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Sample records for linear extrapolation method

  1. Technique of Critical Current Density Measurement of Bulk Superconductor with Linear Extrapolation Method

    Adi, Wisnu Ari; Sukirman, Engkir; Winatapura, Didin S.

    2000-01-01

    Technique of critical current density measurement (Jc) of HTc bulk ceramic superconductor has been performed by using linear extrapolation with four-point probes method. The measurement of critical current density HTc bulk ceramic superconductor usually causes damage in contact resistance. In order to decrease this damage factor, we introduce extrapolation method. The extrapolating data show that the critical current density Jc for YBCO (123) and BSCCO (2212) at 77 K are 10,85(6) Amp.cm - 2 and 14,46(6) Amp.cm - 2, respectively. This technique is easier, simpler, and the use of the current flow is low, so it will not damage the contact resistance of the sample. We expect that the method can give a better solution for bulk superconductor application. Key words. : superconductor, critical temperature, and critical current density

  2. Linear extrapolation distance for a black cylindrical control rod with the pulsed neutron method

    Loewenhielm, G.

    1978-03-01

    The objective of this experiment was to measure the linear extrapolation distance for a central black cylindrical control rod in a cylindrical water moderator. The radius for both the control rod and the moderator was varied. The pulsed neutron technique was used and the decay constant was measured for both a homogeneous and a heterogeneous system. From the difference in the decay constants the extrapolation distance could be calculated. The conclusion is that within experimental error it is safe to use the approximate formula given by Pellaud or the more exact one given by Kavenoky. We can also conclude that linear anisotropic scattering is accounted for in a correct way in the approximate formula given by Pellaud and Prinja and Williams

  3. Novel method of interpolation and extrapolation of functions by a linear initial value problem

    Shatalov, M

    2008-09-01

    Full Text Available A novel method of function approximation using an initial value, linear, ordinary differential equation (ODE) is presented. The main advantage of this method is to obtain the approximation expressions in a closed form. This technique can be taught...

  4. Extrapolation methods theory and practice

    Brezinski, C

    1991-01-01

    This volume is a self-contained, exhaustive exposition of the extrapolation methods theory, and of the various algorithms and procedures for accelerating the convergence of scalar and vector sequences. Many subroutines (written in FORTRAN 77) with instructions for their use are provided on a floppy disk in order to demonstrate to those working with sequences the advantages of the use of extrapolation methods. Many numerical examples showing the effectiveness of the procedures and a consequent chapter on applications are also provided - including some never before published results and applicat

  5. The optimizied expansion method for wavefield extrapolation

    Wu, Zedong

    2013-01-01

    Spectral methods are fast becoming an indispensable tool for wave-field extrapolation, especially in anisotropic media, because of its dispersion and artifact free, as well as highly accurate, solutions of the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain operator.In this abstract, we propose an optimized expansion method that can approximate this operator with its low rank representation. The rank defines the number of inverse FFT required per time extrapolation step, and thus, a lower rank admits faster extrapolations. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its low rank representation.Thus,we obtain more accurate wave-fields using lower rank representation, and thus cheaper extrapolations. The optimization operation to define the low rank representation depends only on the velocity model, and this is done only once, and valid for a full reverse time migration (many shots) or one iteration of full waveform inversion. Applications on the BP model yielded superior results than those obtained using the decomposition approach. For transversely isotopic media, the solutions were free of the shear wave artifacts, and does not require that eta>0.

  6. Extrapolations of nuclear binding energies from new linear mass relations

    Hove, D.; Jensen, A. S.; Riisager, K.

    2013-01-01

    We present a method to extrapolate nuclear binding energies from known values for neighboring nuclei. We select four specific mass relations constructed to eliminate smooth variation of the binding energy as function nucleon numbers. The fast odd-even variations are avoided by comparing nuclei...

  7. π π scattering by pole extrapolation methods

    Lott, F.W. III.

    1978-01-01

    A 25-inch hydrogen bubble chamber was used at the Lawrence Berkeley Laboratory Bevatron to produce 300,000 pictures of π + p interactions at an incident momentum of the π + of 2.67 GeV/c. The 2-prong events were processed using the FSD and the FOG-CLOUDY-FAIR data reduction system. Events of the nature π + p→π + pπ 0 and π + p→π + π + n with values of momentum transfer to the proton of -t less than or equal to 0.238 GeV 2 were selected. These events were used to extrapolate to the pion pole (t = m/sub π/ 2 ) in order to investigate the π π interaction with isospins of both T=1 and T=2. Two methods were used to do the extrapolation: the original Chew-Low method developed in 1959 and the Durr-Pilkuhn method developed in 1965, which takes into account centrifugal barrier penetration factors. At first it seemed that, while the Durr-Pilkuhn method gave better values for the total π π cross section, the Chew-Low method gave better values for the angular distribution. Further analysis, however, showed that, if the requirement of total OPE (one-pion-exchange) was dropped, then the Durr-Pilkuhn method gave more reasonable values of the angular distribution as well as for the total π π cross section

  8. π π scattering by pole extrapolation methods

    Lott, F.W. III.

    1977-01-01

    A 25-inch hydrogen bubble chamber was used at the Lawrence Berkeley Laboratory Bevatron to produce 300,000 pictures of π + p interactions at an incident momentum of the π + of 2.67 GeV/c. The 2-prong events were processed using the FSD and the FOG-CLOUDY-FAIR data reduction system. Events of the nature π + p → π + pπ 0 and π + p → π + π + n with values of momentum transfer to the proton of -t less than or equal to 0.238 GeV 2 were selected. These events were used to extrapolate to the pion pole (t = m/sub π/ 2 ) in order to investigate the π π interaction with isospins of both T = 1 and T = 2. Two methods were used to do the extrapolation: the original Chew-Low method developed in 1959 and the Durr-Pilkuhn method developed in 1965 which takes into account centrifugal barrier penetration factors. At first it seemed that, while the Durr-Pilkuhn method gave better values for the total π π cross section, the Chew-Low method gave better values for the angular distribution. Further analysis, however, showed that if the requirement of total OPE (one-pion-exchange) were dropped, then the Durr-Pilkuhn method gave more reasonable values of the angular distribution as well as for the total π π cross section

  9. Extrapolated stabilized explicit Runge-Kutta methods

    Martín-Vaquero, J.; Kleefeld, B.

