosity in warm dense matter are presented with an emphasis on obtaining numerical convergence and a careful evaluation of the standard deviation. The transport coefficients are computed with the Green-Kubo relation and orbital-free molecular dynamics at the Thomas-Fermi-Dirac level. The numerical parameters are varied until the Green-Kubo integral is equal to a constant in the t→+∞ limit; the transport coefficients are deduced from this constant and not by extrapolation of the Green-Kubo integral. The latter method, which gives rise to an unknown error, is tested for the computation of viscosity; it appears that it should be used with caution. In the large domain of coupling constant considered, both the self-diffusion coefficient and viscosity turn out to be well approximated by simple analytical laws using a single effective atomic number calculated in the average-atom model.

Numerical convergence of the self-diffusion coefficient and viscosity obtained with Thomas-Fermi-Dirac molecular dynamics

NASA Astrophysics Data System (ADS)

Danel, J.-F.; Kazandjian, L.; Zérah, G.

2012-06-01

Computations of the self-diffusion coefficient and viscosity in warm dense matter are presented with an emphasis on obtaining numerical convergence and a careful evaluation of the standard deviation. The transport coefficients are computed with the Green-Kubo relation and orbital-free molecular dynamics at the Thomas-Fermi-Dirac level. The numerical parameters are varied until the Green-Kubo integral is equal to a constant in the t→+∞ limit; the transport coefficients are deduced from this constant and not by extrapolation of the Green-Kubo integral. The latter method, which gives rise to an unknown error, is tested for the computation of viscosity; it appears that it should be used with caution. In the large domain of coupling constant considered, both the self-diffusion coefficient and viscosity turn out to be well approximated by simple analytical laws using a single effective atomic number calculated in the average-atom model.

Residents' numeric inputting error in computerized physician order entry prescription.

PubMed

Wu, Xue; Wu, Changxu; Zhang, Kan; Wei, Dong

2016-04-01

Computerized physician order entry (CPOE) system with embedded clinical decision support (CDS) can significantly reduce certain types of prescription error. However, prescription errors still occur. Various factors such as the numeric inputting methods in human computer interaction (HCI) produce different error rates and types, but has received relatively little attention. This study aimed to examine the effects of numeric inputting methods and urgency levels on numeric inputting errors of prescription, as well as categorize the types of errors. Thirty residents participated in four prescribing tasks in which two factors were manipulated: numeric inputting methods (numeric row in the main keyboard vs. numeric keypad) and urgency levels (urgent situation vs. non-urgent situation). Multiple aspects of participants' prescribing behavior were measured in sober prescribing situations. The results revealed that in urgent situations, participants were prone to make mistakes when using the numeric row in the main keyboard. With control of performance in the sober prescribing situation, the effects of the input methods disappeared, and urgency was found to play a significant role in the generalized linear model. Most errors were either omission or substitution types, but the proportion of transposition and intrusion error types were significantly higher than that of the previous research. Among numbers 3, 8, and 9, which were the less common digits used in prescription, the error rate was higher, which was a great risk to patient safety. Urgency played a more important role in CPOE numeric typing error-making than typing skills and typing habits. It was recommended that inputting with the numeric keypad had lower error rates in urgent situation. An alternative design could consider increasing the sensitivity of the keys with lower frequency of occurrence and decimals. To improve the usability of CPOE, numeric keyboard design and error detection could benefit from spatial incidence of errors found in this study. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Numerical integration of the extended variable generalized Langevin equation with a positive Prony representable memory kernel.

PubMed

Baczewski, Andrew D; Bond, Stephen D

2013-07-28

Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.

Degenerate variational integrators for magnetic field line flow and guiding center trajectories

NASA Astrophysics Data System (ADS)

Ellison, C. L.; Finn, J. M.; Burby, J. W.; Kraus, M.; Qin, H.; Tang, W. M.

2018-05-01

Symplectic integrators offer many benefits for numerically approximating solutions to Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two important Hamiltonian systems encountered in plasma physics—the flow of magnetic field lines and the guiding center motion of magnetized charged particles—resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates. New algorithms were recently developed using the variational integration formalism; however, those integrators were found to admit parasitic mode instabilities due to their multistep character. This work eliminates the multistep character, and therefore the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem "degenerate variational integration." Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that the resultant Euler-Lagrange equations are systems of first-order ordinary differential equations. We show that retaining the same degree of degeneracy when constructing discrete Lagrangians yields one-step variational integrators preserving a non-canonical symplectic structure. Numerical examples demonstrate the benefits of the new algorithms, including superior stability relative to the existing variational integrators for these systems and superior qualitative behavior relative to non-conservative algorithms.

Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes

NASA Astrophysics Data System (ADS)

Calvo, M.; González-Pinto, S.; Montijano, J. I.

2008-09-01

Modern codes for the numerical solution of Initial Value Problems (IVPs) in ODEs are based in adaptive methods that, for a user supplied tolerance [delta], attempt to advance the integration selecting the size of each step so that some measure of the local error is [similar, equals][delta]. Although this policy does not ensure that the global errors are under the prescribed tolerance, after the early studies of Stetter [Considerations concerning a theory for ODE-solvers, in: R. Burlisch, R.D. Grigorieff, J. Schröder (Eds.), Numerical Treatment of Differential Equations, Proceedings of Oberwolfach, 1976, Lecture Notes in Mathematics, vol. 631, Springer, Berlin, 1978, pp. 188-200; Tolerance proportionality in ODE codes, in: R. März (Ed.), Proceedings of the Second Conference on Numerical Treatment of Ordinary Differential Equations, Humbold University, Berlin, 1980, pp. 109-123] and the extensions of Higham [Global error versus tolerance for explicit Runge-Kutta methods, IMA J. Numer. Anal. 11 (1991) 457-480; The tolerance proportionality of adaptive ODE solvers, J. Comput. Appl. Math. 45 (1993) 227-236; The reliability of standard local error control algorithms for initial value ordinary differential equations, in: Proceedings: The Quality of Numerical Software: Assessment and Enhancement, IFIP Series, Springer, Berlin, 1997], it has been proved that in many existing explicit Runge-Kutta codes the global errors behave asymptotically as some rational power of [delta]. This step-size policy, for a given IVP, determines at each grid point tn a new step-size hn+1=h(tn;[delta]) so that h(t;[delta]) is a continuous function of t. In this paper a study of the tolerance proportionality property under a discontinuous step-size policy that does not allow to change the size of the step if the step-size ratio between two consecutive steps is close to unity is carried out. This theory is applied to obtain global error estimations in a few problems that have been solved with the code Gauss2 [S. Gonzalez-Pinto, R. Rojas-Bello, Gauss2, a Fortran 90 code for second order initial value problems, ], based on an adaptive two stage Runge-Kutta-Gauss method with this discontinuous step-size policy.

On the Latent Regression Model of Item Response Theory. Research Report. ETS RR-07-12

ERIC Educational Resources Information Center

Antal, Tamás

2007-01-01

Full account of the latent regression model for the National Assessment of Educational Progress is given. The treatment includes derivation of the EM algorithm, Newton-Raphson method, and the asymptotic standard errors. The paper also features the use of the adaptive Gauss-Hermite numerical integration method as a basic tool to evaluate…

A modified adjoint-based grid adaptation and error correction method for unstructured grid

NASA Astrophysics Data System (ADS)

Cui, Pengcheng; Li, Bin; Tang, Jing; Chen, Jiangtao; Deng, Youqi

2018-05-01

Grid adaptation is an important strategy to improve the accuracy of output functions (e.g. drag, lift, etc.) in computational fluid dynamics (CFD) analysis and design applications. This paper presents a modified robust grid adaptation and error correction method for reducing simulation errors in integral outputs. The procedure is based on discrete adjoint optimization theory in which the estimated global error of output functions can be directly related to the local residual error. According to this relationship, local residual error contribution can be used as an indicator in a grid adaptation strategy designed to generate refined grids for accurately estimating the output functions. This grid adaptation and error correction method is applied to subsonic and supersonic simulations around three-dimensional configurations. Numerical results demonstrate that the sensitive grids to output functions are detected and refined after grid adaptation, and the accuracy of output functions is obviously improved after error correction. The proposed grid adaptation and error correction method is shown to compare very favorably in terms of output accuracy and computational efficiency relative to the traditional featured-based grid adaptation.

A modified precise integration method for transient dynamic analysis in structural systems with multiple damping models

NASA Astrophysics Data System (ADS)

Ding, Zhe; Li, Li; Hu, Yujin

2018-01-01

Sophisticated engineering systems are usually assembled by subcomponents with significantly different levels of energy dissipation. Therefore, these damping systems often contain multiple damping models and lead to great difficulties in analyzing. This paper aims at developing a time integration method for structural systems with multiple damping models. The dynamical system is first represented by a generally damped model. Based on this, a new extended state-space method for the damped system is derived. A modified precise integration method with Gauss-Legendre quadrature is then proposed. The numerical stability and accuracy of the proposed integration method are discussed in detail. It is verified that the method is conditionally stable and has inherent algorithmic damping, period error and amplitude decay. Numerical examples are provided to assess the performance of the proposed method compared with other methods. It is demonstrated that the method is more accurate than other methods with rather good efficiency and the stable condition is easy to be satisfied in practice.

SENS-5D trajectory and wind-sensitivity calculations for unguided rockets

NASA Technical Reports Server (NTRS)

Singh, R. P.; Huang, L. C. P.; Cook, R. A.

1975-01-01

A computational procedure is described which numerically integrates the equations of motion of an unguided rocket. Three translational and two angular (roll discarded) degrees of freedom are integrated through the final burnout; and then, through impact, only three translational motions are considered. Input to the routine is: initial time, altitude and velocity, vehicle characteristics, and other defined options. Input format has a wide range of flexibility for special calculations. Output is geared mainly to the wind-weighting procedure, and includes summary of trajectory at burnout, apogee and impact, summary of spent-stage trajectories, detailed position and vehicle data, unit-wind effects for head, tail and cross winds, coriolis deflections, range derivative, and the sensitivity curves (the so called F(Z) and DF(Z) curves). The numerical integration procedure is a fourth-order, modified Adams-Bashforth Predictor-Corrector method. This method is supplemented by a fourth-order Runge-Kutta method to start the integration at t=0 and whenever error criteria demand a change in step size.

Numerical Issues Associated with Compensating and Competing Processes in Climate Models: an Example from ECHAM-HAM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wan, Hui; Rasch, Philip J.; Zhang, Kai

2013-06-26

The purpose of this paper is to draw attention to the need for appropriate numerical techniques to represent process interactions in climate models. In two versions of the ECHAM-HAM model, different time integration methods are used to solve the sulfuric acid (H2SO4) gas evolution equation, which lead to substantially different results in the H2SO4 gas concentration and the aerosol nucleation rate. Using convergence tests and sensitivity simulations performed with various time stepping schemes, it is confirmed that numerical errors in the second model version are significantly smaller than those in version one. The use of sequential operator splitting in combinationmore » with long time step is identified as the main reason for the large systematic biases in the old model. The remaining errors in version two in the nucleation rate, related to the competition between condensation and nucleation, have a clear impact on the simulated concentration of cloud condensation nuclei in the lower troposphere. These errors can be significantly reduced by employing an implicit solver that handles production, condensation and nucleation at the same time. Lessons learned in this work underline the need for more caution when treating multi-time-scale problems involving compensating and competing processes, a common occurrence in current climate models.« less

An Improved Neutron Transport Algorithm for HZETRN2006

NASA Astrophysics Data System (ADS)

Slaba, Tony

NASA's new space exploration initiative includes plans for long term human presence in space thereby placing new emphasis on space radiation analyses. In particular, a systematic effort of verification, validation and uncertainty quantification of the tools commonly used for radiation analysis for vehicle design and mission planning has begun. In this paper, the numerical error associated with energy discretization in HZETRN2006 is addressed; large errors in the low-energy portion of the neutron fluence spectrum are produced due to a numerical truncation error in the transport algorithm. It is shown that the truncation error results from the narrow energy domain of the neutron elastic spectral distributions, and that an extremely fine energy grid is required in order to adequately resolve the problem under the current formulation. Since adding a sufficient number of energy points will render the code computationally inefficient, we revisit the light-ion transport theory developed for HZETRN2006 and focus on neutron elastic interactions. The new approach that is developed numerically integrates with adequate resolution in the energy domain without affecting the run-time of the code and is easily incorporated into the current code. Efforts were also made to optimize the computational efficiency of the light-ion propagator; a brief discussion of the efforts is given along with run-time comparisons between the original and updated codes. Convergence testing is then completed by running the code for various environments and shielding materials with many different energy grids to ensure stability of the proposed method.

Accuracy of unmodified Stokes' integration in the R-C-R procedure for geoid computation

NASA Astrophysics Data System (ADS)

Ismail, Zahra; Jamet, Olivier

2015-06-01

Geoid determinations by the Remove-Compute-­Restore (R-C-R) technique involves the application of Stokes' integral on reduced gravity anomalies. Numerical Stokes' integration produces an error depending on the choice of the integration radius, grid resolution and Stokes' kernel function. In this work, we aim to evaluate the accuracy of Stokes' integral through a study on synthetic gravitational signals derived from EGM2008 on three different landscape areas with respect to the size of the integration domain and the resolution of the anomaly grid. The influence of the integration radius was studied earlier by several authors. Using real data, they found that the choice of relatively small radii (less than 1°) enables to reach an optimal accuracy. We observe a general behaviour coherent with these earlier studies. On the other hand, we notice that increasing the integration radius up to 2° or 2.5° might bring significantly better results. We note that, unlike the smallest radius corresponding to a local minimum of the error curve, the optimal radius in the range 0° to 6° depends on the terrain characteristics. We also find that the high frequencies, from degree 600, improve continuously with the integration radius in both semi-­mountainous and mountain areas. Finally, we note that the relative error of the computed geoid heights depends weakly on the anomaly spherical harmonic degree in the range from degree 200 to 2000. It remains greater than 10 % for any integration radii up to 6°. This result tends to prove that a one centimetre accuracy cannot be reached in semi-mountainous and mountainous regions with the unmodified Stokes' kernel.

Sensitivity analysis and optimization method for the fabrication of one-dimensional beam-splitting phase gratings

PubMed Central

Pacheco, Shaun; Brand, Jonathan F.; Zaverton, Melissa; Milster, Tom; Liang, Rongguang

2015-01-01

A method to design one-dimensional beam-spitting phase gratings with low sensitivity to fabrication errors is described. The method optimizes the phase function of a grating by minimizing the integrated variance of the energy of each output beam over a range of fabrication errors. Numerical results for three 1x9 beam splitting phase gratings are given. Two optimized gratings with low sensitivity to fabrication errors were compared with a grating designed for optimal efficiency. These three gratings were fabricated using gray-scale photolithography. The standard deviation of the 9 outgoing beam energies in the optimized gratings were 2.3 and 3.4 times lower than the optimal efficiency grating. PMID:25969268

Frequency-independent approach to calculate physical optics radiations with the quadratic concave phase variations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Yu Mao, E-mail: yumaowu@fudan.edu.cn; Teng, Si Jia, E-mail: sjteng12@fudan.edu.cn

In this work, we develop the numerical steepest descent path (NSDP) method to calculate the physical optics (PO) radiations with the quadratic concave phase variations. With the surface integral equation method, the physical optics (PO) scattered fields are formulated and further reduced to the surface integrals. The high frequency physical critical points contributions, including the stationary phase points, the boundary resonance points and the vertex points are comprehensively studied via the proposed NSDP method. The key contributions of this work are twofold. One is that together with the PO integrals taking the quadratic parabolic and hyperbolic phase terms, this workmore » makes the NSDP theory be complete for treating the PO integrals with quadratic phase variations. Another is that, in order to illustrate the transition effect of the high frequency physical critical points, in this work, we consider and further extend the NSDP method to calculate the PO integrals with the coalescence of the high frequency critical points. Numerical results for the highly oscillatory PO integral with the coalescence of the critical points are given to verify the efficiency of the proposed NSDP method. The NSDP method could achieve the frequency independent computational workload and error controllable accuracy in all the numerical experiments, especially for the case of the coalescence of the high frequency critical points.« less

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Designing an algorithm to preserve privacy for medical record linkage with error-prone data.

PubMed

Pal, Doyel; Chen, Tingting; Zhong, Sheng; Khethavath, Praveen

2014-01-20

Linking medical records across different medical service providers is important to the enhancement of health care quality and public health surveillance. In records linkage, protecting the patients' privacy is a primary requirement. In real-world health care databases, records may well contain errors due to various reasons such as typos. Linking the error-prone data and preserving data privacy at the same time are very difficult. Existing privacy preserving solutions for this problem are only restricted to textual data. To enable different medical service providers to link their error-prone data in a private way, our aim was to provide a holistic solution by designing and developing a medical record linkage system for medical service providers. To initiate a record linkage, one provider selects one of its collaborators in the Connection Management Module, chooses some attributes of the database to be matched, and establishes the connection with the collaborator after the negotiation. In the Data Matching Module, for error-free data, our solution offered two different choices for cryptographic schemes. For error-prone numerical data, we proposed a newly designed privacy preserving linking algorithm named the Error-Tolerant Linking Algorithm, that allows the error-prone data to be correctly matched if the distance between the two records is below a threshold. We designed and developed a comprehensive and user-friendly software system that provides privacy preserving record linkage functions for medical service providers, which meets the regulation of Health Insurance Portability and Accountability Act. It does not require a third party and it is secure in that neither entity can learn the records in the other's database. Moreover, our novel Error-Tolerant Linking Algorithm implemented in this software can work well with error-prone numerical data. We theoretically proved the correctness and security of our Error-Tolerant Linking Algorithm. We have also fully implemented the software. The experimental results showed that it is reliable and efficient. The design of our software is open so that the existing textual matching methods can be easily integrated into the system. Designing algorithms to enable medical records linkage for error-prone numerical data and protect data privacy at the same time is difficult. Our proposed solution does not need a trusted third party and is secure in that in the linking process, neither entity can learn the records in the other's database.

Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

NASA Technical Reports Server (NTRS)

Radhakrishnan, K.

1984-01-01

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency.

Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

NASA Astrophysics Data System (ADS)

Trinkle, Dallas R.

2017-10-01

A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to the sum of a few analytic functions and numerical integration of a smooth function over the Brillouin zone for arbitrary crystals. The Dyson equation solves for the Green function in the presence of a solute with arbitrary but finite interaction range to compute the transport coefficients accurately, efficiently and automatically, including cases with very large differences in solute-vacancy exchange rates. The methodology takes advantage of the space group symmetry of a crystal to reduce the complexity of the matrix inversion in the Dyson equation. An open-source implementation of the algorithm is available, and numerical results are presented for the convergence of the integration error of the bare vacancy Green function, and tracer correlation factors for a variety of crystals including wurtzite (hexagonal diamond) and garnet.

An ultra-accurate numerical method in the design of liquid phononic crystals with hard inclusion

NASA Astrophysics Data System (ADS)

Li, Eric; He, Z. C.; Wang, G.; Liu, G. R.

2017-12-01

The phononics crystals (PCs) are periodic man-made composite materials. In this paper, a mass-redistributed finite element method (MR-FEM) is formulated to study the wave propagation within liquid PCs with hard inclusion. With a perfect balance between stiffness and mass in the MR-FEM model, the dispersion error of longitudinal wave is minimized by redistribution of mass. Such tuning can be easily achieved by adjusting the parameter r that controls the location of integration points of mass matrix. More importantly, the property of mass conservation in the MR-FEM model indicates that the locations of integration points inside or outside the element are immaterial. Four numerical examples are studied in this work, including liquid PCs with cross and circle hard inclusions, different size of inclusion and defect. Compared with standard finite element method, the numerical results have verified the accuracy and effectiveness of MR-FEM. The proposed MR-FEM is a unique and innovative numerical approach with its outstanding features, which has strong potentials to study the stress wave within multi-physics PCs.

Integral Method of Boundary Characteristics: Neumann Condition

NASA Astrophysics Data System (ADS)

Kot, V. A.

2018-05-01

A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary conditions with the use of this algorithm are presented. The solutions obtained with it can be considered as exact because their errors comprise hundredths and ten-thousandths of a persent for a wide range of change in the parameters of a problem.

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

1997-01-01

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Integrated guidance and control for microsatellite real-time automated proximity operations

NASA Astrophysics Data System (ADS)

Chen, Ying; He, Zhen; Zhou, Ding; Yu, Zhenhua; Li, Shunli

2018-07-01

This paper investigates the trajectory planning and control of autonomous spacecraft proximity operations with impulsive dynamics. A new integrated guidance and control scheme is developed to perform automated close-range rendezvous for underactuated microsatellites. To efficiently prevent collision, a modified RRT* trajectory planning algorithm is proposed under this context. Several engineering constraints such as collision avoidance, plume impingement, field of view and control feasibility are considered simultaneously. Then, the feedback controller that employs a turn-burn-turn strategy with a combined impulsive orbital control and finite-time attitude control is designed to ensure the implementation of planned trajectory. Finally, the performance of trajectory planner and controller are evaluated through numerical tests. Simulation results indicate the real-time implementability of the proposed integrated guidance and control scheme with position control error less than 0.5 m and velocity control error less than 0.05 m/s. Consequently, the proposed scheme offers the potential for wide applications, such as on-orbit maintenance, space surveillance and debris removal.

A New Adaptive H-Infinity Filtering Algorithm for the GPS/INS Integrated Navigation

PubMed Central

Jiang, Chen; Zhang, Shu-Bi; Zhang, Qiu-Zhao

2016-01-01

The Kalman filter is an optimal estimator with numerous applications in technology, especially in systems with Gaussian distributed noise. Moreover, the adaptive Kalman filtering algorithms, based on the Kalman filter, can control the influence of dynamic model errors. In contrast to the adaptive Kalman filtering algorithms, the H-infinity filter is able to address the interference of the stochastic model by minimization of the worst-case estimation error. In this paper, a novel adaptive H-infinity filtering algorithm, which integrates the adaptive Kalman filter and the H-infinity filter in order to perform a comprehensive filtering algorithm, is presented. In the proposed algorithm, a robust estimation method is employed to control the influence of outliers. In order to verify the proposed algorithm, experiments with real data of the Global Positioning System (GPS) and Inertial Navigation System (INS) integrated navigation, were conducted. The experimental results have shown that the proposed algorithm has multiple advantages compared to the other filtering algorithms. PMID:27999361

A New Adaptive H-Infinity Filtering Algorithm for the GPS/INS Integrated Navigation.

PubMed

Jiang, Chen; Zhang, Shu-Bi; Zhang, Qiu-Zhao

2016-12-19

The Kalman filter is an optimal estimator with numerous applications in technology, especially in systems with Gaussian distributed noise. Moreover, the adaptive Kalman filtering algorithms, based on the Kalman filter, can control the influence of dynamic model errors. In contrast to the adaptive Kalman filtering algorithms, the H-infinity filter is able to address the interference of the stochastic model by minimization of the worst-case estimation error. In this paper, a novel adaptive H-infinity filtering algorithm, which integrates the adaptive Kalman filter and the H-infinity filter in order to perform a comprehensive filtering algorithm, is presented. In the proposed algorithm, a robust estimation method is employed to control the influence of outliers. In order to verify the proposed algorithm, experiments with real data of the Global Positioning System (GPS) and Inertial Navigation System (INS) integrated navigation, were conducted. The experimental results have shown that the proposed algorithm has multiple advantages compared to the other filtering algorithms.

Analyses of integrated aircraft cabin contaminant monitoring network based on Kalman consensus filter.

PubMed

Wang, Rui; Li, Yanxiao; Sun, Hui; Chen, Zengqiang

2017-11-01

The modern civil aircrafts use air ventilation pressurized cabins subject to the limited space. In order to monitor multiple contaminants and overcome the hypersensitivity of the single sensor, the paper constructs an output correction integrated sensor configuration using sensors with different measurement theories after comparing to other two different configurations. This proposed configuration works as a node in the contaminant distributed wireless sensor monitoring network. The corresponding measurement error models of integrated sensors are also proposed by using the Kalman consensus filter to estimate states and conduct data fusion in order to regulate the single sensor measurement results. The paper develops the sufficient proof of the Kalman consensus filter stability when considering the system and the observation noises and compares the mean estimation and the mean consensus errors between Kalman consensus filter and local Kalman filter. The numerical example analyses show the effectiveness of the algorithm. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Proton upsets in LSI memories in space

NASA Technical Reports Server (NTRS)

Mcnulty, P. J.; Wyatt, R. C.; Filz, R. C.; Rothwell, P. L.; Farrell, G. E.

1980-01-01

Two types of large scale integrated dynamic random access memory devices were tested and found to be subject to soft errors when exposed to protons incident at energies between 18 and 130 MeV. These errors are shown to differ significantly from those induced in the same devices by alphas from an Am-241 source. There is considerable variation among devices in their sensitivity to proton-induced soft errors, even among devices of the same type. For protons incident at 130 MeV, the soft error cross sections measured in these experiments varied from 10 to the -8th to 10 to the -6th sq cm/proton. For individual devices, however, the soft error cross section consistently increased with beam energy from 18-130 MeV. Analysis indicates that the soft errors induced by energetic protons result from spallation interactions between the incident protons and the nuclei of the atoms comprising the device. Because energetic protons are the most numerous of both the galactic and solar cosmic rays and form the inner radiation belt, proton-induced soft errors have potentially serious implications for many electronic systems flown in space.

Evaluation of Optimal Formulas for Gravitational Tensors up to Gravitational Curvatures of a Tesseroid

NASA Astrophysics Data System (ADS)

Deng, Xiao-Le; Shen, Wen-Bin

2018-01-01

The forward modeling of the topographic effects of the gravitational parameters in the gravity field is a fundamental topic in geodesy and geophysics. Since the gravitational effects, including for instance the gravitational potential (GP), the gravity vector (GV) and the gravity gradient tensor (GGT), of the topographic (or isostatic) mass reduction have been expanded by adding the gravitational curvatures (GC) in geoscience, it is crucial to find efficient numerical approaches to evaluate these effects. In this paper, the GC formulas of a tesseroid in Cartesian integral kernels are derived in 3D/2D forms. Three generally used numerical approaches for computing the topographic effects (e.g., GP, GV, GGT, GC) of a tesseroid are studied, including the Taylor Series Expansion (TSE), Gauss-Legendre Quadrature (GLQ) and Newton-Cotes Quadrature (NCQ) approaches. Numerical investigations show that the GC formulas in Cartesian integral kernels are more efficient if compared to the previously given GC formulas in spherical integral kernels: by exploiting the 3D TSE second-order formulas, the computational burden associated with the former is 46%, as an average, of that associated with the latter. The GLQ behaves better than the 3D/2D TSE and NCQ in terms of accuracy and computational time. In addition, the effects of a spherical shell's thickness and large-scale geocentric distance on the GP, GV, GGT and GC functionals have been studied with the 3D TSE second-order formulas as well. The relative approximation errors of the GC functionals are larger with the thicker spherical shell, which are the same as those of the GP, GV and GGT. Finally, the very-near-area problem and polar singularity problem have been considered by the numerical methods of the 3D TSE, GLQ and NCQ. The relative approximation errors of the GC components are larger than those of the GP, GV and GGT, especially at the very near area. Compared to the GC formulas in spherical integral kernels, these new GC formulas can avoid the polar singularity problem.

A Strapdown Interial Navigation System/Beidou/Doppler Velocity Log Integrated Navigation Algorithm Based on a Cubature Kalman Filter

PubMed Central

Gao, Wei; Zhang, Ya; Wang, Jianguo

2014-01-01

The integrated navigation system with strapdown inertial navigation system (SINS), Beidou (BD) receiver and Doppler velocity log (DVL) can be used in marine applications owing to the fact that the redundant and complementary information from different sensors can markedly improve the system accuracy. However, the existence of multisensor asynchrony will introduce errors into the system. In order to deal with the problem, conventionally the sampling interval is subdivided, which increases the computational complexity. In this paper, an innovative integrated navigation algorithm based on a Cubature Kalman filter (CKF) is proposed correspondingly. A nonlinear system model and observation model for the SINS/BD/DVL integrated system are established to more accurately describe the system. By taking multi-sensor asynchronization into account, a new sampling principle is proposed to make the best use of each sensor's information. Further, CKF is introduced in this new algorithm to enable the improvement of the filtering accuracy. The performance of this new algorithm has been examined through numerical simulations. The results have shown that the positional error can be effectively reduced with the new integrated navigation algorithm. Compared with the traditional algorithm based on EKF, the accuracy of the SINS/BD/DVL integrated navigation system is improved, making the proposed nonlinear integrated navigation algorithm feasible and efficient. PMID:24434842

Accuracy of Time Integration Approaches for Stiff Magnetohydrodynamics Problems

NASA Astrophysics Data System (ADS)

Knoll, D. A.; Chacon, L.

2003-10-01

The simulation of complex physical processes with multiple time scales presents a continuing challenge to the computational plasma physisist due to the co-existence of fast and slow time scales. Within computational plasma physics, practitioners have developed and used linearized methods, semi-implicit methods, and time splitting in an attempt to tackle such problems. All of these methods are understood to generate numerical error. We are currently developing algorithms which remove such error for MHD problems [1,2]. These methods do not rely on linearization or time splitting. We are also attempting to analyze the errors introduced by existing ``implicit'' methods using modified equation analysis (MEA) [3]. In this presentation we will briefly cover the major findings in [3]. We will then extend this work further into MHD. This analysis will be augmented with numerical experiments with the hope of gaining insight, particularly into how these errors accumulate over many time steps. [1] L. Chacon,. D.A. Knoll, J.M. Finn, J. Comput. Phys., vol. 178, pp. 15-36 (2002) [2] L. Chacon and D.A. Knoll, J. Comput. Phys., vol. 188, pp. 573-592 (2003) [3] D.A. Knoll , L. Chacon, L.G. Margolin, V.A. Mousseau, J. Comput. Phys., vol. 185, pp. 583-611 (2003)

A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation

PubMed Central

Wang, Jinfeng; Li, Hong; Fang, Zhichao

2014-01-01

We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen's expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L 2-norm for the scalar unknown u and a priori error estimates in (L 2)2-norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in H 1-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method. PMID:24701153

IBM system/360 assembly language interval arithmetic software

NASA Technical Reports Server (NTRS)

Phillips, E. J.

1972-01-01

Computer software designed to perform interval arithmetic is described. An interval is defined as the set of all real numbers between two given numbers including or excluding one or both endpoints. Interval arithmetic consists of the various elementary arithmetic operations defined on the set of all intervals, such as interval addition, subtraction, union, etc. One of the main applications of interval arithmetic is in the area of error analysis of computer calculations. For example, it has been used sucessfully to compute bounds on sounding errors in the solution of linear algebraic systems, error bounds in numerical solutions of ordinary differential equations, as well as integral equations and boundary value problems. The described software enables users to implement algorithms of the type described in references efficiently on the IBM 360 system.

On the implementation of an accurate and efficient solver for convection-diffusion equations

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from the finite element solution.

An efficient method for the computation of Legendre moments.

PubMed

Yap, Pew-Thian; Paramesran, Raveendran

2005-12-01

Legendre moments are continuous moments, hence, when applied to discrete-space images, numerical approximation is involved and error occurs. This paper proposes a method to compute the exact values of the moments by mathematically integrating the Legendre polynomials over the corresponding intervals of the image pixels. Experimental results show that the values obtained match those calculated theoretically, and the image reconstructed from these moments have lower error than that of the conventional methods for the same order. Although the same set of exact Legendre moments can be obtained indirectly from the set of geometric moments, the computation time taken is much longer than the proposed method.

Simplified formula for mean cycle-slip time of phase-locked loops with steady-state phase error.

NASA Technical Reports Server (NTRS)

Tausworthe, R. C.

1972-01-01

Previous work shows that the mean time from lock to a slipped cycle of a phase-locked loop is given by a certain double integral. Accurate numerical evaluation of this formula for the second-order loop is extremely vexing because the difference between exponentially large quantities is involved. The presented article demonstrates a method in which a much-reduced precision program can be used to obtain the mean first-cycle slip time for a loop of arbitrary degree tracking at a specified SNR and steady-state phase error. It also presents a simple approximate formula that is asymptotically tight at higher loop SNR.

Optimization of Pockels electric field in transverse modulated optical voltage sensor

NASA Astrophysics Data System (ADS)

Huang, Yifan; Xu, Qifeng; Chen, Kun-Long; Zhou, Jie

2018-05-01

This paper investigates the possibilities of optimizing the Pockels electric field in a transverse modulated optical voltage sensor with a spherical electrode structure. The simulations show that due to the edge effect and the electric field concentrations and distortions, the electric field distributions in the crystal are non-uniform. In this case, a tiny variation in the light path leads to an integral error of more than 0.5%. Moreover, a 2D model cannot effectively represent the edge effect, so a 3D model is employed to optimize the electric field distributions. Furthermore, a new method to attach a quartz crystal to the electro-optic crystal along the electric field direction is proposed to improve the non-uniformity of the electric field. The integral error is reduced therefore from 0.5% to 0.015% and less. The proposed method is simple, practical and effective, and it has been validated by numerical simulations and experimental tests.

Integrated Power and Attitude Control for a Spacecraft with Flywheels and Control Moment Gyroscopes

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Karlgaard, Christopher D.; Kumar, Renjith R.; Bose, David M.

2003-01-01

A law is designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as all integrated set of actuators for attitude control. General. nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as it means of compensating for damping exerted by rotor bearings. Two flywheel 'steering laws' are developed such that torque commanded by all attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude and illustrate the benefits of kinetic energy error feedback.

Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

NASA Technical Reports Server (NTRS)

Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)

2000-01-01

This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

Selective Attention to Semantic and Syntactic Features Modulates Sentence Processing Networks in Anterior Temporal Cortex

PubMed Central

Rogalsky, Corianne

2009-01-01

Numerous studies have identified an anterior temporal lobe (ATL) region that responds preferentially to sentence-level stimuli. It is unclear, however, whether this activity reflects a response to syntactic computations or some form of semantic integration. This distinction is difficult to investigate with the stimulus manipulations and anomaly detection paradigms traditionally implemented. The present functional magnetic resonance imaging study addresses this question via a selective attention paradigm. Subjects monitored for occasional semantic anomalies or occasional syntactic errors, thus directing their attention to semantic integration, or syntactic properties of the sentences. The hemodynamic response in the sentence-selective ATL region (defined with a localizer scan) was examined during anomaly/error-free sentences only, to avoid confounds due to error detection. The majority of the sentence-specific region of interest was equally modulated by attention to syntactic or compositional semantic features, whereas a smaller subregion was only modulated by the semantic task. We suggest that the sentence-specific ATL region is sensitive to both syntactic and integrative semantic functions during sentence processing, with a smaller portion of this area preferentially involved in the later. This study also suggests that selective attention paradigms may be effective tools to investigate the functional diversity of networks involved in sentence processing. PMID:18669589

The impact of pharmacy services on opioid prescribing in dental practice.

PubMed

Stewart, Autumn; Zborovancik, Kelsey J; Stiely, Kara L

To compare rates of dental opioid prescribing between periods of full and partial integration of pharmacy services and periods of no integration. This observational study used a retrospective chart review of opioid prescriptions written by dental providers practicing in a free dental clinic for the medically underserved over a period of 74 months. Pharmacy services were fully integrated into the practice model for 48 of the 74 months under study. During this time frame, all dental opioid orders required review by the pharmacy department before prescribing. Outcomes related to prescribing rates and errors were compared between groups, which were defined by the level of integrated pharmacy services. Demographic and prescription-specific data (drug name, dose, quantity, directions, professional designation of individual entering order) and clinic appointment data were collected and analyzed with the use of descriptive and inferential statistics. A total of 102 opioids were prescribed to 89 patients; hydrocodone-acetaminophen combination products were the most frequently used. Opioid prescribing rates were 5 times greater when pharmacy services were not integrated (P <0.001); and dentists were 81% less likely to prescribe opioids when pharmacy was fully integrated (odds ratio 0.19, 95% confidence interval 0.124-0.293; P <0.001). Frequency of hydrocodone use compared with other opioids did not decrease after the rescheduling of hydrocodone to a Schedule II controlled substance. The frequency of prescribing errors was not statistically different between groups, although there were numerically fewer errors with integrated pharmacy services. The literature reports that dentists are the third most frequent prescribers of opioids. The findings from this study suggest that collaboration between pharmacists and dentists has the potential to decrease opioid utilization in primary dental practice. Copyright © 2017 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

Improved Uncertainty Quantification in Groundwater Flux Estimation Using GRACE

NASA Astrophysics Data System (ADS)

Reager, J. T., II; Rao, P.; Famiglietti, J. S.; Turmon, M.

2015-12-01

Groundwater change is difficult to monitor over large scales. One of the most successful approaches is in the remote sensing of time-variable gravity using NASA Gravity Recovery and Climate Experiment (GRACE) mission data, and successful case studies have created the opportunity to move towards a global groundwater monitoring framework for the world's largest aquifers. To achieve these estimates, several approximations are applied, including those in GRACE processing corrections, the formulation of the formal GRACE errors, destriping and signal recovery, and the numerical model estimation of snow water, surface water and soil moisture storage states used to isolate a groundwater component. A major weakness in these approaches is inconsistency: different studies have used different sources of primary and ancillary data, and may achieve different results based on alternative choices in these approximations. In this study, we present two cases of groundwater change estimation in California and the Colorado River basin, selected for their good data availability and varied climates. We achieve a robust numerical estimate of post-processing uncertainties resulting from land-surface model structural shortcomings and model resolution errors. Groundwater variations should demonstrate less variability than the overlying soil moisture state does, as groundwater has a longer memory of past events due to buffering by infiltration and drainage rate limits. We apply a model ensemble approach in a Bayesian framework constrained by the assumption of decreasing signal variability with depth in the soil column. We also discuss time variable errors vs. time constant errors, across-scale errors v. across-model errors, and error spectral content (across scales and across model). More robust uncertainty quantification for GRACE-based groundwater estimates would take all of these issues into account, allowing for more fair use in management applications and for better integration of GRACE-based measurements with observations from other sources.

Numerical Analysis of Orbital Perturbation Effects on Inclined Geosynchronous SAR

PubMed Central

Dong, Xichao; Hu, Cheng; Long, Teng; Li, Yuanhao

2016-01-01

The geosynchronous synthetic aperture radar (GEO SAR) is susceptible to orbit perturbations, leading to orbit drifts and variations. The influences behave very differently from those in low Earth orbit (LEO) SAR. In this paper, the impacts of perturbations on GEO SAR orbital elements are modelled based on the perturbed dynamic equations, and then, the focusing is analyzed theoretically and numerically by using the Systems Tool Kit (STK) software. The accurate GEO SAR slant range histories can be calculated according to the perturbed orbit positions in STK. The perturbed slant range errors are mainly the first and second derivatives, leading to image drifts and defocusing. Simulations of the point target imaging are performed to validate the aforementioned analysis. In the GEO SAR with an inclination of 53° and an argument of perigee of 90°, the Doppler parameters and the integration time are different and dependent on the geometry configurations. Thus, the influences are varying at different orbit positions: at the equator, the first-order phase errors should be mainly considered; at the perigee and apogee, the second-order phase errors should be mainly considered; at other positions, first-order and second-order exist simultaneously. PMID:27598168

Designing an Algorithm to Preserve Privacy for Medical Record Linkage With Error-Prone Data

PubMed Central

Pal, Doyel; Chen, Tingting; Khethavath, Praveen

2014-01-01

Background Linking medical records across different medical service providers is important to the enhancement of health care quality and public health surveillance. In records linkage, protecting the patients’ privacy is a primary requirement. In real-world health care databases, records may well contain errors due to various reasons such as typos. Linking the error-prone data and preserving data privacy at the same time are very difficult. Existing privacy preserving solutions for this problem are only restricted to textual data. Objective To enable different medical service providers to link their error-prone data in a private way, our aim was to provide a holistic solution by designing and developing a medical record linkage system for medical service providers. Methods To initiate a record linkage, one provider selects one of its collaborators in the Connection Management Module, chooses some attributes of the database to be matched, and establishes the connection with the collaborator after the negotiation. In the Data Matching Module, for error-free data, our solution offered two different choices for cryptographic schemes. For error-prone numerical data, we proposed a newly designed privacy preserving linking algorithm named the Error-Tolerant Linking Algorithm, that allows the error-prone data to be correctly matched if the distance between the two records is below a threshold. Results We designed and developed a comprehensive and user-friendly software system that provides privacy preserving record linkage functions for medical service providers, which meets the regulation of Health Insurance Portability and Accountability Act. It does not require a third party and it is secure in that neither entity can learn the records in the other’s database. Moreover, our novel Error-Tolerant Linking Algorithm implemented in this software can work well with error-prone numerical data. We theoretically proved the correctness and security of our Error-Tolerant Linking Algorithm. We have also fully implemented the software. The experimental results showed that it is reliable and efficient. The design of our software is open so that the existing textual matching methods can be easily integrated into the system. Conclusions Designing algorithms to enable medical records linkage for error-prone numerical data and protect data privacy at the same time is difficult. Our proposed solution does not need a trusted third party and is secure in that in the linking process, neither entity can learn the records in the other’s database. PMID:25600786

Optimizing Cubature for Efficient Integration of Subspace Deformations

PubMed Central

An, Steven S.; Kim, Theodore; James, Doug L.

2009-01-01

We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r2) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration. CR Categories: I.6.8 [Simulation and Modeling]: Types of Simulation—Animation, I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling G.1.4 [Mathematics of Computing]: Numerical Analysis—Quadrature and Numerical Differentiation PMID:19956777

Investigation of ODE integrators using interactive graphics. [Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Brown, R. L.

1978-01-01

Two FORTRAN programs using an interactive graphic terminal to generate accuracy and stability plots for given multistep ordinary differential equation (ODE) integrators are described. The first treats the fixed stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution, as well as the linear stability region. The second generates an analog to the stability region for classes of non-linear ODE's as well as accuracy plots. Both systems can compute method coefficients from a simple specification of the method. Example plots are given.

Wind Power Forecasting Error Frequency Analyses for Operational Power System Studies: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Florita, A.; Hodge, B. M.; Milligan, M.

2012-08-01

The examination of wind power forecasting errors is crucial for optimal unit commitment and economic dispatch of power systems with significant wind power penetrations. This scheduling process includes both renewable and nonrenewable generators, and the incorporation of wind power forecasts will become increasingly important as wind fleets constitute a larger portion of generation portfolios. This research considers the Western Wind and Solar Integration Study database of wind power forecasts and numerical actualizations. This database comprises more than 30,000 locations spread over the western United States, with a total wind power capacity of 960 GW. Error analyses for individual sites andmore » for specific balancing areas are performed using the database, quantifying the fit to theoretical distributions through goodness-of-fit metrics. Insights into wind-power forecasting error distributions are established for various levels of temporal and spatial resolution, contrasts made among the frequency distribution alternatives, and recommendations put forth for harnessing the results. Empirical data are used to produce more realistic site-level forecasts than previously employed, such that higher resolution operational studies are possible. This research feeds into a larger work of renewable integration through the links wind power forecasting has with various operational issues, such as stochastic unit commitment and flexible reserve level determination.« less

Error and Uncertainty Quantification in the Numerical Simulation of Complex Fluid Flows

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2010-01-01

The failure of numerical simulation to predict physical reality is often a direct consequence of the compounding effects of numerical error arising from finite-dimensional approximation and physical model uncertainty resulting from inexact knowledge and/or statistical representation. In this topical lecture, we briefly review systematic theories for quantifying numerical errors and restricted forms of model uncertainty occurring in simulations of fluid flow. A goal of this lecture is to elucidate both positive and negative aspects of applying these theories to practical fluid flow problems. Finite-element and finite-volume calculations of subsonic and hypersonic fluid flow are presented to contrast the differing roles of numerical error and model uncertainty. for these problems.

A semi-analytic theory for the motion of a close-earth artificial satellite with drag

NASA Technical Reports Server (NTRS)

Liu, J. J. F.; Alford, R. L.

1979-01-01

A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.

Prediction of discretization error using the error transport equation

NASA Astrophysics Data System (ADS)

Celik, Ismail B.; Parsons, Don Roscoe

2017-06-01

This study focuses on an approach to quantify the discretization error associated with numerical solutions of partial differential equations by solving an error transport equation (ETE). The goal is to develop a method that can be used to adequately predict the discretization error using the numerical solution on only one grid/mesh. The primary problem associated with solving the ETE is the formulation of the error source term which is required for accurately predicting the transport of the error. In this study, a novel approach is considered which involves fitting the numerical solution with a series of locally smooth curves and then blending them together with a weighted spline approach. The result is a continuously differentiable analytic expression that can be used to determine the error source term. Once the source term has been developed, the ETE can easily be solved using the same solver that is used to obtain the original numerical solution. The new methodology is applied to the two-dimensional Navier-Stokes equations in the laminar flow regime. A simple unsteady flow case is also considered. The discretization error predictions based on the methodology presented in this study are in good agreement with the 'true error'. While in most cases the error predictions are not quite as accurate as those from Richardson extrapolation, the results are reasonable and only require one numerical grid. The current results indicate that there is much promise going forward with the newly developed error source term evaluation technique and the ETE.

Running coupling constant from lattice studies of gluon and ghost propagators

NASA Astrophysics Data System (ADS)

Cucchieri, A.; Mendes, T.

2004-12-01

We present a numerical study of the running coupling constant in four-dimensional pure-SU(2) lattice gauge theory. The running coupling is evaluated by fitting data for the gluon and ghost propagators in minimal Landau gauge. Following Refs. [1, 2], the fitting formulae are obtained by a simultaneous integration of the β function and of a function coinciding with the anomalous dimension of the propagator in the momentum subtraction scheme. We consider these formulae at three and four loops. The fitting method works well, especially for the ghost case, for which statistical error and hyper-cubic effects are very small. Our present result for ΛMS is 200-40+60 MeV, where the error is purely systematic. We are currently extending this analysis to five loops in order to reduce this systematic error.

A Discrete Constraint for Entropy Conservation and Sound Waves in Cloud-Resolving Modeling

NASA Technical Reports Server (NTRS)

Zeng, Xi-Ping; Tao, Wei-Kuo; Simpson, Joanne

2003-01-01

Ideal cloud-resolving models contain little-accumulative errors. When their domain is so large that synoptic large-scale circulations are accommodated, they can be used for the simulation of the interaction between convective clouds and the large-scale circulations. This paper sets up a framework for the models, using moist entropy as a prognostic variable and employing conservative numerical schemes. The models possess no accumulative errors of thermodynamic variables when they comply with a discrete constraint on entropy conservation and sound waves. Alternatively speaking, the discrete constraint is related to the correct representation of the large-scale convergence and advection of moist entropy. Since air density is involved in entropy conservation and sound waves, the challenge is how to compute sound waves efficiently under the constraint. To address the challenge, a compensation method is introduced on the basis of a reference isothermal atmosphere whose governing equations are solved analytically. Stability analysis and numerical experiments show that the method allows the models to integrate efficiently with a large time step.

A collaborative inventory model for vendor-buyer system with inspection errors, unequal sized shipment, and repairable item

NASA Astrophysics Data System (ADS)

Hamdani, Irfan Hilmi; Jauhari, Wakhid Ahmad; Rosyidi, Cucuk Nur

2017-11-01

This paper develops an integrated inventory model consisting of single-vendor and single-buyer system. The demand in buyer side is deterministic and the production process is imperfect and produces a certain number of defective items. The delivery within a single production batch from vendor to buyer is increasing by a fixed factor. After the delivery arrives at the buyer, an inspection process is conducted. The inspection process in not perfect. Errors may occur when the inspector is misclassifies a non-defective item as defective ne, or incorrectly classifies a defective item as non-defective. All the product which defective will be repair by repair-shop. After the defective arrives at repair shop, will perfect inspection. The defective item will repair and back to buyer. This model provides an optimal solution for the expected integrated total annual cost of the vendor and the buyer. The result from numerical examples shows that the integrated model will result in lower joint total cost in comparison with the equal-sized policy.