    2016-12-01

    Extrapolated Stabilized Explicit Runge-Kutta methods (ESERK) are proposed to solve multi-dimensional nonlinear partial differential equations (PDEs). In such methods it is necessary to evaluate the function nt times per step, but the stability region is O (nt2). Hence, the computational cost is O (nt) times lower than for a traditional explicit algorithm. In that way stiff problems can be integrated by the use of simple explicit evaluations in which case implicit methods usually had to be used. Therefore, they are especially well-suited for the method of lines (MOL) discretizations of parabolic nonlinear multi-dimensional PDEs. In this work, first s-stages first-order methods with extended stability along the negative real axis are obtained. They have slightly shorter stability regions than other traditional first-order stabilized explicit Runge-Kutta algorithms (also called Runge-Kutta-Chebyshev codes). Later, they are used to derive nt-stages second- and fourth-order schemes using Richardson extrapolation. The stability regions of these fourth-order codes include the interval [ - 0.01nt2, 0 ] (nt being the number of total functions evaluations), which are shorter than stability regions of ROCK4 methods, for example. However, the new algorithms neither suffer from propagation of errors (as other Runge-Kutta-Chebyshev codes as ROCK4 or DUMKA) nor internal instabilities. Additionally, many other types of higher-order (and also lower-order) methods can be obtained easily in a similar way. These methods also allow adaptation of the length step with no extra cost. Hence, the stability domain is adapted precisely to the spectrum of the problem at the current time of integration in an optimal way, i.e., with minimal number of additional stages. We compare the new techniques with other well-known algorithms with good results in very stiff diffusion or reaction-diffusion multi-dimensional nonlinear equations.

  10. A regularization method for extrapolation of solar potential magnetic fields

    Gary, G. A.; Musielak, Z. E.

    1992-01-01

    The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

  11. A Method for Extrapolation of Atmospheric Soundings

    2014-05-01

    case are not shown here. We also briefly examined data for the Anchorage, AK ( PANC ), radiosonde site for the case of the inversion height equal to...or greater than the extrapolation depth (i.e., hinv ≥ hext). PANC lies at the end of a broad inlet extending northward from the Gulf of Alaska at...type of terrain can affect the model and in turn affect the extrapolation. We examined a sounding from PANC (61.16 N and –150.01 W, elevation of 40

  12. Extrapolation Method for System Reliability Assessment

    Qin, Jianjun; Nishijima, Kazuyoshi; Faber, Michael Havbro

    2012-01-01

    of integrals with scaled domains. The performance of this class of approximation depends on the approach applied for the scaling and the functional form utilized for the extrapolation. A scheme for this task is derived here taking basis in the theory of asymptotic solutions to multinormal probability integrals......The present paper presents a new scheme for probability integral solution for system reliability analysis, which takes basis in the approaches by Naess et al. (2009) and Bucher (2009). The idea is to evaluate the probability integral by extrapolation, based on a sequence of MC approximations...... that the proposed scheme is efficient and adds to generality for this class of approximations for probability integrals....

  13. Multiparameter extrapolation and deflation methods for solving equation systems

    A. J. Hughes Hallett

    1984-01-01

    Full Text Available Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss-Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson's generalised method and the deflation method for detecting successive solutions in nonlinear equation systems are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.

  14. The optimizied expansion method for wavefield extrapolation

    Wu, Zedong; Alkhalifah, Tariq Ali

    2013-01-01

    , for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain operator.In this abstract, we propose an optimized expansion method that can approximate this operator with its low rank representation. The rank defines the number

  15. Assessment of load extrapolation methods for wind turbines

    Toft, H.S.; Sørensen, John Dalsgaard; Veldkamp, D.

    2010-01-01

    an approximate analytical solution for the distribution of the peaks is given by Rice. In the present paper three different methods for statistical load extrapolation are compared with the analytical solution for one mean wind speed. The methods considered are global maxima, block maxima and the peak over...

  16. Assessment of Load Extrapolation Methods for Wind Turbines

    Toft, Henrik Stensgaard; Sørensen, John Dalsgaard; Veldkamp, Dick

    2011-01-01

    , an approximate analytical solution for the distribution of the peaks is given by Rice. In the present paper, three different methods for statistical load extrapolation are compared with the analytical solution for one mean wind speed. The methods considered are global maxima, block maxima, and the peak over...

  17. Linearization Method and Linear Complexity

    Tanaka, Hidema

    We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.

  18. Novel extrapolation method in the Monte Carlo shell model

    Shimizu, Noritaka; Abe, Takashi; Utsuno, Yutaka; Mizusaki, Takahiro; Otsuka, Takaharu; Honma, Michio

    2010-01-01

    We propose an extrapolation method utilizing energy variance in the Monte Carlo shell model to estimate the energy eigenvalue and observables accurately. We derive a formula for the energy variance with deformed Slater determinants, which enables us to calculate the energy variance efficiently. The feasibility of the method is demonstrated for the full pf-shell calculation of 56 Ni, and the applicability of the method to a system beyond the current limit of exact diagonalization is shown for the pf+g 9/2 -shell calculation of 64 Ge.

  19. Standardization of electron-capture and complex beta-gamma radionuclides by the efficiency extrapolation method

    Grigorescu, L.