De-Aliasing Through Over-Integration Applied to the Flux Reconstruction and Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Spiegel, Seth C.; Huynh, H. T.; DeBonis, James R.

2015-01-01

High-order methods are quickly becoming popular for turbulent flows as the amount of computer processing power increases. The flux reconstruction (FR) method presents a unifying framework for a wide class of high-order methods including discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV). It offers a simple, efficient, and easy way to implement nodal-based methods that are derived via the differential form of the governing equations. Whereas high-order methods have enjoyed recent success, they have been known to introduce numerical instabilities due to polynomial aliasing when applied to under-resolved nonlinear problems. Aliasing errors have been extensively studied in reference to DG methods; however, their study regarding FR methods has mostly been limited to the selection of the nodal points used within each cell. Here, we extend some of the de-aliasing techniques used for DG methods, primarily over-integration, to the FR framework. Our results show that over-integration does remove aliasing errors but may not remove all instabilities caused by insufficient resolution (for FR as well as DG).

Abnormal Error Monitoring in Math-Anxious Individuals: Evidence from Error-Related Brain Potentials

PubMed Central

Suárez-Pellicioni, Macarena; Núñez-Peña, María Isabel; Colomé, Àngels

2013-01-01

This study used event-related brain potentials to investigate whether math anxiety is related to abnormal error monitoring processing. Seventeen high math-anxious (HMA) and seventeen low math-anxious (LMA) individuals were presented with a numerical and a classical Stroop task. Groups did not differ in terms of trait or state anxiety. We found enhanced error-related negativity (ERN) in the HMA group when subjects committed an error on the numerical Stroop task, but not on the classical Stroop task. Groups did not differ in terms of the correct-related negativity component (CRN), the error positivity component (Pe), classical behavioral measures or post-error measures. The amplitude of the ERN was negatively related to participants’ math anxiety scores, showing a more negative amplitude as the score increased. Moreover, using standardized low resolution electromagnetic tomography (sLORETA) we found greater activation of the insula in errors on a numerical task as compared to errors in a non-numerical task only for the HMA group. The results were interpreted according to the motivational significance theory of the ERN. PMID:24236212

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

Nonparametric probability density estimation by optimization theoretic techniques

NASA Technical Reports Server (NTRS)

Scott, D. W.

1976-01-01

Two nonparametric probability density estimators are considered. The first is the kernel estimator. The problem of choosing the kernel scaling factor based solely on a random sample is addressed. An interactive mode is discussed and an algorithm proposed to choose the scaling factor automatically. The second nonparametric probability estimate uses penalty function techniques with the maximum likelihood criterion. A discrete maximum penalized likelihood estimator is proposed and is shown to be consistent in the mean square error. A numerical implementation technique for the discrete solution is discussed and examples displayed. An extensive simulation study compares the integrated mean square error of the discrete and kernel estimators. The robustness of the discrete estimator is demonstrated graphically.

Shape sensing using multi-core fiber optic cable and parametric curve solutions.

PubMed

Moore, Jason P; Rogge, Matthew D

2012-01-30

The shape of a multi-core optical fiber is calculated by numerically solving a set of Frenet-Serret equations describing the path of the fiber in three dimensions. Included in the Frenet-Serret equations are curvature and bending direction functions derived from distributed fiber Bragg grating strain measurements in each core. The method offers advantages over prior art in that it determines complex three-dimensional fiber shape as a continuous parametric solution rather than an integrated series of discrete planar bends. Results and error analysis of the method using a tri-core optical fiber is presented. Maximum error expressed as a percentage of fiber length was found to be 7.2%.

Performance Comparison of Orthogonal and Quasi-orthogonal Codes in Quasi-Synchronous Cellular CDMA Communication

NASA Astrophysics Data System (ADS)

Jos, Sujit; Kumar, Preetam; Chakrabarti, Saswat

Orthogonal and quasi-orthogonal codes are integral part of any DS-CDMA based cellular systems. Orthogonal codes are ideal for use in perfectly synchronous scenario like downlink cellular communication. Quasi-orthogonal codes are preferred over orthogonal codes in the uplink communication where perfect synchronization cannot be achieved. In this paper, we attempt to compare orthogonal and quasi-orthogonal codes in presence of timing synchronization error. This will give insight into the synchronization demands in DS-CDMA systems employing the two classes of sequences. The synchronization error considered is smaller than chip duration. Monte-Carlo simulations have been carried out to verify the analytical and numerical results.

DYNAMIC STABILITY OF THE SOLAR SYSTEM: STATISTICALLY INCONCLUSIVE RESULTS FROM ENSEMBLE INTEGRATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zeebe, Richard E., E-mail: zeebe@soest.hawaii.edu

Due to the chaotic nature of the solar system, the question of its long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of nearby orbits. Destabilization of the inner planets, leading to close encounters and/or collisions can be initiated through a large increase in Mercury's eccentricity, with a currently assumed likelihood of ∼1%. However, little is known at present about the robustness of this number. Here I report ensemble integrations of the full equations of motion of the eight planets and Pluto over 5 Gyr, including contributions from general relativity. The resultsmore » show that different numerical algorithms lead to statistically different results for the evolution of Mercury's eccentricity (e{sub M}). For instance, starting at present initial conditions (e{sub M}≃0.21), Mercury's maximum eccentricity achieved over 5 Gyr is, on average, significantly higher in symplectic ensemble integrations using heliocentric rather than Jacobi coordinates and stricter error control. In contrast, starting at a possible future configuration (e{sub M}≃0.53), Mercury's maximum eccentricity achieved over the subsequent 500 Myr is, on average, significantly lower using heliocentric rather than Jacobi coordinates. For example, the probability for e{sub M} to increase beyond 0.53 over 500 Myr is >90% (Jacobi) versus only 40%-55% (heliocentric). This poses a dilemma because the physical evolution of the real system—and its probabilistic behavior—cannot depend on the coordinate system or the numerical algorithm chosen to describe it. Some tests of the numerical algorithms suggest that symplectic integrators using heliocentric coordinates underestimate the odds for destabilization of Mercury's orbit at high initial e{sub M}.« less

Evaluation of integration methods for hybrid simulation of complex structural systems through collapse

NASA Astrophysics Data System (ADS)

Del Carpio R., Maikol; Hashemi, M. Javad; Mosqueda, Gilberto

2017-10-01

This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration (iterative) and the operator-splitting (non-iterative) is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom (SDOF) cantilever column with replaceable steel coupons that provides repeatable highlynonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1:2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model of a 1:2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.

Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

NASA Astrophysics Data System (ADS)

Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

2010-10-01

Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

Detailed modeling of the statistical uncertainty of Thomson scattering measurements

NASA Astrophysics Data System (ADS)

Morton, L. A.; Parke, E.; Den Hartog, D. J.

2013-11-01

The uncertainty of electron density and temperature fluctuation measurements is determined by statistical uncertainty introduced by multiple noise sources. In order to quantify these uncertainties precisely, a simple but comprehensive model was made of the noise sources in the MST Thomson scattering system and of the resulting variance in the integrated scattered signals. The model agrees well with experimental and simulated results. The signal uncertainties are then used by our existing Bayesian analysis routine to find the most likely electron temperature and density, with confidence intervals. In the model, photonic noise from scattered light and plasma background light is multiplied by the noise enhancement factor (F) of the avalanche photodiode (APD). Electronic noise from the amplifier and digitizer is added. The amplifier response function shapes the signal and induces correlation in the noise. The data analysis routine fits a characteristic pulse to the digitized signals from the amplifier, giving the integrated scattered signals. A finite digitization rate loses information and can cause numerical integration error. We find a formula for the variance of the scattered signals in terms of the background and pulse amplitudes, and three calibration constants. The constants are measured easily under operating conditions, resulting in accurate estimation of the scattered signals' uncertainty. We measure F ≈ 3 for our APDs, in agreement with other measurements for similar APDs. This value is wavelength-independent, simplifying analysis. The correlated noise we observe is reproduced well using a Gaussian response function. Numerical integration error can be made negligible by using an interpolated characteristic pulse, allowing digitization rates as low as the detector bandwidth. The effect of background noise is also determined.

On the chaotic diffusion in multidimensional Hamiltonian systems

NASA Astrophysics Data System (ADS)

Cincotta, P. M.; Giordano, C. M.; Martí, J. G.; Beaugé, C.

2018-01-01

We present numerical evidence that diffusion in the herein studied multidimensional near-integrable Hamiltonian systems departs from a normal process, at least for realistic timescales. Therefore, the derivation of a diffusion coefficient from a linear fit on the variance evolution of the unperturbed integrals fails. We review some topics on diffusion in the Arnold Hamiltonian and yield numerical and theoretical arguments to show that in the examples we considered, a standard coefficient would not provide a good estimation of the speed of diffusion. However, numerical experiments concerning diffusion would provide reliable information about the stability of the motion within chaotic regions of the phase space. In this direction, we present an extension of previous results concerning the dynamical structure of the Laplace resonance in Gliese-876 planetary system considering variations of the orbital parameters accordingly to the error introduced by the radial velocity determination. We found that a slight variation of the eccentricity of planet c would destabilize the inner region of the resonance that, though chaotic, shows stable when adopting the best fit values for the parameters.

Precise and Fast Computation of the Gravitational Field of a General Finite Body and Its Application to the Gravitational Study of Asteroid Eros

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fukushima, Toshio, E-mail: Toshio.Fukushima@nao.ac.jp

In order to obtain the gravitational field of a general finite body inside its Brillouin sphere, we developed a new method to compute the field accurately. First, the body is assumed to consist of some layers in a certain spherical polar coordinate system and the volume mass density of each layer is expanded as a Maclaurin series of the radial coordinate. Second, the line integral with respect to the radial coordinate is analytically evaluated in a closed form. Third, the resulting surface integrals are numerically integrated by the split quadrature method using the double exponential rule. Finally, the associated gravitationalmore » acceleration vector is obtained by numerically differentiating the numerically integrated potential. Numerical experiments confirmed that the new method is capable of computing the gravitational field independently of the location of the evaluation point, namely whether inside, on the surface of, or outside the body. It can also provide sufficiently precise field values, say of 14–15 digits for the potential and of 9–10 digits for the acceleration. Furthermore, its computational efficiency is better than that of the polyhedron approximation. This is because the computational error of the new method decreases much faster than that of the polyhedron models when the number of required transcendental function calls increases. As an application, we obtained the gravitational field of 433 Eros from its shape model expressed as the 24 × 24 spherical harmonic expansion by assuming homogeneity of the object.« less

Probabilistic numerics and uncertainty in computations

PubMed Central

Hennig, Philipp; Osborne, Michael A.; Girolami, Mark

2015-01-01

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations. PMID:26346321

Probabilistic numerics and uncertainty in computations.

PubMed

Hennig, Philipp; Osborne, Michael A; Girolami, Mark

2015-07-08

We deliver a call to arms for probabilistic numerical methods : algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

Data Mining on Numeric Error in Computerized Physician Order Entry System Prescriptions.

PubMed

Wu, Xue; Wu, Changxu

2017-01-01

This study revealed the numeric error patterns related to dosage when doctors prescribed in computerized physician order entry system. Error categories showed that the '6','7', and '9' key produced a higher incidence of errors in Numpad typing, while the '2','3', and '0' key produced a higher incidence of errors in main keyboard digit line typing. Errors categorized as omission and substitution were higher in prevalence than transposition and intrusion.

Ocean regional circulation model sensitizes to resolution of the lateral boundary conditions

NASA Astrophysics Data System (ADS)

Pham, Van Sy; Hwang, Jin Hwan

2017-04-01

Dynamical downscaling with nested regional oceanographic models is an effective approach for forecasting operationally coastal weather and projecting long term climate on the ocean. Nesting procedures deliver the unwanted in dynamic downscaling due to the differences of numerical grid sizes and updating steps. Therefore, such unavoidable errors restrict the application of the Ocean Regional Circulation Model (ORCMs) in both short-term forecasts and long-term projections. The current work identifies the effects of errors induced by computational limitations during nesting procedures on the downscaled results of the ORCMs. The errors are quantitatively evaluated for each error source and its characteristics by the Big-Brother Experiments (BBE). The BBE separates identified errors from each other and quantitatively assess the amount of uncertainties employing the same model to simulate for both nesting and nested model. Here, we focus on discussing errors resulting from two main matters associated with nesting procedures. They should be the spatial grids' differences and the temporal updating steps. After the diverse cases from separately running of the BBE, a Taylor diagram was adopted to analyze the results and suggest an optimization intern of grid size and updating period and domain sizes. Key words: lateral boundary condition, error, ocean regional circulation model, Big-Brother Experiment. Acknowledgement: This research was supported by grants from the Korean Ministry of Oceans and Fisheries entitled "Development of integrated estuarine management system" and a National Research Foundation of Korea (NRF) Grant (No. 2015R1A5A 7037372) funded by MSIP of Korea. The authors thank the Integrated Research Institute of Construction and Environmental Engineering of Seoul National University for administrative support.

Accurate fluid force measurement based on control surface integration

NASA Astrophysics Data System (ADS)

Lentink, David

2018-01-01

Nonintrusive 3D fluid force measurements are still challenging to conduct accurately for freely moving animals, vehicles, and deforming objects. Two techniques, 3D particle image velocimetry (PIV) and a new technique, the aerodynamic force platform (AFP), address this. Both rely on the control volume integral for momentum; whereas PIV requires numerical integration of flow fields, the AFP performs the integration mechanically based on rigid walls that form the control surface. The accuracy of both PIV and AFP measurements based on the control surface integration is thought to hinge on determining the unsteady body force associated with the acceleration of the volume of displaced fluid. Here, I introduce a set of non-dimensional error ratios to show which fluid and body parameters make the error negligible. The unsteady body force is insignificant in all conditions where the average density of the body is much greater than the density of the fluid, e.g., in gas. Whenever a strongly deforming body experiences significant buoyancy and acceleration, the error is significant. Remarkably, this error can be entirely corrected for with an exact factor provided that the body has a sufficiently homogenous density or acceleration distribution, which is common in liquids. The correction factor for omitting the unsteady body force, {{{ {ρ f}} {1 - {ρ f} ( {{ρ b}+{ρ f}} )}.{( {{{{ρ }}b}+{ρ f}} )}}} , depends only on the fluid, {ρ f}, and body, {{ρ }}b, density. Whereas these straightforward solutions work even at the liquid-gas interface in a significant number of cases, they do not work for generalized bodies undergoing buoyancy in combination with appreciable body density inhomogeneity, volume change (PIV), or volume rate-of-change (PIV and AFP). In these less common cases, the 3D body shape needs to be measured and resolved in time and space to estimate the unsteady body force. The analysis shows that accounting for the unsteady body force is straightforward to non-intrusively and accurately determine fluid force in most applications.

Comparison of transport properties models for numerical simulations of Mars entry vehicles

NASA Astrophysics Data System (ADS)

Hao, Jiaao; Wang, Jingying; Gao, Zhenxun; Jiang, Chongwen; Lee, Chunhian

2017-01-01

Effects of two different models for transport properties, including the approximate model and the collision integral model, on hypersonic flow simulations of Mars entry vehicles are numerically investigated. A least square fitting is firstly performed using the best-available data of collision integrals for Martian atmosphere species within the temperature range of 300-20,000 K. Then, the performance of these two transport properties models are compared for an equilibrium Martian atmosphere gas mixture at 10 kPa and temperatures ranging from 1000 to 10,000 K. Finally, four flight conditions chosen from the trajectory of the Mars Pathfinder entry vehicle are numerically simulated. It is indicated that the approximate model is capable of accurately providing the distributions of species mass fractions and temperatures in the flowfield. Both models give similar translational-rotational and vibrational heat fluxes. However, the chemical diffusion heat fluxes predicted by the approximate model are significantly larger than the results computed by the collision integral model, particularly in the vicinity of the forebody stagnation point, whose maximum relative error of 15% for the super-catalytic case. The diffusion model employed in the approximate model is responsible to the discrepancy. In addition, the wake structure is largely unaffected by the transport properties models.

Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow

NASA Astrophysics Data System (ADS)

Henshaw, William D.; Schwendeman, Donald W.

2006-08-01

We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows that demonstrate the use and accuracy of the numerical approach.

A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

NASA Technical Reports Server (NTRS)

Radhadrishnan, Krishnan

1993-01-01

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

PubMed

Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

2014-10-01

Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Arnold, Andrea; Calvetti, Daniela; Somersalo, Erkki

2014-10-01

A commonly encountered problem in numerous areas of applications is to estimate the unknown coefficients of a dynamical system from direct or indirect observations at discrete times of some of the components of the state vector. A related problem is to estimate unobserved components of the state. An egregious example of such a problem is provided by metabolic models, in which the numerous model parameters and the concentrations of the metabolites in tissue are to be estimated from concentration data in the blood. A popular method for addressing similar questions in stochastic and turbulent dynamics is the ensemble Kalman filter (EnKF), a particle-based filtering method that generalizes classical Kalman filtering. In this work, we adapt the EnKF algorithm for deterministic systems in which the numerical approximation error is interpreted as a stochastic drift with variance based on classical error estimates of numerical integrators. This approach, which is particularly suitable for stiff systems where the stiffness may depend on the parameters, allows us to effectively exploit the parallel nature of particle methods. Moreover, we demonstrate how spatial prior information about the state vector, which helps the stability of the computed solution, can be incorporated into the filter. The viability of the approach is shown by computed examples, including a metabolic system modeling an ischemic episode in skeletal muscle, with a high number of unknown parameters.

Fuzzy Adaptive Cubature Kalman Filter for Integrated Navigation Systems.

PubMed

Tseng, Chien-Hao; Lin, Sheng-Fuu; Jwo, Dah-Jing

2016-07-26

This paper presents a sensor fusion method based on the combination of cubature Kalman filter (CKF) and fuzzy logic adaptive system (FLAS) for the integrated navigation systems, such as the GPS/INS (Global Positioning System/inertial navigation system) integration. The third-degree spherical-radial cubature rule applied in the CKF has been employed to avoid the numerically instability in the system model. In processing navigation integration, the performance of nonlinear filter based estimation of the position and velocity states may severely degrade caused by modeling errors due to dynamics uncertainties of the vehicle. In order to resolve the shortcoming for selecting the process noise covariance through personal experience or numerical simulation, a scheme called the fuzzy adaptive cubature Kalman filter (FACKF) is presented by introducing the FLAS to adjust the weighting factor of the process noise covariance matrix. The FLAS is incorporated into the CKF framework as a mechanism for timely implementing the tuning of process noise covariance matrix based on the information of degree of divergence (DOD) parameter. The proposed FACKF algorithm shows promising accuracy improvement as compared to the extended Kalman filter (EKF), unscented Kalman filter (UKF), and CKF approaches.

Fuzzy Adaptive Cubature Kalman Filter for Integrated Navigation Systems

PubMed Central

Tseng, Chien-Hao; Lin, Sheng-Fuu; Jwo, Dah-Jing

2016-01-01

This paper presents a sensor fusion method based on the combination of cubature Kalman filter (CKF) and fuzzy logic adaptive system (FLAS) for the integrated navigation systems, such as the GPS/INS (Global Positioning System/inertial navigation system) integration. The third-degree spherical-radial cubature rule applied in the CKF has been employed to avoid the numerically instability in the system model. In processing navigation integration, the performance of nonlinear filter based estimation of the position and velocity states may severely degrade caused by modeling errors due to dynamics uncertainties of the vehicle. In order to resolve the shortcoming for selecting the process noise covariance through personal experience or numerical simulation, a scheme called the fuzzy adaptive cubature Kalman filter (FACKF) is presented by introducing the FLAS to adjust the weighting factor of the process noise covariance matrix. The FLAS is incorporated into the CKF framework as a mechanism for timely implementing the tuning of process noise covariance matrix based on the information of degree of divergence (DOD) parameter. The proposed FACKF algorithm shows promising accuracy improvement as compared to the extended Kalman filter (EKF), unscented Kalman filter (UKF), and CKF approaches. PMID:27472336

Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme

NASA Astrophysics Data System (ADS)

Mandziuk, Margaret; Schlick, Tamar

1995-05-01

The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- ( Δt) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance ( Δt ≈ 7 fs here) leads to instability, and higher-order resonances ( n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.

Geometric Integration of Weakly Dissipative Systems

NASA Astrophysics Data System (ADS)

Modin, K.; Führer, C.; Soöderlind, G.

2009-09-01

Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.

Spectral combination of spherical gravitational curvature boundary-value problems

NASA Astrophysics Data System (ADS)

PitoÅák, Martin; Eshagh, Mehdi; Šprlák, Michal; Tenzer, Robert; Novák, Pavel

2018-04-01

Four solutions of the spherical gravitational curvature boundary-value problems can be exploited for the determination of the Earth's gravitational potential. In this article we discuss the combination of simulated satellite gravitational curvatures, i.e., components of the third-order gravitational tensor, by merging these solutions using the spectral combination method. For this purpose, integral estimators of biased- and unbiased-types are derived. In numerical studies, we investigate the performance of the developed mathematical models for the gravitational field modelling in the area of Central Europe based on simulated satellite measurements. Firstly, we verify the correctness of the integral estimators for the spectral downward continuation by a closed-loop test. Estimated errors of the combined solution are about eight orders smaller than those from the individual solutions. Secondly, we perform a numerical experiment by considering the Gaussian noise with the standard deviation of 6.5× 10-17 m-1s-2 in the input data at the satellite altitude of 250 km above the mean Earth sphere. This value of standard deviation is equivalent to a signal-to-noise ratio of 10. Superior results with respect to the global geopotential model TIM-r5 are obtained by the spectral downward continuation of the vertical-vertical-vertical component with the standard deviation of 2.104 m2s-2, but the root mean square error is the largest and reaches 9.734 m2s-2. Using the spectral combination of all gravitational curvatures the root mean square error is more than 400 times smaller but the standard deviation reaches 17.234 m2s-2. The combination of more components decreases the root mean square error of the corresponding solutions while the standard deviations of the combined solutions do not improve as compared to the solution from the vertical-vertical-vertical component. The presented method represents a weight mean in the spectral domain that minimizes the root mean square error of the combined solutions and improves standard deviation of the solution based only on the least accurate components.

Windowed Green function method for the Helmholtz equation in the presence of multiply layered media

NASA Astrophysics Data System (ADS)

Bruno, O. P.; Pérez-Arancibia, C.

2017-06-01

This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in the presence of an arbitrary number of penetrable layers. Relying on the use of certain slow-rise windowing functions, the proposed windowed Green function approach efficiently evaluates oscillatory integrals over unbounded domains, with high accuracy, without recourse to the highly expensive Sommerfeld integrals that have typically been used to account for the effect of underlying planar multilayer structures. The proposed methodology, whose theoretical basis was presented in the recent contribution (Bruno et al. 2016 SIAM J. Appl. Math. 76, 1871-1898. (doi:10.1137/15M1033782)), is fast, accurate, flexible and easy to implement. Our numerical experiments demonstrate that the numerical errors resulting from the proposed approach decrease faster than any negative power of the window size. In a number of examples considered in this paper, the proposed method is up to thousands of times faster, for a given accuracy, than corresponding methods based on the use of Sommerfeld integrals.

Windowed Green function method for the Helmholtz equation in the presence of multiply layered media.

PubMed

Bruno, O P; Pérez-Arancibia, C

2017-06-01

This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in the presence of an arbitrary number of penetrable layers. Relying on the use of certain slow-rise windowing functions, the proposed windowed Green function approach efficiently evaluates oscillatory integrals over unbounded domains, with high accuracy, without recourse to the highly expensive Sommerfeld integrals that have typically been used to account for the effect of underlying planar multilayer structures. The proposed methodology, whose theoretical basis was presented in the recent contribution (Bruno et al. 2016 SIAM J. Appl. Math. 76 , 1871-1898. (doi:10.1137/15M1033782)), is fast, accurate, flexible and easy to implement. Our numerical experiments demonstrate that the numerical errors resulting from the proposed approach decrease faster than any negative power of the window size. In a number of examples considered in this paper, the proposed method is up to thousands of times faster, for a given accuracy, than corresponding methods based on the use of Sommerfeld integrals.

Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Jinxing; Pu Zuyin; Xie Lun

Charged particle dynamics in magnetosphere has temporal and spatial multiscale; therefore, numerical accuracy over a long integration time is required. A variational symplectic integrator (VSI) [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008) and H. Qin, X. Guan, and W. M. Tang, Phys. Plasmas 16, 042510 (2009)] for the guiding-center motion of charged particles in general magnetic field is applied to study the dynamics of charged particles in magnetosphere. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing themore » dynamics. The VSI conserves exactly a discrete Lagrangian symplectic structure and has better numerical properties over a long integration time, compared with standard integrators, such as the standard and adaptive fourth order Runge-Kutta (RK4) methods. Applying the VSI method to guiding-center dynamics in the inner magnetosphere, we can accurately calculate the particles'orbits for an arbitrary long simulating time with good conservation property. When a time-independent convection and corotation electric field is considered, the VSI method can give the accurate single particle orbit, while the RK4 method gives an incorrect orbit due to its intrinsic error accumulation over a long integrating time.« less

Nonspinning numerical relativity waveform surrogates: assessing the model

NASA Astrophysics Data System (ADS)

Field, Scott; Blackman, Jonathan; Galley, Chad; Scheel, Mark; Szilagyi, Bela; Tiglio, Manuel

2015-04-01

Recently, multi-modal gravitational waveform surrogate models have been built directly from data numerically generated by the Spectral Einstein Code (SpEC). I will describe ways in which the surrogate model error can be quantified. This task, in turn, requires (i) characterizing differences between waveforms computed by SpEC with those predicted by the surrogate model and (ii) estimating errors associated with the SpEC waveforms from which the surrogate is built. Both pieces can have numerous sources of numerical and systematic errors. We make an attempt to study the most dominant error sources and, ultimately, the surrogate model's fidelity. These investigations yield information about the surrogate model's uncertainty as a function of time (or frequency) and parameter, and could be useful in parameter estimation studies which seek to incorporate model error. Finally, I will conclude by comparing the numerical relativity surrogate model to other inspiral-merger-ringdown models. A companion talk will cover the building of multi-modal surrogate models.

Automatic alignment for three-dimensional tomographic reconstruction

NASA Astrophysics Data System (ADS)

van Leeuwen, Tristan; Maretzke, Simon; Joost Batenburg, K.

2018-02-01

In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to reconstruct the object. Given noisy and incomplete measurements, the inverse problem is typically solved through a regularized least-squares approach. A challenge for both approaches is that in practice the exact directions and offsets of the x-rays are only known approximately due to, e.g. calibration errors. Such errors lead to artifacts in the reconstructed image. In the case of sufficient sampling and geometrically simple misalignment, the measurements can be corrected by exploiting so-called consistency conditions. In other cases, such conditions may not apply and we have to solve an additional inverse problem to retrieve the angles and shifts. In this paper we propose a general algorithmic framework for retrieving these parameters in conjunction with an algebraic reconstruction technique. The proposed approach is illustrated by numerical examples for both simulated data and an electron tomography dataset.

A new smooth robust control design for uncertain nonlinear systems with non-vanishing disturbances

NASA Astrophysics Data System (ADS)

Xian, Bin; Zhang, Yao

2016-06-01

In this paper, we consider the control problem for a general class of nonlinear system subjected to uncertain dynamics and non-varnishing disturbances. A smooth nonlinear control algorithm is presented to tackle these uncertainties and disturbances. The proposed control design employs the integral of a nonlinear sigmoid function to compensate the uncertain dynamics, and achieve a uniformly semi-global practical asymptotic stable tracking control of the system outputs. A novel Lyapunov-based stability analysis is employed to prove the convergence of the tracking errors and the stability of the closed-loop system. Numerical simulation results on a two-link robot manipulator are presented to illustrate the performance of the proposed control algorithm comparing with the layer-boundary sliding mode controller and the robust of integration of sign of error control design. Furthermore, real-time experiment results for the attitude control of a quadrotor helicopter are also included to confirm the effectiveness of the proposed algorithm.

Eulerian-Lagrangian Simulations of Transonic Flutter Instabilities

NASA Technical Reports Server (NTRS)

Bendiksen, Oddvar O.

1994-01-01

This paper presents an overview of recent applications of Eulerian-Lagrangian computational schemes in simulating transonic flutter instabilities. This approach, the fluid-structure system is treated as a single continuum dynamics problem, by switching from an Eulerian to a Lagrangian formulation at the fluid-structure boundary. This computational approach effectively eliminates the phase integration errors associated with previous methods, where the fluid and structure are integrated sequentially using different schemes. The formulation is based on Hamilton's Principle in mixed coordinates, and both finite volume and finite element discretization schemes are considered. Results from numerical simulations of transonic flutter instabilities are presented for isolated wings, thin panels, and turbomachinery blades. The results suggest that the method is capable of reproducing the energy exchange between the fluid and the structure with significantly less error than existing methods. Localized flutter modes and panel flutter modes involving traveling waves can also be simulated effectively with no a priori knowledge of the type of instability involved.

Multi-Objective Control Optimization for Greenhouse Environment Using Evolutionary Algorithms

PubMed Central

Hu, Haigen; Xu, Lihong; Wei, Ruihua; Zhu, Bingkun

2011-01-01

This paper investigates the issue of tuning the Proportional Integral and Derivative (PID) controller parameters for a greenhouse climate control system using an Evolutionary Algorithm (EA) based on multiple performance measures such as good static-dynamic performance specifications and the smooth process of control. A model of nonlinear thermodynamic laws between numerous system variables affecting the greenhouse climate is formulated. The proposed tuning scheme is tested for greenhouse climate control by minimizing the integrated time square error (ITSE) and the control increment or rate in a simulation experiment. The results show that by tuning the gain parameters the controllers can achieve good control performance through step responses such as small overshoot, fast settling time, and less rise time and steady state error. Besides, it can be applied to tuning the system with different properties, such as strong interactions among variables, nonlinearities and conflicting performance criteria. The results implicate that it is a quite effective and promising tuning method using multi-objective optimization algorithms in the complex greenhouse production. PMID:22163927

An optimization-based integrated controls-structures design methodology for flexible space structures

NASA Technical Reports Server (NTRS)

Maghami, Peiman G.; Joshi, Suresh M.; Armstrong, Ernest S.

1993-01-01

An approach for an optimization-based integrated controls-structures design is presented for a class of flexible spacecraft that require fine attitude pointing and vibration suppression. The integrated design problem is posed in the form of simultaneous optimization of both structural and control design variables. The approach is demonstrated by application to the integrated design of a generic space platform and to a model of a ground-based flexible structure. The numerical results obtained indicate that the integrated design approach can yield spacecraft designs that have substantially superior performance over a conventional design wherein the structural and control designs are performed sequentially. For example, a 40-percent reduction in the pointing error is observed along with a slight reduction in mass, or an almost twofold increase in the controlled performance is indicated with more than a 5-percent reduction in the overall mass of the spacecraft (a reduction of hundreds of kilograms).

Towards efficient backward-in-time adjoint computations using data compression techniques

DOE PAGES

Cyr, E. C.; Shadid, J. N.; Wildey, T.

2014-12-16

In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for themore » difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.« less

Estimating Coastal Digital Elevation Model (DEM) Uncertainty

NASA Astrophysics Data System (ADS)

Amante, C.; Mesick, S.

2017-12-01

Integrated bathymetric-topographic digital elevation models (DEMs) are representations of the Earth's solid surface and are fundamental to the modeling of coastal processes, including tsunami, storm surge, and sea-level rise inundation. Deviations in elevation values from the actual seabed or land surface constitute errors in DEMs, which originate from numerous sources, including: (i) the source elevation measurements (e.g., multibeam sonar, lidar), (ii) the interpolative gridding technique (e.g., spline, kriging) used to estimate elevations in areas unconstrained by source measurements, and (iii) the datum transformation used to convert bathymetric and topographic data to common vertical reference systems. The magnitude and spatial distribution of the errors from these sources are typically unknown, and the lack of knowledge regarding these errors represents the vertical uncertainty in the DEM. The National Oceanic and Atmospheric Administration (NOAA) National Centers for Environmental Information (NCEI) has developed DEMs for more than 200 coastal communities. This study presents a methodology developed at NOAA NCEI to derive accompanying uncertainty surfaces that estimate DEM errors at the individual cell-level. The development of high-resolution (1/9th arc-second), integrated bathymetric-topographic DEMs along the southwest coast of Florida serves as the case study for deriving uncertainty surfaces. The estimated uncertainty can then be propagated into the modeling of coastal processes that utilize DEMs. Incorporating the uncertainty produces more reliable modeling results, and in turn, better-informed coastal management decisions.

A characteristic based volume penalization method for general evolution problems applied to compressible viscous flows

NASA Astrophysics Data System (ADS)

Brown-Dymkoski, Eric; Kasimov, Nurlybek; Vasilyev, Oleg V.

2014-04-01

In order to introduce solid obstacles into flows, several different methods are used, including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations. One well known method is Brinkman penalization, which models solid obstacles as porous media. While it has been adapted for compressible, incompressible, viscous and inviscid flows, it is limited in the types of boundary conditions that it imposes, as are most volume penalization methods. Typically, approaches are limited to Dirichlet boundary conditions. In this paper, Brinkman penalization is extended for generalized Neumann and Robin boundary conditions by introducing hyperbolic penalization terms with characteristics pointing inward on solid obstacles. This Characteristic-Based Volume Penalization (CBVP) method is a comprehensive approach to conditions on immersed boundaries, providing for homogeneous and inhomogeneous Dirichlet, Neumann, and Robin boundary conditions on hyperbolic and parabolic equations. This CBVP method can be used to impose boundary conditions for both integrated and non-integrated variables in a systematic manner that parallels the prescription of exact boundary conditions. Furthermore, the method does not depend upon a physical model, as with porous media approach for Brinkman penalization, and is therefore flexible for various physical regimes and general evolutionary equations. Here, the method is applied to scalar diffusion and to direct numerical simulation of compressible, viscous flows. With the Navier-Stokes equations, both homogeneous and inhomogeneous Neumann boundary conditions are demonstrated through external flow around an adiabatic and heated cylinder. Theoretical and numerical examination shows that the error from penalized Neumann and Robin boundary conditions can be rigorously controlled through an a priori penalization parameter η. The error on a transient boundary is found to converge as O(η), which is more favorable than the error convergence of the already established Dirichlet boundary condition.

The orbit of asteroid (99942) Apophis as determined from optical and radar observations

NASA Astrophysics Data System (ADS)

Vinogradova, T. A.; Kochetova, O. M.; Chernetenko, Yu. A.; Shor, V. A.; Yagudina, E. I.

2008-08-01

The results of improving the orbit accuracy for the asteroid Apophis and the circumstances of its approach to Earth in 2029 are described. Gravitational perturbations from all of the major planets and Pluto, Ceres, Pallas, and Vesta are taken into account in the equations of motion of the asteroid. Relativistic perturbations from the Sun and perturbations due to the oblateness of the Sun and Earth and due to the light pressure are also included in the model. Perturbations from the Earth and Moon are considered separately. The coordinates of the perturbing bodies are calculated using DE405. The phase correction and the gravitational deflection of light are taken into account. The numerical integration of the equations of motion and equations in variations is performed by the 15th-order Everhart method. The error of the numerical integration over the 2005 2029 interval, estimated using forward and backward computations, is not more than 3 × 10-11 AU. Improved coordinates and velocities at epoch JD2454200.5 (April 10, 2007) were obtained applying the weighted leastsquares fit. For the period from March 15, 2004, to August 16, 2006, 989 optical and 7 radar observations were used. The resulting system represents the optical observations with an error of 0.37 (66 conditional equations were rejected). The residuals of the radar observations are an order, or more, smaller than their errors. The system of Apophis’ elements and the estimates of their precision obtained in this study are in perfect agreement with the results published by other authors. The minimum Apophis-Earth distance is about 38 200 km on April 13, 2029. This estimate agrees to within 20 km with those calculated based on other published systems of elements. The effect of some model components on the minimum distance is estimated.

An Empirical Evaluation of Five Circular Error Probable Estimation Techniques and a Method for Improving Them

DTIC Science & Technology

1993-03-10

template which runs a Romberg algorithm in the background to numerically integrate the BVN [12:257]. Appendix A als- lists the results from two other...for computing these values: a Taylor series expansion, the Romberg algorithm , and the CBN technique. Appendix A lists CEPpop. values for eleven...determining factor in this selection process. Of the 175 populations ex- amined in the experiment, the MathCAD version of the Romberg algorithm failed

Comparison of Aircraft Models and Integration Schemes for Interval Management in the TRACON

NASA Technical Reports Server (NTRS)

Neogi, Natasha; Hagen, George E.; Herencia-Zapana, Heber

2012-01-01

Reusable models of common elements for communication, computation, decision and control in air traffic management are necessary in order to enable simulation, analysis and assurance of emergent properties, such as safety and stability, for a given operational concept. Uncertainties due to faults, such as dropped messages, along with non-linearities and sensor noise are an integral part of these models, and impact emergent system behavior. Flight control algorithms designed using a linearized version of the flight mechanics will exhibit error due to model uncertainty, and may not be stable outside a neighborhood of the given point of linearization. Moreover, the communication mechanism by which the sensed state of an aircraft is fed back to a flight control system (such as an ADS-B message) impacts the overall system behavior; both due to sensor noise as well as dropped messages (vacant samples). Additionally simulation of the flight controller system can exhibit further numerical instability, due to selection of the integration scheme and approximations made in the flight dynamics. We examine the theoretical and numerical stability of a speed controller under the Euler and Runge-Kutta schemes of integration, for the Maintain phase for a Mid-Term (2035-2045) Interval Management (IM) Operational Concept for descent and landing operations. We model uncertainties in communication due to missed ADS-B messages by vacant samples in the integration schemes, and compare the emergent behavior of the system, in terms of stability, via the boundedness of the final system state. Any bound on the errors incurred by these uncertainties will play an essential part in a composable assurance argument required for real-time, flight-deck guidance and control systems,. Thus, we believe that the creation of reusable models, which possess property guarantees, such as safety and stability, is an innovative and essential requirement to assessing the emergent properties of novel airspace concepts of operation.

Computation of Sound Propagation by Boundary Element Method

NASA Technical Reports Server (NTRS)

Guo, Yueping

2005-01-01

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Distance Measurement Error in Time-of-Flight Sensors Due to Shot Noise

PubMed Central

Illade-Quinteiro, Julio; Brea, Víctor M.; López, Paula; Cabello, Diego; Doménech-Asensi, Gines

2015-01-01

Unlike other noise sources, which can be reduced or eliminated by different signal processing techniques, shot noise is an ever-present noise component in any imaging system. In this paper, we present an in-depth study of the impact of shot noise on time-of-flight sensors in terms of the error introduced in the distance estimation. The paper addresses the effect of parameters, such as the size of the photosensor, the background and signal power or the integration time, and the resulting design trade-offs. The study is demonstrated with different numerical examples, which show that, in general, the phase shift determination technique with two background measurements approach is the most suitable for pixel arrays of large resolution. PMID:25723141

Quantifying errors in trace species transport modeling.

PubMed

Prather, Michael J; Zhu, Xin; Strahan, Susan E; Steenrod, Stephen D; Rodriguez, Jose M

2008-12-16

One expectation when computationally solving an Earth system model is that a correct answer exists, that with adequate physical approximations and numerical methods our solutions will converge to that single answer. With such hubris, we performed a controlled numerical test of the atmospheric transport of CO(2) using 2 models known for accurate transport of trace species. Resulting differences were unexpectedly large, indicating that in some cases, scientific conclusions may err because of lack of knowledge of the numerical errors in tracer transport models. By doubling the resolution, thereby reducing numerical error, both models show some convergence to the same answer. Now, under realistic conditions, we identify a practical approach for finding the correct answer and thus quantifying the advection error.

Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes

NASA Astrophysics Data System (ADS)

Clark, Martyn P.; Kavetski, Dmitri

2010-10-01

A major neglected weakness of many current hydrological models is the numerical method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping schemes in terms of numerical reliability and computational efficiency in the context of conceptual hydrological modeling. Numerical experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the numerical errors of fixed-step explicit schemes commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where numerical errors compensate for model structural errors. Simply running fixed-step explicit schemes with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit schemes with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping schemes investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of numerical errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust numerical implementation.

IMPROVED PERFORMANCES IN SUBSONIC FLOWS OF AN SPH SCHEME WITH GRADIENTS ESTIMATED USING AN INTEGRAL APPROACH

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valdarnini, R., E-mail: valda@sissa.it

In this paper, we present results from a series of hydrodynamical tests aimed at validating the performance of a smoothed particle hydrodynamics (SPH) formulation in which gradients are derived from an integral approach. We specifically investigate the code behavior with subsonic flows, where it is well known that zeroth-order inconsistencies present in standard SPH make it particularly problematic to correctly model the fluid dynamics. In particular, we consider the Gresho–Chan vortex problem, the growth of Kelvin–Helmholtz instabilities, the statistics of driven subsonic turbulence and the cold Keplerian disk problem. We compare simulation results for the different tests with those obtained,more » for the same initial conditions, using standard SPH. We also compare the results with the corresponding ones obtained previously with other numerical methods, such as codes based on a moving-mesh scheme or Godunov-type Lagrangian meshless methods. We quantify code performances by introducing error norms and spectral properties of the particle distribution, in a way similar to what was done in other works. We find that the new SPH formulation exhibits strongly reduced gradient errors and outperforms standard SPH in all of the tests considered. In fact, in terms of accuracy, we find good agreement between the simulation results of the new scheme and those produced using other recently proposed numerical schemes. These findings suggest that the proposed method can be successfully applied for many astrophysical problems in which the presence of subsonic flows previously limited the use of SPH, with the new scheme now being competitive in these regimes with other numerical methods.« less

Neural system for heartbeats recognition using genetically integrated ensemble of classifiers.

PubMed

Osowski, Stanislaw; Siwek, Krzysztof; Siroic, Robert

2011-03-01

This paper presents the application of genetic algorithm for the integration of neural classifiers combined in the ensemble for the accurate recognition of heartbeat types on the basis of ECG registration. The idea presented in this paper is that using many classifiers arranged in the form of ensemble leads to the increased accuracy of the recognition. In such ensemble the important problem is the integration of all classifiers into one effective classification system. This paper proposes the use of genetic algorithm. It was shown that application of the genetic algorithm is very efficient and allows to reduce significantly the total error of heartbeat recognition. This was confirmed by the numerical experiments performed on the MIT BIH Arrhythmia Database. Copyright © 2011 Elsevier Ltd. All rights reserved.

Analytical approximation of a distorted reflector surface defined by a discrete set of points

NASA Technical Reports Server (NTRS)

Acosta, Roberto J.; Zaman, Afroz A.

1988-01-01

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

An improved lambda-scheme for one-dimensional flows

NASA Technical Reports Server (NTRS)

Moretti, G.; Dipiano, M. T.

1983-01-01

A code for the calculation of one-dimensional flows is presented, which combines a simple and efficient version of the lambda-scheme with tracking of discontinuities. The latter is needed to identify points where minor departures from the basic integration scheme are applied to prevent infiltration of numerical errors. Such a tracking is obtained via a systematic application of Boolean algebra. It is, therefore, very efficient. Fifteen examples are presented and discussed in detail. The results are exceptionally good. All discontinuites are captured within one mesh interval.

Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kube, Susanna; Lasser, Caroline; Weber, Marcus

2009-04-01

The article addresses the achievable accuracy for a Monte Carlo sampling of Wigner functions in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The approximation of Wigner functions is realized by an adaption of the Metropolis algorithm for real-valued functions with disconnected support. The integration, which is necessary for computing values of the Wigner function, uses importance sampling with a Gaussian weight function. The numerical experiments agree with theoretical considerations and show an error of 2-3%.

Addressing global uncertainty and sensitivity in first-principles based microkinetic models by an adaptive sparse grid approach

NASA Astrophysics Data System (ADS)

Döpking, Sandra; Plaisance, Craig P.; Strobusch, Daniel; Reuter, Karsten; Scheurer, Christoph; Matera, Sebastian

2018-01-01

In the last decade, first-principles-based microkinetic modeling has been developed into an important tool for a mechanistic understanding of heterogeneous catalysis. A commonly known, but hitherto barely analyzed issue in this kind of modeling is the presence of sizable errors from the use of approximate Density Functional Theory (DFT). We here address the propagation of these errors to the catalytic turnover frequency (TOF) by global sensitivity and uncertainty analysis. Both analyses require the numerical quadrature of high-dimensional integrals. To achieve this efficiently, we utilize and extend an adaptive sparse grid approach and exploit the confinement of the strongly non-linear behavior of the TOF to local regions of the parameter space. We demonstrate the methodology on a model of the oxygen evolution reaction at the Co3O4 (110)-A surface, using a maximum entropy error model that imposes nothing but reasonable bounds on the errors. For this setting, the DFT errors lead to an absolute uncertainty of several orders of magnitude in the TOF. We nevertheless find that it is still possible to draw conclusions from such uncertain models about the atomistic aspects controlling the reactivity. A comparison with derivative-based local sensitivity analysis instead reveals that this more established approach provides incomplete information. Since the adaptive sparse grids allow for the evaluation of the integrals with only a modest number of function evaluations, this approach opens the way for a global sensitivity analysis of more complex models, for instance, models based on kinetic Monte Carlo simulations.

An evaluation of programmed treatment-integrity errors during discrete-trial instruction.

PubMed

Carroll, Regina A; Kodak, Tiffany; Fisher, Wayne W

2013-01-01

This study evaluated the effects of programmed treatment-integrity errors on skill acquisition for children with an autism spectrum disorder (ASD) during discrete-trial instruction (DTI). In Study 1, we identified common treatment-integrity errors that occur during academic instruction in schools. In Study 2, we simultaneously manipulated 3 integrity errors during DTI. In Study 3, we evaluated the effects of each of the 3 integrity errors separately on skill acquisition during DTI. Results showed that participants either demonstrated slower skill acquisition or did not acquire the target skills when instruction included treatment-integrity errors. © Society for the Experimental Analysis of Behavior.

Transforming high-dimensional potential energy surfaces into sum-of-products form using Monte Carlo methods

NASA Astrophysics Data System (ADS)

Schröder, Markus; Meyer, Hans-Dieter

2017-08-01

We propose a Monte Carlo method, "Monte Carlo Potfit," for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Tucker form. To this end we use a variational ansatz in which we replace numerically exact integrals with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows a treatment of surfaces up to 15-18 degrees of freedom. We furthermore show that the error made with this ansatz can be controlled and vanishes in certain limits. We present calculations on the potential of HFCO to demonstrate the features of the algorithm. To demonstrate the power of the method, we transformed a 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form and calculated the ground and lowest 26 vibrationally excited states of the Zundel cation with the multi-configuration time-dependent Hartree method.

Zero in the brain: A voxel-based lesion-symptom mapping study in right hemisphere damaged patients.

PubMed

Benavides-Varela, Silvia; Passarini, Laura; Butterworth, Brian; Rolma, Giuseppe; Burgio, Francesca; Pitteri, Marco; Meneghello, Francesca; Shallice, Tim; Semenza, Carlo

2016-04-01

Transcoding numerals containing zero is more problematic than transcoding numbers formed by non-zero digits. However, it is currently unknown whether this is due to zeros requiring brain areas other than those traditionally associated with number representation. Here we hypothesize that transcoding zeros entails visuo-spatial and integrative processes typically associated with the right hemisphere. The investigation involved 22 right-brain-damaged patients and 20 healthy controls who completed tests of reading and writing Arabic numbers. As expected, the most significant deficit among patients involved a failure to cope with zeros. Moreover, a voxel-based lesion-symptom mapping (VLSM) analysis showed that the most common zero-errors were maximally associated to the right insula which was previously related to sensorimotor integration, attention, and response selection, yet for the first time linked to transcoding processes. Error categories involving other digits corresponded to the so-called Neglect errors, which however, constituted only about 10% of the total reading and 3% of the writing mistakes made by the patients. We argue that damage to the right hemisphere impairs the mechanism of parsing, and the ability to set-up empty-slot structures required for processing zeros in complex numbers; moreover, we suggest that the brain areas located in proximity to the right insula play a role in the integration of the information resulting from the temporary application of transcoding procedures. Copyright © 2016 Elsevier Ltd. All rights reserved.