    1976-07-01

    The efficiency extrapolation method was improved by establishing ''linearity conditions'' for the discrimination on the gamma channel of the coincidence equipment. These conditions were proved to eliminate the systematic error of the method. A control procedure for the fulfilment of linearity conditions and estimation of residual systematic error was given. For law-energy gamma transitions an ''equivalent scheme principle'' was established, which allow for a correct application of the method. Solutions of Cs-134, Co-57, Ba-133 and Zn-65 were standardized with an ''effective standard deviation'' of 0.3-0.7 per cent. For Zn-65 ''special linearity conditions'' were applied. (author)

  20. Dead time corrections using the backward extrapolation method

    Gilad, E., E-mail: gilade@bgu.ac.il [The Unit of Nuclear Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Dubi, C. [Department of Physics, Nuclear Research Center NEGEV (NRCN), Beer-Sheva 84190 (Israel); Geslot, B.; Blaise, P. [DEN/CAD/DER/SPEx/LPE, CEA Cadarache, Saint-Paul-les-Durance 13108 (France); Kolin, A. [Department of Physics, Nuclear Research Center NEGEV (NRCN), Beer-Sheva 84190 (Israel)

    2017-05-11

    Dead time losses in neutron detection, caused by both the detector and the electronics dead time, is a highly nonlinear effect, known to create high biasing in physical experiments as the power grows over a certain threshold, up to total saturation of the detector system. Analytic modeling of the dead time losses is a highly complicated task due to the different nature of the dead time in the different components of the monitoring system (e.g., paralyzing vs. non paralyzing), and the stochastic nature of the fission chains. In the present study, a new technique is introduced for dead time corrections on the sampled Count Per Second (CPS), based on backward extrapolation of the losses, created by increasingly growing artificially imposed dead time on the data, back to zero. The method has been implemented on actual neutron noise measurements carried out in the MINERVE zero power reactor, demonstrating high accuracy (of 1–2%) in restoring the corrected count rate. - Highlights: • A new method for dead time corrections is introduced and experimentally validated. • The method does not depend on any prior calibration nor assumes any specific model. • Different dead times are imposed on the signal and the losses are extrapolated to zero. • The method is implemented and validated using neutron measurements from the MINERVE. • Result show very good correspondence to empirical results.

  1. A generalized sound extrapolation method for turbulent flows

    Zhong, Siyang; Zhang, Xin

    2018-02-01

    Sound extrapolation methods are often used to compute acoustic far-field directivities using near-field flow data in aeroacoustics applications. The results may be erroneous if the volume integrals are neglected (to save computational cost), while non-acoustic fluctuations are collected on the integration surfaces. In this work, we develop a new sound extrapolation method based on an acoustic analogy using Taylor's hypothesis (Taylor 1938 Proc. R. Soc. Lon. A 164, 476-490. (doi:10.1098/rspa.1938.0032)). Typically, a convection operator is used to filter out the acoustically inefficient components in the turbulent flows, and an acoustics dominant indirect variable Dcp‧ is solved. The sound pressure p' at the far field is computed from Dcp‧ based on the asymptotic properties of the Green's function. Validations results for benchmark problems with well-defined sources match well with the exact solutions. For aeroacoustics applications: the sound predictions by the aerofoil-gust interaction are close to those by an earlier method specially developed to remove the effect of vortical fluctuations (Zhong & Zhang 2017 J. Fluid Mech. 820, 424-450. (doi:10.1017/jfm.2017.219)); for the case of vortex shedding noise from a cylinder, the off-body predictions by the proposed method match well with the on-body Ffowcs-Williams and Hawkings result; different integration surfaces yield close predictions (of both spectra and far-field directivities) for a co-flowing jet case using an established direct numerical simulation database. The results suggest that the method may be a potential candidate for sound projection in aeroacoustics applications.

  2. The effects of different expansions of the exit distribution on the extrapolation length for linearly anisotropic scattering

    Bulut, S.; Guelecyuez, M.C.; Kaskas, A.; Tezcan, C.

    2007-01-01

    H N and singular eigenfunction methods are used to determine the neutron distribution everywhere in a source-free half space with zero incident flux for a linearly anisotropic scattering kernel. The singular eigenfunction expansion of the method of elementary solutions is used. The orthogonality relations of the discrete and continuous eigenfunctions for linearly anisotropic scattering provides the determination of the expansion coefficients. Different expansions of the exit distribution are used: the expansion in powers of μ, the expansion in terms of Legendre polynomials and the expansion in powers of 1/(1+μ). The results are compared to each other. In the second part of our work, the transport equation and the infinite medium Green function are used. The numerical results of the extrapolation length obtained for the different expansions is discussed. (orig.)

  3. Application of the largest Lyapunov exponent and non-linear fractal extrapolation algorithm to short-term load forecasting

    Wang Jianzhou; Jia Ruiling; Zhao Weigang; Wu Jie; Dong Yao

    2012-01-01

    Highlights: ► The maximal predictive step size is determined by the largest Lyapunov exponent. ► A proper forecasting step size is applied to load demand forecasting. ► The improved approach is validated by the actual load demand data. ► Non-linear fractal extrapolation method is compared with three forecasting models. ► Performance of the models is evaluated by three different error measures. - Abstract: Precise short-term load forecasting (STLF) plays a key role in unit commitment, maintenance and economic dispatch problems. Employing a subjective and arbitrary predictive step size is one of the most important factors causing the low forecasting accuracy. To solve this problem, the largest Lyapunov exponent is adopted to estimate the maximal predictive step size so that the step size in the forecasting is no more than this maximal one. In addition, in this paper a seldom used forecasting model, which is based on the non-linear fractal extrapolation (NLFE) algorithm, is considered to develop the accuracy of predictions. The suitability and superiority of the two solutions are illustrated through an application to real load forecasting using New South Wales electricity load data from the Australian National Electricity Market. Meanwhile, three forecasting models: the gray model, the seasonal autoregressive integrated moving average approach and the support vector machine method, which received high approval in STLF, are selected to compare with the NLFE algorithm. Comparison results also show that the NLFE model is outstanding, effective, practical and feasible.