Computation of rapidly varied unsteady, free-surface flow

USGS Publications Warehouse

Basco, D.R.

1987-01-01

Many unsteady flows in hydraulics occur with relatively large gradients in free surface profiles. The assumption of hydrostatic pressure distribution with depth is no longer valid. These are rapidly-varied unsteady flows (RVF) of classical hydraulics and also encompass short wave propagation of coastal hydraulics. The purpose of this report is to present an introductory review of the Boussinnesq-type differential equations that describe these flows and to discuss methods for their numerical integration. On variable slopes and for large scale (finite-amplitude) disturbances, three independent derivational methods all gave differences in the motion equation for higher order terms. The importance of these higher-order terms for riverine applications must be determined by numerical experiments. Care must be taken in selection of the appropriate finite-difference scheme to minimize truncation error effects and the possibility of diverging (double mode) numerical solutions. It is recommended that practical hydraulics cases be established and tested numerically to demonstrate the order of differences in solution with those obtained from the long wave equations of St. Venant. (USGS)

Numerical Calculation of the Propagation of Spatial Coherence from Partially Coherent Sources.

DTIC Science & Technology

1982-10-01

can determine appropriate wj, aj, and n such that, for a given error e, I ° - 2~ jI "ja(E -E2) j Wj GoE1P -21,aj) < C,4 where x <a .(x,a) (5) 10 x > a...Since the major work in evaluating the integrand of JI (PI is in evaluating J[Efla(P2)], it is natural to express the integral in polar coordinates...The last step follows from observing that since OR w, OR 0’ < 2w- (OR + e’)- (4) eR e,0 < 0, eR + 61 >W The integration is treated as follows: JOR

Five-equation and robust three-equation methods for solution verification of large eddy simulation

NASA Astrophysics Data System (ADS)

Dutta, Rabijit; Xing, Tao

2018-02-01

This study evaluates the recently developed general framework for solution verification methods for large eddy simulation (LES) using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids. The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared with the numerical and modeling errors and therefore can be neglected. The authors recommend five-equation method based on Hypothesis II, which shows a monotonic convergence behavior of the predicted numerical benchmark ( S C ), and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predict the error trends. It was also observed that the numerical and modeling errors usually have opposite signs, which suggests error cancellation play an essential role in LES. When Reynolds averaged Navier-Stokes (RANS) based error estimation method is applied, it shows significant error in the prediction of S C on coarse meshes. However, it predicts reasonable S C when the grids resolve at least 80% of the total turbulent kinetic energy.

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-04-01

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integrationmore » methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.« less

An efficient HZETRN (a galactic cosmic ray transport code)

NASA Technical Reports Server (NTRS)

Shinn, Judy L.; Wilson, John W.

1992-01-01

An accurate and efficient engineering code for analyzing the shielding requirements against the high-energy galactic heavy ions is needed. The HZETRN is a deterministic code developed at Langley Research Center that is constantly under improvement both in physics and numerical computation and is targeted for such use. One problem area connected with the space-marching technique used in this code is the propagation of the local truncation error. By improving the numerical algorithms for interpolation, integration, and grid distribution formula, the efficiency of the code is increased by a factor of eight as the number of energy grid points is reduced. The numerical accuracy of better than 2 percent for a shield thickness of 150 g/cm(exp 2) is found when a 45 point energy grid is used. The propagating step size, which is related to the perturbation theory, is also reevaluated.

Two-Photon Transitions in Hydrogen-Like Atoms

NASA Astrophysics Data System (ADS)

Martinis, Mladen; Stojić, Marko

Different methods for evaluating two-photon transition amplitudes in hydrogen-like atoms are compared with the improved method of direct summation. Three separate contributions to the two-photon transition probabilities in hydrogen-like atoms are calculated. The first one coming from the summation over discrete intermediate states is performed up to nc(max) = 35. The second contribution from the integration over the continuum states is performed numerically. The third contribution coming from the summation from nc(max) to infinity is calculated in an approximate way using the mean level energy for this region. It is found that the choice of nc(max) controls the numerical error in the calculations and can be used to increase the accuracy of the results much more efficiently than in other methods.

Error analysis in some Gauss-Turan-Radau and Gauss-Turan-Lobatto quadratures for analytic functions

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2004-03-01

We consider the generalized Gauss-Turan quadrature formulae of Radau and Lobatto type for approximating . The aim of this paper is to analyze the remainder term in the case when f is an analytic function in some region of the complex plane containing the interval [-1,1] in its interior. The remainder term is presented in the form of a contour integral over confocal ellipses (cf. SIAM J. Numer. Anal. 80 (1983) 1170). Sufficient conditions on the convergence for some of such quadratures, associated with the generalized Chebyshev weight functions, are found. Using some ideas from Hunter (BIT 35 (1995) 64) we obtain new estimates of the remainder term, which are very exact. Some numerical results and illustrations are shown.

On the error propagation of semi-Lagrange and Fourier methods for advection problems☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2015-01-01

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme. PMID:25844018

Controlling Reflections from Mesh Refinement Interfaces in Numerical Relativity

NASA Technical Reports Server (NTRS)

Baker, John G.; Van Meter, James R.

2005-01-01

A leading approach to improving the accuracy on numerical relativity simulations of black hole systems is through fixed or adaptive mesh refinement techniques. We describe a generic numerical error which manifests as slowly converging, artificial reflections from refinement boundaries in a broad class of mesh-refinement implementations, potentially limiting the effectiveness of mesh- refinement techniques for some numerical relativity applications. We elucidate this numerical effect by presenting a model problem which exhibits the phenomenon, but which is simple enough that its numerical error can be understood analytically. Our analysis shows that the effect is caused by variations in finite differencing error generated across low and high resolution regions, and that its slow convergence is caused by the presence of dramatic speed differences among propagation modes typical of 3+1 relativity. Lastly, we resolve the problem, presenting a class of finite-differencing stencil modifications which eliminate this pathology in both our model problem and in numerical relativity examples.

PACOM: A Versatile Tool for Integrating, Filtering, Visualizing, and Comparing Multiple Large Mass Spectrometry Proteomics Data Sets.

PubMed

Martínez-Bartolomé, Salvador; Medina-Aunon, J Alberto; López-García, Miguel Ángel; González-Tejedo, Carmen; Prieto, Gorka; Navajas, Rosana; Salazar-Donate, Emilio; Fernández-Costa, Carolina; Yates, John R; Albar, Juan Pablo

2018-04-06

Mass-spectrometry-based proteomics has evolved into a high-throughput technology in which numerous large-scale data sets are generated from diverse analytical platforms. Furthermore, several scientific journals and funding agencies have emphasized the storage of proteomics data in public repositories to facilitate its evaluation, inspection, and reanalysis. (1) As a consequence, public proteomics data repositories are growing rapidly. However, tools are needed to integrate multiple proteomics data sets to compare different experimental features or to perform quality control analysis. Here, we present a new Java stand-alone tool, Proteomics Assay COMparator (PACOM), that is able to import, combine, and simultaneously compare numerous proteomics experiments to check the integrity of the proteomic data as well as verify data quality. With PACOM, the user can detect source of errors that may have been introduced in any step of a proteomics workflow and that influence the final results. Data sets can be easily compared and integrated, and data quality and reproducibility can be visually assessed through a rich set of graphical representations of proteomics data features as well as a wide variety of data filters. Its flexibility and easy-to-use interface make PACOM a unique tool for daily use in a proteomics laboratory. PACOM is available at https://github.com/smdb21/pacom .

Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

NASA Astrophysics Data System (ADS)

Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

2013-09-01

Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

Improving the satellite communication efficiency of the accumulative acknowledgement strategies

NASA Astrophysics Data System (ADS)

Duarte, Otto Carlos M. B.; de Lima, Heliomar Medeiros

The performances of two finite buffer error recovery strategies are analyzed. In both strategies the retransmission request decision between selective repeat and continuous retransmission is based on an imminent buffer overflow condition. These are accumulative acknowledgment schemes, but in the second strategy the selective-repeat control frame is uniquely an individual negative acknowledgment. The two strategies take advantage of the availability of a greater buffer capacity, making the most of the selective repeat, postponing the sending of a continuous retransmission request. Numerical results show a better performance very close to the ideal, but it does not integrally conform to the high-level data link control (HDLC) procedures. It is shown that these strategies are well suited for high-speed data transfer in the high-error-rate satellite environment.

Beam collimation and focusing and error analysis of LD and fiber coupling system based on ZEMAX

NASA Astrophysics Data System (ADS)

Qiao, Lvlin; Zhou, Dejian; Xiao, Lei

2017-10-01

Laser diodde has many advantages, such as high efficiency, small volume, low cost and easy integration, so it is widely used. Because of its poor beam quality, the application of semiconductor laser has also been seriously hampered. In view of the poor beam quality, the ZEMAX optical design software is used to simulate the far field characteristics of the semiconductor laser beam, and the coupling module of the semiconductor laser and the optical fiber is designed and optimized. And the beam is coupled into the fiber core diameter d=200µm, the numerical aperture NA=0.22 optical fiber, the output power can reach 95%. Finally, the influence of the three docking errors on the coupling efficiency during the installation process is analyzed.

On the accuracy and precision of numerical waveforms: effect of waveform extraction methodology

NASA Astrophysics Data System (ADS)

Chu, Tony; Fong, Heather; Kumar, Prayush; Pfeiffer, Harald P.; Boyle, Michael; Hemberger, Daniel A.; Kidder, Lawrence E.; Scheel, Mark A.; Szilagyi, Bela

2016-08-01

We present a new set of 95 numerical relativity simulations of non-precessing binary black holes (BBHs). The simulations sample comprehensively both black-hole spins up to spin magnitude of 0.9, and cover mass ratios 1-3. The simulations cover on average 24 inspiral orbits, plus merger and ringdown, with low initial orbital eccentricities e\\lt {10}-4. A subset of the simulations extends the coverage of non-spinning BBHs up to mass ratio q = 10. Gravitational waveforms at asymptotic infinity are computed with two independent techniques: extrapolation and Cauchy characteristic extraction. An error analysis based on noise-weighted inner products is performed. We find that numerical truncation error, error due to gravitational wave extraction, and errors due to the Fourier transformation of signals with finite length of the numerical waveforms are of similar magnitude, with gravitational wave extraction errors dominating at noise-weighted mismatches of ˜ 3× {10}-4. This set of waveforms will serve to validate and improve aligned-spin waveform models for gravitational wave science.

A constrained-gradient method to control divergence errors in numerical MHD

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2016-10-01

In numerical magnetohydrodynamics (MHD), a major challenge is maintaining nabla \\cdot {B}=0. Constrained transport (CT) schemes achieve this but have been restricted to specific methods. For more general (meshless, moving-mesh, ALE) methods, `divergence-cleaning' schemes reduce the nabla \\cdot {B} errors; however they can still be significant and can lead to systematic errors which converge away slowly. We propose a new constrained gradient (CG) scheme which augments these with a projection step, and can be applied to any numerical scheme with a reconstruction. This iteratively approximates the least-squares minimizing, globally divergence-free reconstruction of the fluid. Unlike `locally divergence free' methods, this actually minimizes the numerically unstable nabla \\cdot {B} terms, without affecting the convergence order of the method. We implement this in the mesh-free code GIZMO and compare various test problems. Compared to cleaning schemes, our CG method reduces the maximum nabla \\cdot {B} errors by ˜1-3 orders of magnitude (˜2-5 dex below typical errors if no nabla \\cdot {B} cleaning is used). By preventing large nabla \\cdot {B} at discontinuities, this eliminates systematic errors at jumps. Our CG results are comparable to CT methods; for practical purposes, the nabla \\cdot {B} errors are eliminated. The cost is modest, ˜30 per cent of the hydro algorithm, and the CG correction can be implemented in a range of numerical MHD methods. While for many problems, we find Dedner-type cleaning schemes are sufficient for good results, we identify a range of problems where using only Powell or `8-wave' cleaning can produce order-of-magnitude errors.

Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems

DOE PAGES

Najm, Habib N.; Valorani, Mauro

2014-04-12

We explore the relation between the development of a non-negligible probability of negative states and the instability of numerical integration of the intrusive Galerkin ordinary differential equation system describing uncertain chemical ignition. To prevent this instability without resorting to either multi-element local polynomial chaos (PC) methods or increasing the order of the PC representation in time, we propose a procedure aimed at modifying the amplitude of the PC modes to bring the probability of negative state values below a user-defined threshold. This modification can be effectively described as a filtering procedure of the spectral PC coefficients, which is applied on-the-flymore » during the numerical integration when the current value of the probability of negative states exceeds the prescribed threshold. We demonstrate the filtering procedure using a simple model of an ignition process in a batch reactor. This is carried out by comparing different observables and error measures as obtained by non-intrusive Monte Carlo and Gauss-quadrature integration and the filtered intrusive procedure. Lastly, the filtering procedure has been shown to effectively stabilize divergent intrusive solutions, and also to improve the accuracy of stable intrusive solutions which are close to the stability limits.« less

Case Mis-Conceptualization in Psychological Treatment: An Enduring Clinical Problem.

PubMed

Ridley, Charles R; Jeffrey, Christina E; Roberson, Richard B

2017-04-01

Case conceptualization, an integral component of mental health treatment, aims to facilitate therapeutic gains by formulating a clear picture of a client's psychological presentation. However, despite numerous attempts to improve this clinical activity, it remains unclear how well existing methods achieve their purported purpose. Case formulation is inconsistently defined in the literature and implemented in practice, with many methods varying in complexity, theoretical grounding, and empirical support. In addition, many of the methods demand a precise clinical acumen that is easily influenced by judgmental and inferential errors. These errors occur regardless of clinicians' level of training or amount of clinical experience. Overall, the lack of a consensus definition, a diversity of methods, and susceptibility of clinicians to errors are manifestations of the state of crisis in case conceptualization. This article, the 2nd in a series of 5 on thematic mapping, argues the need for more reliable and valid models of case conceptualization. © 2017 Wiley Periodicals, Inc.

Simulated forecast error and climate drift resulting from the omission of the upper stratosphere in numerical models

NASA Technical Reports Server (NTRS)

Boville, Byron A.; Baumhefner, David P.

1990-01-01

Using an NCAR community climate model, Version I, the forecast error growth and the climate drift resulting from the omission of the upper stratosphere are investigated. In the experiment, the control simulation is a seasonal integration of a medium horizontal general circulation model with 30 levels extending from the surface to the upper mesosphere, while the main experiment uses an identical model, except that only the bottom 15 levels (below 10 mb) are retained. It is shown that both random and systematic errors develop rapidly in the lower stratosphere with some local propagation into the troposphere in the 10-30-day time range. The random growth rate in the troposphere in the case of the altered upper boundary was found to be slightly faster than that for the initial-condition uncertainty alone. However, this is not likely to make a significant impact in operational forecast models, because the initial-condition uncertainty is very large.

Activity in the fronto-parietal network indicates numerical inductive reasoning beyond calculation: An fMRI study combined with a cognitive model

PubMed Central

Liang, Peipeng; Jia, Xiuqin; Taatgen, Niels A.; Borst, Jelmer P.; Li, Kuncheng

2016-01-01

Numerical inductive reasoning refers to the process of identifying and extrapolating the rule involved in numeric materials. It is associated with calculation, and shares the common activation of the fronto-parietal regions with calculation, which suggests that numerical inductive reasoning may correspond to a general calculation process. However, compared with calculation, rule identification is critical and unique to reasoning. Previous studies have established the central role of the fronto-parietal network for relational integration during rule identification in numerical inductive reasoning. The current question of interest is whether numerical inductive reasoning exclusively corresponds to calculation or operates beyond calculation, and whether it is possible to distinguish between them based on the activity pattern in the fronto-parietal network. To directly address this issue, three types of problems were created: numerical inductive reasoning, calculation, and perceptual judgment. Our results showed that the fronto-parietal network was more active in numerical inductive reasoning which requires more exchanges between intermediate representations and long-term declarative knowledge during rule identification. These results survived even after controlling for the covariates of response time and error rate. A computational cognitive model was developed using the cognitive architecture ACT-R to account for the behavioral results and brain activity in the fronto-parietal network. PMID:27193284

Activity in the fronto-parietal network indicates numerical inductive reasoning beyond calculation: An fMRI study combined with a cognitive model.

PubMed

Liang, Peipeng; Jia, Xiuqin; Taatgen, Niels A; Borst, Jelmer P; Li, Kuncheng

2016-05-19

Numerical inductive reasoning refers to the process of identifying and extrapolating the rule involved in numeric materials. It is associated with calculation, and shares the common activation of the fronto-parietal regions with calculation, which suggests that numerical inductive reasoning may correspond to a general calculation process. However, compared with calculation, rule identification is critical and unique to reasoning. Previous studies have established the central role of the fronto-parietal network for relational integration during rule identification in numerical inductive reasoning. The current question of interest is whether numerical inductive reasoning exclusively corresponds to calculation or operates beyond calculation, and whether it is possible to distinguish between them based on the activity pattern in the fronto-parietal network. To directly address this issue, three types of problems were created: numerical inductive reasoning, calculation, and perceptual judgment. Our results showed that the fronto-parietal network was more active in numerical inductive reasoning which requires more exchanges between intermediate representations and long-term declarative knowledge during rule identification. These results survived even after controlling for the covariates of response time and error rate. A computational cognitive model was developed using the cognitive architecture ACT-R to account for the behavioral results and brain activity in the fronto-parietal network.

An interval precise integration method for transient unbalance response analysis of rotor system with uncertainty

NASA Astrophysics Data System (ADS)

Fu, Chao; Ren, Xingmin; Yang, Yongfeng; Xia, Yebao; Deng, Wangqun

2018-07-01

A non-intrusive interval precise integration method (IPIM) is proposed in this paper to analyze the transient unbalance response of uncertain rotor systems. The transfer matrix method (TMM) is used to derive the deterministic equations of motion of a hollow-shaft overhung rotor. The uncertain transient dynamic problem is solved by combing the Chebyshev approximation theory with the modified precise integration method (PIM). Transient response bounds are calculated by interval arithmetic of the expansion coefficients. Theoretical error analysis of the proposed method is provided briefly, and its accuracy is further validated by comparing with the scanning method in simulations. Numerical results show that the IPIM can keep good accuracy in vibration prediction of the start-up transient process. Furthermore, the proposed method can also provide theoretical guidance to other transient dynamic mechanical systems with uncertainties.

Discrepancy-based error estimates for Quasi-Monte Carlo III. Error distributions and central limits

NASA Astrophysics Data System (ADS)

Hoogland, Jiri; Kleiss, Ronald

1997-04-01

In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-random point sets, we derive various results on the probability distribution of the integration error, which can be compared to the standard Central Limit Theorem for normal stochastic sampling. In many cases, a Gaussian error distribution is obtained.

Reducing oral and maxillofacial surgery resident risk exposure: lessons from graduate medical education reform.

PubMed

Buhrow, Suzanne Morse; Buhrow, Jack A

2013-12-01

It is estimated that, in the United States, more than 40,000 patients are injured each day because of preventable medical errors. Although numerous studies examine the causes of medical trainee errors and efforts to mitigate patient injuries in this population, little research exists on adverse events experienced by oral and maxillofacial surgery (OMFS) residents or strategies to improve patient safety awareness in OMFS residency programs. The authors conducted a retrospective literature review of contemporary studies on medical trainees' reported risk exposure and the impact of integrating evidence-based patient safety training into residency curricula. A review of the literature suggests that OMFS residents face similar risks as medical trainees in medical, surgical, and anesthesia residency programs and may benefit from integrating competency-based safety training in the OMFS residency curriculum. OMFS trainees face particular challenges when transitioning from dental student to surgical resident, particularly related to their limited clinical exposure to high-reliability organizations, which may place them at higher risk than other medical trainees. OMFS educators should establish resident competence in patient safety principles and system improvement strategies throughout the training period.

A periodic review integrated inventory model with controllable setup cost, imperfect items, and inspection errors under service level constraint

NASA Astrophysics Data System (ADS)

Saga, R. S.; Jauhari, W. A.; Laksono, P. W.

2017-11-01

This paper presents an integrated inventory model which consists of single vendor and buyer. The buyer managed its inventory periodically and orders products from the vendor to satisfy the end customer’s demand, where the annual demand and the ordering cost were in the fuzzy environment. The buyer used a service level constraint instead of the stock-out cost term, so that the stock-out level per cycle was bounded. Then, the vendor produced and delivered products to the buyer. The vendor had a choice to commit an investment to reduce the setup cost. However, the vendor’s production process was imperfect, thus the lot delivered contained some defective products. Moreover, the buyer’s inspection process was not error-free since the inspector could be mistaken in categorizing the product’s quality. The objective was to find the optimum value for the review period, the setup cost, and the number of deliveries in one production cycle which might minimize the joint total cost. Furthermore, the algorithm and numerical example were provided to illustrate the application of the model.

Marcus canonical integral for non-Gaussian processes and its computation: pathwise simulation and tau-leaping algorithm.

PubMed

Li, Tiejun; Min, Bin; Wang, Zhiming

2013-03-14

The stochastic integral ensuring the Newton-Leibnitz chain rule is essential in stochastic energetics. Marcus canonical integral has this property and can be understood as the Wong-Zakai type smoothing limit when the driving process is non-Gaussian. However, this important concept seems not well-known for physicists. In this paper, we discuss Marcus integral for non-Gaussian processes and its computation in the context of stochastic energetics. We give a comprehensive introduction to Marcus integral and compare three equivalent definitions in the literature. We introduce the exact pathwise simulation algorithm and give the error analysis. We show how to compute the thermodynamic quantities based on the pathwise simulation algorithm. We highlight the information hidden in the Marcus mapping, which plays the key role in determining thermodynamic quantities. We further propose the tau-leaping algorithm, which advance the process with deterministic time steps when tau-leaping condition is satisfied. The numerical experiments and its efficiency analysis show that it is very promising.

Numerical Experiments in Error Control for Sound Propagation Using a Damping Layer Boundary Treatment

NASA Technical Reports Server (NTRS)

Goodrich, John W.

2017-01-01

This paper presents results from numerical experiments for controlling the error caused by a damping layer boundary treatment when simulating the propagation of an acoustic signal from a continuous pressure source. The computations are with the 2D Linearized Euler Equations (LEE) for both a uniform mean flow and a steady parallel jet. The numerical experiments are with algorithms that are third, fifth, seventh and ninth order accurate in space and time. The numerical domain is enclosed in a damping layer boundary treatment. The damping is implemented in a time accurate manner, with simple polynomial damping profiles of second, fourth, sixth and eighth power. At the outer boundaries of the damping layer the propagating solution is uniformly set to zero. The complete boundary treatment is remarkably simple and intrinsically independant from the dimension of the spatial domain. The reported results show the relative effect on the error from the boundary treatment by varying the damping layer width, damping profile power, damping amplitude, propagtion time, grid resolution and algorithm order. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error in the numerical solution from the complete boundary treatment can be controlled. We report maximum relative absolute errors from just the boundary treatment that range from O[10-2] to O[10-7].

Air-Sea Interaction Processes in Low and High-Resolution Coupled Climate Model Simulations for the Southeast Pacific

NASA Astrophysics Data System (ADS)

Porto da Silveira, I.; Zuidema, P.; Kirtman, B. P.

2017-12-01

The rugged topography of the Andes Cordillera along with strong coastal upwelling, strong sea surface temperatures (SST) gradients and extensive but geometrically-thin stratocumulus decks turns the Southeast Pacific (SEP) into a challenge for numerical modeling. In this study, hindcast simulations using the Community Climate System Model (CCSM4) at two resolutions were analyzed to examine the importance of resolution alone, with the parameterizations otherwise left unchanged. The hindcasts were initialized on January 1 with the real-time oceanic and atmospheric reanalysis (CFSR) from 1982 to 2003, forming a 10-member ensemble. The two resolutions are (0.1o oceanic and 0.5o atmospheric) and (1.125o oceanic and 0.9o atmospheric). The SST error growth in the first six days of integration (fast errors) and those resulted from model drift (saturated errors) are assessed and compared towards evaluating the model processes responsible for the SST error growth. For the high-resolution simulation, SST fast errors are positive (+0.3oC) near the continental borders and negative offshore (-0.1oC). Both are associated with a decrease in cloud cover, a weakening of the prevailing southwesterly winds and a reduction of latent heat flux. The saturated errors possess a similar spatial pattern, but are larger and are more spatially concentrated. This suggests that the processes driving the errors already become established within the first week, in contrast to the low-resolution simulations. These, instead, manifest too-warm SSTs related to too-weak upwelling, driven by too-strong winds and Ekman pumping. Nevertheless, the ocean surface tends to be cooler in the low-resolution simulation than the high-resolution due to a higher cloud cover. Throughout the integration, saturated SST errors become positive and could reach values up to +4oC. These are accompanied by upwelling dumping and a decrease in cloud cover. High and low resolution models presented notable differences in how SST errors variability drove atmospheric changes, especially because the high resolution is sensitive to resurgence regions. This allows the model to resolve cloud heights and establish different radiative feedbacks.

Stochastic Evolution Equations Driven by Fractional Noises

DTIC Science & Technology

2016-11-28

rate of convergence to zero or the error and the limit in distribution of the error fluctuations. We have studied time discrete numerical schemes...error fluctuations. We have studied time discrete numerical schemes based on Taylor expansions for rough differential equations and for stochastic...variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian

Numerical stability in problems of linear algebra.

NASA Technical Reports Server (NTRS)

Babuska, I.

1972-01-01

Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

A flexible importance sampling method for integrating subgrid processes

DOE PAGES

Raut, E. K.; Larson, V. E.

2016-01-29

Numerical models of weather and climate need to compute grid-box-averaged rates of physical processes such as microphysics. These averages are computed by integrating subgrid variability over a grid box. For this reason, an important aspect of atmospheric modeling is spatial integration over subgrid scales. The needed integrals can be estimated by Monte Carlo integration. Monte Carlo integration is simple and general but requires many evaluations of the physical process rate. To reduce the number of function evaluations, this paper describes a new, flexible method of importance sampling. It divides the domain of integration into eight categories, such as the portion that containsmore » both precipitation and cloud, or the portion that contains precipitation but no cloud. It then allows the modeler to prescribe the density of sample points within each of the eight categories. The new method is incorporated into the Subgrid Importance Latin Hypercube Sampler (SILHS). Here, the resulting method is tested on drizzling cumulus and stratocumulus cases. In the cumulus case, the sampling error can be considerably reduced by drawing more sample points from the region of rain evaporation.« less

Comprehensive Anti-error Study on Power Grid Dispatching Based on Regional Regulation and Integration

NASA Astrophysics Data System (ADS)

Zhang, Yunju; Chen, Zhongyi; Guo, Ming; Lin, Shunsheng; Yan, Yinyang

2018-01-01

With the large capacity of the power system, the development trend of the large unit and the high voltage, the scheduling operation is becoming more frequent and complicated, and the probability of operation error increases. This paper aims at the problem of the lack of anti-error function, single scheduling function and low working efficiency for technical support system in regional regulation and integration, the integrated construction of the error prevention of the integrated architecture of the system of dispatching anti - error of dispatching anti - error of power network based on cloud computing has been proposed. Integrated system of error prevention of Energy Management System, EMS, and Operation Management System, OMS have been constructed either. The system architecture has good scalability and adaptability, which can improve the computational efficiency, reduce the cost of system operation and maintenance, enhance the ability of regional regulation and anti-error checking with broad development prospects.

Prediction of daily spring hydrographs for future climatic scenarios based on an integrated numerical modelling approach: Application on a snow-governed semi- arid karst catchment area.

NASA Astrophysics Data System (ADS)

Doummar, J.; Kassem, A.; Gurdak, J. J.

2017-12-01

In the framework of a three-year USAID/NSF- funded PEER Science project, flow in a karst system in Lebanon (Assal Spring; discharge 0.2-2.5 m3/s yearly volume of 22-30 Mm3) dominated by snow and semi arid conditions was simulated using an integrated numerical model (Mike She 2016). The calibrated model (Nash-Sutcliffe coefficient of 0.77) is based on high resolution input data (2014-2017) and detailed catchment characterization. The approach is to assess the influence of various model parameters on recharge signals in the different hydrological karst compartments (Atmosphere, unsaturated zone, and saturated zone) based on an integrated numerical model. These parameters include precipitation intensity and magnitude, temperature, snow-melt parameters, in addition to karst specific spatially distributed features such as fast infiltration points, soil properties and thickness, topographical slopes, Epikarst and thickness of unsaturated zone, and hydraulic conductivity among others. Moreover, the model is currently simulated forward using various scenarios for future climate (Global Climate Models GCM; daily downscaled temperature and precipitation time series for Lebanon 2020-2045) in order to depict the flow rates expected in the future and the effect of climate change on hydrographs recession coefficients, discharge maxima and minima, and total spring discharge volume . Additionally, a sensitivity analysis of individual or coupled major parameters allows quantifying their impact on recharge or indirectly on the vulnerability of the system (soil thickness, soil and rock hydraulic conductivity appear to be amongst the highly sensitive parameters). This study particularly unravels the normalized single effect of rain magnitude and intensity, snow, and temperature change on the flow rate (e.g., a change of temperature of 3° on the catchment yields a Residual Mean Square Error RMSE of 0.15 m3/s in the spring discharge and a 16% error in the total annual volume with respect to the calibrated model). Finally, such a study can allow decision makers to implement best informed management practices, especially in complex karst systems, to overcome impacts of climate change on water resources.

High-precision numerical integration of equations in dynamics

NASA Astrophysics Data System (ADS)

Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

2018-05-01

An important requirement for the process of solving differential equations in Dynamics, such as the equations of the motion of celestial bodies and, in particular, the motion of cosmic robotic systems is high accuracy at large time intervals. One of effective tools for obtaining such solutions is the Taylor series method. In this connection, we note that it is very advantageous to reduce the given equations of Dynamics to systems with polynomial (in unknowns) right-hand sides. This allows us to obtain effective algorithms for finding the Taylor coefficients, a priori error estimates at each step of integration, and an optimal choice of the order of the approximation used. In the paper, these questions are discussed and appropriate algorithms are considered.

Sequential ranging integration times in the presence of CW interference in the ranging channel

NASA Technical Reports Server (NTRS)

Mathur, Ashok; Nguyen, Tien

1986-01-01

The Deep Space Network (DSN), managed by the Jet Propulsion Laboratory for NASA, is used primarily for communication with interplanetary spacecraft. The high sensitivity required to achieve planetary communications makes the DSN very susceptible to radio-frequency interference (RFI). In this paper, an analytical model is presented of the performance degradation of the DSN sequential ranging subsystem in the presence of downlink CW interference in the ranging channel. A trade-off between the ranging component integration times and the ranging signal-to-noise ratio to achieve a desired level of range measurement accuracy and the probability of error in the code components is also presented. Numerical results presented illustrate the required trade-offs under various interference conditions.

A proportional integral estimator-based clock synchronization protocol for wireless sensor networks.

PubMed

Yang, Wenlun; Fu, Minyue

2017-11-01

Clock synchronization is an issue of vital importance in applications of WSNs. This paper proposes a proportional integral estimator-based protocol (EBP) to achieve clock synchronization for wireless sensor networks. As each local clock skew gradually drifts, synchronization accuracy will decline over time. Compared with existing consensus-based approaches, the proposed synchronization protocol improves synchronization accuracy under time-varying clock skews. Moreover, by restricting synchronization error of clock skew into a relative small quantity, it could reduce periodic re-synchronization frequencies. At last, a pseudo-synchronous implementation for skew compensation is introduced as synchronous protocol is unrealistic in practice. Numerical simulations are shown to illustrate the performance of the proposed protocol. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Modeling global vector fields of chaotic systems from noisy time series with the aid of structure-selection techniques.

PubMed

Xu, Daolin; Lu, Fangfang

2006-12-01

We address the problem of reconstructing a set of nonlinear differential equations from chaotic time series. A method that combines the implicit Adams integration and the structure-selection technique of an error reduction ratio is proposed for system identification and corresponding parameter estimation of the model. The structure-selection technique identifies the significant terms from a pool of candidates of functional basis and determines the optimal model through orthogonal characteristics on data. The technique with the Adams integration algorithm makes the reconstruction available to data sampled with large time intervals. Numerical experiment on Lorenz and Rossler systems shows that the proposed strategy is effective in global vector field reconstruction from noisy time series.

Applications of integrated human error identification techniques on the chemical cylinder change task.

PubMed

Cheng, Ching-Min; Hwang, Sheue-Ling

2015-03-01

This paper outlines the human error identification (HEI) techniques that currently exist to assess latent human errors. Many formal error identification techniques have existed for years, but few have been validated to cover latent human error analysis in different domains. This study considers many possible error modes and influential factors, including external error modes, internal error modes, psychological error mechanisms, and performance shaping factors, and integrates several execution procedures and frameworks of HEI techniques. The case study in this research was the operational process of changing chemical cylinders in a factory. In addition, the integrated HEI method was used to assess the operational processes and the system's reliability. It was concluded that the integrated method is a valuable aid to develop much safer operational processes and can be used to predict human error rates on critical tasks in the plant. Copyright © 2014 Elsevier Ltd and The Ergonomics Society. All rights reserved.

Multigrid Approach to Incompressible Viscous Cavity Flows

NASA Technical Reports Server (NTRS)

Wood, William A.

1996-01-01

Two-dimensional incompressible viscous driven-cavity flows are computed for Reynolds numbers on the range 100-20,000 using a loosely coupled, implicit, second-order centrally-different scheme. Mesh sequencing and three-level V-cycle multigrid error smoothing are incorporated into the symmetric Gauss-Seidel time-integration algorithm. Parametrics on the numerical parameters are performed, achieving reductions in solution times by more than 60 percent with the full multigrid approach. Details of the circulation patterns are investigated in cavities of 2-to-1, 1-to-1, and 1-to-2 depth to width ratios.

Multisynchronization of chaotic oscillators via nonlinear observer approach.

PubMed

Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L

2014-01-01

The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.

Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach

PubMed Central

Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L.

2014-01-01

The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology. PMID:24578671

Leader–follower fixed-time consensus of multi-agent systems with high-order integrator dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tian, Bailing; Zuo, Zongyu; Wang, Hong

The leader-follower fixed-time consensus of high-order multi-agent systems with external disturbances is investigated in this paper. A novel sliding manifold is designed to ensure that the tracking errors converge to zero in a fixed-time during the sliding motion. Then, a distributed control law is designed based on Lyapunov technique to drive the system states to the sliding manifold in finite-time independent of initial conditions. Finally, the efficiency of the proposed method is illustrated by numerical simulations.

Faster and More Accurate Transport Procedures for HZETRN

NASA Technical Reports Server (NTRS)

Slaba, Tony C.; Blattnig, Steve R.; Badavi, Francis F.

2010-01-01

Several aspects of code verification are examined for HZETRN. First, a detailed derivation of the numerical marching algorithms is given. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of various coding errors is also given, and the impact of these errors on exposure quantities is shown. Finally, a coupled convergence study is conducted. From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is also determined that almost all of the discretization error in HZETRN is caused by charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons are given for three applications in which HZETRN is commonly used. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations.

Gauss-Legendre quadrature method used to evaluate the spatio-temporal intensity of ultrashort pulses in the focal region of lenses.

PubMed

García-Martínez, L; Rosete-Aguilar, M; Garduño-Mejia, J

2012-01-20

We analyze the spatio-temporal intensity of sub-20 femtosecond pulses with a carrier wavelength of 810 nm along the optical axis of low numerical aperture achromatic and apochromatic doublets designed in the IR region by using the scalar diffraction theory. The diffraction integral is solved by expanding the wave number around the carrier frequency of the pulse in a Taylor series up to third order, and then the integral over the frequencies is solved by using the Gauss-Legendre quadrature method. The numerical errors in this method are negligible by taking 96 nodes and the computational time is reduced by 95% compared to the integration method by rectangles. We will show that the third-order group velocity dispersion (GVD) is not negligible for 10 fs pulses at 810 nm propagating through the low numerical aperture doublets, and its effect is more important than the propagation time difference (PTD). This last effect, however, is also significant. For sub-20 femtosecond pulses, these two effects make the use of a pulse shaper necessary to correct for second and higher-order GVD terms and also the use of apochromatic optics to correct the PTD effect. The design of an apochromatic doublet is presented in this paper and the spatio-temporal intensity of the pulse at the focal region of this doublet is compared to that given by the achromatic doublet. © 2012 Optical Society of America

Errare machinale est: the use of error-related potentials in brain-machine interfaces

PubMed Central

Chavarriaga, Ricardo; Sobolewski, Aleksander; Millán, José del R.

2014-01-01

The ability to recognize errors is crucial for efficient behavior. Numerous studies have identified electrophysiological correlates of error recognition in the human brain (error-related potentials, ErrPs). Consequently, it has been proposed to use these signals to improve human-computer interaction (HCI) or brain-machine interfacing (BMI). Here, we present a review of over a decade of developments toward this goal. This body of work provides consistent evidence that ErrPs can be successfully detected on a single-trial basis, and that they can be effectively used in both HCI and BMI applications. We first describe the ErrP phenomenon and follow up with an analysis of different strategies to increase the robustness of a system by incorporating single-trial ErrP recognition, either by correcting the machine's actions or by providing means for its error-based adaptation. These approaches can be applied both when the user employs traditional HCI input devices or in combination with another BMI channel. Finally, we discuss the current challenges that have to be overcome in order to fully integrate ErrPs into practical applications. This includes, in particular, the characterization of such signals during real(istic) applications, as well as the possibility of extracting richer information from them, going beyond the time-locked decoding that dominates current approaches. PMID:25100937

How Angular Velocity Features and Different Gyroscope Noise Types Interact and Determine Orientation Estimation Accuracy.

PubMed

Pasciuto, Ilaria; Ligorio, Gabriele; Bergamini, Elena; Vannozzi, Giuseppe; Sabatini, Angelo Maria; Cappozzo, Aurelio

2015-09-18

In human movement analysis, 3D body segment orientation can be obtained through the numerical integration of gyroscope signals. These signals, however, are affected by errors that, for the case of micro-electro-mechanical systems, are mainly due to: constant bias, scale factor, white noise, and bias instability. The aim of this study is to assess how the orientation estimation accuracy is affected by each of these disturbances, and whether it is influenced by the angular velocity magnitude and 3D distribution across the gyroscope axes. Reference angular velocity signals, either constant or representative of human walking, were corrupted with each of the four noise types within a simulation framework. The magnitude of the angular velocity affected the error in the orientation estimation due to each noise type, except for the white noise. Additionally, the error caused by the constant bias was also influenced by the angular velocity 3D distribution. As the orientation error depends not only on the noise itself but also on the signal it is applied to, different sensor placements could enhance or mitigate the error due to each disturbance, and special attention must be paid in providing and interpreting measures of accuracy for orientation estimation algorithms.

How Angular Velocity Features and Different Gyroscope Noise Types Interact and Determine Orientation Estimation Accuracy

PubMed Central

Pasciuto, Ilaria; Ligorio, Gabriele; Bergamini, Elena; Vannozzi, Giuseppe; Sabatini, Angelo Maria; Cappozzo, Aurelio

2015-01-01

In human movement analysis, 3D body segment orientation can be obtained through the numerical integration of gyroscope signals. These signals, however, are affected by errors that, for the case of micro-electro-mechanical systems, are mainly due to: constant bias, scale factor, white noise, and bias instability. The aim of this study is to assess how the orientation estimation accuracy is affected by each of these disturbances, and whether it is influenced by the angular velocity magnitude and 3D distribution across the gyroscope axes. Reference angular velocity signals, either constant or representative of human walking, were corrupted with each of the four noise types within a simulation framework. The magnitude of the angular velocity affected the error in the orientation estimation due to each noise type, except for the white noise. Additionally, the error caused by the constant bias was also influenced by the angular velocity 3D distribution. As the orientation error depends not only on the noise itself but also on the signal it is applied to, different sensor placements could enhance or mitigate the error due to each disturbance, and special attention must be paid in providing and interpreting measures of accuracy for orientation estimation algorithms. PMID:26393606

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

NASA Astrophysics Data System (ADS)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

Design and Stress Analysis of Low-Noise Adjusted Bearing Contact Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Litvin, Faydor L.; Fuentes, Alfonso; Mullins, Baxter R.; Woods, Ron

2002-01-01

An integrated computerized approach for design and stress analysis of low-noise spiral bevel gear drives with adjusted bearing contact has been developed. The computation procedure is an iterative process, requiring four separate steps that provide: (a) a parabolic function of transmission errors that is able to reduce the effect of errors of alignment, and (b) reduction of the shift of bearing contact caused by misalignment. Application of finite element analysis permits the contact and bending stresses to be determined and investigate the formation of the bearing contact. The design of finite element models and boundary conditions is automated and does not require an intermediate CAD computer program. A commercially available finite element analysis computer program with contact capability was used to conduct the stress analysis. The theory developed is illustrated with numerical examples.

Dependence of surface tension on curvature obtained from a diffuse-interface approach

NASA Astrophysics Data System (ADS)

Badillo, Arnoldo; Lafferty, Nathan; Matar, Omar K.

2017-11-01

From a sharp-interface viewpoint, the surface tension force is f = σκδ (x -xi) n , where σ is the surface tension, κ the local interface curvature, δ the delta function, and n the unit normal vector. The numerical implementation of this force on discrete domains poses challenges that arise from the calculation of the curvature. The continuous surface tension force model, proposed by Brackbill et al. (1992), is an alternative, used commonly in two-phase computational models. In this model, δ is replaced by the gradient of a phase indicator field, whose integral across a diffuse-interface equals unity. An alternative to the Brackbill model are Phase-Field models, which do not require an explicit calculation of the curvature. However, and just as in Brackbill's approach, there are numerical errors that depend on the thickness of the diffuse interface, the grid spacing, and the curvature. We use differential geometry to calculate the leading errors in this force when obtained from a diffuse-interface approach, and outline possible routes to eliminate them. Our results also provide a simple geometrical explanation to the dependence of surface tension on curvature, and to the problem of line tension.

The development and validation of a numerical integration method for non-linear viscoelastic modeling

PubMed Central

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

Evaluation of gravitational curvatures of a tesseroid in spherical integral kernels

NASA Astrophysics Data System (ADS)

Deng, Xiao-Le; Shen, Wen-Bin

2018-04-01

Proper understanding of how the Earth's mass distributions and redistributions influence the Earth's gravity field-related functionals is crucial for numerous applications in geodesy, geophysics and related geosciences. Calculations of the gravitational curvatures (GC) have been proposed in geodesy in recent years. In view of future satellite missions, the sixth-order developments of the gradients are becoming requisite. In this paper, a set of 3D integral GC formulas of a tesseroid mass body have been provided by spherical integral kernels in the spatial domain. Based on the Taylor series expansion approach, the numerical expressions of the 3D GC formulas are provided up to sixth order. Moreover, numerical experiments demonstrate the correctness of the 3D Taylor series approach for the GC formulas with order as high as sixth order. Analogous to other gravitational effects (e.g., gravitational potential, gravity vector, gravity gradient tensor), numerically it is found that there exist the very-near-area problem and polar singularity problem in the GC east-east-radial, north-north-radial and radial-radial-radial components in spatial domain, and compared to the other gravitational effects, the relative approximation errors of the GC components are larger due to not only the influence of the geocentric distance but also the influence of the latitude. This study shows that the magnitude of each term for the nonzero GC functionals by a grid resolution 15^' } } × 15^' }} at GOCE satellite height can reach of about 10^{-16} m^{-1} s2 for zero order, 10^{-24 } or 10^{-23} m^{-1} s2 for second order, 10^{-29} m^{-1} s2 for fourth order and 10^{-35} or 10^{-34} m^{-1} s2 for sixth order, respectively.

On a more rigorous gravity field processing for future LL-SST type gravity satellite missions

NASA Astrophysics Data System (ADS)

Daras, I.; Pail, R.; Murböck, M.

2013-12-01

In order to meet the augmenting demands of the user community concerning accuracies of temporal gravity field models, future gravity missions of low-low satellite-to-satellite tracking (LL-SST) type are planned to carry more precise sensors than their precedents. A breakthrough is planned with the improved LL-SST measurement link, where the traditional K-band microwave instrument of 1μm accuracy will be complemented by an inter-satellite ranging instrument of several nm accuracy. This study focuses on investigations concerning the potential performance of the new sensors and their impact in gravity field solutions. The processing methods for gravity field recovery have to meet the new sensor standards and be able to take full advantage of the new accuracies that they provide. We use full-scale simulations in a realistic environment to investigate whether the standard processing techniques suffice to fully exploit the new sensors standards. We achieve that by performing full numerical closed-loop simulations based on the Integral Equation approach. In our simulation scheme, we simulate dynamic orbits in a conventional tracking analysis to compute pseudo inter-satellite ranges or range-rates that serve as observables. Each part of the processing is validated separately with special emphasis on numerical errors and their impact in gravity field solutions. We demonstrate that processing with standard precision may be a limiting factor for taking full advantage of new generation sensors that future satellite missions will carry. Therefore we have created versions of our simulator with enhanced processing precision with primarily aim to minimize round-off system errors. Results using the enhanced precision show a big reduction of system errors that were present at the standard precision processing even for the error-free scenario, and reveal the improvements the new sensors will bring into the gravity field solutions. As a next step, we analyze the contribution of individual error sources to the system's error budget. More specifically we analyze sensor noise from the laser interferometer and the accelerometers, errors in the kinematic orbits and the background fields as well as temporal and spatial aliasing errors. We give special care on the assessment of error sources with stochastic behavior, such as the laser interferometer and the accelerometers, and their consistent stochastic modeling in frame of the adjustment process.

Numerical Uncertainties in the Simulation of Reversible Isentropic Processes and Entropy Conservation.

NASA Astrophysics Data System (ADS)

Johnson, Donald R.; Lenzen, Allen J.; Zapotocny, Tom H.; Schaack, Todd K.

2000-11-01

A challenge common to weather, climate, and seasonal numerical prediction is the need to simulate accurately reversible isentropic processes in combination with appropriate determination of sources/sinks of energy and entropy. Ultimately, this task includes the distribution and transport of internal, gravitational, and kinetic energies, the energies of water substances in all forms, and the related thermodynamic processes of phase changes involved with clouds, including condensation, evaporation, and precipitation processes.All of the processes noted above involve the entropies of matter, radiation, and chemical substances, conservation during transport, and/or changes in entropies by physical processes internal to the atmosphere. With respect to the entropy of matter, a means to study a model's accuracy in simulating internal hydrologic processes is to determine its capability to simulate the appropriate conservation of potential and equivalent potential temperature as surrogates of dry and moist entropy under reversible adiabatic processes in which clouds form, evaporate, and precipitate. In this study, a statistical strategy utilizing the concept of `pure error' is set forth to assess the numerical accuracies of models to simulate reversible processes during 10-day integrations of the global circulation corresponding to the global residence time of water vapor. During the integrations, the sums of squared differences between equivalent potential temperature e numerically simulated by the governing equations of mass, energy, water vapor, and cloud water and a proxy equivalent potential temperature te numerically simulated as a conservative property are monitored. Inspection of the differences of e and te in time and space and the relative frequency distribution of the differences details bias and random errors that develop from nonlinear numerical inaccuracies in the advection and transport of potential temperature and water substances within the global atmosphere.A series of nine global simulations employing various versions of Community Climate Models CCM2 and CCM3-all Eulerian spectral numerics, all semi-Lagrangian numerics, mixed Eulerian spectral, and semi-Lagrangian numerics-and the University of Wisconsin-Madison (UW) isentropic-sigma gridpoint model provides an interesting comparison of numerical accuracies in the simulation of reversibility. By day 10, large bias and random differences were identified in the simulation of reversible processes in all of the models except for the UW isentropic-sigma model. The CCM2 and CCM3 simulations yielded systematic differences that varied zonally, vertically, and temporally. Within the comparison, the UW isentropic-sigma model was superior in transporting water vapor and cloud water/ice and in simulating reversibility involving the conservation of dry and moist entropy. The only relative frequency distribution of differences that appeared optimal, in that the distribution remained unbiased and equilibrated with minimal variance as it remained statistically stationary, was the distribution from the UW isentropic-sigma model. All other distributions revealed nonstationary characteristics with spreading and/or shifting of the maxima as the biases and variances of the numerical differences of e and te amplified.