  4. An efficient wave extrapolation method for anisotropic media with tilt

    Waheed, Umair bin

    2015-03-23

    Wavefield extrapolation operators for elliptically anisotropic media offer significant cost reduction compared with that for the transversely isotropic case, particularly when the axis of symmetry exhibits tilt (from the vertical). However, elliptical anisotropy does not provide accurate wavefield representation or imaging for transversely isotropic media. Therefore, we propose effective elliptically anisotropic models that correctly capture the kinematic behaviour of wavefields for transversely isotropic media. Specifically, we compute source-dependent effective velocities for the elliptic medium using kinematic high-frequency representation of the transversely isotropic wavefield. The effective model allows us to use cheaper elliptic wave extrapolation operators. Despite the fact that the effective models are obtained by matching kinematics using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy trade-off for wavefield computations in transversely isotropic media, particularly for media of low to moderate complexity. In addition, the wavefield solution is free from shear-wave artefacts as opposed to the conventional finite-difference-based transversely isotropic wave extrapolation scheme. We demonstrate these assertions through numerical tests on synthetic tilted transversely isotropic models.

  5. An efficient wave extrapolation method for anisotropic media with tilt

    Waheed, Umair bin; Alkhalifah, Tariq Ali

    2015-01-01

    Wavefield extrapolation operators for elliptically anisotropic media offer significant cost reduction compared with that for the transversely isotropic case, particularly when the axis of symmetry exhibits tilt (from the vertical). However, elliptical anisotropy does not provide accurate wavefield representation or imaging for transversely isotropic media. Therefore, we propose effective elliptically anisotropic models that correctly capture the kinematic behaviour of wavefields for transversely isotropic media. Specifically, we compute source-dependent effective velocities for the elliptic medium using kinematic high-frequency representation of the transversely isotropic wavefield. The effective model allows us to use cheaper elliptic wave extrapolation operators. Despite the fact that the effective models are obtained by matching kinematics using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy trade-off for wavefield computations in transversely isotropic media, particularly for media of low to moderate complexity. In addition, the wavefield solution is free from shear-wave artefacts as opposed to the conventional finite-difference-based transversely isotropic wave extrapolation scheme. We demonstrate these assertions through numerical tests on synthetic tilted transversely isotropic models.

  6. The Extrapolation-Accelerated Multilevel Aggregation Method in PageRank Computation

    Bing-Yuan Pu

    2013-01-01

    Full Text Available An accelerated multilevel aggregation method is presented for calculating the stationary probability vector of an irreducible stochastic matrix in PageRank computation, where the vector extrapolation method is its accelerator. We show how to periodically combine the extrapolation method together with the multilevel aggregation method on the finest level for speeding up the PageRank computation. Detailed numerical results are given to illustrate the behavior of this method, and comparisons with the typical methods are also made.

  7. A high precision extrapolation method in multiphase-field model for simulating dendrite growth

    Yang, Cong; Xu, Qingyan; Liu, Baicheng

    2018-05-01

    The phase-field method coupling with thermodynamic data has become a trend for predicting the microstructure formation in technical alloys. Nevertheless, the frequent access to thermodynamic database and calculation of local equilibrium conditions can be time intensive. The extrapolation methods, which are derived based on Taylor expansion, can provide approximation results with a high computational efficiency, and have been proven successful in applications. This paper presents a high precision second order extrapolation method for calculating the driving force in phase transformation. To obtain the phase compositions, different methods in solving the quasi-equilibrium condition are tested, and the M-slope approach is chosen for its best accuracy. The developed second order extrapolation method along with the M-slope approach and the first order extrapolation method are applied to simulate dendrite growth in a Ni-Al-Cr ternary alloy. The results of the extrapolation methods are compared with the exact solution with respect to the composition profile and dendrite tip position, which demonstrate the high precision and efficiency of the newly developed algorithm. To accelerate the phase-field and extrapolation computation, the graphic processing unit (GPU) based parallel computing scheme is developed. The application to large-scale simulation of multi-dendrite growth in an isothermal cross-section has demonstrated the ability of the developed GPU-accelerated second order extrapolation approach for multiphase-field model.

  8. Extrapolation method in the Monte Carlo Shell Model and its applications

    Shimizu, Noritaka; Abe, Takashi; Utsuno, Yutaka; Mizusaki, Takahiro; Otsuka, Takaharu; Honma, Michio

    2011-01-01

    We demonstrate how the energy-variance extrapolation method works using the sequence of the approximated wave functions obtained by the Monte Carlo Shell Model (MCSM), taking 56 Ni with pf-shell as an example. The extrapolation method is shown to work well even in the case that the MCSM shows slow convergence, such as 72 Ge with f5pg9-shell. The structure of 72 Se is also studied including the discussion of the shape-coexistence phenomenon.

  9. extrap: Software to assist the selection of extrapolation methods for moving-boat ADCP streamflow measurements

    Mueller, David S.

    2013-04-01

    Selection of the appropriate extrapolation methods for computing the discharge in the unmeasured top and bottom parts of a moving-boat acoustic Doppler current profiler (ADCP) streamflow measurement is critical to the total discharge computation. The software tool, extrap, combines normalized velocity profiles from the entire cross section and multiple transects to determine a mean profile for the measurement. The use of an exponent derived from normalized data from the entire cross section is shown to be valid for application of the power velocity distribution law in the computation of the unmeasured discharge in a cross section. Selected statistics are combined with empirically derived criteria to automatically select the appropriate extrapolation methods. A graphical user interface (GUI) provides the user tools to visually evaluate the automatically selected extrapolation methods and manually change them, as necessary. The sensitivity of the total discharge to available extrapolation methods is presented in the GUI. Use of extrap by field hydrographers has demonstrated that extrap is a more accurate and efficient method of determining the appropriate extrapolation methods compared with tools currently (2012) provided in the ADCP manufacturers' software.

  10. Standardization of I-125 solution by extrapolation of an efficiency wave obtained by coincidence X-(X-γ) counting method

    Iwahara, A.

    1989-01-01

    The activity concentration of 125 I was determined by X-(X-α) coincidence counting method and efficiency extrapolation curve. The measurement system consists of 2 thin NaI(T1) scintillation detectors which are horizontally movable on a track. The efficiency curve is obtained by symmetricaly changing the distance between the source and the detectors and the activity is determined by applying a linear efficiency extrapolation curve. All sum-coincidence events are included between 10 and 100 KeV window counting and the main source of uncertainty is coming from poor counting statistic around zero efficiency. The consistence of results with other methods shows that this technique can be applied to photon cascade emitters and are not discriminating by the detectors. It has been also determined the 35,5 KeV gamma-ray emission probability of 125 I by using a Gamma-X type high purity germanium detector. (author) [pt

  11. The optimized expansion based low-rank method for wavefield extrapolation

    Wu, Zedong

    2014-03-01

    Spectral methods are fast becoming an indispensable tool for wavefield extrapolation, especially in anisotropic media because it tends to be dispersion and artifact free as well as highly accurate when solving the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain extrapolation operator efficiently. To solve this problem, we evaluated an optimized expansion method that can approximate this operator with a low-rank variable separation representation. The rank defines the number of inverse Fourier transforms for each time extrapolation step, and thus, the lower the rank, the faster the extrapolation. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its explicit low-rank representation. As a result, we obtain lower rank representations compared with the standard low-rank method within reasonable accuracy and thus cheaper extrapolations. Additional bounds set on the range of propagated wavenumbers to adhere to the physical wave limits yield unconditionally stable extrapolations regardless of the time step. An application on the BP model provided superior results compared to those obtained using the decomposition approach. For transversely isotopic media, because we used the pure P-wave dispersion relation, we obtained solutions that were free of the shear wave artifacts, and the algorithm does not require that n > 0. In addition, the required rank for the optimization approach to obtain high accuracy in anisotropic media was lower than that obtained by the decomposition approach, and thus, it was more efficient. A reverse time migration result for the BP tilted transverse isotropy model using this method as a wave propagator demonstrated the ability of the algorithm.

  12. Evaluation of extrapolation methods for actual state expenditures on health care in Russian Federation

    S. A. Banin

    2016-01-01

    Full Text Available Forecasting methods, extrapolation ones in particular, are used in health care for medical, biological and clinical research. The author, using accessible internet space, has not met a single publication devoted to extrapolation of financial parameters of health care activities. This determined the relevance of the material presented in the article: based on health care financing dynamics in Russia in 2000–2010 the author examined possibility of application of basic perspective extrapolation methods - moving average, exponential smoothing and least squares. It is hypothesized that all three methods can equally forecast actual public expenditures on health care in medium term in Russia’s current financial and economic conditions. The study result was evaluated in two time periods: within the studied interval and a five-year period. It was found that within the study period all methods have an average relative extrapolation error of 3–5%, which means high precision of the forecast. The study shown a specific feature of the least squares method which were gradually accumulating results so their economic interpretation became possible only in the end of the studied period. That is why the extrapolating results obtained by least squares method are not applicable in an entire study period and rather have a theoretical value. Beyond the study period, however, this feature was found to be the most corresponding to the real situation. It was the least squares method that proved to be the most appropriate for economic interpretation of the forecast results of actual public expenditures on health care. The hypothesis was not confirmed, the author received three differently directed results, while each method had independent significance and its application depended on evaluation study objectives and real social, economic and financial situation in Russian health care system.

  13. Parametric methods of describing and extrapolating the characteristics of long-term strength of refractory materials

    Tsvilyuk, I.S.; Avramenko, D.S.

    1986-01-01

    This paper carries out the comparative analysis of the suitability of parametric methods for describing and extrapolating the results of longterm tests on refractory materials. Diagrams are presented of the longterm strength of niobium based alloys tested in a vacuum of 1.3 X 10 -3 Pa. The predicted values and variance of the estimate of endurance of refractory alloys are presented by parametric dependences. The longterm strength characteristics can be described most adequately by the Manson-Sakkop and Sherby-Dorn methods. Several methods must be used to ensure the reliable extrapolation of the longterm strength characteristics to the time period an order of magnitude longer than the experimental data. The most suitable method cannot always be selected on the basis of the correlation ratio

  14. Evaluation of functioning of an extrapolation chamber using Monte Carlo method

    Oramas Polo, I.; Alfonso Laguardia, R.

    2015-01-01

    The extrapolation chamber is a parallel plate chamber and variable volume based on the Braff-Gray theory. It determines in absolute mode, with high accuracy the dose absorbed by the extrapolation of the ionization current measured for a null distance between the electrodes. This camera is used for dosimetry of external beta rays for radiation protection. This paper presents a simulation for evaluating the functioning of an extrapolation chamber type 23392 of PTW, using the MCNPX Monte Carlo method. In the simulation, the fluence in the air collector cavity of the chamber was obtained. The influence of the materials that compose the camera on its response against beta radiation beam was also analysed. A comparison of the contribution of primary and secondary radiation was performed. The energy deposition in the air collector cavity for different depths was calculated. The component with the higher energy deposition is the Polymethyl methacrylate block. The energy deposition in the air collector cavity for chamber depth 2500 μm is greater with a value of 9.708E-07 MeV. The fluence in the air collector cavity decreases with depth. It's value is 1.758E-04 1/cm 2 for chamber depth 500 μm. The values reported are for individual electron and photon histories. The graphics of simulated parameters are presented in the paper. (Author)

  15. A comparison between progressive extension method (PEM) and iterative method (IM) for magnetic field extrapolations in the solar atmosphere

    Wu, S. T.; Sun, M. T.; Sakurai, Takashi

    1990-01-01

    This paper presents a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, viz the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized, and the accuracy and numerical instability are discussed. On the basis of this investigation, it is claimed that the two methods do resemble each other qualitatively.