Lagrangian numerical techniques for modelling multicomponent flow in the presence of large viscosity contrasts: Markers-in-bulk versus Markers-in-chain

NASA Astrophysics Data System (ADS)

Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard

2015-04-01

Many problems in geodynamic applications may be described as viscous flow of chemically heterogeneous materials. Examples include subduction of compositionally stratified lithospheric plates, folding of rheologically layered rocks, and thermochemical convection of the Earth's mantle. The associated time scales are significantly shorter than that of chemical diffusion, which justifies the commonly featured phenomena in geodynamic flow models termed contact discontinuities. These are spatially sharp interfaces separating regions of different material properties. Numerical modelling of advection of fields with sharp interfaces is challenging. Typical errors include numerical diffusion, which arises due to the repeated action of numerical interpolation. Mathematically, a material field can be represented by discrete indicator functions, whose values are interpreted as logical statements (e.g. whether or not the location is occupied by a given material). Interpolation of a discrete function boils down to determining where in the intermediate node-positions one material ends, and the other begins. The numerical diffusion error thus manifests itself as an erroneous location of the material-interface. Lagrangian advection-schemes are known to be less prone to numerical diffusion errors, compared to their Eulerian counterparts. The tracer-ratio method, where Lagrangian markers are used to discretize the bulk of materials filling the entire domain, is a popular example of such methods. The Stokes equation in this case is solved on a separate, static grid, and in order to do it - material properties must be interpolated from the markers to the grid. This involves the difficulty related to interpolation of discrete fields. The material distribution, and thus material-properties like viscosity and density, seen by the grid is polluted by the interpolation error, which enters the solution of the momentum equation. Errors due to the uncertainty of interface-location can be avoided when using interface tracking methods for advection. Marker-chain method is one such approach, where rather than discretizing the volume of each material, only their interface is discretized by a connected set of markers. Together with the boundary of the domain, the marker-chain constitutes closed polygon-boundaries which enclose the regions spanned by each material. Communicating material properties to the static grid can be done by determining which polygon each grid-node (or integration point) falls into, eliminating the need for interpolation. In our chosen implementation, an efficient parallelized algorithm for the point-in-polygon location is used, so this part of the code takes up only a small fraction of the CPU-time spent on each time step, and allows for spatial resolution of the compositional field beyond that which is practical with markers-in-bulk methods. An additional advantage of using marker-chains for material advection is that it offers a possibility to use some of its markers, or even edges, to generate a FEM grid. One can tailor a grid for obtaining a Stokes solution with optimal accuracy, while controlling the quality and size of its elements. Where geometry of the interface allows - element-edges may be aligned with it, which is known to significantly improve the quality of Stokes solution, compared to when the interface cuts through the elements (Moresi et al., 1996; Deubelbeiss and Kaus, 2008). In more geometrically complex interface-regions, the grid may simply be refined to reduce the error. As materials get deformed in the course of a simulation, the interface may get stretched and entangled. Addition of new markers along the chain may be required in order to properly resolve the increasingly complicated geometry. Conversely, some markers may be removed from regions where they get clustered. Such resampling of the interface requires additional computational effort (although small compared to other parts of the code), and introduces an error in the interface-location (similar to numerical diffusion). Our implementation of this procedure, which utilizes an auxiliary high-resolution structured grid, allows a high degree of control on the magnitude of this error, although cannot eliminate it completely. We will present our chosen numerical implementation of the markers-in-bulk and markers-in-chain methods outlined above, together with the simulation results of the especially designed benchmarks that demonstrate the relative successes and limitations of these methods.

Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.; Carpenter, Mark H.

2001-01-01

Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations. First, accuracy, stability, conservation, and dense output are considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, N = 2, additive Runge-Kutta ARK2 methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms are of equal order to those of the elemental methods. Derived ARK2 methods have vanishing stability functions for very large values of the stiff scaled eigenvalue, z(exp [I]) goes to infinity, and retain high stability efficiency in the absence of stiffness, z(exp [I]) goes to zero. Extrapolation-type stage-value predictors are provided based on dense-output formulae. Optimized methods minimize both leading order ARK2 error terms and Butcher coefficient magnitudes as well as maximize conservation properties. Numerical tests of the new schemes on a CDR problem show negligible stiffness leakage and near classical order convergence rates. However, tests on three simple singular-perturbation problems reveal generally predictable order reduction. Error control is best managed with a PID-controller. While results for the fifth-order method are disappointing, both the new third- and fourth-order methods are at least as efficient as existing ARK2 methods while offering error control and stage-value predictors.

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering

NASA Technical Reports Server (NTRS)

Deepak, A.; Fluellen, A.

1978-01-01

An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.

An accurate European option pricing model under Fractional Stable Process based on Feynman Path Integral

NASA Astrophysics Data System (ADS)

Ma, Chao; Ma, Qinghua; Yao, Haixiang; Hou, Tiancheng

2018-03-01

In this paper, we propose to use the Fractional Stable Process (FSP) for option pricing. The FSP is one of the few candidates to directly model a number of desired empirical properties of asset price risk neutral dynamics. However, pricing the vanilla European option under FSP is difficult and problematic. In the paper, built upon the developed Feynman Path Integral inspired techniques, we present a novel computational model for option pricing, i.e. the Fractional Stable Process Path Integral (FSPPI) model under a general fractional stable distribution that tackles this problem. Numerical and empirical experiments show that the proposed pricing model provides a correction of the Black-Scholes pricing error - overpricing long term options, underpricing short term options; overpricing out-of-the-money options, underpricing in-the-money options without any additional structures such as stochastic volatility and a jump process.

The vertical variability of hyporheic fluxes inferred from riverbed temperature data

NASA Astrophysics Data System (ADS)

Cranswick, Roger H.; Cook, Peter G.; Shanafield, Margaret; Lamontagne, Sebastien

2014-05-01

We present detailed profiles of vertical water flux from the surface to 1.2 m beneath the Haughton River in the tropical northeast of Australia. A 1-D numerical model is used to estimate vertical flux based on raw temperature time series observations from within downwelling, upwelling, neutral, and convergent sections of the hyporheic zone. A Monte Carlo analysis is used to derive error bounds for the fluxes based on temperature measurement error and uncertainty in effective thermal diffusivity. Vertical fluxes ranged from 5.7 m d-1 (downward) to -0.2 m d-1 (upward) with the lowest relative errors for values between 0.3 and 6 m d-1. Our 1-D approach provides a useful alternative to 1-D analytical and other solutions because it does not incorporate errors associated with simplified boundary conditions or assumptions of purely vertical flow, hydraulic parameter values, or hydraulic conditions. To validate the ability of this 1-D approach to represent the vertical fluxes of 2-D flow fields, we compare our model with two simple 2-D flow fields using a commercial numerical model. These comparisons showed that: (1) the 1-D vertical flux was equivalent to the mean vertical component of flux irrespective of a changing horizontal flux; and (2) the subsurface temperature data inherently has a "spatial footprint" when the vertical flux profiles vary spatially. Thus, the mean vertical flux within a 2-D flow field can be estimated accurately without requiring the flow to be purely vertical. The temperature-derived 1-D vertical flux represents the integrated vertical component of flux along the flow path intersecting the observation point. This article was corrected on 6 JUN 2014. See the end of the full text for details.

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Reliability-Based Stability Analysis of Rock Slopes Using Numerical Analysis and Response Surface Method

NASA Astrophysics Data System (ADS)

Dadashzadeh, N.; Duzgun, H. S. B.; Yesiloglu-Gultekin, N.

2017-08-01

While advanced numerical techniques in slope stability analysis are successfully used in deterministic studies, they have so far found limited use in probabilistic analyses due to their high computation cost. The first-order reliability method (FORM) is one of the most efficient probabilistic techniques to perform probabilistic stability analysis by considering the associated uncertainties in the analysis parameters. However, it is not possible to directly use FORM in numerical slope stability evaluations as it requires definition of a limit state performance function. In this study, an integrated methodology for probabilistic numerical modeling of rock slope stability is proposed. The methodology is based on response surface method, where FORM is used to develop an explicit performance function from the results of numerical simulations. The implementation of the proposed methodology is performed by considering a large potential rock wedge in Sumela Monastery, Turkey. The accuracy of the developed performance function to truly represent the limit state surface is evaluated by monitoring the slope behavior. The calculated probability of failure is compared with Monte Carlo simulation (MCS) method. The proposed methodology is found to be 72% more efficient than MCS, while the accuracy is decreased with an error of 24%.

Technical Note: A direct ray-tracing method to compute integral depth dose in pencil beam proton radiography with a multilayer ionization chamber.

PubMed

Farace, Paolo; Righetto, Roberto; Deffet, Sylvain; Meijers, Arturs; Vander Stappen, Francois

2016-12-01

To introduce a fast ray-tracing algorithm in pencil proton radiography (PR) with a multilayer ionization chamber (MLIC) for in vivo range error mapping. Pencil beam PR was obtained by delivering spots uniformly positioned in a square (45 × 45 mm 2 field-of-view) of 9 × 9 spots capable of crossing the phantoms (210 MeV). The exit beam was collected by a MLIC to sample the integral depth dose (IDD MLIC ). PRs of an electron-density and of a head phantom were acquired by moving the couch to obtain multiple 45 × 45 mm 2 frames. To map the corresponding range errors, the two-dimensional set of IDD MLIC was compared with (i) the integral depth dose computed by the treatment planning system (TPS) by both analytic (IDD TPS ) and Monte Carlo (IDD MC ) algorithms in a volume of water simulating the MLIC at the CT, and (ii) the integral depth dose directly computed by a simple ray-tracing algorithm (IDD direct ) through the same CT data. The exact spatial position of the spot pattern was numerically adjusted testing different in-plane positions and selecting the one that minimized the range differences between IDD direct and IDD MLIC . Range error mapping was feasible by both the TPS and the ray-tracing methods, but very sensitive to even small misalignments. In homogeneous regions, the range errors computed by the direct ray-tracing algorithm matched the results obtained by both the analytic and the Monte Carlo algorithms. In both phantoms, lateral heterogeneities were better modeled by the ray-tracing and the Monte Carlo algorithms than by the analytic TPS computation. Accordingly, when the pencil beam crossed lateral heterogeneities, the range errors mapped by the direct algorithm matched better the Monte Carlo maps than those obtained by the analytic algorithm. Finally, the simplicity of the ray-tracing algorithm allowed to implement a prototype procedure for automated spatial alignment. The ray-tracing algorithm can reliably replace the TPS method in MLIC PR for in vivo range verification and it can be a key component to develop software tools for spatial alignment and correction of CT calibration.

A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices

NASA Astrophysics Data System (ADS)

AlQurashi, Ahmed; Selvakumar, C. R.

2018-06-01

There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices.

A Hybrid Strategy for the Lattice Evaluation of the Leading Order Hadronic Contribution to (g - 2)μ

NASA Astrophysics Data System (ADS)

Golterman, Maarten; Maltman, Kim; Peris, Santiago

2016-04-01

The leading-order hadronic contribution to the muon anomalous magentic moment, aμLO,HVP, can be expressed as an integral over Euclidean Q2 of the vacuum polarization function. We point out that a simple trapezoid-rule numerical integration of the current lattice data is good enough to produce a result with a less-than-1% error for the contribution from the interval above Q2 ≳ 0.1 - 0.2GeV2. This leaves the interval below this value of Q2 as the one to focus on in the future. In order to achieve an accurate result also in this lower window Q2 ≲ 0.1 - 0.2GeV2, we indicate the usefulness of three possible tools. These are: Padé Approximants, polynomials in a conformal variable and a NNLO Chiral Perturbation Theory representation supplemented by a Q4 term. The combination of the numerical integration in the upper Q2 interval together with the use of these tools in the lower Q2 interval provides a hybrid strategy which looks promising as a means of reaching the desired goal on the lattice of a sub-percent precision in the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

Modelling wetting and drying effects over complex topography

NASA Astrophysics Data System (ADS)

Tchamen, G. W.; Kahawita, R. A.

1998-06-01

The numerical simulation of free surface flows that alternately flood and dry out over complex topography is a formidable task. The model equation set generally used for this purpose is the two-dimensional (2D) shallow water wave model (SWWM). Simplified forms of this system such as the zero inertia model (ZIM) can accommodate specific situations like slowly evolving floods over gentle slopes. Classical numerical techniques, such as finite differences (FD) and finite elements (FE), have been used for their integration over the last 20-30 years. Most of these schemes experience some kind of instability and usually fail when some particular domain under specific flow conditions is treated. The numerical instability generally manifests itself in the form of an unphysical negative depth that subsequently causes a run-time error at the computation of the celerity and/or the friction slope. The origins of this behaviour are diverse and may be generally attributed to:1. The use of a scheme that is inappropriate for such complex flow conditions (mixed regimes).2. Improper treatment of a friction source term or a large local curvature in topography.3. Mishandling of a cell that is partially wet/dry.In this paper, a tentative attempt has been made to gain a better understanding of the genesis of the instabilities, their implications and the limits to the proposed solutions. Frequently, the enforcement of robustness is made at the expense of accuracy. The need for a positive scheme, that is, a scheme that always predicts positive depths when run within the constraints of some practical stability limits, is fundamental. It is shown here how a carefully chosen scheme (in this case, an adaptation of the solver to the SWWM) can preserve positive values of water depth under both explicit and implicit time integration, high velocities and complex topography that may include dry areas. However, the treatment of the source terms: friction, Coriolis and particularly the bathymetry, are also of prime importance and must not be overlooked. Linearization with a combination of switching between explicit-implicit integration can overcome the stiffness of the friction and Coriolis terms and provide stable numerical integration. The treatment of the bathymetry source term is much more delicate. For cells undergoing a transient wet-dry process, the imposition of zero velocity stabilizes most of the approximations. However, this artificial zero velocity condition can be the cause of considerable error, especially when fast moving fronts are involved. Besides these difficulties linked with the internal position of the front within a cell versus the limited resolution of a numerical grid, it appears that the second derivative that defines whether the bed is locally convex or concave is a key indicator for stability. A convex bottom may lead to unbounded solutions. It appears that this behaviour is not linked to the numerics (numerical scheme) but rather to the mathematical theory of the SWWM. These concerns about stability have taken precedence, until now, over the crucial and related question of accuracy, especially near a moving front, and how these possible inaccuracies at the leading edge may affect the solution at interior points within the domain.This paper presents an in depth, fully two-dimensional space analysis of the aforementioned problem that has not been addressed before. The purpose of the present communication is not to propose what could be viewed as a final solution, but rather to provide some key considerations that may reveal the ingredients and insight necessary for the development of accurate and robust solutions in the future.

Measuring and modeling high-resolution topographic change at archaeological sites in Grand Canyon National Park, Arizona, U.S.A.

NASA Astrophysics Data System (ADS)

Collins, B. D.; Corbett, S. C.; Fairley, H. C.

2012-04-01

Erosion of archaeological sites within Grand Canyon National Park (GCNP) Arizona, located in the southwestern United States is a subject of continuing interest to land and resource managers. This is partly fueled by an ongoing debate about whether and to what degree controlled releases from Glen Canyon Dam, located immediately upstream of GCNP, are affecting the physical integrity of archaeological sites. Long-term topographic change due to natural sources is typical in the desert southwest region. However, continuing erosion, which may be related in-part to anthropogenic factors, threatens both the preservation of archaeological sites as well as our ability to study evidence of past human habitation in GCNP that dates back at least 8,000 years before present. To quantitatively identify changes to archaeological sites in this region, and with the broader intention of developing numerical models to predict how and under what circumstances dam-controlled flows influence archaeological sites, we undertook a detailed terrestrial-lidar based monitoring program at thirteen sites between 2006 and 2010. Our studies looked specifically at sites located along the Colorado River that are potentially subject to changes related to dam operations. This could occur, for example, by limited sediment supply to sand bars which in turn contribute aeolian sediment to archaeologic sites. Each site was several hundred to several thousand square meters in size and was surveyed multiple times during the 5-year period. Our monitoring program shows how various data registration and georeferencing techniques result in varying degrees of topographic surface model accuracy. For example, surveys performed between 2006 and 2007 used point cloud registration methods and resulted in estimated change detection thresholds of 8 cm between repeat surveys. In 2010, surveys at the same sites used control point registration methods and resulted in estimated change detection thresholds of 3 cm. Error thresholds were determined using two types of change detection error analyses. The first used the absolute errors inherent in each step of the lidar data collection process (i.e., directly combining laser, survey, and registration errors) and provides a conservative estimate of potential errors. The second used an empirical metric based on the closest point-to-point match between known fixed objects (e.g., large boulders) and results in a more realistic error bound. Our data indicate that some sites changed significantly during the monitored time period. These measurements provide much of the essential data required for developing an in-house, physically-based, numerical sediment transport model that can provide estimates on the likelihood for future archaeological site change in GCNP. Thus far, we are finding that the data provided by typical terrestrial lidar surveys is likely overly-dense for numerical model requirements with respect to computational efficiency. Despite this, we also find that high-resolution data is necessary to perform change detection at the accuracy required for model calibration and to document changes before they have progressed beyond the point when site integrity is compromised. The results of the study will provide land and resource managers with the pertinent information needed to oversee these archaeological resources in the best way possible.

Numerical Demons in Monte Carlo Estimation of Bayesian Model Evidence with Application to Soil Respiration Models

NASA Astrophysics Data System (ADS)

Elshall, A. S.; Ye, M.; Niu, G. Y.; Barron-Gafford, G.

2016-12-01

Bayesian multimodel inference is increasingly being used in hydrology. Estimating Bayesian model evidence (BME) is of central importance in many Bayesian multimodel analysis such as Bayesian model averaging and model selection. BME is the overall probability of the model in reproducing the data, accounting for the trade-off between the goodness-of-fit and the model complexity. Yet estimating BME is challenging, especially for high dimensional problems with complex sampling space. Estimating BME using the Monte Carlo numerical methods is preferred, as the methods yield higher accuracy than semi-analytical solutions (e.g. Laplace approximations, BIC, KIC, etc.). However, numerical methods are prone the numerical demons arising from underflow of round off errors. Although few studies alluded to this issue, to our knowledge this is the first study that illustrates these numerical demons. We show that the precision arithmetic can become a threshold on likelihood values and Metropolis acceptance ratio, which results in trimming parameter regions (when likelihood function is less than the smallest floating point number that a computer can represent) and corrupting of the empirical measures of the random states of the MCMC sampler (when using log-likelihood function). We consider two of the most powerful numerical estimators of BME that are the path sampling method of thermodynamic integration (TI) and the importance sampling method of steppingstone sampling (SS). We also consider the two most widely used numerical estimators, which are the prior sampling arithmetic mean (AS) and posterior sampling harmonic mean (HM). We investigate the vulnerability of these four estimators to the numerical demons. Interesting, the most biased estimator, namely the HM, turned out to be the least vulnerable. While it is generally assumed that AM is a bias-free estimator that will always approximate the true BME by investing in computational effort, we show that arithmetic underflow can hamper AM resulting in severe underestimation of BME. TI turned out to be the most vulnerable, resulting in BME overestimation. Finally, we show how SS can be largely invariant to rounding errors, yielding the most accurate and computational efficient results. These research results are useful for MC simulations to estimate Bayesian model evidence.

Automatic Error Analysis Using Intervals

ERIC Educational Resources Information Center

Rothwell, E. J.; Cloud, M. J.

2012-01-01

A technique for automatic error analysis using interval mathematics is introduced. A comparison to standard error propagation methods shows that in cases involving complicated formulas, the interval approach gives comparable error estimates with much less effort. Several examples are considered, and numerical errors are computed using the INTLAB…

Revised and improved value of the QED tenth-order electron anomalous magnetic moment

NASA Astrophysics Data System (ADS)

Aoyama, Tatsumi; Kinoshita, Toichiro; Nio, Makiko

2018-02-01

In order to improve the theoretical prediction of the electron anomalous magnetic moment ae we have carried out a new numerical evaluation of the 389 integrals of Set V, which represent 6,354 Feynman vertex diagrams without lepton loops. During this work, we found that one of the integrals, called X 024 , was given a wrong value in the previous calculation due to an incorrect assignment of integration variables. The correction of this error causes a shift of -1.26 to the Set V contribution, and hence to the tenth-order universal (i.e., mass-independent) term A1(10 ). The previous evaluation of all other 388 integrals is free from errors and consistent with the new evaluation. Combining the new and the old (excluding X 024 ) calculations statistically, we obtain 7.606 (192 )(α /π )5 as the best estimate of the Set V contribution. Including the contribution of the diagrams with fermion loops, the improved tenth-order universal term becomes A1(10 )=6.675 (192 ) . Adding hadronic and electroweak contributions leads to the theoretical prediction ae(theory)=1 159 652 182.032 (720 )×10-12 . From this and the best measurement of ae, we obtain the inverse fine-structure constant α-1(ae)=137.035 999 1491 (331 ) . The theoretical prediction of the muon anomalous magnetic moment is also affected by the update of QED contribution and the new value of α , but the shift is much smaller than the theoretical uncertainty.

Some Surprising Errors in Numerical Differentiation

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2012-01-01

Data analysis methods, both numerical and visual, are used to discover a variety of surprising patterns in the errors associated with successive approximations to the derivatives of sinusoidal and exponential functions based on the Newton difference-quotient. L'Hopital's rule and Taylor polynomial approximations are then used to explain why these…

Computational investigations and grid refinement study of 3D transient flow in a cylindrical tank using OpenFOAM

NASA Astrophysics Data System (ADS)

Mohd Sakri, F.; Mat Ali, M. S.; Sheikh Salim, S. A. Z.

2016-10-01

The study of physic fluid for a liquid draining inside a tank is easily accessible using numerical simulation. However, numerical simulation is expensive when the liquid draining involves the multi-phase problem. Since an accurate numerical simulation can be obtained if a proper method for error estimation is accomplished, this paper provides systematic assessment of error estimation due to grid convergence error using OpenFOAM. OpenFOAM is an open source CFD-toolbox and it is well-known among the researchers and institutions because of its free applications and ready to use. In this study, three types of grid resolution are used: coarse, medium and fine grids. Grid Convergence Index (GCI) is applied to estimate the error due to the grid sensitivity. A monotonic convergence condition is obtained in this study that shows the grid convergence error has been progressively reduced. The fine grid has the GCI value below 1%. The extrapolated value from Richardson Extrapolation is in the range of the GCI obtained.

Interferometric correction system for a numerically controlled machine

DOEpatents

Burleson, Robert R.

1978-01-01

An interferometric correction system for a numerically controlled machine is provided to improve the positioning accuracy of a machine tool, for example, for a high-precision numerically controlled machine. A laser interferometer feedback system is used to monitor the positioning of the machine tool which is being moved by command pulses to a positioning system to position the tool. The correction system compares the commanded position as indicated by a command pulse train applied to the positioning system with the actual position of the tool as monitored by the laser interferometer. If the tool position lags the commanded position by a preselected error, additional pulses are added to the pulse train applied to the positioning system to advance the tool closer to the commanded position, thereby reducing the lag error. If the actual tool position is leading in comparison to the commanded position, pulses are deleted from the pulse train where the advance error exceeds the preselected error magnitude to correct the position error of the tool relative to the commanded position.

Discretization vs. Rounding Error in Euler's Method

ERIC Educational Resources Information Center

Borges, Carlos F.

2011-01-01

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, David

In the January 2002 edition of SIAM News, Nick Trefethen announced the '$100, 100-Digit Challenge'. In this note he presented ten easy-to-state but hard-to-solve problems of numerical analysis, and challenged readers to find each answer to ten-digit accuracy. Trefethen closed with the enticing comment: 'Hint: They're hard! If anyone gets 50 digits in total, I will be impressed.' This challenge obviously struck a chord in hundreds of numerical mathematicians worldwide, as 94 teams from 25 nations later submitted entries. Many of these submissions exceeded the target of 50 correct digits; in fact, 20 teams achieved a perfect score of 100more » correct digits. Trefethen had offered $100 for the best submission. Given the overwhelming response, a generous donor (William Browning, founder of Applied Mathematics, Inc.) provided additional funds to provide a $100 award to each of the 20 winning teams. Soon after the results were out, four participants, each from a winning team, got together and agreed to write a book about the problems and their solutions. The team is truly international: Bornemann is from Germany, Laurie is from South Africa, Wagon is from the USA, and Waldvogel is from Switzerland. This book provides some mathematical background for each problem, and then shows in detail how each of them can be solved. In fact, multiple solution techniques are mentioned in each case. The book describes how to extend these solutions to much larger problems and much higher numeric precision (hundreds or thousands of digit accuracy). The authors also show how to compute error bounds for the results, so that one can say with confidence that one's results are accurate to the level stated. Numerous numerical software tools are demonstrated in the process, including the commercial products Mathematica, Maple and Matlab. Computer programs that perform many of the algorithms mentioned in the book are provided, both in an appendix to the book and on a website. In the process, the authors take the reader on a wide-ranging tour of modern numerical mathematics, with enough background material so that even readers with little or no training in numerical analysis can follow. Here is a list of just a few of the topics visited: numerical quadrature (i.e., numerical integration), series summation, sequence extrapolation, contour integration, Fourier integrals, high-precision arithmetic, interval arithmetic, symbolic computing, numerical linear algebra, perturbation theory, Euler-Maclaurin summation, global minimization, eigenvalue methods, evolutionary algorithms, matrix preconditioning, random walks, special functions, elliptic functions, Monte-Carlo methods, and numerical differentiation.« less

Impact of PBL and convection parameterization schemes for prediction of severe land-falling Bay of Bengal cyclones using WRF-ARW model

NASA Astrophysics Data System (ADS)

Singh, K. S.; Bhaskaran, Prasad K.

2017-12-01

This study evaluates the performance of the Advanced Research Weather Research and Forecasting (WRF-ARW) model for prediction of land-falling Bay of Bengal (BoB) tropical cyclones (TCs). Model integration was performed using two-way interactive double nested domains at 27 and 9 km resolutions. The present study comprises two major components. Firstly, the study explores the impact of five different planetary boundary layer (PBL) and six cumulus convection (CC) schemes on seven land-falling BoB TCs. A total of 85 numerical simulations were studied in detail, and the results signify that the model simulated better both the track and intensity by using a combination of Yonsei University (YSU) PBL and the old simplified Arakawa-Schubert CC scheme. Secondly, the study also investigated the model performance based on the best possible combinations of model physics on the real-time forecasts of four BoB cyclones (Phailin, Helen, Lehar, and Madi) that made landfall during 2013 based on another 15 numerical simulations. The predicted mean track error during 2013 was about 71 km, 114 km, 133 km, 148 km, and 130 km respectively from day-1 to day-5. The Root Mean Square Error (RMSE) for Minimum Central Pressure (MCP) was about 6 hPa and the same noticed for Maximum Surface Wind (MSW) was about 4.5 m s-1 noticed during the entire simulation period. In addition the study also reveals that the predicted track errors during 2013 cyclones improved respectively by 43%, 44%, and 52% from day-1 to day-3 as compared to cyclones simulated during the period 2006-2011. The improvements noticed can be attributed due to relatively better quality data that was specified for the initial mean position error (about 48 km) during 2013. Overall the study signifies that the track and intensity forecast for 2013 cyclones using the specified combinations listed in the first part of this study performed relatively better than the other NWP (Numerical Weather Prediction) models, and thereby finds application in real-time forecast.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE PAGES

Steyer, Andrew J.; Van Vleck, Erik S.

2018-04-13

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

A network of spiking neurons for computing sparse representations in an energy efficient way

PubMed Central

Hu, Tao; Genkin, Alexander; Chklovskii, Dmitri B.

2013-01-01

Computing sparse redundant representations is an important problem both in applied mathematics and neuroscience. In many applications, this problem must be solved in an energy efficient way. Here, we propose a hybrid distributed algorithm (HDA), which solves this problem on a network of simple nodes communicating via low-bandwidth channels. HDA nodes perform both gradient-descent-like steps on analog internal variables and coordinate-descent-like steps via quantized external variables communicated to each other. Interestingly, such operation is equivalent to a network of integrate-and-fire neurons, suggesting that HDA may serve as a model of neural computation. We compare the numerical performance of HDA with existing algorithms and show that in the asymptotic regime the representation error of HDA decays with time, t, as 1/t. We show that HDA is stable against time-varying noise, specifically, the representation error decays as 1/t for Gaussian white noise. PMID:22920853

Hyper-X Post-Flight Trajectory Reconstruction

NASA Technical Reports Server (NTRS)

Karlgaard, Christopher D.; Tartabini, Paul V.; Blanchard, RobertC.; Kirsch, Michael; Toniolo, Matthew D.

2004-01-01

This paper discusses the formulation and development of a trajectory reconstruction tool for the NASA X{43A/Hyper{X high speed research vehicle, and its implementation for the reconstruction and analysis of ight test data. Extended Kalman ltering techniques are employed to reconstruct the trajectory of the vehicle, based upon numerical integration of inertial measurement data along with redundant measurements of the vehicle state. The equations of motion are formulated in order to include the effects of several systematic error sources, whose values may also be estimated by the ltering routines. Additionally, smoothing algorithms have been implemented in which the nal value of the state (or an augmented state that includes other systematic error parameters to be estimated) and covariance are propagated back to the initial time to generate the best-estimated trajectory, based upon all available data. The methods are applied to the problem of reconstructing the trajectory of the Hyper-X vehicle from ight data.

A network of spiking neurons for computing sparse representations in an energy-efficient way.

PubMed

Hu, Tao; Genkin, Alexander; Chklovskii, Dmitri B

2012-11-01

Computing sparse redundant representations is an important problem in both applied mathematics and neuroscience. In many applications, this problem must be solved in an energy-efficient way. Here, we propose a hybrid distributed algorithm (HDA), which solves this problem on a network of simple nodes communicating by low-bandwidth channels. HDA nodes perform both gradient-descent-like steps on analog internal variables and coordinate-descent-like steps via quantized external variables communicated to each other. Interestingly, the operation is equivalent to a network of integrate-and-fire neurons, suggesting that HDA may serve as a model of neural computation. We show that the numerical performance of HDA is on par with existing algorithms. In the asymptotic regime, the representation error of HDA decays with time, t, as 1/t. HDA is stable against time-varying noise; specifically, the representation error decays as 1/√t for gaussian white noise.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steyer, Andrew J.; Van Vleck, Erik S.

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Synchronisation, electronic circuit implementation, and fractional-order analysis of 5D ordinary differential equations with hidden hyperchaotic attractors

NASA Astrophysics Data System (ADS)

Wei, Zhouchao; Rajagopal, Karthikeyan; Zhang, Wei; Kingni, Sifeu Takougang; Akgül, Akif

2018-04-01

Hidden hyperchaotic attractors can be generated with three positive Lyapunov exponents in the proposed 5D hyperchaotic Burke-Shaw system with only one stable equilibrium. To the best of our knowledge, this feature has rarely been previously reported in any other higher-dimensional systems. Unidirectional linear error feedback coupling scheme is used to achieve hyperchaos synchronisation, which will be estimated by using two indicators: the normalised average root-mean squared synchronisation error and the maximum cross-correlation coefficient. The 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integration. In addition, fractional-order hidden hyperchaotic system will be considered from the following three aspects: stability, bifurcation analysis and FPGA implementation. Such implementations in real time represent hidden hyperchaotic attractors with important consequences for engineering applications.

Online machining error estimation method of numerical control gear grinding machine tool based on data analysis of internal sensors

NASA Astrophysics Data System (ADS)

Zhao, Fei; Zhang, Chi; Yang, Guilin; Chen, Chinyin

2016-12-01

This paper presents an online estimation method of cutting error by analyzing of internal sensor readings. The internal sensors of numerical control (NC) machine tool are selected to avoid installation problem. The estimation mathematic model of cutting error was proposed to compute the relative position of cutting point and tool center point (TCP) from internal sensor readings based on cutting theory of gear. In order to verify the effectiveness of the proposed model, it was simulated and experimented in gear generating grinding process. The cutting error of gear was estimated and the factors which induce cutting error were analyzed. The simulation and experiments verify that the proposed approach is an efficient way to estimate the cutting error of work-piece during machining process.

Application of Energy Function as a Measure of Error in the Numerical Solution for Online Transient Stability Assessment

NASA Astrophysics Data System (ADS)

Sarojkumar, K.; Krishna, S.

2016-08-01

Online dynamic security assessment (DSA) is a computationally intensive task. In order to reduce the amount of computation, screening of contingencies is performed. Screening involves analyzing the contingencies with the system described by a simpler model so that computation requirement is reduced. Screening identifies those contingencies which are sure to not cause instability and hence can be eliminated from further scrutiny. The numerical method and the step size used for screening should be chosen with a compromise between speed and accuracy. This paper proposes use of energy function as a measure of error in the numerical solution used for screening contingencies. The proposed measure of error can be used to determine the most accurate numerical method satisfying the time constraint of online DSA. Case studies on 17 generator system are reported.

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

NASA Astrophysics Data System (ADS)

Wu, Zedong; Alkhalifah, Tariq

2018-07-01

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

Aerodynamic influence coefficient method using singularity splines.

NASA Technical Reports Server (NTRS)

Mercer, J. E.; Weber, J. A.; Lesferd, E. P.

1973-01-01

A new numerical formulation with computed results, is presented. This formulation combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of the loading function methods. The formulation employs a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfies all of the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise (termed 'spline'). Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral.

Found in translation: Integrating laboratory and clinical oncology research

PubMed Central

Wagner, H

2008-01-01

Translational research in medicine aims to inform the clinic and the laboratory with the results of each other’s work, and to bring promising and validated new therapies into clinical application. While laudable in intent, this is complicated in practice and the current state of translational research in cancer shows both striking success stories and examples of the numerous potential obstacles as well as opportunities for delays and errors in translation. This paper reviews the premises, promises, and problems of translational research with a focus on radiation oncology and suggests opportunities for improvements in future research design. PMID:21611010

Stabilization of computational procedures for constrained dynamical systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Chiou, J. C.

1988-01-01

A new stabilization method of treating constraints in multibody dynamical systems is presented. By tailoring a penalty form of the constraint equations, the method achieves stabilization without artificial damping and yields a companion matrix differential equation for the constraint forces; hence, the constraint forces are obtained by integrating the companion differential equation for the constraint forces in time. A principal feature of the method is that the errors committed in each constraint condition decay with its corresponding characteristic time scale associated with its constraint force. Numerical experiments indicate that the method yields a marked improvement over existing techniques.

Structure and structure-preserving algorithms for plasma physics

NASA Astrophysics Data System (ADS)

Morrison, P. J.

2016-10-01

Conventional simulation studies of plasma physics are based on numerically solving the underpinning differential (or integro-differential) equations. Usual algorithms in general do not preserve known geometric structure of the physical systems, such as the local energy-momentum conservation law, Casimir invariants, and the symplectic structure (Poincaré invariants). As a consequence, numerical errors may accumulate coherently with time and long-term simulation results may be unreliable. Recently, a series of geometric algorithms that preserve the geometric structures resulting from the Hamiltonian and action principle (HAP) form of theoretical models in plasma physics have been developed by several authors. The superiority of these geometric algorithms has been demonstrated with many test cases. For example, symplectic integrators for guiding-center dynamics have been constructed to preserve the noncanonical symplectic structures and bound the energy-momentum errors for all simulation time-steps; variational and symplectic algorithms have been discovered and successfully applied to the Vlasov-Maxwell system, MHD, and other magnetofluid equations as well. Hamiltonian truncations of the full Vlasov-Maxwell system have opened the field of discrete gyrokinetics and led to the GEMPIC algorithm. The vision that future numerical capabilities in plasma physics should be based on structure-preserving geometric algorithms will be presented. It will be argued that the geometric consequences of HAP form and resulting geometric algorithms suitable for plasma physics studies cannot be adapted from existing mathematical literature but, rather, need to be discovered and worked out by theoretical plasma physicists. The talk will review existing HAP structures of plasma physics for a variety of models, and how they have been adapted for numerical implementation. Supported by DOE DE-FG02-04ER-54742.

EasyLCMS: an asynchronous web application for the automated quantification of LC-MS data

PubMed Central

2012-01-01

Background Downstream applications in metabolomics, as well as mathematical modelling, require data in a quantitative format, which may also necessitate the automated and simultaneous quantification of numerous metabolites. Although numerous applications have been previously developed for metabolomics data handling, automated calibration and calculation of the concentrations in terms of μmol have not been carried out. Moreover, most of the metabolomics applications are designed for GC-MS, and would not be suitable for LC-MS, since in LC, the deviation in the retention time is not linear, which is not taken into account in these applications. Moreover, only a few are web-based applications, which could improve stand-alone software in terms of compatibility, sharing capabilities and hardware requirements, even though a strong bandwidth is required. Furthermore, none of these incorporate asynchronous communication to allow real-time interaction with pre-processed results. Findings Here, we present EasyLCMS (http://www.easylcms.es/), a new application for automated quantification which was validated using more than 1000 concentration comparisons in real samples with manual operation. The results showed that only 1% of the quantifications presented a relative error higher than 15%. Using clustering analysis, the metabolites with the highest relative error distributions were identified and studied to solve recurrent mistakes. Conclusions EasyLCMS is a new web application designed to quantify numerous metabolites, simultaneously integrating LC distortions and asynchronous web technology to present a visual interface with dynamic interaction which allows checking and correction of LC-MS raw data pre-processing results. Moreover, quantified data obtained with EasyLCMS are fully compatible with numerous downstream applications, as well as for mathematical modelling in the systems biology field. PMID:22884039

Asymmetric Memory Circuit Would Resist Soft Errors

NASA Technical Reports Server (NTRS)

Buehler, Martin G.; Perlman, Marvin

1990-01-01

Some nonlinear error-correcting codes more efficient in presence of asymmetry. Combination of circuit-design and coding concepts expected to make integrated-circuit random-access memories more resistant to "soft" errors (temporary bit errors, also called "single-event upsets" due to ionizing radiation). Integrated circuit of new type made deliberately more susceptible to one kind of bit error than to other, and associated error-correcting code adapted to exploit this asymmetry in error probabilities.

[What Surgeons Should Know about Risk Management].

PubMed

Strametz, R; Tannheimer, M; Rall, M

2017-02-01

Background: The fact that medical treatment is associated with errors has long been recognized. Based on the principle of "first do no harm", numerous efforts have since been made to prevent such errors or limit their impact. However, recent statistics show that these measures do not sufficiently prevent grave mistakes with serious consequences. Preventable mistakes such as wrong patient or wrong site surgery still frequently occur in error statistics. Methods: Based on insight from research on human error, in due consideration of recent legislative regulations in Germany, the authors give an overview of the clinical risk management tools needed to identify risks in surgery, analyse their causes, and determine adequate measures to manage those risks depending on their relevance. The use and limitations of critical incident reporting systems (CIRS), safety checklists and crisis resource management (CRM) are highlighted. Also the rationale for IT systems to support the risk management process is addressed. Results/Conclusion: No single tool of risk management can be effective as a standalone instrument, but unfolds its effect only when embedded in a superordinate risk management system, which integrates tailor-made elements to increase patient safety into the workflows of each organisation. Competence in choosing adequate tools, effective IT systems to support the risk management process as well as leadership and commitment to constructive handling of human error are crucial components to establish a safety culture in surgery. Georg Thieme Verlag KG Stuttgart · New York.

The Effects of Discrete-Trial Training Commission Errors on Learner Outcomes: An Extension

ERIC Educational Resources Information Center

Jenkins, Sarah R.; Hirst, Jason M.; DiGennaro Reed, Florence D.

2015-01-01

We conducted a parametric analysis of treatment integrity errors during discrete-trial training and investigated the effects of three integrity conditions (0, 50, or 100 % errors of commission) on performance in the presence and absence of programmed errors. The presence of commission errors impaired acquisition for three of four participants.…

Numerical stability of the error diffusion concept

NASA Astrophysics Data System (ADS)

Weissbach, Severin; Wyrowski, Frank

1992-10-01

The error diffusion algorithm is an easy implementable mean to handle nonlinearities in signal processing, e.g. in picture binarization and coding of diffractive elements. The numerical stability of the algorithm depends on the choice of the diffusion weights. A criterion for the stability of the algorithm is presented and evaluated for some examples.

Numerical ‘health check’ for scientific codes: the CADNA approach

NASA Astrophysics Data System (ADS)

Scott, N. S.; Jézéquel, F.; Denis, C.; Chesneaux, J.-M.

2007-04-01

Scientific computation has unavoidable approximations built into its very fabric. One important source of error that is difficult to detect and control is round-off error propagation which originates from the use of finite precision arithmetic. We propose that there is a need to perform regular numerical 'health checks' on scientific codes in order to detect the cancerous effect of round-off error propagation. This is particularly important in scientific codes that are built on legacy software. We advocate the use of the CADNA library as a suitable numerical screening tool. We present a case study to illustrate the practical use of CADNA in scientific codes that are of interest to the Computer Physics Communications readership. In doing so we hope to stimulate a greater awareness of round-off error propagation and present a practical means by which it can be analyzed and managed.

Consistency and convergence for numerical radiation conditions

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1990-01-01

The problem of imposing radiation conditions at artificial boundaries for the numerical simulation of wave propagation is considered. Emphasis is on the behavior and analysis of the error which results from the restriction of the domain. The theory of error estimation is briefly outlined for boundary conditions. Use is made of the asymptotic analysis of propagating wave groups to derive and analyze boundary operators. For dissipative problems this leads to local, accurate conditions, but falls short in the hyperbolic case. A numerical experiment on the solution of the wave equation with cylindrical symmetry is described. A unified presentation of a number of conditions which have been proposed in the literature is given and the time dependence of the error which results from their use is displayed. The results are in qualitative agreement with theoretical considerations. It was found, however, that for this model problem it is particularly difficult to force the error to decay rapidly in time.

Optimum employment of satellite indirect soundings as numerical model input

NASA Technical Reports Server (NTRS)

Horn, L. H.; Derber, J. C.; Koehler, T. L.; Schmidt, B. D.

1981-01-01

The characteristics of satellite-derived temperature soundings that would significantly affect their use as input for numerical weather prediction models were examined. Independent evaluations of satellite soundings were emphasized to better define error characteristics. Results of a Nimbus-6 sounding study reveal an underestimation of the strength of synoptic scale troughs and ridges, and associated gradients in isobaric height and temperature fields. The most significant errors occurred near the Earth's surface and the tropopause. Soundings from the TIROS-N and NOAA-6 satellites were also evaluated. Results again showed an underestimation of upper level trough amplitudes leading to weaker thermal gradient depictions in satellite-only fields. These errors show a definite correlation to the synoptic flow patterns. In a satellite-only analysis used to initialize a numerical model forecast, it was found that these synoptically correlated errors were retained in the forecast sequence.

Error modeling for surrogates of dynamical systems using machine learning: Machine-learning-based error model for surrogates of dynamical systems

DOE PAGES

Trehan, Sumeet; Carlberg, Kevin T.; Durlofsky, Louis J.

2017-07-14

A machine learning–based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (eg, random forests, and LASSO) to map a large set of inexpensively computed “error indicators” (ie, features) produced by the surrogate model at a given time instance to a prediction of the surrogate-model error in a quantity of interest (QoI). This eliminates the need for the user to hand-select a small number of informative features. The methodology requires a training set of parameter instances at which the time-dependent surrogate-model error is computed bymore » simulating both the high-fidelity and surrogate models. Using these training data, the method first determines regression-model locality (via classification or clustering) and subsequently constructs a “local” regression model to predict the time-instantaneous error within each identified region of feature space. We consider 2 uses for the resulting error model: (1) as a correction to the surrogate-model QoI prediction at each time instance and (2) as a way to statistically model arbitrary functions of the time-dependent surrogate-model error (eg, time-integrated errors). We then apply the proposed framework to model errors in reduced-order models of nonlinear oil-water subsurface flow simulations, with time-varying well-control (bottom-hole pressure) parameters. The reduced-order models used in this work entail application of trajectory piecewise linearization in conjunction with proper orthogonal decomposition. Moreover, when the first use of the method is considered, numerical experiments demonstrate consistent improvement in accuracy in the time-instantaneous QoI prediction relative to the original surrogate model, across a large number of test cases. When the second use is considered, results show that the proposed method provides accurate statistical predictions of the time- and well-averaged errors.« less

Error modeling for surrogates of dynamical systems using machine learning: Machine-learning-based error model for surrogates of dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trehan, Sumeet; Carlberg, Kevin T.; Durlofsky, Louis J.

A machine learning–based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (eg, random forests, and LASSO) to map a large set of inexpensively computed “error indicators” (ie, features) produced by the surrogate model at a given time instance to a prediction of the surrogate-model error in a quantity of interest (QoI). This eliminates the need for the user to hand-select a small number of informative features. The methodology requires a training set of parameter instances at which the time-dependent surrogate-model error is computed bymore » simulating both the high-fidelity and surrogate models. Using these training data, the method first determines regression-model locality (via classification or clustering) and subsequently constructs a “local” regression model to predict the time-instantaneous error within each identified region of feature space. We consider 2 uses for the resulting error model: (1) as a correction to the surrogate-model QoI prediction at each time instance and (2) as a way to statistically model arbitrary functions of the time-dependent surrogate-model error (eg, time-integrated errors). We then apply the proposed framework to model errors in reduced-order models of nonlinear oil-water subsurface flow simulations, with time-varying well-control (bottom-hole pressure) parameters. The reduced-order models used in this work entail application of trajectory piecewise linearization in conjunction with proper orthogonal decomposition. Moreover, when the first use of the method is considered, numerical experiments demonstrate consistent improvement in accuracy in the time-instantaneous QoI prediction relative to the original surrogate model, across a large number of test cases. When the second use is considered, results show that the proposed method provides accurate statistical predictions of the time- and well-averaged errors.« less

A revised radiation package of G-packed McICA and two-stream approximation: Performance evaluation in a global weather forecasting model

NASA Astrophysics Data System (ADS)

Baek, Sunghye

2017-07-01

For more efficient and accurate computation of radiative flux, improvements have been achieved in two aspects, integration of the radiative transfer equation over space and angle. First, the treatment of the Monte Carlo-independent column approximation (MCICA) is modified focusing on efficiency using a reduced number of random samples ("G-packed") within a reconstructed and unified radiation package. The original McICA takes 20% of CPU time of radiation in the Global/Regional Integrated Model systems (GRIMs). The CPU time consumption of McICA is reduced by 70% without compromising accuracy. Second, parameterizations of shortwave two-stream approximations are revised to reduce errors with respect to the 16-stream discrete ordinate method. Delta-scaled two-stream approximation (TSA) is almost unanimously used in Global Circulation Model (GCM) but contains systematic errors which overestimate forward peak scattering as solar elevation decreases. These errors are alleviated by adjusting the parameterizations of each scattering element—aerosol, liquid, ice and snow cloud particles. Parameterizations are determined with 20,129 atmospheric columns of the GRIMs data and tested with 13,422 independent data columns. The result shows that the root-mean-square error (RMSE) over the all atmospheric layers is decreased by 39% on average without significant increase in computational time. Revised TSA developed and validated with a separate one-dimensional model is mounted on GRIMs for mid-term numerical weather forecasting. Monthly averaged global forecast skill scores are unchanged with revised TSA but the temperature at lower levels of the atmosphere (pressure ≥ 700 hPa) is slightly increased (< 0.5 K) with corrected atmospheric absorption.