  16. Explorative methods in linear models

    Høskuldsson, Agnar

    2004-01-01

    The author has developed the H-method of mathematical modeling that builds up the model by parts, where each part is optimized with respect to prediction. Besides providing with better predictions than traditional methods, these methods provide with graphic procedures for analyzing different feat...... features in data. These graphic methods extend the well-known methods and results of Principal Component Analysis to any linear model. Here the graphic procedures are applied to linear regression and Ridge Regression....

  17. A method of creep rupture data extrapolation based on physical processes

    Leinster, M.G.

    2008-01-01

    There is a need for a reliable method to extrapolate generic creep rupture data to failure times in excess of the currently published times. A method based on well-understood and mathematically described physical processes is likely to be stable and reliable. Creep process descriptions have been developed based on accepted theory, to the extent that good fits with published data have been obtained. Methods have been developed to apply these descriptions to extrapolate creep rupture data to stresses below the published values. The relationship creep life parameter=f(ln(sinh(stress))) has been shown to be justifiable over the stress ranges of most interest, and gives realistic results at high temperatures and long times to failure. In the interests of continuity with past and present practice, the suggested method is intended to extend existing polynomial descriptions of life parameters at low stress. Where no polynomials exist, the method can be used to describe the behaviour of life parameters throughout the full range of a particular failure mode in the published data

  18. Correction method for critical extrapolation of control-rods-rising during physical start-up of reactor

    Zhang Fan; Chen Wenzhen; Yu Lei

    2008-01-01

    During physical start-up of nuclear reactor, the curve got by lifting the con- trol rods to extrapolate to the critical state is often in protruding shape, by which the supercritical phenomena is led. In the paper, the reason why the curve was in protruding was analyzed. A correction method was introduced, and the calculations were carried out by the practical data used in a nuclear power plant. The results show that the correction method reverses the protruding shape of the extrapolating curve, and the risk of reactor supercritical phenomena can be reduced using the extrapolated curve got by the correction method during physical start-up of the reactor. (authors)

  19. EXTRAPOLATION METHOD FOR MAXIMAL AND 24-H AVERAGE LTE TDD EXPOSURE ESTIMATION.

    Franci, D; Grillo, E; Pavoncello, S; Coltellacci, S; Buccella, C; Aureli, T

    2018-01-01

    The Long-Term Evolution (LTE) system represents the evolution of the Universal Mobile Telecommunication System technology. This technology introduces two duplex modes: Frequency Division Duplex and Time Division Duplex (TDD). Despite having experienced a limited expansion in the European countries since the debut of the LTE technology, a renewed commercial interest for LTE TDD technology has recently been shown. Therefore, the development of extrapolation procedures optimised for TDD systems becomes crucial, especially for the regulatory authorities. This article presents an extrapolation method aimed to assess the exposure to LTE TDD sources, based on the detection of the Cell-Specific Reference Signal power level. The method introduces a βTDD parameter intended to quantify the fraction of the LTE TDD frame duration reserved for downlink transmission. The method has been validated by experimental measurements performed on signals generated by both a vector signal generator and a test Base Transceiver Station installed at Linkem S.p.A facility in Rome. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

  20. An Efficient Method of Reweighting and Reconstructing Monte Carlo Molecular Simulation Data for Extrapolation to Different Temperature and Density Conditions

    Sun, Shuyu

    2013-06-01

    This paper introduces an efficient technique to generate new molecular simulation Markov chains for different temperature and density conditions, which allow for rapid extrapolation of canonical ensemble averages at a range of temperatures and densities different from the original conditions where a single simulation is conducted. Obtained information from the original simulation are reweighted and even reconstructed in order to extrapolate our knowledge to the new conditions. Our technique allows not only the extrapolation to a new temperature or density, but also the double extrapolation to both new temperature and density. The method was implemented for Lennard-Jones fluid with structureless particles in single-gas phase region. Extrapolation behaviors as functions of extrapolation ranges were studied. Limits of extrapolation ranges showed a remarkable capability especially along isochors where only reweighting is required. Various factors that could affect the limits of extrapolation ranges were investigated and compared. In particular, these limits were shown to be sensitive to the number of particles used and starting point where the simulation was originally conducted.

  1. An Efficient Method of Reweighting and Reconstructing Monte Carlo Molecular Simulation Data for Extrapolation to Different Temperature and Density Conditions

    Sun, Shuyu; Kadoura, Ahmad Salim; Salama, Amgad

    2013-01-01

    This paper introduces an efficient technique to generate new molecular simulation Markov chains for different temperature and density conditions, which allow for rapid extrapolation of canonical ensemble averages at a range of temperatures and densities different from the original conditions where a single simulation is conducted. Obtained information from the original simulation are reweighted and even reconstructed in order to extrapolate our knowledge to the new conditions. Our technique allows not only the extrapolation to a new temperature or density, but also the double extrapolation to both new temperature and density. The method was implemented for Lennard-Jones fluid with structureless particles in single-gas phase region. Extrapolation behaviors as functions of extrapolation ranges were studied. Limits of extrapolation ranges showed a remarkable capability especially along isochors where only reweighting is required. Various factors that could affect the limits of extrapolation ranges were investigated and compared. In particular, these limits were shown to be sensitive to the number of particles used and starting point where the simulation was originally conducted.