Chemical Transport in a Fissured Rock: Verification of a Numerical Model

NASA Astrophysics Data System (ADS)

Rasmuson, A.; Narasimhan, T. N.; Neretnieks, I.

1982-10-01

Numerical models for simulating chemical transport in fissured rocks constitute powerful tools for evaluating the acceptability of geological nuclear waste repositories. Due to the very long-term, high toxicity of some nuclear waste products, the models are required to predict, in certain cases, the spatial and temporal distribution of chemical concentration less than 0.001% of the concentration released from the repository. Whether numerical models can provide such accuracies is a major question addressed in the present work. To this end we have verified a numerical model, TRUMP, which solves the advective diffusion equation in general three dimensions, with or without decay and source terms. The method is based on an integrated finite difference approach. The model was verified against known analytic solution of the one-dimensional advection-diffusion problem, as well as the problem of advection-diffusion in a system of parallel fractures separated by spherical particles. The studies show that as long as the magnitude of advectance is equal to or less than that of conductance for the closed surface bounding any volume element in the region (that is, numerical Peclet number <2), the numerical method can indeed match the analytic solution within errors of ±10-3% or less. The realistic input parameters used in the sample calculations suggest that such a range of Peclet numbers is indeed likely to characterize deep groundwater systems in granitic and ancient argillaceous systems. Thus TRUMP in its present form does provide a viable tool for use in nuclear waste evaluation studies. A sensitivity analysis based on the analytic solution suggests that the errors in prediction introduced due to uncertainties in input parameters are likely to be larger than the computational inaccuracies introduced by the numerical model. Currently, a disadvantage in the TRUMP model is that the iterative method of solving the set of simultaneous equations is rather slow when time constants vary widely over the flow region. Although the iterative solution may be very desirable for large three-dimensional problems in order to minimize computer storage, it seems desirable to use a direct solver technique in conjunction with the mixed explicit-implicit approach whenever possible. Work in this direction is in progress.

A reduced order model based on Kalman filtering for sequential data assimilation of turbulent flows

NASA Astrophysics Data System (ADS)

Meldi, M.; Poux, A.

2017-10-01

A Kalman filter based sequential estimator is presented in this work. The estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows. This technique provides an augmented flow state integrating available observation in the CFD model, naturally preserving a zero-divergence condition for the velocity field. Because of the prohibitive costs associated with a complete Kalman Filter application, two model reduction strategies have been proposed and assessed. These strategies dramatically reduce the increase in computational costs of the model, which can be quantified in an augmentation of 10%- 15% with respect to the classical numerical simulation. In addition, an extended analysis of the behavior of the numerical model covariance Q has been performed. Optimized values are strongly linked to the truncation error of the discretization procedure. The estimator has been applied to the analysis of a number of test cases exhibiting increasing complexity, including turbulent flow configurations. The results show that the augmented flow successfully improves the prediction of the physical quantities investigated, even when the observation is provided in a limited region of the physical domain. In addition, the present work suggests that these Data Assimilation techniques, which are at an embryonic stage of development in CFD, may have the potential to be pushed even further using the augmented prediction as a powerful tool for the optimization of the free parameters in the numerical simulation.

An Evaluation of Programmed Treatment-integrity Errors during Discrete-trial Instruction

ERIC Educational Resources Information Center

Carroll, Regina A.; Kodak, Tiffany; Fisher, Wayne W.

2013-01-01

This study evaluated the effects of programmed treatment-integrity errors on skill acquisition for children with an autism spectrum disorder (ASD) during discrete-trial instruction (DTI). In Study 1, we identified common treatment-integrity errors that occur during academic instruction in schools. In Study 2, we simultaneously manipulated 3…

ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.

USGS Publications Warehouse

Hromadka, T.V.

1987-01-01

Besides providing an exact solution for steady-state heat conduction processes (Laplace-Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil-water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximate boundary generation.

A simple analytical infiltration model for short-duration rainfall

NASA Astrophysics Data System (ADS)

Wang, Kaiwen; Yang, Xiaohua; Liu, Xiaomang; Liu, Changming

2017-12-01

Many infiltration models have been proposed to simulate infiltration process. Different initial soil conditions and non-uniform initial water content can lead to infiltration simulation errors, especially for short-duration rainfall (SHR). Few infiltration models are specifically derived to eliminate the errors caused by the complex initial soil conditions. We present a simple analytical infiltration model for SHR infiltration simulation, i.e., Short-duration Infiltration Process model (SHIP model). The infiltration simulated by 5 models (i.e., SHIP (high) model, SHIP (middle) model, SHIP (low) model, Philip model and Parlange model) were compared based on numerical experiments and soil column experiments. In numerical experiments, SHIP (middle) and Parlange models had robust solutions for SHR infiltration simulation of 12 typical soils under different initial soil conditions. The absolute values of percent bias were less than 12% and the values of Nash and Sutcliffe efficiency were greater than 0.83. Additionally, in soil column experiments, infiltration rate fluctuated in a range because of non-uniform initial water content. SHIP (high) and SHIP (low) models can simulate an infiltration range, which successfully covered the fluctuation range of the observed infiltration rate. According to the robustness of solutions and the coverage of fluctuation range of infiltration rate, SHIP model can be integrated into hydrologic models to simulate SHR infiltration process and benefit the flood forecast.

Molecular dynamics with rigid bodies: Alternative formulation and assessment of its limitations when employed to simulate liquid water

NASA Astrophysics Data System (ADS)

Silveira, Ana J.; Abreu, Charlles R. A.

2017-09-01

Sets of atoms collectively behaving as rigid bodies are often used in molecular dynamics to model entire molecules or parts thereof. This is a coarse-graining strategy that eliminates degrees of freedom and supposedly admits larger time steps without abandoning the atomistic character of a model. In this paper, we rely on a particular factorization of the rotation matrix to simplify the mechanical formulation of systems containing rigid bodies. We then propose a new derivation for the exact solution of torque-free rotations, which are employed as part of a symplectic numerical integration scheme for rigid-body dynamics. We also review methods for calculating pressure in systems of rigid bodies with pairwise-additive potentials and periodic boundary conditions. Finally, simulations of liquid phases, with special focus on water, are employed to analyze the numerical aspects of the proposed methodology. Our results show that energy drift is avoided for time step sizes up to 5 fs, but only if a proper smoothing is applied to the interatomic potentials. Despite this, the effects of discretization errors are relevant, even for smaller time steps. These errors induce, for instance, a systematic failure of the expected equipartition of kinetic energy between translational and rotational degrees of freedom.

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

NASA Technical Reports Server (NTRS)

Barth, Timothy; Saini, Subhash (Technical Monitor)

1999-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

A Novel Robust H∞ Filter Based on Krein Space Theory in the SINS/CNS Attitude Reference System.

PubMed

Yu, Fei; Lv, Chongyang; Dong, Qianhui

2016-03-18

Owing to their numerous merits, such as compact, autonomous and independence, the strapdown inertial navigation system (SINS) and celestial navigation system (CNS) can be used in marine applications. What is more, due to the complementary navigation information obtained from two different kinds of sensors, the accuracy of the SINS/CNS integrated navigation system can be enhanced availably. Thus, the SINS/CNS system is widely used in the marine navigation field. However, the CNS is easily interfered with by the surroundings, which will lead to the output being discontinuous. Thus, the uncertainty problem caused by the lost measurement will reduce the system accuracy. In this paper, a robust H∞ filter based on the Krein space theory is proposed. The Krein space theory is introduced firstly, and then, the linear state and observation models of the SINS/CNS integrated navigation system are established reasonably. By taking the uncertainty problem into account, in this paper, a new robust H∞ filter is proposed to improve the robustness of the integrated system. At last, this new robust filter based on the Krein space theory is estimated by numerical simulations and actual experiments. Additionally, the simulation and experiment results and analysis show that the attitude errors can be reduced by utilizing the proposed robust filter effectively when the measurements are missing discontinuous. Compared to the traditional Kalman filter (KF) method, the accuracy of the SINS/CNS integrated system is improved, verifying the robustness and the availability of the proposed robust H∞ filter.

Performance Improvement of Receivers Based on Ultra-Tight Integration in GNSS-Challenged Environments

PubMed Central

Qin, Feng; Zhan, Xingqun; Du, Gang

2013-01-01

Ultra-tight integration was first proposed by Abbott in 2003 with the purpose of integrating a global navigation satellite system (GNSS) and an inertial navigation system (INS). This technology can improve the tracking performances of a receiver by reconfiguring the tracking loops in GNSS-challenged environments. In this paper, the models of all error sources known to date in the phase lock loops (PLLs) of a standard receiver and an ultra-tightly integrated GNSS/INS receiver are built, respectively. Based on these models, the tracking performances of the two receivers are compared to verify the improvement due to the ultra-tight integration. Meanwhile, the PLL error distributions of the two receivers are also depicted to analyze the error changes of the tracking loops. These results show that the tracking error is significantly reduced in the ultra-tightly integrated GNSS/INS receiver since the receiver's dynamics are estimated and compensated by an INS. Moreover, the mathematical relationship between the tracking performances of the ultra-tightly integrated GNSS/INS receiver and the quality of the selected inertial measurement unit (IMU) is derived from the error models and proved by the error comparisons of four ultra-tightly integrated GNSS/INS receivers aided by different grade IMUs.

Comment on 'Shang S. 2012. Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step. Hydrological Processes 26: 3338-3343. DOI: 10.1002/hyp.8405'

NASA Technical Reports Server (NTRS)

Yatheendradas, Soni; Narapusetty, Balachandrudu; Peters-Lidard, Christa; Funk, Christopher; Verdin, James

2014-01-01

A previous study analyzed errors in the numerical calculation of actual crop evapotranspiration (ET(sub a)) under soil water stress. Assuming no irrigation or precipitation, it constructed equations for ET(sub a) over limited soil-water ranges in a root zone drying out due to evapotranspiration. It then used a single crop-soil composite to provide recommendations about the appropriate usage of numerical methods under different values of the time step and the maximum crop evapotranspiration (ET(sub c)). This comment reformulates those ET(sub a) equations for applicability over the full range of soil water values, revealing a dependence of the relative error in numerical ET(sub a) on the initial soil water that was not seen in the previous study. It is shown that the recommendations based on a single crop-soil composite can be invalid for other crop-soil composites. Finally, a consideration of the numerical error in the time-cumulative value of ET(sub a) is discussed besides the existing consideration of that error over individual time steps as done in the previous study. This cumulative ET(sub a) is more relevant to the final crop yield.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sudiarta, I. Wayan; Angraini, Lily Maysari, E-mail: lilyangraini@unram.ac.id

We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.

Approximation of the exponential integral (well function) using sampling methods

NASA Astrophysics Data System (ADS)

Baalousha, Husam Musa

2015-04-01

Exponential integral (also known as well function) is often used in hydrogeology to solve Theis and Hantush equations. Many methods have been developed to approximate the exponential integral. Most of these methods are based on numerical approximations and are valid for a certain range of the argument value. This paper presents a new approach to approximate the exponential integral. The new approach is based on sampling methods. Three different sampling methods; Latin Hypercube Sampling (LHS), Orthogonal Array (OA), and Orthogonal Array-based Latin Hypercube (OA-LH) have been used to approximate the function. Different argument values, covering a wide range, have been used. The results of sampling methods were compared with results obtained by Mathematica software, which was used as a benchmark. All three sampling methods converge to the result obtained by Mathematica, at different rates. It was found that the orthogonal array (OA) method has the fastest convergence rate compared with LHS and OA-LH. The root mean square error RMSE of OA was in the order of 1E-08. This method can be used with any argument value, and can be used to solve other integrals in hydrogeology such as the leaky aquifer integral.

Optimization of planar PIV-based pressure estimates in laminar and turbulent wakes

NASA Astrophysics Data System (ADS)

McClure, Jeffrey; Yarusevych, Serhiy

2017-05-01

The performance of four pressure estimation techniques using Eulerian material acceleration estimates from planar, two-component Particle Image Velocimetry (PIV) data were evaluated in a bluff body wake. To allow for the ground truth comparison of the pressure estimates, direct numerical simulations of flow over a circular cylinder were used to obtain synthetic velocity fields. Direct numerical simulations were performed for Re_D = 100, 300, and 1575, spanning laminar, transitional, and turbulent wake regimes, respectively. A parametric study encompassing a range of temporal and spatial resolutions was performed for each Re_D. The effect of random noise typical of experimental velocity measurements was also evaluated. The results identified optimal temporal and spatial resolutions that minimize the propagation of random and truncation errors to the pressure field estimates. A model derived from linear error propagation through the material acceleration central difference estimators was developed to predict these optima, and showed good agreement with the results from common pressure estimation techniques. The results of the model are also shown to provide acceptable first-order approximations for sampling parameters that reduce error propagation when Lagrangian estimations of material acceleration are employed. For pressure integration based on planar PIV, the effect of flow three-dimensionality was also quantified, and shown to be most pronounced at higher Reynolds numbers downstream of the vortex formation region, where dominant vortices undergo substantial three-dimensional deformations. The results of the present study provide a priori recommendations for the use of pressure estimation techniques from experimental PIV measurements in vortex dominated laminar and turbulent wake flows.

A new flux-conserving numerical scheme for the steady, incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.

1994-01-01

This paper is concerned with the continued development of a new numerical method, the space-time solution element (STS) method, for solving conservation laws. The present work focuses on the two-dimensional, steady, incompressible Navier-Stokes equations. Using first an integral approach, and then a differential approach, the discrete flux conservation equations presented in a recent paper are rederived. Here a simpler method for determining the flux expressions at cell interfaces is given; a systematic and rigorous derivation of the conditions used to simulate the differential form of the governing conservation law(s) is provided; necessary and sufficient conditions for a discrete approximation to satisfy a conservation law in E2 are derived; and an estimate of the local truncation error is given. A specific scheme is then constructed for the solution of the thin airfoil boundary layer problem. Numerical results are presented which demonstrate the ability of the scheme to accurately resolve the developing boundary layer and wake regions using grids which are much coarser than those employed by other numerical methods. It is shown that ten cells in the cross-stream direction are sufficient to accurately resolve the developing airfoil boundary layer.

Efficient and precise calculation of the b-matrix elements in diffusion-weighted imaging pulse sequences.

PubMed

Zubkov, Mikhail; Stait-Gardner, Timothy; Price, William S

2014-06-01

Precise NMR diffusion measurements require detailed knowledge of the cumulative dephasing effect caused by the numerous gradient pulses present in most NMR pulse sequences. This effect, which ultimately manifests itself as the diffusion-related NMR signal attenuation, is usually described by the b-value or the b-matrix in the case of multidirectional diffusion weighting, the latter being common in diffusion-weighted NMR imaging. Neglecting some of the gradient pulses introduces an error in the calculated diffusion coefficient reaching in some cases 100% of the expected value. Therefore, ensuring the b-matrix calculation includes all the known gradient pulses leads to significant error reduction. Calculation of the b-matrix for simple gradient waveforms is rather straightforward, yet it grows cumbersome when complexly shaped and/or numerous gradient pulses are introduced. Making three broad assumptions about the gradient pulse arrangement in a sequence results in an efficient framework for calculation of b-matrices as well providing some insight into optimal gradient pulse placement. The framework allows accounting for the diffusion-sensitising effect of complexly shaped gradient waveforms with modest computational time and power. This is achieved by using the b-matrix elements of the simple unmodified pulse sequence and minimising the integration of the complexly shaped gradient waveform in the modified sequence. Such re-evaluation of the b-matrix elements retains all the analytical relevance of the straightforward approach, yet at least halves the amount of symbolic integration required. The application of the framework is demonstrated with the evaluation of the expression describing the diffusion-sensitizing effect, caused by different bipolar gradient pulse modules. Copyright © 2014 Elsevier Inc. All rights reserved.

A Floating Node Method for the Modelling of Discontinuities Within a Finite Element

NASA Technical Reports Server (NTRS)

Pinho, Silvestre T.; Chen, B. Y.; DeCarvalho, Nelson V.; Baiz, P. M.; Tay, T. E.

2013-01-01

This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.

Efficient field-theoretic simulation of polymer solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Villet, Michael C.; Fredrickson, Glenn H., E-mail: ghf@mrl.ucsb.edu; Department of Materials, University of California, Santa Barbara, California 93106

2014-12-14

We present several developments that facilitate the efficient field-theoretic simulation of polymers by complex Langevin sampling. A regularization scheme using finite Gaussian excluded volume interactions is used to derive a polymer solution model that appears free of ultraviolet divergences and hence is well-suited for lattice-discretized field theoretic simulation. We show that such models can exhibit ultraviolet sensitivity, a numerical pathology that dramatically increases sampling error in the continuum lattice limit, and further show that this pathology can be eliminated by appropriate model reformulation by variable transformation. We present an exponential time differencing algorithm for integrating complex Langevin equations for fieldmore » theoretic simulation, and show that the algorithm exhibits excellent accuracy and stability properties for our regularized polymer model. These developments collectively enable substantially more efficient field-theoretic simulation of polymers, and illustrate the importance of simultaneously addressing analytical and numerical pathologies when implementing such computations.« less

Pre-University Students' Errors in Integration of Rational Functions and Implications for Classroom Teaching

ERIC Educational Resources Information Center

Yee, Ng Kin; Lam, Toh Tin

2008-01-01

This paper reports on students' errors in performing integration of rational functions, a topic of calculus in the pre-university mathematics classrooms. Generally the errors could be classified as those due to the students' weak algebraic concepts and their lack of understanding of the concept of integration. With the students' inability to link…

Using integrating spheres with wavelength modulation spectroscopy: effect of pathlength distribution on 2nd harmonic signals

NASA Astrophysics Data System (ADS)

Hodgkinson, J.; Masiyano, D.; Tatam, R. P.

2013-02-01

We have studied the effect on 2nd harmonic wavelength modulation spectroscopy of the use of integrating spheres as multipass gas cells. The gas lineshape becomes distorted at high concentrations, as a consequence of the exponential pathlength distribution of the sphere, introducing nonlinearity beyond that expected from the Beer-Lambert law. We have modelled this numerically for methane absorption at 1.651 μm, with gas concentrations in the range of 0-2.5 %vol in air. The results of this model compare well with experimental measurements. The nonlinearity for the 2 fWMS measurements is larger than that for direct scan measurements; if this additional effect were not accounted for, the resulting error would be approximately 20 % of the reading at a concentration of 2.5 %vol methane.

A precision analogue integrator system for heavy current measurement in MFDC resistance spot welding

NASA Astrophysics Data System (ADS)

Xia, Yu-Jun; Zhang, Zhong-Dian; Xia, Zhen-Xin; Zhu, Shi-Liang; Zhang, Rui

2016-02-01

In order to control and monitor the quality of middle frequency direct current (MFDC) resistance spot welding (RSW), precision measurement of the welding current up to 100 kA is required, for which Rogowski coils are the only viable current transducers at present. Thus, a highly accurate analogue integrator is the key to restoring the converted signals collected from the Rogowski coils. Previous studies emphasised that the integration drift is a major factor that influences the performance of analogue integrators, but capacitive leakage error also has a significant impact on the result, especially in long-time pulse integration. In this article, new methods of measuring and compensating capacitive leakage error are proposed to fabricate a precision analogue integrator system for MFDC RSW. A voltage holding test is carried out to measure the integration error caused by capacitive leakage, and an original integrator with a feedback adder is designed to compensate capacitive leakage error in real time. The experimental results and statistical analysis show that the new analogue integrator system could constrain both drift and capacitive leakage error, of which the effect is robust to different voltage levels of output signals. The total integration error is limited within  ±0.09 mV s-1 0.005% s-1 or full scale at a 95% confidence level, which makes it possible to achieve the precision measurement of the welding current of MFDC RSW with Rogowski coils of 0.1% accuracy class.

The State Geologic Map Compilation (SGMC) geodatabase of the conterminous United States

USGS Publications Warehouse

Horton, John D.; San Juan, Carma A.; Stoeser, Douglas B.

2017-06-30

The State Geologic Map Compilation (SGMC) geodatabase of the conterminous United States (https://doi. org/10.5066/F7WH2N65) represents a seamless, spatial database of 48 State geologic maps that range from 1:50,000 to 1:1,000,000 scale. A national digital geologic map database is essential in interpreting other datasets that support numerous types of national-scale studies and assessments, such as those that provide geochemistry, remote sensing, or geophysical data. The SGMC is a compilation of the individual U.S. Geological Survey releases of the Preliminary Integrated Geologic Map Databases for the United States. The SGMC geodatabase also contains updated data for seven States and seven entirely new State geologic maps that have been added since the preliminary databases were published. Numerous errors have been corrected and enhancements added to the preliminary datasets using thorough quality assurance/quality control procedures. The SGMC is not a truly integrated geologic map database because geologic units have not been reconciled across State boundaries. However, the geologic data contained in each State geologic map have been standardized to allow spatial analyses of lithology, age, and stratigraphy at a national scale.

Deep Kalman Filter: Simultaneous Multi-Sensor Integration and Modelling; A GNSS/IMU Case Study

PubMed Central

Hosseinyalamdary, Siavash

2018-01-01

Bayes filters, such as the Kalman and particle filters, have been used in sensor fusion to integrate two sources of information and obtain the best estimate of unknowns. The efficient integration of multiple sensors requires deep knowledge of their error sources. Some sensors, such as Inertial Measurement Unit (IMU), have complicated error sources. Therefore, IMU error modelling and the efficient integration of IMU and Global Navigation Satellite System (GNSS) observations has remained a challenge. In this paper, we developed deep Kalman filter to model and remove IMU errors and, consequently, improve the accuracy of IMU positioning. To achieve this, we added a modelling step to the prediction and update steps of the Kalman filter, so that the IMU error model is learned during integration. The results showed our deep Kalman filter outperformed the conventional Kalman filter and reached a higher level of accuracy. PMID:29695119

Deep Kalman Filter: Simultaneous Multi-Sensor Integration and Modelling; A GNSS/IMU Case Study.

PubMed

Hosseinyalamdary, Siavash

2018-04-24

Bayes filters, such as the Kalman and particle filters, have been used in sensor fusion to integrate two sources of information and obtain the best estimate of unknowns. The efficient integration of multiple sensors requires deep knowledge of their error sources. Some sensors, such as Inertial Measurement Unit (IMU), have complicated error sources. Therefore, IMU error modelling and the efficient integration of IMU and Global Navigation Satellite System (GNSS) observations has remained a challenge. In this paper, we developed deep Kalman filter to model and remove IMU errors and, consequently, improve the accuracy of IMU positioning. To achieve this, we added a modelling step to the prediction and update steps of the Kalman filter, so that the IMU error model is learned during integration. The results showed our deep Kalman filter outperformed the conventional Kalman filter and reached a higher level of accuracy.

Lost in Translation: the Case for Integrated Testing

NASA Technical Reports Server (NTRS)

Young, Aaron

2017-01-01

The building of a spacecraft is complex and often involves multiple suppliers and companies that have their own designs and processes. Standards have been developed across the industries to reduce the chances for critical flight errors at the system level, but the spacecraft is still vulnerable to the introduction of critical errors during integration of these systems. Critical errors can occur at any time during the process and in many cases, human reliability analysis (HRA) identifies human error as a risk driver. Most programs have a test plan in place that is intended to catch these errors, but it is not uncommon for schedule and cost stress to result in less testing than initially planned. Therefore, integrated testing, or "testing as you fly," is essential as a final check on the design and assembly to catch any errors prior to the mission. This presentation will outline the unique benefits of integrated testing by catching critical flight errors that can otherwise go undetected, discuss HRA methods that are used to identify opportunities for human error, lessons learned and challenges over ownership of testing will be discussed.

A POSTERIORI ERROR ANALYSIS OF TWO STAGE COMPUTATION METHODS WITH APPLICATION TO EFFICIENT DISCRETIZATION AND THE PARAREAL ALGORITHM.

PubMed

Chaudhry, Jehanzeb Hameed; Estep, Don; Tavener, Simon; Carey, Varis; Sandelin, Jeff

2016-01-01

We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute "dual-weighted" a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.

A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

NASA Astrophysics Data System (ADS)

Huang, Weizhang; Kamenski, Lennard; Lang, Jens

2010-03-01

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauß-Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.

Finite Element A Posteriori Error Estimation for Heat Conduction. Degree awarded by George Washington Univ.

NASA Technical Reports Server (NTRS)

Lang, Christapher G.; Bey, Kim S. (Technical Monitor)

2002-01-01

This research investigates residual-based a posteriori error estimates for finite element approximations of heat conduction in single-layer and multi-layered materials. The finite element approximation, based upon hierarchical modelling combined with p-version finite elements, is described with specific application to a two-dimensional, steady state, heat-conduction problem. Element error indicators are determined by solving an element equation for the error with the element residual as a source, and a global error estimate in the energy norm is computed by collecting the element contributions. Numerical results of the performance of the error estimate are presented by comparisons to the actual error. Two methods are discussed and compared for approximating the element boundary flux. The equilibrated flux method provides more accurate results for estimating the error than the average flux method. The error estimation is applied to multi-layered materials with a modification to the equilibrated flux method to approximate the discontinuous flux along a boundary at the material interfaces. A directional error indicator is developed which distinguishes between the hierarchical modeling error and the finite element error. Numerical results are presented for single-layered materials which show that the directional indicators accurately determine which contribution to the total error dominates.

Improving the Numerical Stability of Fast Matrix Multiplication

DOE PAGES

Ballard, Grey; Benson, Austin R.; Druinsky, Alex; ...

2016-10-04

Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications. However, there exist many practical alternatives to Strassen's algorithm with varying performance and numerical properties. Fast algorithms are known to be numerically stable, but because their error bounds are slightly weaker than the classical algorithm, they are not used even in cases where they provide a performance benefit. We argue in this study that the numerical sacrifice of fastmore » algorithms, particularly for the typical use cases of practical algorithms, is not prohibitive, and we explore ways to improve the accuracy both theoretically and empirically. The numerical accuracy of fast matrix multiplication depends on properties of the algorithm and of the input matrices, and we consider both contributions independently. We generalize and tighten previous error analyses of fast algorithms and compare their properties. We discuss algorithmic techniques for improving the error guarantees from two perspectives: manipulating the algorithms, and reducing input anomalies by various forms of diagonal scaling. In conclusion, we benchmark performance and demonstrate our improved numerical accuracy.« less

Error Control with Perfectly Matched Layer or Damping Layer Treatments for Computational Aeroacoustics with Jet Flows

NASA Technical Reports Server (NTRS)

Goodrich, John W.

2009-01-01

In this paper we show by means of numerical experiments that the error introduced in a numerical domain because of a Perfectly Matched Layer or Damping Layer boundary treatment can be controlled. These experimental demonstrations are for acoustic propagation with the Linearized Euler Equations with both uniform and steady jet flows. The propagating signal is driven by a time harmonic pressure source. Combinations of Perfectly Matched and Damping Layers are used with different damping profiles. These layer and profile combinations allow the relative error introduced by a layer to be kept as small as desired, in principle. Tradeoffs between error and cost are explored.

General linear codes for fault-tolerant matrix operations on processor arrays

NASA Technical Reports Server (NTRS)

Nair, V. S. S.; Abraham, J. A.

1988-01-01

Various checksum codes have been suggested for fault-tolerant matrix computations on processor arrays. Use of these codes is limited due to potential roundoff and overflow errors. Numerical errors may also be misconstrued as errors due to physical faults in the system. In this a set of linear codes is identified which can be used for fault-tolerant matrix operations such as matrix addition, multiplication, transposition, and LU-decomposition, with minimum numerical error. Encoding schemes are given for some of the example codes which fall under the general set of codes. With the help of experiments, a rule of thumb for the selection of a particular code for a given application is derived.

Stochastic Integration H∞ Filter for Rapid Transfer Alignment of INS.

PubMed

Zhou, Dapeng; Guo, Lei

2017-11-18

The performance of an inertial navigation system (INS) operated on a moving base greatly depends on the accuracy of rapid transfer alignment (RTA). However, in practice, the coexistence of large initial attitude errors and uncertain observation noise statistics poses a great challenge for the estimation accuracy of misalignment angles. This study aims to develop a novel robust nonlinear filter, namely the stochastic integration H ∞ filter (SIH ∞ F) for improving both the accuracy and robustness of RTA. In this new nonlinear H ∞ filter, the stochastic spherical-radial integration rule is incorporated with the framework of the derivative-free H ∞ filter for the first time, and the resulting SIH ∞ F simultaneously attenuates the negative effect in estimations caused by significant nonlinearity and large uncertainty. Comparisons between the SIH ∞ F and previously well-known methodologies are carried out by means of numerical simulation and a van test. The results demonstrate that the newly-proposed method outperforms the cubature H ∞ filter. Moreover, the SIH ∞ F inherits the benefit of the traditional stochastic integration filter, but with more robustness in the presence of uncertainty.

Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers

NASA Technical Reports Server (NTRS)

Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)

2001-01-01

A method of minimizing numerical errors, and improving nonlinear stability and accuracy associated with low Mach number computational aeroacoustics (CAA) is proposed. The method consists of two levels. From the governing equation level, we condition the Euler equations in two steps. The first step is to split the inviscid flux derivatives into a conservative and a non-conservative portion that satisfies a so called generalized energy estimate. This involves the symmetrization of the Euler equations via a transformation of variables that are functions of the physical entropy. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the second step is to reformulate the split Euler equations in perturbation form with the new unknowns as the small changes of the conservative variables with respect to their large stagnation values. From the numerical scheme level, a stable sixth-order central interior scheme with a third-order boundary schemes that satisfies the discrete analogue of the integration-by-parts procedure used in the continuous energy estimate (summation-by-parts property) is employed.

A microkernel design for component-based parallel numerical software systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balay, S.

1999-01-13

What is the minimal software infrastructure and what type of conventions are needed to simplify development of sophisticated parallel numerical application codes using a variety of software components that are not necessarily available as source code? We propose an opaque object-based model where the objects are dynamically loadable from the file system or network. The microkernel required to manage such a system needs to include, at most: (1) a few basic services, namely--a mechanism for loading objects at run time via dynamic link libraries, and consistent schemes for error handling and memory management; and (2) selected methods that all objectsmore » share, to deal with object life (destruction, reference counting, relationships), and object observation (viewing, profiling, tracing). We are experimenting with these ideas in the context of extensible numerical software within the ALICE (Advanced Large-scale Integrated Computational Environment) project, where we are building the microkernel to manage the interoperability among various tools for large-scale scientific simulations. This paper presents some preliminary observations and conclusions from our work with microkernel design.« less

Numerical and experimental study of a high port-density WDM optical packet switch architecture for data centers.

PubMed

Di Lucente, S; Luo, J; Centelles, R Pueyo; Rohit, A; Zou, S; Williams, K A; Dorren, H J S; Calabretta, N

2013-01-14

Data centers have to sustain the rapid growth of data traffic due to the increasing demand of bandwidth-hungry internet services. The current intra-data center fat tree topology causes communication bottlenecks in the server interaction process, power-hungry O-E-O conversions that limit the minimum latency and the power efficiency of these systems. In this paper we numerically and experimentally investigate an optical packet switch architecture with modular structure and highly distributed control that allow configuration times in the order of nanoseconds. Numerical results indicate that the candidate architecture scaled over 4000 ports, provides an overall throughput over 50 Tb/s and a packet loss rate below 10(-6) while assuring sub-microsecond latency. We present experimental results that demonstrate the feasibility of a 16x16 optical packet switch based on parallel 1x4 integrated optical cross-connect modules. Error-free operations can be achieved with 4 dB penalty while the overall energy consumption is of 66 pJ/b. Based on those results, we discuss feasibility to scale the architecture to a much larger port count.

Probabilistic In Situ Stress Estimation and Forecasting using Sequential Data Assimilation

NASA Astrophysics Data System (ADS)

Fichtner, A.; van Dinther, Y.; Kuensch, H. R.

2017-12-01

Our physical understanding and forecasting ability of earthquakes, and other solid Earth dynamic processes, is significantly hampered by limited indications on the evolving state of stress and strength on faults. Integrating observations and physics-based numerical modeling to quantitatively estimate this evolution of a fault's state is crucial. However, systematic attempts are limited and tenuous, especially in light of the scarcity and uncertainty of natural data and the difficulty of modelling the physics governing earthquakes. We adopt the statistical framework of sequential data assimilation - extensively developed for weather forecasting - to efficiently integrate observations and prior knowledge in a forward model, while acknowledging errors in both. To prove this concept we perform a perfect model test in a simplified subduction zone setup, where we assimilate synthetic noised data on velocities and stresses from a single location. Using an Ensemble Kalman Filter, these data and their errors are assimilated to update 150 ensemble members from a Partial Differential Equation-driven seismic cycle model. Probabilistic estimates of fault stress and dynamic strength evolution capture the truth exceptionally well. This is possible, because the sampled error covariance matrix contains prior information from the physics that relates velocities, stresses and pressure at the surface to those at the fault. During the analysis step, stress and strength distributions are thus reconstructed such that fault coupling can be updated to either inhibit or trigger events. In the subsequent forecast step the physical equations are solved to propagate the updated states forward in time and thus provide probabilistic information on the occurrence of the next event. At subsequent assimilation steps, the system's forecasting ability turns out to be significantly better than that of a periodic recurrence model (requiring an alarm 17% vs. 68% of the time). This thus provides distinct added value with respect to using observations or numerical models separately. Although several challenges for applications to a natural setting remain, these first results indicate the large potential of data assimilation techniques for probabilistic seismic hazard assessment and other challenges in dynamic solid earth systems.

Photorealistic ray tracing to visualize automobile side mirror reflective scenes.

PubMed

Lee, Hocheol; Kim, Kyuman; Lee, Gang; Lee, Sungkoo; Kim, Jingu

2014-10-20

We describe an interactive visualization procedure for determining the optimal surface of a special automobile side mirror, thereby removing the blind spot, without the need for feedback from the error-prone manufacturing process. If the horizontally progressive curvature distributions are set to the semi-mathematical expression for a free-form surface, the surface point set can then be derived through numerical integration. This is then converted to a NURBS surface while retaining the surface curvature. Then, reflective scenes from the driving environment can be virtually realized using photorealistic ray tracing, in order to evaluate how these reflected images would appear to drivers.

Application of the Discrete Regularization Method to the Inverse of the Chord Vibration Equation

NASA Astrophysics Data System (ADS)

Wang, Linjun; Han, Xu; Wei, Zhouchao

The inverse problem of the initial condition about the boundary value of the chord vibration equation is ill-posed. First, we transform it into a Fredholm integral equation. Second, we discretize it by the trapezoidal formula method, and then obtain a severely ill-conditioned linear equation, which is sensitive to the disturbance of the data. In addition, the tiny error of right data causes the huge concussion of the solution. We cannot obtain good results by the traditional method. In this paper, we solve this problem by the Tikhonov regularization method, and the numerical simulations demonstrate that this method is feasible and effective.

Climate Prediction for Brazil's Nordeste: Performance of Empirical and Numerical Modeling Methods.

NASA Astrophysics Data System (ADS)

Moura, Antonio Divino; Hastenrath, Stefan

2004-07-01

Comparisons of performance of climate forecast methods require consistency in the predictand and a long common reference period. For Brazil's Nordeste, empirical methods developed at the University of Wisconsin use preseason (October January) rainfall and January indices of the fields of meridional wind component and sea surface temperature (SST) in the tropical Atlantic and the equatorial Pacific as input to stepwise multiple regression and neural networking. These are used to predict the March June rainfall at a network of 27 stations. An experiment at the International Research Institute for Climate Prediction, Columbia University, with a numerical model (ECHAM4.5) used global SST information through February to predict the March June rainfall at three grid points in the Nordeste. The predictands for the empirical and numerical model forecasts are correlated at +0.96, and the period common to the independent portion of record of the empirical prediction and the numerical modeling is 1968 99. Over this period, predicted versus observed rainfall are evaluated in terms of correlation, root-mean-square error, absolute error, and bias. Performance is high for both approaches. Numerical modeling produces a correlation of +0.68, moderate errors, and strong negative bias. For the empirical methods, errors and bias are small, and correlations of +0.73 and +0.82 are reached between predicted and observed rainfall.

More on Systematic Error in a Boyle's Law Experiment

ERIC Educational Resources Information Center

McCall, Richard P.

2012-01-01

A recent article in "The Physics Teacher" describes a method for analyzing a systematic error in a Boyle's law laboratory activity. Systematic errors are important to consider in physics labs because they tend to bias the results of measurements. There are numerous laboratory examples and resources that discuss this common source of error.

Fluorescence errors in integrating sphere measurements of remote phosphor type LED light sources

NASA Astrophysics Data System (ADS)

Keppens, A.; Zong, Y.; Podobedov, V. B.; Nadal, M. E.; Hanselaer, P.; Ohno, Y.

2011-05-01

The relative spectral radiant flux error caused by phosphor fluorescence during integrating sphere measurements is investigated both theoretically and experimentally. Integrating sphere and goniophotometer measurements are compared and used for model validation, while a case study provides additional clarification. Criteria for reducing fluorescence errors to a degree of negligibility as well as a fluorescence error correction method based on simple matrix algebra are presented. Only remote phosphor type LED light sources are studied because of their large phosphor surfaces and high application potential in general lighting.

The combined geodetic network adjusted on the reference ellipsoid - a comparison of three functional models for GNSS observations

NASA Astrophysics Data System (ADS)

Kadaj, Roman

2016-12-01

The adjustment problem of the so-called combined (hybrid, integrated) network created with GNSS vectors and terrestrial observations has been the subject of many theoretical and applied works. The network adjustment in various mathematical spaces was considered: in the Cartesian geocentric system on a reference ellipsoid and on a mapping plane. For practical reasons, it often takes a geodetic coordinate system associated with the reference ellipsoid. In this case, the Cartesian GNSS vectors are converted, for example, into geodesic parameters (azimuth and length) on the ellipsoid, but the simple form of converted pseudo-observations are the direct differences of the geodetic coordinates. Unfortunately, such an approach may be essentially distorted by a systematic error resulting from the position error of the GNSS vector, before its projection on the ellipsoid surface. In this paper, an analysis of the impact of this error on the determined measures of geometric ellipsoid elements, including the differences of geodetic coordinates or geodesic parameters is presented. Assuming that the adjustment of a combined network on the ellipsoid shows that the optimal functional approach in relation to the satellite observation, is to create the observational equations directly for the original GNSS Cartesian vector components, writing them directly as a function of the geodetic coordinates (in numerical applications, we use the linearized forms of observational equations with explicitly specified coefficients). While retaining the original character of the Cartesian vector, one avoids any systematic errors that may occur in the conversion of the original GNSS vectors to ellipsoid elements, for example the vector of the geodesic parameters. The problem is theoretically developed and numerically tested. An example of the adjustment of a subnet loaded from the database of reference stations of the ASG-EUPOS system was considered for the preferred functional model of the GNSS observations.

Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays.

PubMed

Rakkiyappan, R; Sakthivel, N; Cao, Jinde

2015-06-01

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen's inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods. Copyright © 2015 Elsevier Ltd. All rights reserved.

Parametric optimization in virtual prototyping environment of the control device for a robotic system used in thin layers deposition

NASA Astrophysics Data System (ADS)

Enescu (Balaş, M. L.; Alexandru, C.

2016-08-01

The paper deals with the optimal design of the control system for a 6-DOF robot used in thin layers deposition. The optimization is based on parametric technique, by modelling the design objective as a numerical function, and then establishing the optimal values of the design variables so that to minimize the objective function. The robotic system is a mechatronic product, which integrates the mechanical device and the controlled operating device.The mechanical device of the robot was designed in the CAD (Computer Aided Design) software CATIA, the 3D-model being then transferred to the MBS (Multi-Body Systems) environment ADAMS/View. The control system was developed in the concurrent engineering concept, through the integration with the MBS mechanical model, by using the DFC (Design for Control) software solution EASY5. The necessary angular motions in the six joints of the robot, in order to obtain the imposed trajectory of the end-effector, have been established by performing the inverse kinematic analysis. The positioning error in each joint of the robot is used as design objective, the optimization goal being to minimize the root mean square during simulation, which is a measure of the magnitude of the positioning error varying quantity.

Numerically accurate computational techniques for optimal estimator analyses of multi-parameter models

NASA Astrophysics Data System (ADS)

Berger, Lukas; Kleinheinz, Konstantin; Attili, Antonio; Bisetti, Fabrizio; Pitsch, Heinz; Mueller, Michael E.

2018-05-01

Modelling unclosed terms in partial differential equations typically involves two steps: First, a set of known quantities needs to be specified as input parameters for a model, and second, a specific functional form needs to be defined to model the unclosed terms by the input parameters. Both steps involve a certain modelling error, with the former known as the irreducible error and the latter referred to as the functional error. Typically, only the total modelling error, which is the sum of functional and irreducible error, is assessed, but the concept of the optimal estimator enables the separate analysis of the total and the irreducible errors, yielding a systematic modelling error decomposition. In this work, attention is paid to the techniques themselves required for the practical computation of irreducible errors. Typically, histograms are used for optimal estimator analyses, but this technique is found to add a non-negligible spurious contribution to the irreducible error if models with multiple input parameters are assessed. Thus, the error decomposition of an optimal estimator analysis becomes inaccurate, and misleading conclusions concerning modelling errors may be drawn. In this work, numerically accurate techniques for optimal estimator analyses are identified and a suitable evaluation of irreducible errors is presented. Four different computational techniques are considered: a histogram technique, artificial neural networks, multivariate adaptive regression splines, and an additive model based on a kernel method. For multiple input parameter models, only artificial neural networks and multivariate adaptive regression splines are found to yield satisfactorily accurate results. Beyond a certain number of input parameters, the assessment of models in an optimal estimator analysis even becomes practically infeasible if histograms are used. The optimal estimator analysis in this paper is applied to modelling the filtered soot intermittency in large eddy simulations using a dataset of a direct numerical simulation of a non-premixed sooting turbulent flame.

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

NASA Astrophysics Data System (ADS)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates

NASA Astrophysics Data System (ADS)

Läuter, Matthias; Giraldo, Francis X.; Handorf, Dörthe; Dethloff, Klaus

2008-12-01

A global model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge-Kutta discontinuous Galerkin method on an unstructured triangular grid. The shallow water equations on the sphere, a two-dimensional surface in R3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two-dimensional representation of tangential momentum and therefore only two discrete momentum equations. The discontinuous Galerkin method consists of an integral formulation which requires both area (elements) and line (element faces) integrals. Here, we use a Rusanov numerical flux to resolve the discontinuous fluxes at the element faces. A strong stability-preserving third-order Runge-Kutta method is applied for the time discretization. The polynomial space of order k on each curved triangle of the grid is characterized by a Lagrange basis and requires high-order quadature rules for the integration over elements and element faces. For the presented method no mass matrix inversion is necessary, except in a preprocessing step. The validation of the atmospheric model has been done considering standard tests from Williamson et al. [D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211-224], unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream. A convergence rate of O(Δx) was observed in the model experiments. Furthermore, a numerical experiment is presented, for which the third-order time-integration method limits the model error. Thus, the time step Δt is restricted by both the CFL-condition and accuracy demands. Conservation of mass was shown up to machine precision and energy conservation converges for both increasing grid resolution and increasing polynomial order k.

Phobos laser ranging: Numerical Geodesy experiments for Martian system science

NASA Astrophysics Data System (ADS)

Dirkx, D.; Vermeersen, L. L. A.; Noomen, R.; Visser, P. N. A. M.

2014-09-01

Laser ranging is emerging as a technology for use over (inter)planetary distances, having the advantage of high (mm-cm) precision and accuracy and low mass and power consumption. We have performed numerical simulations to assess the science return in terms of geodetic observables of a hypothetical Phobos lander performing active two-way laser ranging with Earth-based stations. We focus our analysis on the estimation of Phobos and Mars gravitational, tidal and rotational parameters. We explicitly include systematic error sources in addition to uncorrelated random observation errors. This is achieved through the use of consider covariance parameters, specifically the ground station position and observation biases. Uncertainties for the consider parameters are set at 5 mm and at 1 mm for the Gaussian uncorrelated observation noise (for an observation integration time of 60 s). We perform the analysis for a mission duration up to 5 years. It is shown that a Phobos Laser Ranging (PLR) can contribute to a better understanding of the Martian system, opening the possibility for improved determination of a variety of physical parameters of Mars and Phobos. The simulations show that the mission concept is especially suited for estimating Mars tidal deformation parameters, estimating degree 2 Love numbers with absolute uncertainties at the 10-2 to 10-4 level after 1 and 4 years, respectively and providing separate estimates for the Martian quality factors at Sun and Phobos-forced frequencies. The estimation of Phobos libration amplitudes and gravity field coefficients provides an estimate of Phobos' relative equatorial and polar moments of inertia with an absolute uncertainty of 10-4 and 10-7, respectively, after 1 year. The observation of Phobos tidal deformation will be able to differentiate between a rubble pile and monolithic interior within 2 years. For all parameters, systematic errors have a much stronger influence (per unit uncertainty) than the uncorrelated Gaussian observation noise. This indicates the need for the inclusion of systematic errors in simulation studies and special attention to the mitigation of these errors in mission and system design.

Simple, accurate formula for the average bit error probability of multiple-input multiple-output free-space optical links over negative exponential turbulence channels.

PubMed

Peppas, Kostas P; Lazarakis, Fotis; Alexandridis, Antonis; Dangakis, Kostas

2012-08-01

In this Letter we investigate the error performance of multiple-input multiple-output free-space optical communication systems employing intensity modulation/direct detection and operating over strong atmospheric turbulence channels. Atmospheric-induced strong turbulence fading is modeled using the negative exponential distribution. For the considered system, an approximate yet accurate analytical expression for the average bit error probability is derived and an efficient method for its numerical evaluation is proposed. Numerically evaluated and computer simulation results are further provided to demonstrate the validity of the proposed mathematical analysis.

Estimating the designated use attainment decision error rates of US Environmental Protection Agency's proposed numeric total phosphorus criteria for Florida, USA, colored lakes.

PubMed

McLaughlin, Douglas B

2012-01-01

The utility of numeric nutrient criteria established for certain surface waters is likely to be affected by the uncertainty that exists in the presence of a causal link between nutrient stressor variables and designated use-related biological responses in those waters. This uncertainty can be difficult to characterize, interpret, and communicate to a broad audience of environmental stakeholders. The US Environmental Protection Agency (USEPA) has developed a systematic planning process to support a variety of environmental decisions, but this process is not generally applied to the development of national or state-level numeric nutrient criteria. This article describes a method for implementing such an approach and uses it to evaluate the numeric total P criteria recently proposed by USEPA for colored lakes in Florida, USA. An empirical, log-linear relationship between geometric mean concentrations of total P (a potential stressor variable) and chlorophyll a (a nutrient-related response variable) in these lakes-that is assumed to be causal in nature-forms the basis for the analysis. The use of the geometric mean total P concentration of a lake to correctly indicate designated use status, defined in terms of a 20 µg/L geometric mean chlorophyll a threshold, is evaluated. Rates of decision errors analogous to the Type I and Type II error rates familiar in hypothesis testing, and a 3rd error rate, E(ni) , referred to as the nutrient criterion-based impairment error rate, are estimated. The results show that USEPA's proposed "baseline" and "modified" nutrient criteria approach, in which data on both total P and chlorophyll a may be considered in establishing numeric nutrient criteria for a given lake within a specified range, provides a means for balancing and minimizing designated use attainment decision errors. Copyright © 2011 SETAC.

Simulation of wave propagation in three-dimensional random media

NASA Technical Reports Server (NTRS)

Coles, William A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1993-01-01

Quantitative error analysis for simulation of wave propagation in three dimensional random media assuming narrow angular scattering are presented for the plane wave and spherical wave geometry. This includes the errors resulting from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive index of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared to the spatial spectra of intensity. The numerical requirements for a simulation of given accuracy are determined for realizations of the field. The numerical requirements for accurate estimation of higher moments of the field are less stringent.

Integral methods of solving boundary-value problems of nonstationary heat conduction and their comparative analysis

NASA Astrophysics Data System (ADS)

Kot, V. A.

2017-11-01

The modern state of approximate integral methods used in applications, where the processes of heat conduction and heat and mass transfer are of first importance, is considered. Integral methods have found a wide utility in different fields of knowledge: problems of heat conduction with different heat-exchange conditions, simulation of thermal protection, Stefantype problems, microwave heating of a substance, problems on a boundary layer, simulation of a fluid flow in a channel, thermal explosion, laser and plasma treatment of materials, simulation of the formation and melting of ice, inverse heat problems, temperature and thermal definition of nanoparticles and nanoliquids, and others. Moreover, polynomial solutions are of interest because the determination of a temperature (concentration) field is an intermediate stage in the mathematical description of any other process. The following main methods were investigated on the basis of the error norms: the Tsoi and Postol’nik methods, the method of integral relations, the Gudman integral method of heat balance, the improved Volkov integral method, the matched integral method, the modified Hristov method, the Mayer integral method, the Kudinov method of additional boundary conditions, the Fedorov boundary method, the method of weighted temperature function, the integral method of boundary characteristics. It was established that the two last-mentioned methods are characterized by high convergence and frequently give solutions whose accuracy is not worse that the accuracy of numerical solutions.

Development of a 3-D Pen Input Device

DTIC Science & Technology

2008-09-01

of a unistroke which can be written on any surface or in the air while correcting integration errors from the...navigation frame of a unistroke, which can be written on any surface or in the air while correcting integration errors from the measurements of the IMU... be written on any surface or in the air while correcting integration errors from the measurements of the IMU (Inertial Measurement Unit) of the

A Novel Robust H∞ Filter Based on Krein Space Theory in the SINS/CNS Attitude Reference System

PubMed Central

Yu, Fei; Lv, Chongyang; Dong, Qianhui

2016-01-01

Owing to their numerous merits, such as compact, autonomous and independence, the strapdown inertial navigation system (SINS) and celestial navigation system (CNS) can be used in marine applications. What is more, due to the complementary navigation information obtained from two different kinds of sensors, the accuracy of the SINS/CNS integrated navigation system can be enhanced availably. Thus, the SINS/CNS system is widely used in the marine navigation field. However, the CNS is easily interfered with by the surroundings, which will lead to the output being discontinuous. Thus, the uncertainty problem caused by the lost measurement will reduce the system accuracy. In this paper, a robust H∞ filter based on the Krein space theory is proposed. The Krein space theory is introduced firstly, and then, the linear state and observation models of the SINS/CNS integrated navigation system are established reasonably. By taking the uncertainty problem into account, in this paper, a new robust H∞ filter is proposed to improve the robustness of the integrated system. At last, this new robust filter based on the Krein space theory is estimated by numerical simulations and actual experiments. Additionally, the simulation and experiment results and analysis show that the attitude errors can be reduced by utilizing the proposed robust filter effectively when the measurements are missing discontinuous. Compared to the traditional Kalman filter (KF) method, the accuracy of the SINS/CNS integrated system is improved, verifying the robustness and the availability of the proposed robust H∞ filter. PMID:26999153

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

A new numerically stable implementation of the T-matrix method for electromagnetic scattering by spheroidal particles

NASA Astrophysics Data System (ADS)

Somerville, W. R. C.; Auguié, B.; Le Ru, E. C.

2013-07-01

We propose, describe, and demonstrate a new numerically stable implementation of the extended boundary-condition method (EBCM) to compute the T-matrix for electromagnetic scattering by spheroidal particles. Our approach relies on the fact that for many of the EBCM integrals in the special case of spheroids, a leading part of the integrand integrates exactly to zero, which causes catastrophic loss of precision in numerical computations. This feature was in fact first pointed out by Waterman in the context of acoustic scattering and electromagnetic scattering by infinite cylinders. We have recently studied it in detail in the case of electromagnetic scattering by particles. Based on this study, the principle of our new implementation is therefore to compute all the integrands without the problematic part to avoid the primary cause of loss of precision. Particular attention is also given to choosing the algorithms that minimise loss of precision in every step of the method, without compromising on speed. We show that the resulting implementation can efficiently compute in double precision arithmetic the T-matrix and therefore optical properties of spheroidal particles to a high precision, often down to a remarkable accuracy (10-10 relative error), over a wide range of parameters that are typically considered problematic. We discuss examples such as high-aspect ratio metallic nanorods and large size parameter (≈35) dielectric particles, which had been previously modelled only using quadruple-precision arithmetic codes.

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.

2003-01-01

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

On synchronisation of a class of complex chaotic systems with complex unknown parameters via integral sliding mode control

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed; Karami-Mollaee, Ali

2018-06-01

Chaotic systems demonstrate complex behaviour in their state variables and their parameters, which generate some challenges and consequences. This paper presents a new synchronisation scheme based on integral sliding mode control (ISMC) method on a class of complex chaotic systems with complex unknown parameters. Synchronisation between corresponding states of a class of complex chaotic systems and also convergence of the errors of the system parameters to zero point are studied. The designed feedback control vector and complex unknown parameter vector are analytically achieved based on the Lyapunov stability theory. Moreover, the effectiveness of the proposed methodology is verified by synchronisation of the Chen complex system and the Lorenz complex systems as the leader and the follower chaotic systems, respectively. In conclusion, some numerical simulations related to the synchronisation methodology is given to illustrate the effectiveness of the theoretical discussions.

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

DOE PAGES

Huang, Lei; Xue, Junpeng; Gao, Bo; ...

2016-12-21

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Multi-boson block factorization of fermions

NASA Astrophysics Data System (ADS)

Giusti, Leonardo; Cè, Marco; Schaefer, Stefan

2018-03-01

The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are baryon masses and matrix elements, the hadronic vacuum polarization and the light-by-light scattering contributions to the muon g - 2, and the form factors of semileptonic B decays. Reliable and precise determinations of these quantities are very difficult if not impractical with state-of-the-art standard Monte Carlo integration schemes. I will review a recent proposal for factorizing the fermion determinant in lattice QCD that leads to a local action in the gauge field and in the auxiliary boson fields. Once combined with the corresponding factorization of the quark propagator, it paves the way for multi-level Monte Carlo integration in the presence of fermions opening new perspectives in lattice QCD. Exploratory results on the impact on the above mentioned observables will be presented.

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Lei; Xue, Junpeng; Gao, Bo

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Performance assessment of static lead-lag feedforward controllers for disturbance rejection in PID control loops.

PubMed

Yu, Zhenpeng; Wang, Jiandong

2016-09-01

This paper assesses the performance of feedforward controllers for disturbance rejection in univariate feedback plus feedforward control loops. The structures of feedback and feedforward controllers are confined to proportional-integral-derivative and static-lead-lag forms, respectively, and the effects of feedback controllers are not considered. The integral squared error (ISE) and total squared variation (TSV) are used as performance metrics. A performance index is formulated by comparing the current ISE and TSV metrics to their own lower bounds as performance benchmarks. A controller performance assessment (CPA) method is proposed to calculate the performance index from measurements. The proposed CPA method resolves two critical limitations in the existing CPA methods, in order to be consistent with industrial scenarios. Numerical and experimental examples illustrate the effectiveness of the obtained results. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Flow Mapping Based on the Motion-Integration Errors of Autonomous Underwater Vehicles

NASA Astrophysics Data System (ADS)

Chang, D.; Edwards, C. R.; Zhang, F.

2016-02-01

Knowledge of a flow field is crucial in the navigation of autonomous underwater vehicles (AUVs) since the motion of AUVs is affected by ambient flow. Due to the imperfect knowledge of the flow field, it is typical to observe a difference between the actual and predicted trajectories of an AUV, which is referred to as a motion-integration error (also known as a dead-reckoning error if an AUV navigates via dead-reckoning). The motion-integration error has been essential for an underwater glider to compute its flow estimate from the travel information of the last leg and to improve navigation performance by using the estimate for the next leg. However, the estimate by nature exhibits a phase difference compared to ambient flow experienced by gliders, prohibiting its application in a flow field with strong temporal and spatial gradients. In our study, to mitigate the phase problem, we have developed a local ocean model by combining the flow estimate based on the motion-integration error with flow predictions from a tidal ocean model. Our model has been used to create desired trajectories of gliders for guidance. Our method is validated by Long Bay experiments in 2012 and 2013 in which we deployed multiple gliders on the shelf of South Atlantic Bight and near the edge of Gulf Stream. In our recent study, the application of the motion-integration error is further extended to create a spatial flow map. Considering that the motion-integration errors of AUVs accumulate along their trajectories, the motion-integration error is formulated as a line integral of ambient flow which is then reformulated into algebraic equations. By solving an inverse problem for these algebraic equations, we obtain the knowledge of such flow in near real time, allowing more effective and precise guidance of AUVs in a dynamic environment. This method is referred to as motion tomography. We provide the results of non-parametric and parametric flow mapping from both simulated and experimental data.

Experimental validation of wireless communication with chaos.

PubMed

Ren, Hai-Peng; Bai, Chao; Liu, Jian; Baptista, Murilo S; Grebogi, Celso

2016-08-01

The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and an integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter.

Hyper-X Mach 10 Trajectory Reconstruction

NASA Technical Reports Server (NTRS)

Karlgaard, Christopher D.; Martin, John G.; Tartabini, Paul V.; Thornblom, Mark N.

2005-01-01

This paper discusses the formulation and development of a trajectory reconstruction tool for the NASA X-43A/Hyper-X high speed research vehicle, and its implementation for the reconstruction and analysis of flight test data. Extended Kalman filtering techniques are employed to reconstruct the trajectory of the vehicle, based upon numerical integration of inertial measurement data along with redundant measurements of the vehicle state. The equations of motion are formulated in order to include the effects of several systematic error sources, whose values may also be estimated by the filtering routines. Additionally, smoothing algorithms have been implemented in which the final value of the state (or an augmented state that includes other systematic error parameters to be estimated) and covariance are propagated back to the initial time to generate the best-estimated trajectory, based upon all available data. The methods are applied to the problem of reconstructing the trajectory of the Hyper-X vehicle from data obtained during the Mach 10 test flight, which occurred on November 16th 2004.

Use of upscaled elevation and surface roughness data in two-dimensional surface water models

USGS Publications Warehouse

Hughes, J.D.; Decker, J.D.; Langevin, C.D.

2011-01-01

In this paper, we present an approach that uses a combination of cell-block- and cell-face-averaging of high-resolution cell elevation and roughness data to upscale hydraulic parameters and accurately simulate surface water flow in relatively low-resolution numerical models. The method developed allows channelized features that preferentially connect large-scale grid cells at cell interfaces to be represented in models where these features are significantly smaller than the selected grid size. The developed upscaling approach has been implemented in a two-dimensional finite difference model that solves a diffusive wave approximation of the depth-integrated shallow surface water equations using preconditioned Newton–Krylov methods. Computational results are presented to show the effectiveness of the mixed cell-block and cell-face averaging upscaling approach in maintaining model accuracy, reducing model run-times, and how decreased grid resolution affects errors. Application examples demonstrate that sub-grid roughness coefficient variations have a larger effect on simulated error than sub-grid elevation variations.

Experimental validation of wireless communication with chaos

NASA Astrophysics Data System (ADS)

Ren, Hai-Peng; Bai, Chao; Liu, Jian; Baptista, Murilo S.; Grebogi, Celso

2016-08-01

The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and an integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter.

Experimental validation of wireless communication with chaos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Hai-Peng; Bai, Chao; Liu, Jian

The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and anmore » integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter.« less

A Bayesian approach to microwave precipitation profile retrieval

NASA Technical Reports Server (NTRS)

Evans, K. Franklin; Turk, Joseph; Wong, Takmeng; Stephens, Graeme L.

1995-01-01

A multichannel passive microwave precipitation retrieval algorithm is developed. Bayes theorem is used to combine statistical information from numerical cloud models with forward radiative transfer modeling. A multivariate lognormal prior probability distribution contains the covariance information about hydrometeor distribution that resolves the nonuniqueness inherent in the inversion process. Hydrometeor profiles are retrieved by maximizing the posterior probability density for each vector of observations. The hydrometeor profile retrieval method is tested with data from the Advanced Microwave Precipitation Radiometer (10, 19, 37, and 85 GHz) of convection over ocean and land in Florida. The CP-2 multiparameter radar data are used to verify the retrieved profiles. The results show that the method can retrieve approximate hydrometeor profiles, with larger errors over land than water. There is considerably greater accuracy in the retrieval of integrated hydrometeor contents than of profiles. Many of the retrieval errors are traced to problems with the cloud model microphysical information, and future improvements to the algorithm are suggested.

Faster and more accurate transport procedures for HZETRN

NASA Astrophysics Data System (ADS)

Slaba, T. C.; Blattnig, S. R.; Badavi, F. F.

2010-12-01

The deterministic transport code HZETRN was developed for research scientists and design engineers studying the effects of space radiation on astronauts and instrumentation protected by various shielding materials and structures. In this work, several aspects of code verification are examined. First, a detailed derivation of the light particle ( A ⩽ 4) and heavy ion ( A > 4) numerical marching algorithms used in HZETRN is given. References are given for components of the derivation that already exist in the literature, and discussions are given for details that may have been absent in the past. The present paper provides a complete description of the numerical methods currently used in the code and is identified as a key component of the verification process. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of round-off error is also given, and the impact of this error on previously predicted exposure quantities is shown. Finally, a coupled convergence study is conducted by refining the discretization parameters (step-size and energy grid-size). From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is determined that almost all of the discretization error in HZETRN is caused by the use of discretization parameters that violate a numerical convergence criterion related to charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms to 100 g/cm 2 in aluminum and water, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons between the old and new algorithms are given for one, two, and three layer slabs of 100 g/cm 2 of aluminum, polyethylene, and water. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations.

Faster and more accurate transport procedures for HZETRN

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slaba, T.C., E-mail: Tony.C.Slaba@nasa.go; Blattnig, S.R., E-mail: Steve.R.Blattnig@nasa.go; Badavi, F.F., E-mail: Francis.F.Badavi@nasa.go

The deterministic transport code HZETRN was developed for research scientists and design engineers studying the effects of space radiation on astronauts and instrumentation protected by various shielding materials and structures. In this work, several aspects of code verification are examined. First, a detailed derivation of the light particle (A {<=} 4) and heavy ion (A > 4) numerical marching algorithms used in HZETRN is given. References are given for components of the derivation that already exist in the literature, and discussions are given for details that may have been absent in the past. The present paper provides a complete descriptionmore » of the numerical methods currently used in the code and is identified as a key component of the verification process. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of round-off error is also given, and the impact of this error on previously predicted exposure quantities is shown. Finally, a coupled convergence study is conducted by refining the discretization parameters (step-size and energy grid-size). From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is determined that almost all of the discretization error in HZETRN is caused by the use of discretization parameters that violate a numerical convergence criterion related to charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms to 100 g/cm{sup 2} in aluminum and water, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons between the old and new algorithms are given for one, two, and three layer slabs of 100 g/cm{sup 2} of aluminum, polyethylene, and water. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations.« less

Comment on ``Scalings for radiation from plasma bubbles'' [Phys. Plasmas 17, 056708 (2010)

NASA Astrophysics Data System (ADS)

Corde, S.; Stordeur, A.; Malka, V.

2011-03-01

Thomas has recently derived scaling laws for x-ray radiation from electrons accelerated in plasma bubbles, as well as a threshold for the self-injection of background electrons into the bubble [A. G. R. Thomas, Phys. Plasmas 17, 056708 (2010)]. To obtain this threshold, the equations of motion for a test electron are studied within the frame of the bubble model, where the bubble is described by prescribed electromagnetic fields and has a perfectly spherical shape. The author affirms that any elliptical trajectory of the form x'2/γp2+y'2=R2 is solution of the equations of motion (in the bubble frame), within the approximation py'2/px'2≪1. In addition, he highlights that his result is different from the work of Kostyukov et al. [Phys. Rev. Lett. 103, 175003 (2009)], and explains the error committed by Kostyukov-Nerush-Pukhov-Seredov (KNPS). In this comment, we show that numerically integrated trajectories, based on the same equations than the analytical work of Thomas, lead to a completely different result for the self-injection threshold, the result published by KNPS [Phys. Rev. Lett. 103, 175003 (2009)]. We explain why the analytical analysis of Thomas fails and we provide a discussion based on numerical simulations which show exactly where the difference arises. We also show that the arguments of Thomas concerning the error of KNPS do not hold, and that their analysis is mathematically correct. Finally, we emphasize that if the KNPS threshold is found not to be verified in PIC (Particle In Cell) simulations or experiments, it is due to a deficiency of the model itself, and not to an error in the mathematical derivation.

A support-operator method for 3-D rupture dynamics

NASA Astrophysics Data System (ADS)

Ely, Geoffrey P.; Day, Steven M.; Minster, Jean-Bernard

2009-06-01

We present a numerical method to simulate spontaneous shear crack propagation within a heterogeneous, 3-D, viscoelastic medium. Wave motions are computed on a logically rectangular hexahedral mesh, using the generalized finite-difference method of Support Operators (SOM). This approach enables modelling of non-planar surfaces and non-planar fault ruptures. Our implementation, the Support Operator Rupture Dynamics (SORD) code, is highly scalable, enabling large-scale, multiprocessors calculations. The fault surface is modelled by coupled double nodes, where rupture occurs as dictated by the local stress conditions and a frictional failure law. The method successfully performs test problems developed for the Southern California Earthquake Center (SCEC)/U.S. Geological Survey (USGS) dynamic earthquake rupture code validation exercise, showing good agreement with semi-analytical boundary integral method results. We undertake further dynamic rupture tests to quantify numerical errors introduced by shear deformations to the hexahedral mesh. We generate a family of meshes distorted by simple shearing, in the along-strike direction, up to a maximum of 73°. For SCEC/USGS validation problem number 3, grid-induced errors increase with mesh shear angle, with the logarithm of error approximately proportional to angle over the range tested. At 73°, rms misfits are about 10 per cent for peak slip rate, and 0.5 per cent for both rupture time and total slip, indicating that the method (which, up to now, we have applied mainly to near-vertical strike-slip faulting) is also capable of handling geometries appropriate to low-angle surface-rupturing thrust earthquakes. Additionally, we demonstrate non-planar rupture effects, by modifying the test geometry to include, respectively, cylindrical curvature and sharp kinks.

Microgrid optimal scheduling considering impact of high penetration wind generation

NASA Astrophysics Data System (ADS)

Alanazi, Abdulaziz

The objective of this thesis is to study the impact of high penetration wind energy in economic and reliable operation of microgrids. Wind power is variable, i.e., constantly changing, and nondispatchable, i.e., cannot be controlled by the microgrid controller. Thus an accurate forecasting of wind power is an essential task in order to study its impacts in microgrid operation. Two commonly used forecasting methods including Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Network (ANN) have been used in this thesis to improve the wind power forecasting. The forecasting error is calculated using a Mean Absolute Percentage Error (MAPE) and is improved using the ANN. The wind forecast is further used in the microgrid optimal scheduling problem. The microgrid optimal scheduling is performed by developing a viable model for security-constrained unit commitment (SCUC) based on mixed-integer linear programing (MILP) method. The proposed SCUC is solved for various wind penetration levels and the relationship between the total cost and the wind power penetration is found. In order to reduce microgrid power transfer fluctuations, an additional constraint is proposed and added to the SCUC formulation. The new constraint would control the time-based fluctuations. The impact of the constraint on microgrid SCUC results is tested and validated with numerical analysis. Finally, the applicability of proposed models is demonstrated through numerical simulations.

WISC-R Examiner Errors: Cause for Concern.

ERIC Educational Resources Information Center

Slate, John R.; Chick, David

1989-01-01

Clinical psychology graduate students (N=14) administered Wechsler Intelligence Scale for Children-Revised. Found numerous scoring and mechanical errors that influenced full-scale intelligence quotient scores on two-thirds of protocols. Particularly prone to error were Verbal subtests of Vocabulary, Comprehension, and Similarities. Noted specific…

Wavefront-aberration measurement and systematic-error analysis of a high numerical-aperture objective

NASA Astrophysics Data System (ADS)

Liu, Zhixiang; Xing, Tingwen; Jiang, Yadong; Lv, Baobin

2018-02-01

A two-dimensional (2-D) shearing interferometer based on an amplitude chessboard grating was designed to measure the wavefront aberration of a high numerical-aperture (NA) objective. Chessboard gratings offer better diffraction efficiencies and fewer disturbing diffraction orders than traditional cross gratings. The wavefront aberration of the tested objective was retrieved from the shearing interferogram using the Fourier transform and differential Zernike polynomial-fitting methods. Grating manufacturing errors, including the duty-cycle and pattern-deviation errors, were analyzed with the Fourier transform method. Then, according to the relation between the spherical pupil and planar detector coordinates, the influence of the distortion of the pupil coordinates was simulated. Finally, the systematic error attributable to grating alignment errors was deduced through the geometrical ray-tracing method. Experimental results indicate that the measuring repeatability (3σ) of the wavefront aberration of an objective with NA 0.4 was 3.4 mλ. The systematic-error results were consistent with previous analyses. Thus, the correct wavefront aberration can be obtained after calibration.

ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.

USGS Publications Warehouse

Hromadka, T.V.; ,

1985-01-01

Besides providing an exact solution for steady-state heat conduction processes (Laplace Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximative boundary generation. This error evaluation can be used to develop highly accurate CVBEM models of the heat transport process, and the resulting model can be used as a test case for evaluating the precision of domain models based on finite elements or finite differences.

Numerical optimization in Hilbert space using inexact function and gradient evaluations

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

Magnetoacoustic Tomography with Magnetic Induction (MAT-MI) for Breast Tumor Imaging: Numerical Modeling and Simulation

PubMed Central

Zhou, Lian; Li, Xu; Zhu, Shanan; He, Bin

2011-01-01

Magnetoacoustic tomography with magnetic induction (MAT-MI) was recently introduced as a noninvasive electrical conductivity imaging approach with high spatial resolution close to ultrasound imaging. In the present study, we test the feasibility of the MAT-MI method for breast tumor imaging using numerical modeling and computer simulation. Using the finite element method, we have built three dimensional numerical breast models with varieties of embedded tumors for this simulation study. In order to obtain an accurate and stable forward solution that does not have numerical errors caused by singular MAT-MI acoustic sources at conductivity boundaries, we first derive an integral forward method for calculating MAT-MI acoustic sources over the entire imaging volume. An inverse algorithm for reconstructing the MAT-MI acoustic source is also derived with spherical measurement aperture, which simulates a practical setup for breast imaging. With the numerical breast models, we have conducted computer simulations under different imaging parameter setups and all the results suggest that breast tumors that have large conductivity contrast to its surrounding tissues as reported in literature may be readily detected in the reconstructed MAT-MI images. In addition, our simulations also suggest that the sensitivity of imaging breast tumors using the presented MAT-MI setup depends more on the tumor location and the conductivity contrast between the tumor and its surrounding tissues than on the tumor size. PMID:21364262

Numerical and analytical bounds on threshold error rates for hypergraph-product codes

NASA Astrophysics Data System (ADS)

Kovalev, Alexey A.; Prabhakar, Sanjay; Dumer, Ilya; Pryadko, Leonid P.

2018-06-01

We study analytically and numerically decoding properties of finite-rate hypergraph-product quantum low density parity-check codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several nontrivial lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models and a minimum-weight decoding threshold of approximately 7 % .

A posteriori error estimates in voice source recovery

NASA Astrophysics Data System (ADS)

Leonov, A. S.; Sorokin, V. N.

2017-12-01

The inverse problem of voice source pulse recovery from a segment of a speech signal is under consideration. A special mathematical model is used for the solution that relates these quantities. A variational method of solving inverse problem of voice source recovery for a new parametric class of sources, that is for piecewise-linear sources (PWL-sources), is proposed. Also, a technique for a posteriori numerical error estimation for obtained solutions is presented. A computer study of the adequacy of adopted speech production model with PWL-sources is performed in solving the inverse problems for various types of voice signals, as well as corresponding study of a posteriori error estimates. Numerical experiments for speech signals show satisfactory properties of proposed a posteriori error estimates, which represent the upper bounds of possible errors in solving the inverse problem. The estimate of the most probable error in determining the source-pulse shapes is about 7-8% for the investigated speech material. It is noted that a posteriori error estimates can be used as a criterion of the quality for obtained voice source pulses in application to speaker recognition.

Robust numerical electromagnetic eigenfunction expansion algorithms

NASA Astrophysics Data System (ADS)

Sainath, Kamalesh

This thesis summarizes developments in rigorous, full-wave, numerical spectral-domain (integral plane wave eigenfunction expansion [PWE]) evaluation algorithms concerning time-harmonic electromagnetic (EM) fields radiated by generally-oriented and positioned sources within planar and tilted-planar layered media exhibiting general anisotropy, thickness, layer number, and loss characteristics. The work is motivated by the need to accurately and rapidly model EM fields radiated by subsurface geophysical exploration sensors probing layered, conductive media, where complex geophysical and man-made processes can lead to micro-laminate and micro-fractured geophysical formations exhibiting, at the lower (sub-2MHz) frequencies typically employed for deep EM wave penetration through conductive geophysical media, bulk-scale anisotropic (i.e., directional) electrical conductivity characteristics. When the planar-layered approximation (layers of piecewise-constant material variation and transversely-infinite spatial extent) is locally, near the sensor region, considered valid, numerical spectral-domain algorithms are suitable due to their strong low-frequency stability characteristic, and ability to numerically predict time-harmonic EM field propagation in media with response characterized by arbitrarily lossy and (diagonalizable) dense, anisotropic tensors. If certain practical limitations are addressed, PWE can robustly model sensors with general position and orientation that probe generally numerous, anisotropic, lossy, and thick layers. The main thesis contributions, leading to a sensor and geophysical environment-robust numerical modeling algorithm, are as follows: (1) Simple, rapid estimator of the region (within the complex plane) containing poles, branch points, and branch cuts (critical points) (Chapter 2), (2) Sensor and material-adaptive azimuthal coordinate rotation, integration contour deformation, integration domain sub-region partition and sub-region-dependent integration order (Chapter 3), (3) Integration partition-extrapolation-based (Chapter 3) and Gauss-Laguerre Quadrature (GLQ)-based (Chapter 4) evaluations of the deformed, semi-infinite-length integration contour tails, (4) Robust in-situ-based (i.e., at the spectral-domain integrand level) direct/homogeneous-medium field contribution subtraction and analytical curbing of the source current spatial spectrum function's ill behavior (Chapter 5), and (5) Analytical re-casting of the direct-field expressions when the source is embedded within a NBAM, short for non-birefringent anisotropic medium (Chapter 6). The benefits of these contributions are, respectively, (1) Avoiding computationally intensive critical-point location and tracking (computation time savings), (2) Sensor and material-robust curbing of the integrand's oscillatory and slow decay behavior, as well as preventing undesirable critical-point migration within the complex plane (computation speed, precision, and instability-avoidance benefits), (3) sensor and material-robust reduction (or, for GLQ, elimination) of integral truncation error, (4) robustly stable modeling of scattered fields and/or fields radiated from current sources modeled as spatially distributed (10 to 1000-fold compute-speed acceleration also realized for distributed-source computations), and (5) numerically stable modeling of fields radiated from sources within NBAM layers. Having addressed these limitations, are PWE algorithms applicable to modeling EM waves in tilted planar-layered geometries too? This question is explored in Chapter 7 using a Transformation Optics-based approach, allowing one to model wave propagation through layered media that (in the sensor's vicinity) possess tilted planar interfaces. The technique leads to spurious wave scattering however, whose induced computation accuracy degradation requires analysis. Mathematical exhibition, and exhaustive simulation-based study and analysis of the limitations of, this novel tilted-layer modeling formulation is Chapter 7's main contribution.

Chemical transport in a fissured rock: Verification of a numerical model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rasmuson, A.; Narasimhan, T. N.; Neretnieks, I.

1982-10-01

Numerical models for simulating chemical transport in fissured rocks constitute powerful tools for evaluating the acceptability of geological nuclear waste repositories. Due to the very long-term, high toxicity of some nuclear waste products, the models are required to predict, in certain cases, the spatial and temporal distribution of chemical concentration less than 0.001% of the concentration released from the repository. Whether numerical models can provide such accuracies is a major question addressed in the present work. To this end, we have verified a numerical model, TRUMP, which solves the advective diffusion equation in general three dimensions with or without decaymore » and source terms. The method is based on an integrated finite-difference approach. The model was verified against known analytic solution of the one-dimensional advection-diffusion problem as well as the problem of advection-diffusion in a system of parallel fractures separated by spherical particles. The studies show that as long as the magnitude of advectance is equal to or less than that of conductance for the closed surface bounding any volume element in the region (that is, numerical Peclet number <2), the numerical method can indeed match the analytic solution within errors of ±10{sup -3} % or less. The realistic input parameters used in the sample calculations suggest that such a range of Peclet numbers is indeed likely to characterize deep groundwater systems in granitic and ancient argillaceous systems. Thus TRUMP in its present form does provide a viable tool for use in nuclear waste evaluation studies. A sensitivity analysis based on the analytic solution suggests that the errors in prediction introduced due to uncertainties in input parameters is likely to be larger than the computational inaccuracies introduced by the numerical model. Currently, a disadvantage in the TRUMP model is that the iterative method of solving the set of simultaneous equations is rather slow when time constants vary widely over the flow region. Although the iterative solution may be very desirable for large three-dimensional problems in order to minimize computer storage, it seems desirable to use a direct solver technique in conjunction with the mixed explicit-implicit approach whenever possible. work in this direction is in progress.« less

Network problem threshold

NASA Technical Reports Server (NTRS)

Gejji, Raghvendra, R.

1992-01-01

Network transmission errors such as collisions, CRC errors, misalignment, etc. are statistical in nature. Although errors can vary randomly, a high level of errors does indicate specific network problems, e.g. equipment failure. In this project, we have studied the random nature of collisions theoretically as well as by gathering statistics, and established a numerical threshold above which a network problem is indicated with high probability.

A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov

NASA Astrophysics Data System (ADS)

Greenough, J. A.; Rider, W. J.

2004-05-01

A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube problem, (3) the "peak" shock tube problem, (4) a version of the Shu and Osher shock entropy wave interaction and (5) the Woodward and Colella interacting shock wave problem. For each problem and method, run times, density error norms and convergence rates are reported for each method as produced from a common code test-bed. The linear problem exhibits the advertised convergence rate for both methods as well as the expected large disparity in overall error levels; WENO5 has the smaller errors and an enormous advantage in overall efficiency (in accuracy per unit CPU time). For the nonlinear problems with discontinuities, however, we generally see both first-order self-convergence of error as compared to an exact solution, or when an analytic solution is not available, a converged solution generated on an extremely fine grid. The overall comparison of error levels shows some variation from problem to problem. For Sod's shock tube, PLMDE has nearly half the error, while on the peak problem the errors are nearly the same. For the interacting blast wave problem the two methods again produce a similar level of error with a slight edge for the PLMDE. On the other hand, for the Shu-Osher problem, the errors are similar on the coarser grids, but favors WENO by a factor of nearly 1.5 on the finer grids used. In all cases holding mesh resolution constant though, PLMDE is less costly in terms of CPU time by approximately a factor of 6. If the CPU cost is taken as fixed, that is run times are equal for both numerical methods, then PLMDE uniformly produces lower errors than WENO for the fixed computation cost on the test problems considered here.

Dopamine prediction error responses integrate subjective value from different reward dimensions

PubMed Central

Lak, Armin; Stauffer, William R.; Schultz, Wolfram

2014-01-01

Prediction error signals enable us to learn through experience. These experiences include economic choices between different rewards that vary along multiple dimensions. Therefore, an ideal way to reinforce economic choice is to encode a prediction error that reflects the subjective value integrated across these reward dimensions. Previous studies demonstrated that dopamine prediction error responses reflect the value of singular reward attributes that include magnitude, probability, and delay. Obviously, preferences between rewards that vary along one dimension are completely determined by the manipulated variable. However, it is unknown whether dopamine prediction error responses reflect the subjective value integrated from different reward dimensions. Here, we measured the preferences between rewards that varied along multiple dimensions, and as such could not be ranked according to objective metrics. Monkeys chose between rewards that differed in amount, risk, and type. Because their choices were complete and transitive, the monkeys chose “as if” they integrated different rewards and attributes into a common scale of value. The prediction error responses of single dopamine neurons reflected the integrated subjective value inferred from the choices, rather than the singular reward attributes. Specifically, amount, risk, and reward type modulated dopamine responses exactly to the extent that they influenced economic choices, even when rewards were vastly different, such as liquid and food. This prediction error response could provide a direct updating signal for economic values. PMID:24453218

Numerical simulation of KdV equation by finite difference method

NASA Astrophysics Data System (ADS)

Yokus, A.; Bulut, H.

2018-05-01

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier-Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L2 and L_{∞} norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration

NASA Astrophysics Data System (ADS)

Hinder, Ian; Buonanno, Alessandra; Boyle, Michael; Etienne, Zachariah B.; Healy, James; Johnson-McDaniel, Nathan K.; Nagar, Alessandro; Nakano, Hiroyuki; Pan, Yi; Pfeiffer, Harald P.; Pürrer, Michael; Reisswig, Christian; Scheel, Mark A.; Schnetter, Erik; Sperhake, Ulrich; Szilágyi, Bela; Tichy, Wolfgang; Wardell, Barry; Zenginoğlu, Anıl; Alic, Daniela; Bernuzzi, Sebastiano; Bode, Tanja; Brügmann, Bernd; Buchman, Luisa T.; Campanelli, Manuela; Chu, Tony; Damour, Thibault; Grigsby, Jason D.; Hannam, Mark; Haas, Roland; Hemberger, Daniel A.; Husa, Sascha; Kidder, Lawrence E.; Laguna, Pablo; London, Lionel; Lovelace, Geoffrey; Lousto, Carlos O.; Marronetti, Pedro; Matzner, Richard A.; Mösta, Philipp; Mroué, Abdul; Müller, Doreen; Mundim, Bruno C.; Nerozzi, Andrea; Paschalidis, Vasileios; Pollney, Denis; Reifenberger, George; Rezzolla, Luciano; Shapiro, Stuart L.; Shoemaker, Deirdre; Taracchini, Andrea; Taylor, Nicholas W.; Teukolsky, Saul A.; Thierfelder, Marcus; Witek, Helvi; Zlochower, Yosef

2013-01-01

The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ˜100-200M⊙, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios ⩽4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.

Evaluation of wave runup predictions from numerical and parametric models

USGS Publications Warehouse

Stockdon, Hilary F.; Thompson, David M.; Plant, Nathaniel G.; Long, Joseph W.

2014-01-01

Wave runup during storms is a primary driver of coastal evolution, including shoreline and dune erosion and barrier island overwash. Runup and its components, setup and swash, can be predicted from a parameterized model that was developed by comparing runup observations to offshore wave height, wave period, and local beach slope. Because observations during extreme storms are often unavailable, a numerical model is used to simulate the storm-driven runup to compare to the parameterized model and then develop an approach to improve the accuracy of the parameterization. Numerically simulated and parameterized runup were compared to observations to evaluate model accuracies. The analysis demonstrated that setup was accurately predicted by both the parameterized model and numerical simulations. Infragravity swash heights were most accurately predicted by the parameterized model. The numerical model suffered from bias and gain errors that depended on whether a one-dimensional or two-dimensional spatial domain was used. Nonetheless, all of the predictions were significantly correlated to the observations, implying that the systematic errors can be corrected. The numerical simulations did not resolve the incident-band swash motions, as expected, and the parameterized model performed best at predicting incident-band swash heights. An assimilated prediction using a weighted average of the parameterized model and the numerical simulations resulted in a reduction in prediction error variance. Finally, the numerical simulations were extended to include storm conditions that have not been previously observed. These results indicated that the parameterized predictions of setup may need modification for extreme conditions; numerical simulations can be used to extend the validity of the parameterized predictions of infragravity swash; and numerical simulations systematically underpredict incident swash, which is relatively unimportant under extreme conditions.

A new numerical approach to solve Thomas-Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming.

PubMed

Raja, Muhammad Asif Zahoor; Zameer, Aneela; Khan, Aziz Ullah; Wazwaz, Abdul Majid

2016-01-01

In this study, a novel bio-inspired computing approach is developed to analyze the dynamics of nonlinear singular Thomas-Fermi equation (TFE) arising in potential and charge density models of an atom by exploiting the strength of finite difference scheme (FDS) for discretization and optimization through genetic algorithms (GAs) hybrid with sequential quadratic programming. The FDS procedures are used to transform the TFE differential equations into a system of nonlinear equations. A fitness function is constructed based on the residual error of constituent equations in the mean square sense and is formulated as the minimization problem. Optimization of parameters for the system is carried out with GAs, used as a tool for viable global search integrated with SQP algorithm for rapid refinement of the results. The design scheme is applied to solve TFE for five different scenarios by taking various step sizes and different input intervals. Comparison of the proposed results with the state of the art numerical and analytical solutions reveals that the worth of our scheme in terms of accuracy and convergence. The reliability and effectiveness of the proposed scheme are validated through consistently getting optimal values of statistical performance indices calculated for a sufficiently large number of independent runs to establish its significance.

Dimensional transitions in thermodynamic properties of ideal Maxwell-Boltzmann gases

NASA Astrophysics Data System (ADS)

Aydin, Alhun; Sisman, Altug

2015-04-01

An ideal Maxwell-Boltzmann gas confined in various rectangular nanodomains is considered under quantum size effects. Thermodynamic quantities are calculated from their relations with the partition function, which consists of triple infinite summations over momentum states in each direction. To obtain analytical expressions, summations are converted to integrals for macrosystems by a continuum approximation, which fails at the nanoscale. To avoid both the numerical calculation of summations and the failure of their integral approximations at the nanoscale, a method which gives an analytical expression for a single particle partition function (SPPF) is proposed. It is shown that a dimensional transition in momentum space occurs at a certain magnitude of confinement. Therefore, to represent the SPPF by lower-dimensional analytical expressions becomes possible, rather than numerical calculation of summations. Considering rectangular domains with different aspect ratios, a comparison of the results of derived expressions with those of summation forms of the SPPF is made. It is shown that analytical expressions for the SPPF give very precise results with maximum relative errors of around 1%, 2% and 3% at exactly the transition point for single, double and triple transitions, respectively. Based on dimensional transitions, expressions for free energy, entropy, internal energy, chemical potential, heat capacity and pressure are given analytically valid for any scale.

Using smartphone pressure sensors to measure vertical velocities of elevators, stairways, and drones

NASA Astrophysics Data System (ADS)

Monteiro, Martín; Martí, Arturo C.

2017-01-01

We measure the vertical velocities of elevators, pedestrians climbing stairs, and drones (flying unmanned aerial vehicles), by means of smartphone pressure sensors. The barometric pressure obtained with the smartphone is related to the altitude of the device via the hydrostatic approximation. From the altitude values, vertical velocities are derived. The approximation considered is valid in the first hundred meters of the inner layers of the atmosphere. In addition to pressure, acceleration values were also recorded using the built-in accelerometer. Numerical integration was performed, obtaining both vertical velocity and altitude. We show that data obtained using the pressure sensor is significantly less noisy than that obtained using the accelerometer. Error accumulation is also evident in the numerical integration of the acceleration values. In the proposed experiments, the pressure sensor also outperforms GPS, because this sensor does not receive satellite signals indoors and, in general, the operating frequency is considerably lower than that of the pressure sensor. In the cases in which it is possible, comparison with reference values taken from the architectural plans of buildings validates the results obtained using the pressure sensor. This proposal is ideally performed as an external or outreach activity with students to gain insight about fundamental questions in mechanics, fluids, and thermodynamics.

Hierarchical Boltzmann simulations and model error estimation

NASA Astrophysics Data System (ADS)

Torrilhon, Manuel; Sarna, Neeraj

2017-08-01

A hierarchical simulation approach for Boltzmann's equation should provide a single numerical framework in which a coarse representation can be used to compute gas flows as accurately and efficiently as in computational fluid dynamics, but a subsequent refinement allows to successively improve the result to the complete Boltzmann result. We use Hermite discretization, or moment equations, for the steady linearized Boltzmann equation for a proof-of-concept of such a framework. All representations of the hierarchy are rotationally invariant and the numerical method is formulated on fully unstructured triangular and quadrilateral meshes using a implicit discontinuous Galerkin formulation. We demonstrate the performance of the numerical method on model problems which in particular highlights the relevance of stability of boundary conditions on curved domains. The hierarchical nature of the method allows also to provide model error estimates by comparing subsequent representations. We present various model errors for a flow through a curved channel with obstacles.

Beyond Error Patterns: A Sociocultural View of Fraction Comparison Errors in Students with Mathematical Learning Disabilities

ERIC Educational Resources Information Center

Lewis, Katherine E.

2016-01-01

Although many students struggle with fractions, students with mathematical learning disabilities (MLDs) experience pervasive difficulties because of neurological differences in how they process numerical information. These students make errors that are qualitatively different than their typically achieving and low-achieving peers. This study…

Numerical modeling of the divided bar measurements

NASA Astrophysics Data System (ADS)

LEE, Y.; Keehm, Y.

2011-12-01

The divided-bar technique has been used to measure thermal conductivity of rocks and fragments in heat flow studies. Though widely used, divided-bar measurements can have errors, which are not systematically quantified yet. We used an FEM and performed a series of numerical studies to evaluate various errors in divided-bar measurements and to suggest more reliable measurement techniques. A divided-bar measurement should be corrected against lateral heat loss on the sides of rock samples, and the thermal resistance at the contacts between the rock sample and the bar. We first investigated how the amount of these corrections would change by the thickness and thermal conductivity of rock samples through numerical modeling. When we fixed the sample thickness as 10 mm and varied thermal conductivity, errors in the measured thermal conductivity ranges from 2.02% for 1.0 W/m/K to 7.95% for 4.0 W/m/K. While we fixed thermal conductivity as 1.38 W/m/K and varied the sample thickness, we found that the error ranges from 2.03% for the 30 mm-thick sample to 11.43% for the 5 mm-thick sample. After corrections, a variety of error analyses for divided-bar measurements were conducted numerically. Thermal conductivity of two thin standard disks (2 mm in thickness) located at the top and the bottom of the rock sample slightly affects the accuracy of thermal conductivity measurements. When the thermal conductivity of a sample is 3.0 W/m/K and that of two standard disks is 0.2 W/m/K, the relative error in measured thermal conductivity is very small (~0.01%). However, the relative error would reach up to -2.29% for the same sample when thermal conductivity of two disks is 0.5 W/m/K. The accuracy of thermal conductivity measurements strongly depends on thermal conductivity and the thickness of thermal compound that is applied to reduce thermal resistance at contacts between the rock sample and the bar. When the thickness of thermal compound (0.29 W/m/K) is 0.03 mm, we found that the relative error in measured thermal conductivity is 4.01%, while the relative error can be very significant (~12.2%) if the thickness increases to 0.1 mm. Then, we fixed the thickness (0.03 mm) and varied thermal conductivity of the thermal compound. We found that the relative error with an 1.0 W/m/K compound is 1.28%, and the relative error with a 0.29 W/m/K is 4.06%. When we repeated this test with a different thickness of the thermal compound (0.1 mm), the relative error with an 1.0 W/m/K compound is 3.93%, and that with a 0.29 W/m/K is 12.2%. In addition, the cell technique by Sass et al.(1971), which is widely used to measure thermal conductivity of rock fragments, was evaluated using the FEM modeling. A total of 483 isotropic and homogeneous spherical rock fragments in the sample holder were used to test numerically the accuracy of the cell technique. The result shows the relative error of -9.61% for rock fragments with the thermal conductivity of 2.5 W/m/K. In conclusion, we report quantified errors in the divided-bar and the cell technique for thermal conductivity measurements for rocks and fragments. We found that the FEM modeling can accurately mimic these measurement techniques and can help us to estimate measurement errors quantitatively.

Conditions for the optical wireless links bit error ratio determination

NASA Astrophysics Data System (ADS)

Kvíčala, Radek

2017-11-01

To determine the quality of the Optical Wireless Links (OWL), there is necessary to establish the availability and the probability of interruption. This quality can be defined by the optical beam bit error rate (BER). Bit error rate BER presents the percentage of successfully transmitted bits. In practice, BER runs into the problem with the integration time (measuring time) determination. For measuring and recording of BER at OWL the bit error ratio tester (BERT) has been developed. The 1 second integration time for the 64 kbps radio links is mentioned in the accessible literature. However, it is impossible to use this integration time for singularity of coherent beam propagation.

Determination of Cole-Cole parameters using only the real part of electrical impedivity measurements.

PubMed

Miranda, David A; Rivera, S A López

2008-05-01

An algorithm is presented to determine the Cole-Cole parameters of electrical impedivity using only measurements of its real part. The algorithm is based on two multi-fold direct inversion methods for the Cole-Cole and Debye equations, respectively, and a genetic algorithm for the optimization of the mean square error between experimental and calculated data. The algorithm has been developed to obtain the Cole-Cole parameters from experimental data, which were used to screen cervical intra-epithelial neoplasia. The proposed algorithm was compared with different numerical integrations of the Kramers-Kronig relation and the result shows that this algorithm is the best. A high immunity to noise was obtained.

On-chip quantum tomography of mechanical nanoscale oscillators with guided Rydberg atoms

NASA Astrophysics Data System (ADS)

Sanz-Mora, A.; Wüster, S.; Rost, J.-M.

2017-07-01

Nanomechanical oscillators as well as Rydberg-atomic waveguides hosted on microfabricated chip surfaces hold promise to become pillars of future quantum technologies. In a hybrid platform with both, we show that beams of Rydberg atoms in waveguides can quantum coherently interrogate and manipulate nanomechanical elements, allowing full quantum state tomography. Central to the tomography are quantum nondemolition measurements using the Rydberg atoms as probes. Quantum coherent displacement of the oscillator is also made possible by driving the atoms with external fields while they interact with the oscillator. We numerically demonstrate the feasibility of this fully integrated on-chip control and read-out suite for quantum nanomechanics, taking into account noise and error sources.

Study on vibration characteristic of the marine beveloid gear RV reducer

NASA Astrophysics Data System (ADS)

Wen, Jianmin; Cui, Haiyue; Yang, Tong

2018-05-01

The paper focuses on the vibration characteristic of the marine beveloid gear RV reducer and provides the theoretical guidance for vibration reduction. The cycloid gears are replaced by the beveloid gears in the transmission system. Considering the impact of the backlash, time-varying meshing stiffness and transmission error, a three-dimensional lumped parameter dynamic model of the marine beveloid gear RV reducer is established. The dynamic differential equations are solved through the 4th-5th order Runge-Kutta numerical integration method. By comparing the change of the time-displacement curves and amplitude curves, the impact of the external and internal excitation on the system vibration characteristic is investigated.

The method of fundamental solutions for computing acoustic interior transmission eigenvalues

NASA Astrophysics Data System (ADS)

Kleefeld, Andreas; Pieronek, Lukas

2018-03-01

We analyze the method of fundamental solutions (MFS) in two different versions with focus on the computation of approximate acoustic interior transmission eigenvalues in 2D for homogeneous media. Our approach is mesh- and integration free, but suffers in general from the ill-conditioning effects of the discretized eigenoperator, which we could then successfully balance using an approved stabilization scheme. Our numerical examples cover many of the common scattering objects and prove to be very competitive in accuracy with the standard methods for PDE-related eigenvalue problems. We finally give an approximation analysis for our framework and provide error estimates, which bound interior transmission eigenvalue deviations in terms of some generalized MFS output.