  2. Low-cost extrapolation method for maximal LTE radio base station exposure estimation: test and validation.

    Verloock, Leen; Joseph, Wout; Gati, Azeddine; Varsier, Nadège; Flach, Björn; Wiart, Joe; Martens, Luc

    2013-06-01

    An experimental validation of a low-cost method for extrapolation and estimation of the maximal electromagnetic-field exposure from long-term evolution (LTE) radio base station installations are presented. No knowledge on downlink band occupation or service characteristics is required for the low-cost method. The method is applicable in situ. It only requires a basic spectrum analyser with appropriate field probes without the need of expensive dedicated LTE decoders. The method is validated both in laboratory and in situ, for a single-input single-output antenna LTE system and a 2×2 multiple-input multiple-output system, with low deviations in comparison with signals measured using dedicated LTE decoders.

  3. Low-cost extrapolation method for maximal lte radio base station exposure estimation: Test and validation

    Verloock, L.; Joseph, W.; Gati, A.; Varsier, N.; Flach, B.; Wiart, J.; Martens, L.

    2013-01-01

    An experimental validation of a low-cost method for extrapolation and estimation of the maximal electromagnetic-field exposure from long-term evolution (LTE) radio base station installations are presented. No knowledge on down-link band occupation or service characteristics is required for the low-cost method. The method is applicable in situ. It only requires a basic spectrum analyser with appropriate field probes without the need of expensive dedicated LTE decoders. The method is validated both in laboratory and in situ, for a single-input single-output antenna LTE system and a 2x2 multiple-input multiple-output system, with low deviations in comparison with signals measured using dedicated LTE decoders. (authors)

  4. Linear methods in band theory

    Andersen, O. Krogh

    1975-01-01

    of Korringa-Kohn-Rostoker, linear-combination-of-atomic-orbitals, and cellular methods; the secular matrix is linear in energy, the overlap integrals factorize as potential parameters and structure constants, the latter are canonical in the sense that they neither depend on the energy nor the cell volume...

  5. Linear Methods for Image Interpolation

    Pascal Getreuer

    2011-01-01

    We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation.

  6. Optimal control linear quadratic methods

    Anderson, Brian D O

    2007-01-01

    This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the

  7. Variational linear algebraic equations method

    Moiseiwitsch, B.L.

    1982-01-01

    A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen. (author)

  8. Bayes linear statistics, theory & methods

    Goldstein, Michael

    2007-01-01

    Bayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodology, and practicalities of this important field. The text provides a thorough coverage of Bayes linear analysis, from the development of the basic language to the collection of algebraic results needed for efficient implementation, with detailed practical examples. The book covers:The importance of partial prior specifications for complex problems where it is difficult to supply a meaningful full prior probability specification...

  9. Linear Methods for Image Interpolation

    Pascal Getreuer

    2011-09-01

    Full Text Available We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation.

  10. A thermal extrapolation method for the effective temperatures and internal energies of activated ions

    Meot-Ner (Mautner), Michael; Somogyi, Árpád

    2007-11-01

    The internal energies of dissociating ions, activated chemically or collisionally, can be estimated using the kinetics of thermal dissociation. The thermal Arrhenius parameters can be combined with the observed dissociation rate of the activated ions using kdiss = Athermalexp(-Ea,thermal/RTeff). This Arrhenius-type relation yields the effective temperature, Teff, at which the ions would dissociate thermally at the same rate, or yield the same product distributions, as the activated ions. In turn, Teff is used to calculate the internal energy of the ions and the energy deposited by the activation process. The method yields an energy deposition efficiency of 10% for a chemical ionization proton transfer reaction and 8-26% for the surface collisions of various peptide ions. Internal energies of ions activated by chemical ionization or by gas phase collisions, and of ions produced by desorption methods such as fast atom bombardment, can be also evaluated. Thermal extrapolation is especially useful for ion-molecule reaction products and for biological ions, where other methods to evaluate internal energies are laborious or unavailable.

  11. Propagation of internal errors in explicit Runge–Kutta methods and internal stability of SSP and extrapolation methods

    Ketcheson, David I.

    2014-04-11

    In practical computation with Runge--Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example that propagation of such errors within a single step can have catastrophic effects for otherwise practical and well-known methods. We perform a general analysis of internal error propagation, emphasizing that it depends significantly on how the method is implemented. We show that for a fixed method, essentially any set of internal stability polynomials can be obtained by modifying the implementation details. We provide bounds on the internal error amplification constants for some classes of methods with many stages, including strong stability preserving methods and extrapolation methods. These results are used to prove error bounds in the presence of roundoff or other internal errors.

  12. Ultrasonic computerized tomography (CT) for temperature measurements with limited projection data based on extrapolated filtered back projection (FBP) method

    Zhu Ning; Jiang Yong; Kato, Seizo

    2005-01-01

    This study uses ultrasound in combination with tomography to obtain three-dimensional temperature measurements using projection data obtained from limited projection angle. The main feature of the new computerized tomography (CT) reconstruction algorithm is to employ extrapolation scheme to make up for the incomplete projection data, it is based on the conventional filtered back projection (FBP) method while on top of that taking into account the correlation between the projection data and Fourier transform-based extrapolation. Computer simulation is conducted to verify the above algorithm. An experimental 3D temperature distribution measurement is also carried out to validate the proposed algorithm. The simulation and experimental results demonstrate that the extrapolated FBP CT algorithm is highly effective in dealing with projection data from limited projection angle

  13. extrap: Software to assist the selection of extrapolation methods for moving-boat ADCP streamflow measurements

    Mueller, David S.