Tracing the source of numerical climate model uncertainties in precipitation simulations using a feature-oriented statistical model

NASA Astrophysics Data System (ADS)

Xu, Y.; Jones, A. D.; Rhoades, A.

2017-12-01

Precipitation is a key component in hydrologic cycles, and changing precipitation regimes contribute to more intense and frequent drought and flood events around the world. Numerical climate modeling is a powerful tool to study climatology and to predict future changes. Despite the continuous improvement in numerical models, long-term precipitation prediction remains a challenge especially at regional scales. To improve numerical simulations of precipitation, it is important to find out where the uncertainty in precipitation simulations comes from. There are two types of uncertainty in numerical model predictions. One is related to uncertainty in the input data, such as model's boundary and initial conditions. These uncertainties would propagate to the final model outcomes even if the numerical model has exactly replicated the true world. But a numerical model cannot exactly replicate the true world. Therefore, the other type of model uncertainty is related the errors in the model physics, such as the parameterization of sub-grid scale processes, i.e., given precise input conditions, how much error could be generated by the in-precise model. Here, we build two statistical models based on a neural network algorithm to predict long-term variation of precipitation over California: one uses "true world" information derived from observations, and the other uses "modeled world" information using model inputs and outputs from the North America Coordinated Regional Downscaling Project (NA CORDEX). We derive multiple climate feature metrics as the predictors for the statistical model to represent the impact of global climate on local hydrology, and include topography as a predictor to represent the local control. We first compare the predictors between the true world and the modeled world to determine the errors contained in the input data. By perturbing the predictors in the statistical model, we estimate how much uncertainty in the model's final outcomes is accounted for by each predictor. By comparing the statistical model derived from true world information and modeled world information, we assess the errors lying in the physics of the numerical models. This work provides a unique insight to assess the performance of numerical climate models, and can be used to guide improvement of precipitation prediction.

Galaxy Strategy for Ligo-Virgo Gravitational Wave Counterpart Searches

NASA Technical Reports Server (NTRS)

Gehrels, Neil; Cannizzo, John K.; Kanner, Jonah; Kasliwal, Mansi M.; Nissanke, Samaya; Singer, Leo P.

2016-01-01

In this work we continue a line of inquiry begun in Kanner et al. which detailed a strategy for utilizing telescopes with narrow fields of view, such as the Swift X-Ray Telescope (XRT), to localize gravity wave (GW) triggers from LIGO (Laser Interferometer Gravitational-Wave Observatory) / Virgo. If one considers the brightest galaxies that produce 50 percent of the light, then the number of galaxies inside typical GW error boxes will be several tens. We have found that this result applies both in the early years of Advanced LIGO when the range is small and the error boxes large, and in the later years when the error boxes will be small and the range large. This strategy has the beneficial property of reducing the number of telescope pointings by a factor 10 to 100 compared with tiling the entire error box. Additional galaxy count reduction will come from a GW rapid distance estimate which will restrict the radial slice in search volume. Combining the bright galaxy strategy with a convolution based on anticipated GW localizations, we find that the searches can be restricted to about 18 plus or minus 5 galaxies for 2015, about 23 plus or minus 4 for 2017, and about 11 plus or minus for 2020. This assumes a distance localization at the putative neutron star-neutron star (NS-NS) merger range mu for each target year, and these totals are integrated out to the range. Integrating out to the horizon would roughly double the totals. For localizations with r (rotation) greatly less than mu the totals would decrease. The galaxy strategy we present in this work will enable numerous sensitive optical and X-ray telescopes with small fields of view to participate meaningfully in searches wherein the prospects for rapidly fading afterglow place a premium on a fast response time.

Improving the trust in results of numerical simulations and scientific data analytics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cappello, Franck; Constantinescu, Emil; Hovland, Paul

This white paper investigates several key aspects of the trust that a user can give to the results of numerical simulations and scientific data analytics. In this document, the notion of trust is related to the integrity of numerical simulations and data analytics applications. This white paper complements the DOE ASCR report on Cybersecurity for Scientific Computing Integrity by (1) exploring the sources of trust loss; (2) reviewing the definitions of trust in several areas; (3) providing numerous cases of result alteration, some of them leading to catastrophic failures; (4) examining the current notion of trust in numerical simulation andmore » scientific data analytics; (5) providing a gap analysis; and (6) suggesting two important research directions and their respective research topics. To simplify the presentation without loss of generality, we consider that trust in results can be lost (or the results’ integrity impaired) because of any form of corruption happening during the execution of the numerical simulation or the data analytics application. In general, the sources of such corruption are threefold: errors, bugs, and attacks. Current applications are already using techniques to deal with different types of corruption. However, not all potential corruptions are covered by these techniques. We firmly believe that the current level of trust that a user has in the results is at least partially founded on ignorance of this issue or the hope that no undetected corruptions will occur during the execution. This white paper explores the notion of trust and suggests recommendations for developing a more scientifically grounded notion of trust in numerical simulation and scientific data analytics. We first formulate the problem and show that it goes beyond previous questions regarding the quality of results such as V&V, uncertainly quantification, and data assimilation. We then explore the complexity of this difficult problem, and we sketch complementary general approaches to address it. This paper does not focus on the trust that the execution will actually complete. The product of simulation or of data analytic executions is the final element of a potentially long chain of transformations, where each stage has the potential to introduce harmful corruptions. These corruptions may produce results that deviate from the user-expected accuracy without notifying the user of this deviation. There are many potential sources of corruption before and during the execution; consequently, in this white paper we do not focus on the protection of the end result after the execution.« less

Study on Network Error Analysis and Locating based on Integrated Information Decision System

NASA Astrophysics Data System (ADS)

Yang, F.; Dong, Z. H.

2017-10-01

Integrated information decision system (IIDS) integrates multiple sub-system developed by many facilities, including almost hundred kinds of software, which provides with various services, such as email, short messages, drawing and sharing. Because the under-layer protocols are different, user standards are not unified, many errors are occurred during the stages of setup, configuration, and operation, which seriously affect the usage. Because the errors are various, which may be happened in different operation phases, stages, TCP/IP communication protocol layers, sub-system software, it is necessary to design a network error analysis and locating tool for IIDS to solve the above problems. This paper studies on network error analysis and locating based on IIDS, which provides strong theory and technology supports for the running and communicating of IIDS.

Long-time stability effects of quadrature and artificial viscosity on nodal discontinuous Galerkin methods for gas dynamics

NASA Astrophysics Data System (ADS)

Durant, Bradford; Hackl, Jason; Balachandar, Sivaramakrishnan

2017-11-01

Nodal discontinuous Galerkin schemes present an attractive approach to robust high-order solution of the equations of fluid mechanics, but remain accompanied by subtle challenges in their consistent stabilization. The effect of quadrature choices (full mass matrix vs spectral elements), over-integration to manage aliasing errors, and explicit artificial viscosity on the numerical solution of a steady homentropic vortex are assessed over a wide range of resolutions and polynomial orders using quadrilateral elements. In both stagnant and advected vortices in periodic and non-periodic domains the need arises for explicit stabilization beyond the numerical surface fluxes of discontinuous Galerkin spectral elements. Artificial viscosity via the entropy viscosity method is assessed as a stabilizing mechanism. It is shown that the regularity of the artificial viscosity field is essential to its use for long-time stabilization of small-scale features in nodal discontinuous Galerkin solutions of the Euler equations of gas dynamics. Supported by the Department of Energy Predictive Science Academic Alliance Program Contract DE-NA0002378.

Divergent expansion, Borel summability and three-dimensional Navier-Stokes equation.

PubMed

Costin, Ovidiu; Luo, Guo; Tanveer, Saleh

2008-08-13

We describe how the Borel summability of a divergent asymptotic expansion can be expanded and applied to nonlinear partial differential equations (PDEs). While Borel summation does not apply for non-analytic initial data, the present approach generates an integral equation (IE) applicable to much more general data. We apply these concepts to the three-dimensional Navier-Stokes (NS) system and show how the IE approach can give rise to local existence proofs. In this approach, the global existence problem in three-dimensional NS systems, for specific initial condition and viscosity, becomes a problem of asymptotics in the variable p (dual to 1/t or some positive power of 1/t). Furthermore, the errors in numerical computations in the associated IE can be controlled rigorously, which is very important for nonlinear PDEs such as NS when solutions are not known to exist globally.Moreover, computation of the solution of the IE over an interval [0,p0] provides sharper control of its p-->infinity behaviour. Preliminary numerical computations give encouraging results.

Krylov Deferred Correction Accelerated Method of Lines Transpose for Parabolic Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jia, Jun; Jingfang, Huang

2008-01-01

In this paper, a new class of numerical methods for the accurate and efficient solutions of parabolic partial differential equations is presented. Unlike traditional method of lines (MoL), the new {\\bf \\it Krylov deferred correction (KDC) accelerated method of lines transpose (MoL^T)} first discretizes the temporal direction using Gaussian type nodes and spectral integration, and symbolically applies low-order time marching schemes to form a preconditioned elliptic system, which is then solved iteratively using Newton-Krylov techniques such as Newton-GMRES or Newton-BiCGStab method. Each function evaluation in the Newton-Krylov method is simply one low-order time-stepping approximation of the error by solving amore » decoupled system using available fast elliptic equation solvers. Preliminary numerical experiments show that the KDC accelerated MoL^T technique is unconditionally stable, can be spectrally accurate in both temporal and spatial directions, and allows optimal time-step sizes in long-time simulations.« less

Aerodynamic influence coefficient method using singularity splines

NASA Technical Reports Server (NTRS)

Mercer, J. E.; Weber, J. A.; Lesferd, E. P.

1974-01-01

A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.

Nonlinear dynamics analysis of the spur gear system for railway locomotive

NASA Astrophysics Data System (ADS)

Wang, Junguo; He, Guangyue; Zhang, Jie; Zhao, Yongxiang; Yao, Yuan

2017-02-01

Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincaré maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

Optimization of processing parameters of UAV integral structural components based on yield response

NASA Astrophysics Data System (ADS)

Chen, Yunsheng

2018-05-01

In order to improve the overall strength of unmanned aerial vehicle (UAV), it is necessary to optimize the processing parameters of UAV structural components, which is affected by initial residual stress in the process of UAV structural components processing. Because machining errors are easy to occur, an optimization model for machining parameters of UAV integral structural components based on yield response is proposed. The finite element method is used to simulate the machining parameters of UAV integral structural components. The prediction model of workpiece surface machining error is established, and the influence of the path of walking knife on residual stress of UAV integral structure is studied, according to the stress of UAV integral component. The yield response of the time-varying stiffness is analyzed, and the yield response and the stress evolution mechanism of the UAV integral structure are analyzed. The simulation results show that this method is used to optimize the machining parameters of UAV integral structural components and improve the precision of UAV milling processing. The machining error is reduced, and the deformation prediction and error compensation of UAV integral structural parts are realized, thus improving the quality of machining.

Refined numerical solution of the transonic flow past a wedge

NASA Technical Reports Server (NTRS)

Liang, S.-M.; Fung, K.-Y.

1985-01-01

A numerical procedure combining the ideas of solving a modified difference equation and of adaptive mesh refinement is introduced. The numerical solution on a fixed grid is improved by using better approximations of the truncation error computed from local subdomain grid refinements. This technique is used to obtain refined solutions of steady, inviscid, transonic flow past a wedge. The effects of truncation error on the pressure distribution, wave drag, sonic line, and shock position are investigated. By comparing the pressure drag on the wedge and wave drag due to the shocks, a supersonic-to-supersonic shock originating from the wedge shoulder is confirmed.

Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving Source

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Turchaninov, V. I.; Tsynkov, S. V.

1999-01-01

We propose a family of algorithms for solving numerically a Cauchy problem for the three-dimensional wave equation. The sources that drive the equation (i.e., the right-hand side) are compactly supported in space for any given time; they, however, may actually move in space with a subsonic speed. The solution is calculated inside a finite domain (e.g., sphere) that also moves with a subsonic speed and always contains the support of the right-hand side. The algorithms employ a standard consistent and stable explicit finite-difference scheme for the wave equation. They allow one to calculate tile solution for arbitrarily long time intervals without error accumulation and with the fixed non-growing amount of tile CPU time and memory required for advancing one time step. The algorithms are inherently three-dimensional; they rely on the presence of lacunae in the solutions of the wave equation in oddly dimensional spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.

Learning mechanisms to limit medication administration errors.

PubMed

Drach-Zahavy, Anat; Pud, Dorit

2010-04-01

This paper is a report of a study conducted to identify and test the effectiveness of learning mechanisms applied by the nursing staff of hospital wards as a means of limiting medication administration errors. Since the influential report ;To Err Is Human', research has emphasized the role of team learning in reducing medication administration errors. Nevertheless, little is known about the mechanisms underlying team learning. Thirty-two hospital wards were randomly recruited. Data were collected during 2006 in Israel by a multi-method (observations, interviews and administrative data), multi-source (head nurses, bedside nurses) approach. Medication administration error was defined as any deviation from procedures, policies and/or best practices for medication administration, and was identified using semi-structured observations of nurses administering medication. Organizational learning was measured using semi-structured interviews with head nurses, and the previous year's reported medication administration errors were assessed using administrative data. The interview data revealed four learning mechanism patterns employed in an attempt to learn from medication administration errors: integrated, non-integrated, supervisory and patchy learning. Regression analysis results demonstrated that whereas the integrated pattern of learning mechanisms was associated with decreased errors, the non-integrated pattern was associated with increased errors. Supervisory and patchy learning mechanisms were not associated with errors. Superior learning mechanisms are those that represent the whole cycle of team learning, are enacted by nurses who administer medications to patients, and emphasize a system approach to data analysis instead of analysis of individual cases.

Integration of Error Compensation of Coordinate Measuring Machines into Feature Measurement: Part I—Model Development

PubMed Central

Calvo, Roque; D’Amato, Roberto; Gómez, Emilio; Domingo, Rosario

2016-01-01

The development of an error compensation model for coordinate measuring machines (CMMs) and its integration into feature measurement is presented. CMMs are widespread and dependable instruments in industry and laboratories for dimensional measurement. From the tip probe sensor to the machine display, there is a complex transformation of probed point coordinates through the geometrical feature model that makes the assessment of accuracy and uncertainty measurement results difficult. Therefore, error compensation is not standardized, conversely to other simpler instruments. Detailed coordinate error compensation models are generally based on CMM as a rigid-body and it requires a detailed mapping of the CMM’s behavior. In this paper a new model type of error compensation is proposed. It evaluates the error from the vectorial composition of length error by axis and its integration into the geometrical measurement model. The non-explained variability by the model is incorporated into the uncertainty budget. Model parameters are analyzed and linked to the geometrical errors and uncertainty of CMM response. Next, the outstanding measurement models of flatness, angle, and roundness are developed. The proposed models are useful for measurement improvement with easy integration into CMM signal processing, in particular in industrial environments where built-in solutions are sought. A battery of implementation tests are presented in Part II, where the experimental endorsement of the model is included. PMID:27690052

Field evaluation of the error arising from inadequate time averaging in the standard use of depth-integrating suspended-sediment samplers

USGS Publications Warehouse

Topping, David J.; Rubin, David M.; Wright, Scott A.; Melis, Theodore S.

2011-01-01

Several common methods for measuring suspended-sediment concentration in rivers in the United States use depth-integrating samplers to collect a velocity-weighted suspended-sediment sample in a subsample of a river cross section. Because depth-integrating samplers are always moving through the water column as they collect a sample, and can collect only a limited volume of water and suspended sediment, they collect only minimally time-averaged data. Four sources of error exist in the field use of these samplers: (1) bed contamination, (2) pressure-driven inrush, (3) inadequate sampling of the cross-stream spatial structure in suspended-sediment concentration, and (4) inadequate time averaging. The first two of these errors arise from misuse of suspended-sediment samplers, and the third has been the subject of previous study using data collected in the sand-bedded Middle Loup River in Nebraska. Of these four sources of error, the least understood source of error arises from the fact that depth-integrating samplers collect only minimally time-averaged data. To evaluate this fourth source of error, we collected suspended-sediment data between 1995 and 2007 at four sites on the Colorado River in Utah and Arizona, using a P-61 suspended-sediment sampler deployed in both point- and one-way depth-integrating modes, and D-96-A1 and D-77 bag-type depth-integrating suspended-sediment samplers. These data indicate that the minimal duration of time averaging during standard field operation of depth-integrating samplers leads to an error that is comparable in magnitude to that arising from inadequate sampling of the cross-stream spatial structure in suspended-sediment concentration. This random error arising from inadequate time averaging is positively correlated with grain size and does not largely depend on flow conditions or, for a given size class of suspended sediment, on elevation above the bed. Averaging over time scales >1 minute is the likely minimum duration required to result in substantial decreases in this error. During standard two-way depth integration, a depth-integrating suspended-sediment sampler collects a sample of the water-sediment mixture during two transits at each vertical in a cross section: one transit while moving from the water surface to the bed, and another transit while moving from the bed to the water surface. As the number of transits is doubled at an individual vertical, this error is reduced by ~30 percent in each size class of suspended sediment. For a given size class of suspended sediment, the error arising from inadequate sampling of the cross-stream spatial structure in suspended-sediment concentration depends only on the number of verticals collected, whereas the error arising from inadequate time averaging depends on both the number of verticals collected and the number of transits collected at each vertical. Summing these two errors in quadrature yields a total uncertainty in an equal-discharge-increment (EDI) or equal-width-increment (EWI) measurement of the time-averaged velocity-weighted suspended-sediment concentration in a river cross section (exclusive of any laboratory-processing errors). By virtue of how the number of verticals and transits influences the two individual errors within this total uncertainty, the error arising from inadequate time averaging slightly dominates that arising from inadequate sampling of the cross-stream spatial structure in suspended-sediment concentration. Adding verticals to an EDI or EWI measurement is slightly more effective in reducing the total uncertainty than adding transits only at each vertical, because a new vertical contributes both temporal and spatial information. However, because collection of depth-integrated samples at more transits at each vertical is generally easier and faster than at more verticals, addition of a combination of verticals and transits is likely a more practical approach to reducing the total uncertainty in most field situatio

Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations: Theory and Implementation

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2014-01-01

Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.

Discussion: Numerical study on the entrainment of bed material into rapid landslides

USGS Publications Warehouse

Iverson, Richard M.

2013-01-01

A paper recently published in this journal (Pirulli & Pastor, 2012) uses numerical modelling to study the important problem of entrainment of bed material by landslides. Unfortunately, some of the basic equations employed in the study are flawed, because they violate the principle of linear momentum conservation. Similar errors exist in some other studies of entrainment, and the errors appear to stem from confusion about the role of bed-sediment inertia in differing frames of reference.

Some Insights of Spectral Optimization in Ocean Color Inversion

NASA Technical Reports Server (NTRS)

Lee, Zhongping; Franz, Bryan; Shang, Shaoling; Dong, Qiang; Arnone, Robert

2011-01-01

In the past decades various algorithms have been developed for the retrieval of water constituents from the measurement of ocean color radiometry, and one of the approaches is spectral optimization. This approach defines an error target (or error function) between the input remote sensing reflectance and the output remote sensing reflectance, with the latter modeled with a few variables that represent the optically active properties (such as the absorption coefficient of phytoplankton and the backscattering coefficient of particles). The values of the variables when the error reach a minimum (optimization is achieved) are considered the properties that form the input remote sensing reflectance; or in other words, the equations are solved numerically. The applications of this approach implicitly assume that the error is a monotonic function of the various variables. Here, with data from numerical simulation and field measurements, we show the shape of the error surface, in a way to justify the possibility of finding a solution of the various variables. In addition, because the spectral properties could be modeled differently, impacts of such differences on the error surface as well as on the retrievals are also presented.

Maximum Correntropy Unscented Kalman Filter for Ballistic Missile Navigation System based on SINS/CNS Deeply Integrated Mode.

PubMed

Hou, Bowen; He, Zhangming; Li, Dong; Zhou, Haiyin; Wang, Jiongqi

2018-05-27

Strap-down inertial navigation system/celestial navigation system ( SINS/CNS) integrated navigation is a high precision navigation technique for ballistic missiles. The traditional navigation method has a divergence in the position error. A deeply integrated mode for SINS/CNS navigation system is proposed to improve the navigation accuracy of ballistic missile. The deeply integrated navigation principle is described and the observability of the navigation system is analyzed. The nonlinearity, as well as the large outliers and the Gaussian mixture noises, often exists during the actual navigation process, leading to the divergence phenomenon of the navigation filter. The new nonlinear Kalman filter on the basis of the maximum correntropy theory and unscented transformation, named the maximum correntropy unscented Kalman filter, is deduced, and the computational complexity is analyzed. The unscented transformation is used for restricting the nonlinearity of the system equation, and the maximum correntropy theory is used to deal with the non-Gaussian noises. Finally, numerical simulation illustrates the superiority of the proposed filter compared with the traditional unscented Kalman filter. The comparison results show that the large outliers and the influence of non-Gaussian noises for SINS/CNS deeply integrated navigation is significantly reduced through the proposed filter.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Massively Parallel Assimilation of TOGA/TAO and Topex/Poseidon Measurements into a Quasi Isopycnal Ocean General Circulation Model Using an Ensemble Kalman Filter

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele; Borovikov, Anna Y.; Suarez, Max

1999-01-01

A massively parallel ensemble Kalman filter (EnKF)is used to assimilate temperature data from the TOGA/TAO array and altimetry from TOPEX/POSEIDON into a Pacific basin version of the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. The EnKF is an approximate Kalman filter in which the error-covariance propagation step is modeled by the integration of multiple instances of a numerical model. An estimate of the true error covariances is then inferred from the distribution of the ensemble of model state vectors. This inplementation of the filter takes advantage of the inherent parallelism in the EnKF algorithm by running all the model instances concurrently. The Kalman filter update step also occurs in parallel by having each processor process the observations that occur in the region of physical space for which it is responsible. The massively parallel data assimilation system is validated by withholding some of the data and then quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The distributions of the forecast and analysis error covariances predicted by the ENKF are also examined.

Speed-constrained three-axes attitude control using kinematic steering

NASA Astrophysics Data System (ADS)

Schaub, Hanspeter; Piggott, Scott

2018-06-01

Spacecraft attitude control solutions typically are torque-level algorithms that simultaneously control both the attitude and angular velocity tracking errors. In contrast, robotic control solutions are kinematic steering commands where rates are treated as the control variable, and a servo-tracking control subsystem is present to achieve the desired control rates. In this paper kinematic attitude steering controls are developed where an outer control loop establishes a desired angular response history to a tracking error, and an inner control loop tracks the commanded body angular rates. The overall stability relies on the separation principle of the inner and outer control loops which must have sufficiently different response time scales. The benefit is that the outer steering law response can be readily shaped to a desired behavior, such as limiting the approach angular velocity when a large tracking error is corrected. A Modified Rodrigues Parameters implementation is presented that smoothly saturates the speed response. A robust nonlinear body rate servo loop is developed which includes integral feedback. This approach provides a convenient modular framework that makes it simple to interchange outer and inner control loops to readily setup new control implementations. Numerical simulations illustrate the expected performance for an aggressive reorientation maneuver subject to an unknown external torque.

Height system unification based on the Fixed Geodetic Boundary Value Problem with limited availability of gravity data

NASA Astrophysics Data System (ADS)

Porz, Lucas; Grombein, Thomas; Seitz, Kurt; Heck, Bernhard; Wenzel, Friedemann

2017-04-01

Regional height reference systems are generally related to individual vertical datums defined by specific tide gauges. The discrepancies of these vertical datums with respect to a unified global datum cause height system biases that range in an order of 1-2 m at a global scale. One approach for unification of height systems relates to the solution of a Geodetic Boundary Value Problem (GBVP). In particular, the fixed GBVP, using gravity disturbances as boundary values, is solved at GNSS/leveling benchmarks, whereupon height datum offsets can be estimated by least squares adjustment. In spherical approximation, the solution of the fixed GBVP is obtained by Hotine's spherical integral formula. However, this method relies on the global availability of gravity data. In practice, gravity data of the necessary resolution and accuracy is not accessible globally. Thus, the integration is restricted to an area within the vicinity of the computation points. The resulting truncation error can reach several meters in height, making height system unification without further consideration of this effect unfeasible. This study analyzes methods for reducing the truncation error by combining terrestrial gravity data with satellite-based global geopotential models and by modifying the integral kernel in order to accelerate the convergence of the resulting potential. For this purpose, EGM2008-derived gravity functionals are used as pseudo-observations to be integrated numerically. Geopotential models of different spectral degrees are implemented using a remove-restore-scheme. Three types of modification are applied to the Hotine-kernel and the convergence of the resulting potential is analyzed. In a further step, the impact of these operations on the estimation of height datum offsets is investigated within a closed loop simulation. A minimum integration radius in combination with a specific modification of the Hotine-kernel is suggested in order to achieve sub-cm accuracy for the estimation of height datum offsets.

On the use of flux limiters in the discrete ordinates method for 3D radiation calculations in absorbing and scattering media

NASA Astrophysics Data System (ADS)

Godoy, William F.; DesJardin, Paul E.

2010-05-01

The application of flux limiters to the discrete ordinates method (DOM), SN, for radiative transfer calculations is discussed and analyzed for 3D enclosures for cases in which the intensities are strongly coupled to each other such as: radiative equilibrium and scattering media. A Newton-Krylov iterative method (GMRES) solves the final systems of linear equations along with a domain decomposition strategy for parallel computation using message passing libraries in a distributed memory system. Ray effects due to angular discretization and errors due to domain decomposition are minimized until small variations are introduced by these effects in order to focus on the influence of flux limiters on errors due to spatial discretization, known as numerical diffusion, smearing or false scattering. Results are presented for the DOM-integrated quantities such as heat flux, irradiation and emission. A variety of flux limiters are compared to "exact" solutions available in the literature, such as the integral solution of the RTE for pure absorbing-emitting media and isotropic scattering cases and a Monte Carlo solution for a forward scattering case. Additionally, a non-homogeneous 3D enclosure is included to extend the use of flux limiters to more practical cases. The overall balance of convergence, accuracy, speed and stability using flux limiters is shown to be superior compared to step schemes for any test case.

Bounded Error Schemes for the Wave Equation on Complex Domains

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Ditkowski, Adi; Yefet, Amir

1998-01-01

This paper considers the application of the method of boundary penalty terms ("SAT") to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g. the staggered Yee scheme) - we achieve a decrease of two orders of magnitude in the level of the L2-error.

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

DOE PAGES

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory; ...

2015-02-25

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

(How) do we learn from errors? A prospective study of the link between the ward's learning practices and medication administration errors.

PubMed

Drach-Zahavy, A; Somech, A; Admi, H; Peterfreund, I; Peker, H; Priente, O

2014-03-01

Attention in the ward should shift from preventing medication administration errors to managing them. Nevertheless, little is known in regard with the practices nursing wards apply to learn from medication administration errors as a means of limiting them. To test the effectiveness of four types of learning practices, namely, non-integrated, integrated, supervisory and patchy learning practices in limiting medication administration errors. Data were collected from a convenient sample of 4 hospitals in Israel by multiple methods (observations and self-report questionnaires) at two time points. The sample included 76 wards (360 nurses). Medication administration error was defined as any deviation from prescribed medication processes and measured by a validated structured observation sheet. Wards' use of medication administration technologies, location of the medication station, and workload were observed; learning practices and demographics were measured by validated questionnaires. Results of the mixed linear model analysis indicated that the use of technology and quiet location of the medication cabinet were significantly associated with reduced medication administration errors (estimate=.03, p<.05 and estimate=-.17, p<.01 correspondingly), while workload was significantly linked to inflated medication administration errors (estimate=.04, p<.05). Of the learning practices, supervisory learning was the only practice significantly linked to reduced medication administration errors (estimate=-.04, p<.05). Integrated and patchy learning were significantly linked to higher levels of medication administration errors (estimate=-.03, p<.05 and estimate=-.04, p<.01 correspondingly). Non-integrated learning was not associated with it (p>.05). How wards manage errors might have implications for medication administration errors beyond the effects of typical individual, organizational and technology risk factors. Head nurse can facilitate learning from errors by "management by walking around" and monitoring nurses' medication administration behaviors. Copyright © 2013 Elsevier Ltd. All rights reserved.

The planning coordinator: A design architecture for autonomous error recovery and on-line planning of intelligent tasks

NASA Technical Reports Server (NTRS)

Farah, Jeffrey J.

1992-01-01

Developing a robust, task level, error recovery and on-line planning architecture is an open research area. There is previously published work on both error recovery and on-line planning; however, none incorporates error recovery and on-line planning into one integrated platform. The integration of these two functionalities requires an architecture that possesses the following characteristics. The architecture must provide for the inclusion of new information without the destruction of existing information. The architecture must provide for the relating of pieces of information, old and new, to one another in a non-trivial rather than trivial manner (e.g., object one is related to object two under the following constraints, versus, yes, they are related; no, they are not related). Finally, the architecture must be not only a stand alone architecture, but also one that can be easily integrated as a supplement to some existing architecture. This thesis proposal addresses architectural development. Its intent is to integrate error recovery and on-line planning onto a single, integrated, multi-processor platform. This intelligent x-autonomous platform, called the Planning Coordinator, will be used initially to supplement existing x-autonomous systems and eventually replace them.

CADNA: a library for estimating round-off error propagation

NASA Astrophysics Data System (ADS)

Jézéquel, Fabienne; Chesneaux, Jean-Marie

2008-06-01

The CADNA library enables one to estimate round-off error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can be performed. CADNA provides new numerical types on which round-off errors can be estimated. Slight modifications are required to control a code with CADNA, mainly changes in variable declarations, input and output. This paper describes the features of the CADNA library and shows how to interpret the information it provides concerning round-off error propagation in a code. Program summaryProgram title:CADNA Catalogue identifier:AEAT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAT_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:53 420 No. of bytes in distributed program, including test data, etc.:566 495 Distribution format:tar.gz Programming language:Fortran Computer:PC running LINUX with an i686 or an ia64 processor, UNIX workstations including SUN, IBM Operating system:LINUX, UNIX Classification:4.14, 6.5, 20 Nature of problem:A simulation program which uses floating-point arithmetic generates round-off errors, due to the rounding performed at each assignment and at each arithmetic operation. Round-off error propagation may invalidate the result of a program. The CADNA library enables one to estimate round-off error propagation in any simulation program and to detect all numerical instabilities that may occur at run time. Solution method:The CADNA library [1] implements Discrete Stochastic Arithmetic [2-4] which is based on a probabilistic model of round-off errors. The program is run several times with a random rounding mode generating different results each time. From this set of results, CADNA estimates the number of exact significant digits in the result that would have been computed with standard floating-point arithmetic. Restrictions:CADNA requires a Fortran 90 (or newer) compiler. In the program to be linked with the CADNA library, round-off errors on complex variables cannot be estimated. Furthermore array functions such as product or sum must not be used. Only the arithmetic operators and the abs, min, max and sqrt functions can be used for arrays. Running time:The version of a code which uses CADNA runs at least three times slower than its floating-point version. This cost depends on the computer architecture and can be higher if the detection of numerical instabilities is enabled. In this case, the cost may be related to the number of instabilities detected. References:The CADNA library, URL address: http://www.lip6.fr/cadna. J.-M. Chesneaux, L'arithmétique Stochastique et le Logiciel CADNA, Habilitation á diriger des recherches, Université Pierre et Marie Curie, Paris, 1995. J. Vignes, A stochastic arithmetic for reliable scientific computation, Math. Comput. Simulation 35 (1993) 233-261. J. Vignes, Discrete stochastic arithmetic for validating results of numerical software, Numer. Algorithms 37 (2004) 377-390.

Errors of Omission and Commission during Alternative Reinforcement of Compliance: The Effects of Varying Levels of Treatment Integrity

ERIC Educational Resources Information Center

Leon, Yanerys; Wilder, David A.; Majdalany, Lina; Myers, Kristin; Saini, Valdeep

2014-01-01

We conducted two experiments to evaluate the effects of errors of omission and commission during alternative reinforcement of compliance in young children. In Experiment 1, we evaluated errors of omission by examining two levels of integrity during alternative reinforcement (20 and 60%) for child compliance following no treatment (baseline) versus…

Error analysis of finite element method for Poisson–Nernst–Planck equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Yuzhou; Sun, Pengtao; Zheng, Bin

A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.

Integrated Wind Power Planning Tool

NASA Astrophysics Data System (ADS)

Rosgaard, Martin; Giebel, Gregor; Skov Nielsen, Torben; Hahmann, Andrea; Sørensen, Poul; Madsen, Henrik

2013-04-01

This poster presents the current state of the public service obligation (PSO) funded project PSO 10464, with the title "Integrated Wind Power Planning Tool". The goal is to integrate a mesoscale numerical weather prediction (NWP) model with purely statistical tools in order to assess wind power fluctuations, with focus on long term power system planning for future wind farms as well as short term forecasting for existing wind farms. Currently, wind power fluctuation models are either purely statistical or integrated with NWP models of limited resolution. Using the state-of-the-art mesoscale NWP model Weather Research & Forecasting model (WRF) the forecast error is sought quantified in dependence of the time scale involved. This task constitutes a preparative study for later implementation of features accounting for NWP forecast errors in the DTU Wind Energy maintained Corwind code - a long term wind power planning tool. Within the framework of PSO 10464 research related to operational short term wind power prediction will be carried out, including a comparison of forecast quality at different mesoscale NWP model resolutions and development of a statistical wind power prediction tool taking input from WRF. The short term prediction part of the project is carried out in collaboration with ENFOR A/S; a Danish company that specialises in forecasting and optimisation for the energy sector. The integrated prediction model will allow for the description of the expected variability in wind power production in the coming hours to days, accounting for its spatio-temporal dependencies, and depending on the prevailing weather conditions defined by the WRF output. The output from the integrated short term prediction tool constitutes scenario forecasts for the coming period, which can then be fed into any type of system model or decision making problem to be solved. The high resolution of the WRF results loaded into the integrated prediction model will ensure a high accuracy data basis is available for use in the decision making process of the Danish transmission system operator. The need for high accuracy predictions will only increase over the next decade as Denmark approaches the goal of 50% wind power based electricity in 2025 from the current 20%.

Variationally consistent discretization schemes and numerical algorithms for contact problems

NASA Astrophysics Data System (ADS)

Wohlmuth, Barbara

We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of possible applications and show the performance of the space discretization scheme, non-linear solver, adaptive refinement process and time integration.

On the Limitations of Variational Bias Correction

NASA Technical Reports Server (NTRS)

Moradi, Isaac; Mccarty, Will; Gelaro, Ronald

2018-01-01

Satellite radiances are the largest dataset assimilated into Numerical Weather Prediction (NWP) models, however the data are subject to errors and uncertainties that need to be accounted for before assimilating into the NWP models. Variational bias correction uses the time series of observation minus background to estimate the observations bias. This technique does not distinguish between the background error, forward operator error, and observations error so that all these errors are summed up together and counted as observation error. We identify some sources of observations errors (e.g., antenna emissivity, non-linearity in the calibration, and antenna pattern) and show the limitations of variational bias corrections on estimating these errors.

Prediction of matching condition for a microstrip subsystem using artificial neural network and adaptive neuro-fuzzy inference system

NASA Astrophysics Data System (ADS)

Salehi, Mohammad Reza; Noori, Leila; Abiri, Ebrahim

2016-11-01

In this paper, a subsystem consisting of a microstrip bandpass filter and a microstrip low noise amplifier (LNA) is designed for WLAN applications. The proposed filter has a small implementation area (49 mm2), small insertion loss (0.08 dB) and wide fractional bandwidth (FBW) (61%). To design the proposed LNA, the compact microstrip cells, an field effect transistor, and only a lumped capacitor are used. It has a low supply voltage and a low return loss (-40 dB) at the operation frequency. The matching condition of the proposed subsystem is predicted using subsystem analysis, artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS). To design the proposed filter, the transmission matrix of the proposed resonator is obtained and analysed. The performance of the proposed ANN and ANFIS models is tested using the numerical data by four performance measures, namely the correlation coefficient (CC), the mean absolute error (MAE), the average percentage error (APE) and the root mean square error (RMSE). The obtained results show that these models are in good agreement with the numerical data, and a small error between the predicted values and numerical solution is obtained.

Problems Associated with Grid Convergence of Functionals

NASA Technical Reports Server (NTRS)

Salas, Manuel D.; Atkins, Harld L.

2008-01-01

The current use of functionals to evaluate order-of-convergence of a numerical scheme can lead to incorrect values. The problem comes about because of interplay between the errors from the evaluation of the functional, e.g., quadrature error, and from the numerical scheme discretization. Alternative procedures for deducing the order-property of a scheme are presented. The problem is studied within the context of the inviscid supersonic flow over a blunt body; however, the problem and solutions presented are not unique to this example.

On Problems Associated with Grid Convergence of Functionals

NASA Technical Reports Server (NTRS)

Salas, Manuael D.; Atkins, Harold L

2009-01-01

The current use of functionals to evaluate order-of-convergence of a numerical scheme can lead to incorrect values. The problem comes about because of interplay between the errors from the evaluation of the functional, e.g., quadrature error, and from the numerical scheme discretization. Alternative procedures for deducing the order property of a scheme are presented. The problems are studied within the context of the inviscid supersonic flow over a blunt body; however, the problems and solutions presented are not unique to this example.

A Modeling Framework for Optimal Computational Resource Allocation Estimation: Considering the Trade-offs between Physical Resolutions, Uncertainty and Computational Costs

NASA Astrophysics Data System (ADS)

Moslehi, M.; de Barros, F.; Rajagopal, R.

2014-12-01

Hydrogeological models that represent flow and transport in subsurface domains are usually large-scale with excessive computational complexity and uncertain characteristics. Uncertainty quantification for predicting flow and transport in heterogeneous formations often entails utilizing a numerical Monte Carlo framework, which repeatedly simulates the model according to a random field representing hydrogeological characteristics of the field. The physical resolution (e.g. grid resolution associated with the physical space) for the simulation is customarily chosen based on recommendations in the literature, independent of the number of Monte Carlo realizations. This practice may lead to either excessive computational burden or inaccurate solutions. We propose an optimization-based methodology that considers the trade-off between the following conflicting objectives: time associated with computational costs, statistical convergence of the model predictions and physical errors corresponding to numerical grid resolution. In this research, we optimally allocate computational resources by developing a modeling framework for the overall error based on a joint statistical and numerical analysis and optimizing the error model subject to a given computational constraint. The derived expression for the overall error explicitly takes into account the joint dependence between the discretization error of the physical space and the statistical error associated with Monte Carlo realizations. The accuracy of the proposed framework is verified in this study by applying it to several computationally extensive examples. Having this framework at hand aims hydrogeologists to achieve the optimum physical and statistical resolutions to minimize the error with a given computational budget. Moreover, the influence of the available computational resources and the geometric properties of the contaminant source zone on the optimum resolutions are investigated. We conclude that the computational cost associated with optimal allocation can be substantially reduced compared with prevalent recommendations in the literature.

Application Of Multi-grid Method On China Seas' Temperature Forecast

NASA Astrophysics Data System (ADS)

Li, W.; Xie, Y.; He, Z.; Liu, K.; Han, G.; Ma, J.; Li, D.

2006-12-01

Correlation scales have been used in traditional scheme of 3-dimensional variational (3D-Var) data assimilation to estimate the background error covariance for the numerical forecast and reanalysis of atmosphere and ocean for decades. However there are still some drawbacks of this scheme. First, the correlation scales are difficult to be determined accurately. Second, the positive definition of the first-guess error covariance matrix cannot be guaranteed unless the correlation scales are sufficiently small. Xie et al. (2005) indicated that a traditional 3D-Var only corrects some certain wavelength errors and its accuracy depends on the accuracy of the first-guess covariance. And in general, short wavelength error can not be well corrected until long one is corrected and then inaccurate first-guess covariance may mistakenly take long wave error as short wave ones and result in erroneous analysis. For the purpose of quickly minimizing the errors of long and short waves successively, a new 3D-Var data assimilation scheme, called multi-grid data assimilation scheme, is proposed in this paper. By assimilating the shipboard SST and temperature profiles data into a numerical model of China Seas, we applied this scheme in two-month data assimilation and forecast experiment which ended in a favorable result. Comparing with the traditional scheme of 3D-Var, the new scheme has higher forecast accuracy and a lower forecast Root-Mean-Square (RMS) error. Furthermore, this scheme was applied to assimilate the SST of shipboard, AVHRR Pathfinder Version 5.0 SST and temperature profiles at the same time, and a ten-month forecast experiment on sea temperature of China Seas was carried out, in which a successful forecast result was obtained. Particularly, the new scheme is demonstrated a great numerical efficiency in these analyses.

Optimized formulas for the gravitational field of a tesseroid

NASA Astrophysics Data System (ADS)

Grombein, Thomas; Seitz, Kurt; Heck, Bernhard

2013-07-01

Various tasks in geodesy, geophysics, and related geosciences require precise information on the impact of mass distributions on gravity field-related quantities, such as the gravitational potential and its partial derivatives. Using forward modeling based on Newton's integral, mass distributions are generally decomposed into regular elementary bodies. In classical approaches, prisms or point mass approximations are mostly utilized. Considering the effect of the sphericity of the Earth, alternative mass modeling methods based on tesseroid bodies (spherical prisms) should be taken into account, particularly in regional and global applications. Expressions for the gravitational field of a point mass are relatively simple when formulated in Cartesian coordinates. In the case of integrating over a tesseroid volume bounded by geocentric spherical coordinates, it will be shown that it is also beneficial to represent the integral kernel in terms of Cartesian coordinates. This considerably simplifies the determination of the tesseroid's potential derivatives in comparison with previously published methodologies that make use of integral kernels expressed in spherical coordinates. Based on this idea, optimized formulas for the gravitational potential of a homogeneous tesseroid and its derivatives up to second-order are elaborated in this paper. These new formulas do not suffer from the polar singularity of the spherical coordinate system and can, therefore, be evaluated for any position on the globe. Since integrals over tesseroid volumes cannot be solved analytically, the numerical evaluation is achieved by means of expanding the integral kernel in a Taylor series with fourth-order error in the spatial coordinates of the integration point. As the structure of the Cartesian integral kernel is substantially simplified, Taylor coefficients can be represented in a compact and computationally attractive form. Thus, the use of the optimized tesseroid formulas particularly benefits from a significant decrease in computation time by about 45 % compared to previously used algorithms. In order to show the computational efficiency and to validate the mathematical derivations, the new tesseroid formulas are applied to two realistic numerical experiments and are compared to previously published tesseroid methods and the conventional prism approach.

Research on the error model of airborne celestial/inertial integrated navigation system

NASA Astrophysics Data System (ADS)

Zheng, Xiaoqiang; Deng, Xiaoguo; Yang, Xiaoxu; Dong, Qiang

2015-02-01

Celestial navigation subsystem of airborne celestial/inertial integrated navigation system periodically correct the positioning error and heading drift of the inertial navigation system, by which the inertial navigation system can greatly improve the accuracy of long-endurance navigation. Thus the navigation accuracy of airborne celestial navigation subsystem directly decides the accuracy of the integrated navigation system if it works for long time. By building the mathematical model of the airborne celestial navigation system based on the inertial navigation system, using the method of linear coordinate transformation, we establish the error transfer equation for the positioning algorithm of airborne celestial system. Based on these we built the positioning error model of the celestial navigation. And then, based on the positioning error model we analyze and simulate the positioning error which are caused by the error of the star tracking platform with the MATLAB software. Finally, the positioning error model is verified by the information of the star obtained from the optical measurement device in range and the device whose location are known. The analysis and simulation results show that the level accuracy and north accuracy of tracking platform are important factors that limit airborne celestial navigation systems to improve the positioning accuracy, and the positioning error have an approximate linear relationship with the level error and north error of tracking platform. The error of the verification results are in 1000m, which shows that the model is correct.

Making Residents Part of the Safety Culture: Improving Error Reporting and Reducing Harms.

PubMed

Fox, Michael D; Bump, Gregory M; Butler, Gabriella A; Chen, Ling-Wan; Buchert, Andrew R

2017-01-30

Reporting medical errors is a focus of the patient safety movement. As frontline physicians, residents are optimally positioned to recognize errors and flaws in systems of care. Previous work highlights the difficulty of engaging residents in identification and/or reduction of medical errors and in integrating these trainees into their institutions' cultures of safety. The authors describe the implementation of a longitudinal, discipline-based, multifaceted curriculum to enhance the reporting of errors by pediatric residents at Children's Hospital of Pittsburgh of University of Pittsburgh Medical Center. The key elements of this curriculum included providing the necessary education to identify medical errors with an emphasis on systems-based causes, modeling of error reporting by faculty, and integrating error reporting and discussion into the residents' daily activities. The authors tracked monthly error reporting rates by residents and other health care professionals, in addition to serious harm event rates at the institution. The interventions resulted in significant increases in error reports filed by residents, from 3.6 to 37.8 per month over 4 years (P < 0.0001). This increase in resident error reporting correlated with a decline in serious harm events, from 15.0 to 8.1 per month over 4 years (P = 0.01). Integrating patient safety into the everyday resident responsibilities encourages frequent reporting and discussion of medical errors and leads to improvements in patient care. Multiple simultaneous interventions are essential to making residents part of the safety culture of their training hospitals.

3-D direct current resistivity anisotropic modelling by goal-oriented adaptive finite element methods

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Qiu, Lewen; Tang, Jingtian; Wu, Xiaoping; Xiao, Xiao; Zhou, Zilong

2018-01-01

Although accurate numerical solvers for 3-D direct current (DC) isotropic resistivity models are current available even for complicated models with topography, reliable numerical solvers for the anisotropic case are still an open question. This study aims to develop a novel and optimal numerical solver for accurately calculating the DC potentials for complicated models with arbitrary anisotropic conductivity structures in the Earth. First, a secondary potential boundary value problem is derived by considering the topography and the anisotropic conductivity. Then, two a posteriori error estimators with one using the gradient-recovery technique and one measuring the discontinuity of the normal component of current density are developed for the anisotropic cases. Combing the goal-oriented and non-goal-oriented mesh refinements and these two error estimators, four different solving strategies are developed for complicated DC anisotropic forward modelling problems. A synthetic anisotropic two-layer model with analytic solutions verified the accuracy of our algorithms. A half-space model with a buried anisotropic cube and a mountain-valley model are adopted to test the convergence rates of these four solving strategies. We found that the error estimator based on the discontinuity of current density shows better performance than the gradient-recovery based a posteriori error estimator for anisotropic models with conductivity contrasts. Both error estimators working together with goal-oriented concepts can offer optimal mesh density distributions and highly accurate solutions.

Therapeutic self-disclosure in integrative psychotherapy: When is this a clinical error?

PubMed

Ziv-Beiman, Sharon; Shahar, Golan

2016-09-01

Ascending to prominence in virtually all forms of psychotherapy, therapist self-disclosure (TSD) has recently been identified as a primarily integrative intervention (Ziv-Beiman, 2013). In the present article, we discuss various instances in which using TSD in integrative psychotherapy might constitute a clinical error. First, we briefly review extant theory and empirical research on TSD, followed by our preferred version of integrative psychotherapy (i.e., a version of Wachtel's Cyclical Psychodynamics [Wachtel, 1977, 1997, 2014]), which we title cognitive existential psychodynamics. Next, we provide and discuss three examples in which implementing TSD constitutes a clinical error. In essence, we submit that using TSD constitutes an error when patients, constrained by their representational structures (object relations), experience the subjectivity of the other as impinging, and thus propels them to "react" instead of "emerge." (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Detecting genotyping errors and describing black bear movement in northern Idaho

Treesearch

Michael K. Schwartz; Samuel A. Cushman; Kevin S. McKelvey; Jim Hayden; Cory Engkjer

2006-01-01

Non-invasive genetic sampling has become a favored tool to enumerate wildlife. Genetic errors, caused by poor quality samples, can lead to substantial biases in numerical estimates of individuals. We demonstrate how the computer program DROPOUT can detect amplification errors (false alleles and allelic dropout) in a black bear (Ursus americanus) dataset collected in...

Using Least Squares for Error Propagation

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2015-01-01

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

A new vertical grid nesting capability in the Weather Research and Forecasting (WRF) Model

DOE PAGES

Daniels, Megan H.; Lundquist, Katherine A.; Mirocha, Jeffrey D.; ...

2016-09-16

Mesoscale atmospheric models are increasingly used for high-resolution (<3 km) simulations to better resolve smaller-scale flow details. Increased resolution is achieved using mesh refinement via grid nesting, a procedure where multiple computational domains are integrated either concurrently or in series. A constraint in the concurrent nesting framework offered by the Weather Research and Forecasting (WRF) Model is that mesh refinement is restricted to the horizontal dimensions. This limitation prevents control of the grid aspect ratio, leading to numerical errors due to poor grid quality and preventing grid optimization. Here, a procedure permitting vertical nesting for one-way concurrent simulation is developedmore » and validated through idealized cases. The benefits of vertical nesting are demonstrated using both mesoscale and large-eddy simulations (LES). Mesoscale simulations of the Terrain-Induced Rotor Experiment (T-REX) show that vertical grid nesting can alleviate numerical errors due to large aspect ratios on coarse grids, while allowing for higher vertical resolution on fine grids. Furthermore, the coarsening of the parent domain does not result in a significant loss of accuracy on the nested domain. LES of neutral boundary layer flow shows that, by permitting optimal grid aspect ratios on both parent and nested domains, use of vertical nesting yields improved agreement with the theoretical logarithmic velocity profile on both domains. Lastly, vertical grid nesting in WRF opens the path forward for multiscale simulations, allowing more accurate simulations spanning a wider range of scales than previously possible.« less

A new vertical grid nesting capability in the Weather Research and Forecasting (WRF) Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Daniels, Megan H.; Lundquist, Katherine A.; Mirocha, Jeffrey D.

Mesoscale atmospheric models are increasingly used for high-resolution (<3 km) simulations to better resolve smaller-scale flow details. Increased resolution is achieved using mesh refinement via grid nesting, a procedure where multiple computational domains are integrated either concurrently or in series. A constraint in the concurrent nesting framework offered by the Weather Research and Forecasting (WRF) Model is that mesh refinement is restricted to the horizontal dimensions. This limitation prevents control of the grid aspect ratio, leading to numerical errors due to poor grid quality and preventing grid optimization. Here, a procedure permitting vertical nesting for one-way concurrent simulation is developedmore » and validated through idealized cases. The benefits of vertical nesting are demonstrated using both mesoscale and large-eddy simulations (LES). Mesoscale simulations of the Terrain-Induced Rotor Experiment (T-REX) show that vertical grid nesting can alleviate numerical errors due to large aspect ratios on coarse grids, while allowing for higher vertical resolution on fine grids. Furthermore, the coarsening of the parent domain does not result in a significant loss of accuracy on the nested domain. LES of neutral boundary layer flow shows that, by permitting optimal grid aspect ratios on both parent and nested domains, use of vertical nesting yields improved agreement with the theoretical logarithmic velocity profile on both domains. Lastly, vertical grid nesting in WRF opens the path forward for multiscale simulations, allowing more accurate simulations spanning a wider range of scales than previously possible.« less

A Generalized Polynomial Chaos-Based Approach to Analyze the Impacts of Process Deviations on MEMS Beams.

PubMed

Gao, Lili; Zhou, Zai-Fa; Huang, Qing-An

2017-11-08

A microstructure beam is one of the fundamental elements in MEMS devices like cantilever sensors, RF/optical switches, varactors, resonators, etc. It is still difficult to precisely predict the performance of MEMS beams with the current available simulators due to the inevitable process deviations. Feasible numerical methods are required and can be used to improve the yield and profits of the MEMS devices. In this work, process deviations are considered to be stochastic variables, and a newly-developed numerical method, i.e., generalized polynomial chaos (GPC), is applied for the simulation of the MEMS beam. The doubly-clamped polybeam has been utilized to verify the accuracy of GPC, compared with our Monte Carlo (MC) approaches. Performance predictions have been made on the residual stress by achieving its distributions in GaAs Monolithic Microwave Integrated Circuit (MMIC)-based MEMS beams. The results show that errors are within 1% for the results of GPC approximations compared with the MC simulations. Appropriate choices of the 4-order GPC expansions with orthogonal terms have also succeeded in reducing the MC simulation labor. The mean value of the residual stress, concluded from experimental tests, shares an error about 1.1% with that of the 4-order GPC method. It takes a probability around 54.3% for the 4-order GPC approximation to attain the mean test value of the residual stress. The corresponding yield occupies over 90 percent around the mean within the twofold standard deviations.

A Generalized Polynomial Chaos-Based Approach to Analyze the Impacts of Process Deviations on MEMS Beams

PubMed Central

Gao, Lili

2017-01-01

A microstructure beam is one of the fundamental elements in MEMS devices like cantilever sensors, RF/optical switches, varactors, resonators, etc. It is still difficult to precisely predict the performance of MEMS beams with the current available simulators due to the inevitable process deviations. Feasible numerical methods are required and can be used to improve the yield and profits of the MEMS devices. In this work, process deviations are considered to be stochastic variables, and a newly-developed numerical method, i.e., generalized polynomial chaos (GPC), is applied for the simulation of the MEMS beam. The doubly-clamped polybeam has been utilized to verify the accuracy of GPC, compared with our Monte Carlo (MC) approaches. Performance predictions have been made on the residual stress by achieving its distributions in GaAs Monolithic Microwave Integrated Circuit (MMIC)-based MEMS beams. The results show that errors are within 1% for the results of GPC approximations compared with the MC simulations. Appropriate choices of the 4-order GPC expansions with orthogonal terms have also succeeded in reducing the MC simulation labor. The mean value of the residual stress, concluded from experimental tests, shares an error about 1.1% with that of the 4-order GPC method. It takes a probability around 54.3% for the 4-order GPC approximation to attain the mean test value of the residual stress. The corresponding yield occupies over 90 percent around the mean within the twofold standard deviations. PMID:29117096

Ensemble Data Assimilation of Photovoltaic Power Information in the Convection-permitting High-Resolution Model COSMO-DE

NASA Astrophysics Data System (ADS)

Declair, Stefan; Saint-Drenan, Yves-Marie; Potthast, Roland

2017-04-01

Determining the amount of weather dependent renewable energy is a demanding task for transmission system operators (TSOs) and wind and photovoltaic (PV) prediction errors require the use of reserve power, which generate costs and can - in extreme cases - endanger the security of supply. In the project EWeLiNE funded by the German government, the German Weather Service and the Fraunhofer Institute on Wind Energy and Energy System Technology develop innovative weather- and power forecasting models and tools for grid integration of weather dependent renewable energy. The key part in energy prediction process chains is the numerical weather prediction (NWP) system. Irradiation forecasts from NWP systems are however subject to several sources of error. For PV power prediction, weaknesses of the NWP model to correctly forecast i.e. low stratus, absorption of condensed water or aerosol optical depths are the main sources of errors. Inaccurate radiation schemes (i.e. the two-stream parametrization) are also known as a deficit of NWP systems with regard to irradiation forecast. To mitigate errors like these, latest observations can be used in a pre-processing technique called data assimilation (DA). In DA, not only the initial fields are provided, but the model is also synchronized with reality - the observations - and hence forecast errors are reduced. Besides conventional observation networks like radiosondes, synoptic observations or air reports of wind, pressure and humidity, the number of observations measuring meteorological information indirectly by means of remote sensing such as satellite radiances, radar reflectivities or GPS slant delays strongly increases. Numerous PV plants installed in Germany potentially represent a dense meteorological network assessing irradiation through their power measurements. Forecast accuracy may thus be enhanced by extending the observations in the assimilation by this new source of information. PV power plants can provide information on clouds, aerosol optical depth or low stratus in terms of remote sensing: the power output is strongly dependent on perturbations along the slant between sun position and PV panel. Since these data are not limited to the vertical column above or below the detector, it may thus complement satellite data and compensate weaknesses in the radiation scheme. In this contribution, the used DA technique (Local Ensemble Transform Kalman Filter, LETKF) is shortly sketched. Furthermore, the computation of the model power equivalents is described and first results are presented and discussed.

A monitor for the laboratory evaluation of control integrity in digital control systems operating in harsh electromagnetic environments

NASA Technical Reports Server (NTRS)

Belcastro, Celeste M.; Fischl, Robert; Kam, Moshe

1992-01-01

This paper presents a strategy for dynamically monitoring digital controllers in the laboratory for susceptibility to electromagnetic disturbances that compromise control integrity. The integrity of digital control systems operating in harsh electromagnetic environments can be compromised by upsets caused by induced transient electrical signals. Digital system upset is a functional error mode that involves no component damage, can occur simultaneously in all channels of a redundant control computer, and is software dependent. The motivation for this work is the need to develop tools and techniques that can be used in the laboratory to validate and/or certify critical aircraft controllers operating in electromagnetically adverse environments that result from lightning, high-intensity radiated fields (HIRF), and nuclear electromagnetic pulses (NEMP). The detection strategy presented in this paper provides dynamic monitoring of a given control computer for degraded functional integrity resulting from redundancy management errors, control calculation errors, and control correctness/effectiveness errors. In particular, this paper discusses the use of Kalman filtering, data fusion, and statistical decision theory in monitoring a given digital controller for control calculation errors.

Linear shoaling of free-surface waves in multi-layer non-hydrostatic models

NASA Astrophysics Data System (ADS)

Bai, Yefei; Cheung, Kwok Fai

2018-01-01

The capability to describe shoaling over sloping bottom is fundamental to modeling of coastal wave transformation. The linear shoaling gradient provides a metric to measure this property in non-hydrostatic models with layer-integrated formulations. The governing equations in Boussinesq form facilitate derivation of the linear shoaling gradient, which is in the form of a [ 2 P + 2 , 2 P ] expansion of the water depth parameter kd with P equal to 1 for a one-layer model and (4 N - 4) for an N-layer model. The expansion reproduces the analytical solution from Airy wave theory at the shallow water limit and maintains a reasonable approximation up to kd = 1.2 and 2 for the one and two-layer models. Additional layers provide rapid and monotonic convergence of the shoaling gradient into deep water. Numerical experiments of wave propagation over a plane slope illustrate manifestation of the shoaling errors through the transformation processes from deep to shallow water. Even though outside the zone of active wave transformation, shoaling errors from deep to intermediate water are cumulative to produce appreciable impact to the wave amplitude in shallow water.

Assessment of the Derivative-Moment Transformation method for unsteady-load estimation

NASA Astrophysics Data System (ADS)

Mohebbian, Ali; Rival, David

2011-11-01

It is often difficult, if not impossible, to measure the aerodynamic or hydrodynamic forces on a moving body. For this reason, a classical control-volume technique is typically applied to extract the unsteady forces instead. However, measuring the acceleration term within the volume of interest using PIV can be limited by optical access, reflections as well as shadows. Therefore in this study an alternative approach, termed the Derivative-Moment Transformation (DMT) method, is introduced and tested on a synthetic data set produced using numerical simulations. The test case involves the unsteady loading of a flat plate in a two-dimensional, laminar periodic gust. The results suggest that the DMT method can accurately predict the acceleration term so long as appropriate spatial and temporal resolutions are maintained. The major deficiency was found to be the determination of pressure in the wake. The effect of control-volume size was investigated suggesting that smaller domains work best by minimizing the associated error with the pressure field. When increasing the control-volume size, the number of calculations necessary for the pressure-gradient integration increases, in turn substantially increasing the error propagation.

Successful choice behavior is associated with distinct and coherent network states in anterior cingulate cortex

PubMed Central

Lapish, Christopher C.; Durstewitz, Daniel; Chandler, L. Judson; Seamans, Jeremy K.

2008-01-01

Successful decision making requires an ability to monitor contexts, actions, and outcomes. The anterior cingulate cortex (ACC) is thought to be critical for these functions, monitoring and guiding decisions especially in challenging situations involving conflict and errors. A number of different single-unit correlates have been observed in the ACC that reflect the diverse cognitive components involved. Yet how ACC neurons function as an integrated network is poorly understood. Here we show, using advanced population analysis of multiple single-unit recordings from the rat ACC during performance of an ecologically valid decision-making task, that ensembles of neurons move through different coherent and dissociable states as the cognitive requirements of the task change. This organization into distinct network patterns with respect to both firing-rate changes and correlations among units broke down during trials with numerous behavioral errors, especially at choice points of the task. These results point to an underlying functional organization into cell assemblies in the ACC that may monitor choices, outcomes, and task contexts, thus tracking the animal's progression through “task space.” PMID:18708525

Development of the functional simulator for the Galileo attitude and articulation control system

NASA Technical Reports Server (NTRS)

Namiri, M. K.

1983-01-01

A simulation program for verifying and checking the performance of the Galileo Spacecraft's Attitude and Articulation Control Subsystem's (AACS) flight software is discussed. The program, which is called Functional Simulator (FUNSIM), provides a simple method of interfacing user-supplied mathematical models coded in FORTRAN which describes spacecraft dynamics, sensors, and actuators; this is done with the AACS flight software, coded in HAL/S (High-level Advanced Language/Shuttle). It is thus able to simulate the AACS flight software accurately to the HAL/S statement level in the environment of a mainframe computer system. FUNSIM also has a command and data subsystem (CDS) simulator. It is noted that the input/output data and timing are simulated with the same precision as the flight microprocessor. FUNSIM uses a variable stepsize numerical integration algorithm complete with individual error bound control on the state variable to solve the equations of motion. The program has been designed to provide both line printer and matrix dot plotting of the variables requested in the run section and to provide error diagnostics.

High Order Numerical Methods for the Investigation of the Two Dimensional Richtmyer-Meshkov Instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Don, W-S; Gotllieb, D; Shu, C-W

2001-11-26

For flows that contain significant structure, high order schemes offer large advantages over low order schemes. Fundamentally, the reason comes from the truncation error of the differencing operators. If one examines carefully the expression for the truncation error, one will see that for a fixed computational cost that the error can be made much smaller by increasing the numerical order than by increasing the number of grid points. One can readily derive the following expression which holds for systems dominated by hyperbolic effects and advanced explicitly in time: flops = const * p{sup 2} * k{sup (d+1)(p+1)/p}/E{sup (d+1)/p} where flopsmore » denotes floating point operations, p denotes numerical order, d denotes spatial dimension, where E denotes the truncation error of the difference operator, and where k denotes the Fourier wavenumber. For flows that contain structure, such as turbulent flows or any calculation where, say, vortices are present, there will be significant energy in the high values of k. Thus, one can see that the rate of growth of the flops is very different for different values of p. Further, the constant in front of the expression is also very different. With a low order scheme, one quickly reaches the limit of the computer. With the high order scheme, one can obtain far more modes before the limit of the computer is reached. Here we examine the application of spectral methods and the Weighted Essentially Non-Oscillatory (WENO) scheme to the Richtmyer-Meshkov Instability. We show the intricate structure that these high order schemes can calculate and we show that the two methods, though very different, converge to the same numerical solution indicating that the numerical solution is very likely physically correct.« less

Numerical time-domain electromagnetics based on finite-difference and convolution

NASA Astrophysics Data System (ADS)

Lin, Yuanqu

Time-domain methods posses a number of advantages over their frequency-domain counterparts for the solution of wideband, nonlinear, and time varying electromagnetic scattering and radiation phenomenon. Time domain integral equation (TDIE)-based methods, which incorporate the beneficial properties of integral equation method, are thus well suited for solving broadband scattering problems for homogeneous scatterers. Widespread adoption of TDIE solvers has been retarded relative to other techniques by their inefficiency, inaccuracy and instability. Moreover, two-dimensional (2D) problems are especially problematic, because 2D Green's functions have infinite temporal support, exacerbating these difficulties. This thesis proposes a finite difference delay modeling (FDDM) scheme for the solution of the integral equations of 2D transient electromagnetic scattering problems. The method discretizes the integral equations temporally using first- and second-order finite differences to map Laplace-domain equations into the Z domain before transforming to the discrete time domain. The resulting procedure is unconditionally stable because of the nature of the Laplace- to Z-domain mapping. The first FDDM method developed in this thesis uses second-order Lagrange basis functions with Galerkin's method for spatial discretization. The second application of the FDDM method discretizes the space using a locally-corrected Nystrom method, which accelerates the precomputation phase and achieves high order accuracy. The Fast Fourier Transform (FFT) is applied to accelerate the marching-on-time process in both methods. While FDDM methods demonstrate impressive accuracy and stability in solving wideband scattering problems for homogeneous scatterers, they still have limitations in analyzing interactions between several inhomogenous scatterers. Therefore, this thesis devises a multi-region finite-difference time-domain (MR-FDTD) scheme based on domain-optimal Green's functions for solving sparsely-populated problems. The scheme uses a discrete Green's function (DGF) on the FDTD lattice to truncate the local subregions, and thus reduces reflection error on the local boundary. A continuous Green's function (CGF) is implemented to pass the influence of external fields into each FDTD region which mitigates the numerical dispersion and anisotropy of standard FDTD. Numerical results will illustrate the accuracy and stability of the proposed techniques.

Numerical Procedure to Forecast the Tsunami Parameters from a Database of Pre-Simulated Seismic Unit Sources

NASA Astrophysics Data System (ADS)

Jiménez, César; Carbonel, Carlos; Rojas, Joel

2018-04-01

We have implemented a numerical procedure to forecast the parameters of a tsunami, such as the arrival time of the front of the first wave and the maximum wave height in real and virtual tidal stations along the Peruvian coast, with this purpose a database of pre-computed synthetic tsunami waveforms (or Green functions) was obtained from numerical simulation of seismic unit sources (dimension: 50 × 50 km2) for subduction zones from southern Chile to northern Mexico. A bathymetry resolution of 30 arc-sec (approximately 927 m) was used. The resulting tsunami waveform is obtained from the superposition of synthetic waveforms corresponding to several seismic unit sources contained within the tsunami source geometry. The numerical procedure was applied to the Chilean tsunami of April 1, 2014. The results show a very good correlation for stations with wave amplitude greater than 1 m, in the case of the Arica tide station an error (from the maximum height of the observed and simulated waveform) of 3.5% was obtained, for Callao station the error was 12% and the largest error was in Chimbote with 53.5%, however, due to the low amplitude of the Chimbote wave (<1 m), the overestimated error, in this case, is not important for evacuation purposes. The aim of the present research is tsunami early warning, where speed is required rather than accuracy, so the results should be taken as preliminary.

Numerical Procedure to Forecast the Tsunami Parameters from a Database of Pre-Simulated Seismic Unit Sources

NASA Astrophysics Data System (ADS)

Jiménez, César; Carbonel, Carlos; Rojas, Joel

2017-09-01

We have implemented a numerical procedure to forecast the parameters of a tsunami, such as the arrival time of the front of the first wave and the maximum wave height in real and virtual tidal stations along the Peruvian coast, with this purpose a database of pre-computed synthetic tsunami waveforms (or Green functions) was obtained from numerical simulation of seismic unit sources (dimension: 50 × 50 km2) for subduction zones from southern Chile to northern Mexico. A bathymetry resolution of 30 arc-sec (approximately 927 m) was used. The resulting tsunami waveform is obtained from the superposition of synthetic waveforms corresponding to several seismic unit sources contained within the tsunami source geometry. The numerical procedure was applied to the Chilean tsunami of April 1, 2014. The results show a very good correlation for stations with wave amplitude greater than 1 m, in the case of the Arica tide station an error (from the maximum height of the observed and simulated waveform) of 3.5% was obtained, for Callao station the error was 12% and the largest error was in Chimbote with 53.5%, however, due to the low amplitude of the Chimbote wave (<1 m), the overestimated error, in this case, is not important for evacuation purposes. The aim of the present research is tsunami early warning, where speed is required rather than accuracy, so the results should be taken as preliminary.

Integrated analysis of error detection and recovery

NASA Technical Reports Server (NTRS)

Shin, K. G.; Lee, Y. H.

1985-01-01

An integrated modeling and analysis of error detection and recovery is presented. When fault latency and/or error latency exist, the system may suffer from multiple faults or error propagations which seriously deteriorate the fault-tolerant capability. Several detection models that enable analysis of the effect of detection mechanisms on the subsequent error handling operations and the overall system reliability were developed. Following detection of the faulty unit and reconfiguration of the system, the contaminated processes or tasks have to be recovered. The strategies of error recovery employed depend on the detection mechanisms and the available redundancy. Several recovery methods including the rollback recovery are considered. The recovery overhead is evaluated as an index of the capabilities of the detection and reconfiguration mechanisms.

Managing operational documentation in the ALICE Detector Control System

NASA Astrophysics Data System (ADS)

Lechman, M.; Augustinus, A.; Bond, P.; Chochula, P.; Kurepin, A.; Pinazza, O.; Rosinsky, P.

2012-12-01

ALICE (A Large Ion Collider Experiment) is one of the big LHC (Large Hadron Collider) experiments at CERN in Geneve, Switzerland. The experiment is composed of 18 sub-detectors controlled by an integrated Detector Control System (DCS) that is implemented using the commercial SCADA package PVSSII. The DCS includes over 1200 network devices, over 1,000,000 monitored parameters and numerous custom made software components that are prepared by over 100 developers from all around the world. This complex system is controlled by a single operator via a central user interface. One of his/her main tasks is the recovery of anomalies and errors that may occur during operation. Therefore, clear, complete and easily accessible documentation is essential to guide the shifter through the expert interfaces of different subsystems. This paper describes the idea of the management of the operational documentation in ALICE using a generic repository that is built on a relational database and is integrated with the control system. The experience gained and the conclusions drawn from the project are also presented.

On singular and highly oscillatory properties of the Green function for ship motions

NASA Astrophysics Data System (ADS)

Chen, Xiao-Bo; Xiong Wu, Guo

2001-10-01

The Green function used for analysing ship motions in waves is the velocity potential due to a point source pulsating and advancing at a uniform forward speed. The behaviour of this function is investigated, in particular for the case when the source is located at or close to the free surface. In the far field, the Green function is represented by a single integral along one closed dispersion curve and two open dispersion curves. The single integral along the open dispersion curves is analysed based on the asymptotic expansion of a complex error function. The singular and highly oscillatory behaviour of the Green function is captured, which shows that the Green function oscillates with indefinitely increasing amplitude and indefinitely decreasing wavelength, when a field point approaches the track of the source point at the free surface. This sheds some light on the nature of the difficulties in the numerical methods used for predicting the motion of a ship advancing in waves.

Explicit methods in extended phase space for inseparable Hamiltonian problems

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2015-03-01

We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator.

A computer program for the simulation of heat and moisture flow in soils

NASA Technical Reports Server (NTRS)

Camillo, P.; Schmugge, T. J.

1981-01-01

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Maximum correntropy square-root cubature Kalman filter with application to SINS/GPS integrated systems.

PubMed

Liu, Xi; Qu, Hua; Zhao, Jihong; Yue, Pengcheng

2018-05-31

For a nonlinear system, the cubature Kalman filter (CKF) and its square-root version are useful methods to solve the state estimation problems, and both can obtain good performance in Gaussian noises. However, their performances often degrade significantly in the face of non-Gaussian noises, particularly when the measurements are contaminated by some heavy-tailed impulsive noises. By utilizing the maximum correntropy criterion (MCC) to improve the robust performance instead of traditional minimum mean square error (MMSE) criterion, a new square-root nonlinear filter is proposed in this study, named as the maximum correntropy square-root cubature Kalman filter (MCSCKF). The new filter not only retains the advantage of square-root cubature Kalman filter (SCKF), but also exhibits robust performance against heavy-tailed non-Gaussian noises. A judgment condition that avoids numerical problem is also given. The results of two illustrative examples, especially the SINS/GPS integrated systems, demonstrate the desirable performance of the proposed filter. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Characterizing traveling-wave collisions in granular chains starting from integrable limits: the case of the Korteweg-de Vries equation and the Toda lattice.

PubMed

Shen, Y; Kevrekidis, P G; Sen, S; Hoffman, A

2014-08-01

Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPU-type lattice through both the Korteweg-de Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both one-soliton and two-soliton solutions in explicit analytical form, we initialize such coherent structures in the granular chain and observe the proximity of the resulting evolution to the underlying integrable (KdV or Toda) model. While the KdV offers the possibility to accurately capture collisions of solitary waves propagating in the same direction, the Toda lattice enables capturing both copropagating and counterpropagating soliton collisions. The error in the approximation is quantified numerically and connections to bounds established in the mathematical literature are also given.

Fully nonlocal inelastic scattering computations for spectroscopical transmission electron microscopy methods

NASA Astrophysics Data System (ADS)

Rusz, Ján; Lubk, Axel; Spiegelberg, Jakob; Tyutyunnikov, Dmitry

2017-12-01

The complex interplay of elastic and inelastic scattering amenable to different levels of approximation constitutes the major challenge for the computation and hence interpretation of TEM-based spectroscopical methods. The two major approaches to calculate inelastic scattering cross sections of fast electrons on crystals—Yoshioka-equations-based forward propagation and the reciprocal wave method—are founded in two conceptually differing schemes—a numerical forward integration of each inelastically scattered wave function, yielding the exit density matrix, and a computation of inelastic scattering matrix elements using elastically scattered initial and final states (double channeling). Here, we compare both approaches and show that the latter is computationally competitive to the former by exploiting analytical integration schemes over multiple excited states. Moreover, we show how to include full nonlocality of the inelastic scattering event, neglected in the forward propagation approaches, at no additional computing costs in the reciprocal wave method. Detailed simulations show in some cases significant errors due to the z -locality approximation and hence pitfalls in the interpretation of spectroscopical TEM results.

ΛCDM Cosmology for Astronomers

NASA Astrophysics Data System (ADS)

Condon, J. J.; Matthews, A. M.

2018-07-01

The homogeneous, isotropic, and flat ΛCDM universe favored by observations of the cosmic microwave background can be described using only Euclidean geometry, locally correct Newtonian mechanics, and the basic postulates of special and general relativity. We present simple derivations of the most useful equations connecting astronomical observables (redshift, flux density, angular diameter, brightness, local space density, ...) with the corresponding intrinsic properties of distant sources (lookback time, distance, spectral luminosity, linear size, specific intensity, source counts, ...). We also present an analytic equation for lookback time that is accurate within 0.1% for all redshifts z. The exact equation for comoving distance is an elliptic integral that must be evaluated numerically, but we found a simple approximation with errors <0.2% for all redshifts up to z ≈ 50.

Numerical trials of HISSE

NASA Technical Reports Server (NTRS)

Peters, C.; Kampe, F. (Principal Investigator)

1980-01-01

The mathematical description and implementation of the statistical estimation procedure known as the Houston integrated spatial/spectral estimator (HISSE) is discussed. HISSE is based on a normal mixture model and is designed to take advantage of spectral and spatial information of LANDSAT data pixels, utilizing the initial classification and clustering information provided by the AMOEBA algorithm. The HISSE calculates parametric estimates of class proportions which reduce the error inherent in estimates derived from typical classify and count procedures common to nonparametric clustering algorithms. It also singles out spatial groupings of pixels which are most suitable for labeling classes. These calculations are designed to aid the analyst/interpreter in labeling patches with a crop class label. Finally, HISSE's initial performance on an actual LANDSAT agricultural ground truth data set is reported.

Compact beam splitters in coupled waveguides using shortcuts to adiabaticity

NASA Astrophysics Data System (ADS)

Chen, Xi; Wen, Rui-Dan; Shi, Jie-Long; Tseng, Shuo-Yen

2018-04-01

There are various works on adiabatic (three) waveguide coupler devices but most are focused on the quantum optical analogies and the physics itself. We successfully apply shortcuts to adiabaticity techniques to the coupled waveguide system with a suitable length for integrated optics devices. Especially, the counter-diabatic driving protocol followed by unitary transformation overcomes the previously unrealistic implemention, and is used to design feasible and robust 1 × 2 and 1 × 3 beam splitters for symmetric and asymmetric three waveguide couplers. Numerical simulations with the beam propagation method demonstrate that these shortcut designs for beam splitters are shorter than the adiabatic ones, and also have a better tolerance than parallel waveguides resonant beam splitters with respect to spacing errors and wavelength variation.

Driven Metadynamics: Reconstructing Equilibrium Free Energies from Driven Adaptive-Bias Simulations

PubMed Central

2013-01-01

We present a novel free-energy calculation method that constructively integrates two distinct classes of nonequilibrium sampling techniques, namely, driven (e.g., steered molecular dynamics) and adaptive-bias (e.g., metadynamics) methods. By employing nonequilibrium work relations, we design a biasing protocol with an explicitly time- and history-dependent bias that uses on-the-fly work measurements to gradually flatten the free-energy surface. The asymptotic convergence of the method is discussed, and several relations are derived for free-energy reconstruction and error estimation. Isomerization reaction of an atomistic polyproline peptide model is used to numerically illustrate the superior efficiency and faster convergence of the method compared with its adaptive-bias and driven components in isolation. PMID:23795244

Precision analysis for standard deviation measurements of immobile single fluorescent molecule images.

PubMed

DeSantis, Michael C; DeCenzo, Shawn H; Li, Je-Luen; Wang, Y M

2010-03-29

Standard deviation measurements of intensity profiles of stationary single fluorescent molecules are useful for studying axial localization, molecular orientation, and a fluorescence imaging system's spatial resolution. Here we report on the analysis of the precision of standard deviation measurements of intensity profiles of single fluorescent molecules imaged using an EMCCD camera.We have developed an analytical expression for the standard deviation measurement error of a single image which is a function of the total number of detected photons, the background photon noise, and the camera pixel size. The theoretical results agree well with the experimental, simulation, and numerical integration results. Using this expression, we show that single-molecule standard deviation measurements offer nanometer precision for a large range of experimental parameters.

Factors Associated With Barcode Medication Administration Technology That Contribute to Patient Safety: An Integrative Review.

PubMed

Strudwick, Gillian; Reisdorfer, Emilene; Warnock, Caroline; Kalia, Kamini; Sulkers, Heather; Clark, Carrie; Booth, Richard

In an effort to prevent medication errors, barcode medication administration technology has been implemented in many health care organizations. An integrative review was conducted to understand the effect of barcode medication administration technology on medication errors, and characteristics of use demonstrated by nurses contribute to medication safety. Addressing poor system use may support improved patient safety through the reduction of medication administration errors.

Error Analysis of p-Version Discontinuous Galerkin Method for Heat Transfer in Built-up Structures

NASA Technical Reports Server (NTRS)

Kaneko, Hideaki; Bey, Kim S.

2004-01-01

The purpose of this paper is to provide an error analysis for the p-version of the discontinuous Galerkin finite element method for heat transfer in built-up structures. As a special case of the results in this paper, a theoretical error estimate for the numerical experiments recently conducted by James Tomey is obtained.

Numerical Differentiation Methods for Computing Error Covariance Matrices in Item Response Theory Modeling: An Evaluation and a New Proposal

ERIC Educational Resources Information Center

Tian, Wei; Cai, Li; Thissen, David; Xin, Tao

2013-01-01

In item response theory (IRT) modeling, the item parameter error covariance matrix plays a critical role in statistical inference procedures. When item parameters are estimated using the EM algorithm, the parameter error covariance matrix is not an automatic by-product of item calibration. Cai proposed the use of Supplemented EM algorithm for…

Integrated numerical modeling of a landslide early warning system in a context of adaptation to future climatic pressures

NASA Astrophysics Data System (ADS)

Khabarov, Nikolay; Huggel, Christian; Obersteiner, Michael; Ramírez, Juan Manuel

2010-05-01

Mountain regions are typically characterized by rugged terrain which is susceptible to different types of landslides during high-intensity precipitation. Landslides account for billions of dollars of damage and many casualties, and are expected to increase in frequency in the future due to a projected increase of precipitation intensity. Early warning systems (EWS) are thought to be a primary tool for related disaster risk reduction and climate change adaptation to extreme climatic events and hydro-meteorological hazards, including landslides. An EWS for hazards such as landslides consist of different components, including environmental monitoring instruments (e.g. rainfall or flow sensors), physical or empirical process models to support decision-making (warnings, evacuation), data and voice communication, organization and logistics-related procedures, and population response. Considering this broad range, EWS are highly complex systems, and it is therefore difficult to understand the effect of the different components and changing conditions on the overall performance, ultimately being expressed as human lives saved or structural damage reduced. In this contribution we present a further development of our approach to assess a landslide EWS in an integral way, both at the system and component level. We utilize a numerical model using 6 hour rainfall data as basic input. A threshold function based on a rainfall-intensity/duration relation was applied as a decision criterion for evacuation. Damage to infrastructure and human lives was defined as a linear function of landslide magnitude, with the magnitude modelled using a power function of landslide frequency. Correct evacuation was assessed with a ‘true' reference rainfall dataset versus a dataset of artificially reduced quality imitating the observation system component. Performance of the EWS using these rainfall datasets was expressed in monetary terms (i.e. damage related to false and correct evacuation). We applied this model to a landslide EWS in Colombia that is currently being implemented within a disaster prevention project. We evaluated the EWS against rainfall data with artificially introduced error and computed with multiple model runs the probabilistic damage functions depending on rainfall error. Then we modified the original precipitation pattern to reflect possible climatic changes e.g. change in annual precipitation as well as change in precipitation intensity with annual values remaining constant. We let the EWS model adapt for changed conditions to function optimally. Our results show that for the same errors in rainfall measurements the system's performance degrades with expected changing climatic conditions. The obtained results suggest that EWS cannot internally adapt to climate change and require exogenous adaptive measures to avoid increase in overall damage. The model represents a first attempt to integrally simulate and evaluate EWS under future possible climatic pressures. Future work will concentrate on refining model components and spatially explicit climate scenarios.

Space-Time Error Representation and Estimation in Navier-Stokes Calculations

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2006-01-01

The mathematical framework for a-posteriori error estimation of functionals elucidated by Eriksson et al. [7] and Becker and Rannacher [3] is revisited in a space-time context. Using these theories, a hierarchy of exact and approximate error representation formulas are presented for use in error estimation and mesh adaptivity. Numerical space-time results for simple model problems as well as compressible Navier-Stokes flow at Re = 300 over a 2D circular cylinder are then presented to demonstrate elements of the error representation theory for time-dependent problems.

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Larson, Mats G.; Barth, Timothy J.

1999-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Error Rate Comparison during Polymerase Chain Reaction by DNA Polymerase

DOE PAGES

McInerney, Peter; Adams, Paul; Hadi, Masood Z.

2014-01-01

As larger-scale cloning projects become more prevalent, there is an increasing need for comparisons among high fidelity DNA polymerases used for PCR amplification. All polymerases marketed for PCR applications are tested for fidelity properties (i.e., error rate determination) by vendors, and numerous literature reports have addressed PCR enzyme fidelity. Nonetheless, it is often difficult to make direct comparisons among different enzymes due to numerous methodological and analytical differences from study to study. We have measured the error rates for 6 DNA polymerases commonly used in PCR applications, including 3 polymerases typically used for cloning applications requiring high fidelity. Error ratemore » measurement values reported here were obtained by direct sequencing of cloned PCR products. The strategy employed here allows interrogation of error rate across a very large DNA sequence space, since 94 unique DNA targets were used as templates for PCR cloning. The six enzymes included in the study, Taq polymerase, AccuPrime-Taq High Fidelity, KOD Hot Start, cloned Pfu polymerase, Phusion Hot Start, and Pwo polymerase, we find the lowest error rates with Pfu , Phusion, and Pwo polymerases. Error rates are comparable for these 3 enzymes and are >10x lower than the error rate observed with Taq polymerase. Mutation spectra are reported, with the 3 high fidelity enzymes displaying broadly similar types of mutations. For these enzymes, transition mutations predominate, with little bias observed for type of transition.« less

Analysis of uncertainties and convergence of the statistical quantities in turbulent wall-bounded flows by means of a physically based criterion

NASA Astrophysics Data System (ADS)

Andrade, João Rodrigo; Martins, Ramon Silva; Thompson, Roney Leon; Mompean, Gilmar; da Silveira Neto, Aristeu

2018-04-01

The present paper provides an analysis of the statistical uncertainties associated with direct numerical simulation (DNS) results and experimental data for turbulent channel and pipe flows, showing a new physically based quantification of these errors, to improve the determination of the statistical deviations between DNSs and experiments. The analysis is carried out using a recently proposed criterion by Thompson et al. ["A methodology to evaluate statistical errors in DNS data of plane channel flows," Comput. Fluids 130, 1-7 (2016)] for fully turbulent plane channel flows, where the mean velocity error is estimated by considering the Reynolds stress tensor, and using the balance of the mean force equation. It also presents how the residual error evolves in time for a DNS of a plane channel flow, and the influence of the Reynolds number on its convergence rate. The root mean square of the residual error is shown in order to capture a single quantitative value of the error associated with the dimensionless averaging time. The evolution in time of the error norm is compared with the final error provided by DNS data of similar Reynolds numbers available in the literature. A direct consequence of this approach is that it was possible to compare different numerical results and experimental data, providing an improved understanding of the convergence of the statistical quantities in turbulent wall-bounded flows.

Chemical library subset selection algorithms: a unified derivation using spatial statistics.

PubMed

Hamprecht, Fred A; Thiel, Walter; van Gunsteren, Wilfred F

2002-01-01

If similar compounds have similar activity, rational subset selection becomes superior to random selection in screening for pharmacological lead discovery programs. Traditional approaches to this experimental design problem fall into two classes: (i) a linear or quadratic response function is assumed (ii) some space filling criterion is optimized. The assumptions underlying the first approach are clear but not always defendable; the second approach yields more intuitive designs but lacks a clear theoretical foundation. We model activity in a bioassay as realization of a stochastic process and use the best linear unbiased estimator to construct spatial sampling designs that optimize the integrated mean square prediction error, the maximum mean square prediction error, or the entropy. We argue that our approach constitutes a unifying framework encompassing most proposed techniques as limiting cases and sheds light on their underlying assumptions. In particular, vector quantization is obtained, in dimensions up to eight, in the limiting case of very smooth response surfaces for the integrated mean square error criterion. Closest packing is obtained for very rough surfaces under the integrated mean square error and entropy criteria. We suggest to use either the integrated mean square prediction error or the entropy as optimization criteria rather than approximations thereof and propose a scheme for direct iterative minimization of the integrated mean square prediction error. Finally, we discuss how the quality of chemical descriptors manifests itself and clarify the assumptions underlying the selection of diverse or representative subsets.

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

NASA Astrophysics Data System (ADS)

Liu, Xianglin; Wang, Yang; Eisenbach, Markus; Stocks, G. Malcolm

2018-03-01

The Green function plays an essential role in the Korringa-Kohn-Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn-Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. By using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xianglin; Wang, Yang; Eisenbach, Markus

The Green function plays an essential role in the Korringa–Kohn–Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn–Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). Themore » pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. Here, by using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.« less

Finite Volume Methods: Foundation and Analysis

NASA Technical Reports Server (NTRS)

Barth, Timothy; Ohlberger, Mario

2003-01-01

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

DOE PAGES

Liu, Xianglin; Wang, Yang; Eisenbach, Markus; ...

2017-10-28

The Green function plays an essential role in the Korringa–Kohn–Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn–Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). Themore » pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. Here, by using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.« less

Errors in finite-difference computations on curvilinear coordinate systems

NASA Technical Reports Server (NTRS)

Mastin, C. W.; Thompson, J. F.

1980-01-01

Curvilinear coordinate systems were used extensively to solve partial differential equations on arbitrary regions. An analysis of truncation error in the computation of derivatives revealed why numerical results may be erroneous. A more accurate method of computing derivatives is presented.

Error analysis of numerical gravitational waveforms from coalescing binary black holes

NASA Astrophysics Data System (ADS)

Fong, Heather; Chu, Tony; Kumar, Prayush; Pfeiffer, Harald; Boyle, Michael; Hemberger, Daniel; Kidder, Lawrence; Scheel, Mark; Szilagyi, Bela; SXS Collaboration

2016-03-01

The Advanced Laser Interferometer Gravitational-wave Observatory (Advanced LIGO) has finished a successful first observation run and will commence its second run this summer. Detection of compact object binaries utilizes matched-filtering, which requires a vast collection of highly accurate gravitational waveforms. This talk will present a set of about 100 new aligned-spin binary black hole simulations. I will discuss their properties, including a detailed error analysis, which demonstrates that the numerical waveforms are sufficiently accurate for gravitational wave detection purposes, as well as for parameter estimation purposes.

A Comparison of Three PML Treatments for CAA (and CFD)

NASA Technical Reports Server (NTRS)

Goodrich, John W.

2008-01-01

In this paper we compare three Perfectly Matched Layer (PML) treatments by means of a series of numerical experiments, using common numerical algorithms, computational grids, and code implementations. These comparisons are with the Linearized Euler Equations, for base uniform base flow. We see that there are two very good PML candidates, and that can both control the introduced error. Furthermore, we also show that corners can be handled with essentially no increase in the introduced error, and that with a good PML, the outer boundary is the most significant source of err

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

Integrating numerical computation into the undergraduate education physics curriculum using spreadsheet excel

NASA Astrophysics Data System (ADS)

Fauzi, Ahmad

2017-11-01

Numerical computation has many pedagogical advantages: it develops analytical skills and problem-solving skills, helps to learn through visualization, and enhances physics education. Unfortunately, numerical computation is not taught to undergraduate education physics students in Indonesia. Incorporate numerical computation into the undergraduate education physics curriculum presents many challenges. The main challenges are the dense curriculum that makes difficult to put new numerical computation course and most students have no programming experience. In this research, we used case study to review how to integrate numerical computation into undergraduate education physics curriculum. The participants of this research were 54 students of the fourth semester of physics education department. As a result, we concluded that numerical computation could be integrated into undergraduate education physics curriculum using spreadsheet excel combined with another course. The results of this research become complements of the study on how to integrate numerical computation in learning physics using spreadsheet excel.

Efficient and accurate time-stepping schemes for integrate-and-fire neuronal networks.

PubMed

Shelley, M J; Tao, L

2001-01-01

To avoid the numerical errors associated with resetting the potential following a spike in simulations of integrate-and-fire neuronal networks, Hansel et al. and Shelley independently developed a modified time-stepping method. Their particular scheme consists of second-order Runge-Kutta time-stepping, a linear interpolant to find spike times, and a recalibration of postspike potential using the spike times. Here we show analytically that such a scheme is second order, discuss the conditions under which efficient, higher-order algorithms can be constructed to treat resets, and develop a modified fourth-order scheme. To support our analysis, we simulate a system of integrate-and-fire conductance-based point neurons with all-to-all coupling. For six-digit accuracy, our modified Runge-Kutta fourth-order scheme needs a time-step of Delta(t) = 0.5 x 10(-3) seconds, whereas to achieve comparable accuracy using a recalibrated second-order or a first-order algorithm requires time-steps of 10(-5) seconds or 10(-9) seconds, respectively. Furthermore, since the cortico-cortical conductances in standard integrate-and-fire neuronal networks do not depend on the value of the membrane potential, we can attain fourth-order accuracy with computational costs normally associated with second-order schemes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Argo, P.E.; DeLapp, D.; Sutherland, C.D.

TRACKER is an extension of a three-dimensional Hamiltonian raytrace code developed some thirty years ago by R. Michael Jones. Subsequent modifications to this code, which is commonly called the {open_quotes}Jones Code,{close_quotes} were documented by Jones and Stephensen (1975). TRACKER incorporates an interactive user`s interface, modern differential equation integrators, graphical outputs, homing algorithms, and the Ionospheric Conductivity and Electron Density (ICED) ionosphere. TRACKER predicts the three-dimensional paths of radio waves through model ionospheres by numerically integrating Hamilton`s equations, which are a differential expression of Fermat`s principle of least time. By using continuous models, the Hamiltonian method avoids false caustics and discontinuousmore » raypath properties often encountered in other raytracing methods. In addition to computing the raypath, TRACKER also calculates the group path (or pulse travel time), the phase path, the geometrical (or {open_quotes}real{close_quotes}) pathlength, and the Doppler shift (if the time variation of the ionosphere is explicitly included). Computational speed can be traded for accuracy by specifying the maximum allowable integration error per step in the integration. Only geometrical optics are included in the main raytrace code; no partial reflections or diffraction effects are taken into account. In addition, TRACKER does not lend itself to statistical descriptions of propagation -- it requires a deterministic model of the ionosphere.« less

Symmetry boost of the fidelity of Shor factoring

NASA Astrophysics Data System (ADS)

Nam, Y. S.; Blümel, R.

2018-05-01

In Shor's algorithm quantum subroutines occur with the structure F U F-1 , where F is a unitary transform and U is performing a quantum computation. Examples are quantum adders and subunits of quantum modulo adders. In this paper we show, both analytically and numerically, that if, in analogy to spin echoes, F and F-1 can be implemented symmetrically when executing Shor's algorithm on actual, imperfect quantum hardware, such that F and F-1 have the same hardware errors, a symmetry boost in the fidelity of the combined F U F-1 quantum operation results when compared to the case in which the errors in F and F-1 are independently random. Running the complete gate-by-gate implemented Shor algorithm, we show that the symmetry-induced fidelity boost can be as large as a factor 4. While most of our analytical and numerical results concern the case of over- and under-rotation of controlled rotation gates, in the numerically accessible case of Shor's algorithm with a small number of qubits, we show explicitly that the symmetry boost is robust with respect to more general types of errors. While, expectedly, additional error types reduce the symmetry boost, we show explicitly, by implementing general off-diagonal SU (N ) errors (N =2 ,4 ,8 ), that the boost factor scales like a Lorentzian in δ /σ , where σ and δ are the error strengths of the diagonal over- and underrotation errors and the off-diagonal SU (N ) errors, respectively. The Lorentzian shape also shows that, while the boost factor may become small with increasing δ , it declines slowly (essentially like a power law) and is never completely erased. We also investigate the effect of diagonal nonunitary errors, which, in analogy to unitary errors, reduce but never erase the symmetry boost. Going beyond the case of small quantum processors, we present analytical scaling results that show that the symmetry boost persists in the practically interesting case of a large number of qubits. We illustrate this result explicitly for the case of Shor factoring of the semiprime RSA-1024, where, analytically, focusing on over- and underrotation errors, we obtain a boost factor of about 10. In addition, we provide a proof of the fidelity product formula, including its range of applicability.

Relating Regime Structure to Probability Distribution and Preferred Structure of Small Errors in a Large Atmospheric GCM

NASA Astrophysics Data System (ADS)

Straus, D. M.

2007-12-01

The probability distribution (pdf) of errors is followed in identical twin studies using the COLA T63 AGCM, integrated with observed SST for 15 recent winters. 30 integrations per winter (for 15 winters) are available with initial errors that are extremely small. The evolution of the pdf is tested for multi-modality, and the results interpreted in terms of clusters / regimes found in: (a) the set of 15x30 integrations mentioned, and (b) a larger ensemble of 55x15 integrations made with the same GCM using the same SSTs. The mapping of pdf evolution and clusters is also carried out for each winter separately, using the clusters found in the 55-member ensemble for the same winter alone. This technique yields information on the change in regimes caused by different boundary forcing (Straus and Molteni, 2004; Straus, Corti and Molteni, 2006). Analysis of the growing errors in terms of baroclinic and barotropic components allows for interpretation of the corresponding instabilities.

Statistical error in simulations of Poisson processes: Example of diffusion in solids

NASA Astrophysics Data System (ADS)

Nilsson, Johan O.; Leetmaa, Mikael; Vekilova, Olga Yu.; Simak, Sergei I.; Skorodumova, Natalia V.

2016-08-01

Simulations of diffusion in solids often produce poor statistics of diffusion events. We present an analytical expression for the statistical error in ion conductivity obtained in such simulations. The error expression is not restricted to any computational method in particular, but valid in the context of simulation of Poisson processes in general. This analytical error expression is verified numerically for the case of Gd-doped ceria by running a large number of kinetic Monte Carlo calculations.