    2013-01-01

    Selection of the appropriate extrapolation methods for computing the discharge in the unmeasured top and bottom parts of a moving-boat acoustic Doppler current profiler (ADCP) streamflow measurement is critical to the total discharge computation. The software tool, extrap, combines normalized velocity

  14. Direct activity determination of Mn-54 and Zn-65 by a non-extrapolation liquid scintillation method

    Simpson, BRS

    2004-02-01

    Full Text Available . The simple decay scheme exhibited by these radionuclides, with the emission of an energetic gamma ray, allows the absolute activity to be determined from 4pie-gamma data by direct calculation without the need for efficiency extrapolation. The method, which...

  15. Acceleration of nodal diffusion code by Chebychev polynomial extrapolation method; Ubrzanje spoljasnjih iteracija difuzionog nodalnog proracuna Chebisevijevom ekstrapolacionom metodom

    Zmijarevic, I; Tomashevic, Dj [Institut za Nuklearne Nauke Boris Kidric, Belgrade (Yugoslavia)

    1988-07-01

    This paper presents Chebychev acceleration of outer iterations of a nodal diffusion code of high accuracy. Extrapolation parameters, unique for all moments are calculated using the node integrated distribution of fission source. Sample calculations are presented indicating the efficiency of method. (author)

  16. Comparison of precipitation nowcasting by extrapolation and statistical-advection methods

    Sokol, Zbyněk; Kitzmiller, D.; Pešice, Petr; Mejsnar, Jan

    2013-01-01

    Roč. 123, 1 April (2013), s. 17-30 ISSN 0169-8095 R&D Projects: GA MŠk ME09033 Institutional support: RVO:68378289 Keywords : Precipitation forecast * Statistical models * Regression * Quantitative precipitation forecast * Extrapolation forecast Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 2.421, year: 2013 http://www.sciencedirect.com/science/article/pii/S0169809512003390

  17. Linear Algebraic Method for Non-Linear Map Analysis

    Yu, L.; Nash, B.

    2009-01-01

    We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.

  18. Measurement of the surface field on open magnetic samples by the extrapolation method

    Perevertov, Oleksiy

    2005-01-01

    Roč. 76, - (2005), 104701/1-104701/7 ISSN 0034-6748 R&D Projects: GA ČR(CZ) GP202/04/P010; GA AV ČR(CZ) 1QS100100508 Institutional research plan: CEZ:AV0Z10100520 Keywords : magnetic field measurement * extrapolation * air gaps * magnetic permeability Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.235, year: 2005

  19. A linear iterative unfolding method

    László, András

    2012-01-01

    A frequently faced task in experimental physics is to measure the probability distribution of some quantity. Often this quantity to be measured is smeared by a non-ideal detector response or by some physical process. The procedure of removing this smearing effect from the measured distribution is called unfolding, and is a delicate problem in signal processing, due to the well-known numerical ill behavior of this task. Various methods were invented which, given some assumptions on the initial probability distribution, try to regularize the unfolding problem. Most of these methods definitely introduce bias into the estimate of the initial probability distribution. We propose a linear iterative method (motivated by the Neumann series / Landweber iteration known in functional analysis), which has the advantage that no assumptions on the initial probability distribution is needed, and the only regularization parameter is the stopping order of the iteration, which can be used to choose the best compromise between the introduced bias and the propagated statistical and systematic errors. The method is consistent: 'binwise' convergence to the initial probability distribution is proved in absence of measurement errors under a quite general condition on the response function. This condition holds for practical applications such as convolutions, calorimeter response functions, momentum reconstruction response functions based on tracking in magnetic field etc. In presence of measurement errors, explicit formulae for the propagation of the three important error terms is provided: bias error (distance from the unknown to-be-reconstructed initial distribution at a finite iteration order), statistical error, and systematic error. A trade-off between these three error terms can be used to define an optimal iteration stopping criterion, and the errors can be estimated there. We provide a numerical C library for the implementation of the method, which incorporates automatic

  20. Comparison of extrapolation methods for creep rupture stresses of 12Cr and 18Cr10NiTi steels

    Ivarsson, B.

    1979-01-01

    As a part of a Soviet-Swedish research programme the creep rupture properties of two heat resisting steels namely a 12% Cr steel and an 18% Cr12% Ni titanium stabilized steel have been studied. One heat from each country of both steels were creep tested. The strength of the 12% Cr steels was similar to earlier reported strength values, the Soviet steel being some-what stronger due to a higher tungsten content. The strength of the Swedish 18/12 Ti steel agreed with earlier results, while the properties of the Soviet steel were inferior to those reported from earlier Soviet creep testings. Three extrapolation methods were compared on creep rupture data collected in both countries. Isothermal extrapolation and an algebraic method of Soviet origin gave in many cases rather similar results, while the parameter method recommended by ISO resulted in higher rupture strength values at longer times. (author)

  1. A comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallel

    Ketcheson, David I.

    2014-06-13

    We compare the three main types of high-order one-step initial value solvers: extrapolation, spectral deferred correction, and embedded Runge–Kutta pairs. We consider orders four through twelve, including both serial and parallel implementations. We cast extrapolation and deferred correction methods as fixed-order Runge–Kutta methods, providing a natural framework for the comparison. The stability and accuracy properties of the methods are analyzed by theoretical measures, and these are compared with the results of numerical tests. In serial, the eighth-order pair of Prince and Dormand (DOP8) is most efficient. But other high-order methods can be more efficient than DOP8 when implemented in parallel. This is demonstrated by comparing a parallelized version of the wellknown ODEX code with the (serial) DOP853 code. For an N-body problem with N = 400, the experimental extrapolation code is as fast as the tuned Runge–Kutta pair at loose tolerances, and is up to two times as fast at tight tolerances.

  2. An efficient wave extrapolation method for tilted orthorhombic media using effective ellipsoidal models

    Waheed, Umair bin; Alkhalifah, Tariq Ali

    2014-01-01

    The wavefield extrapolation operator for ellipsoidally anisotropic (EA) media offers significant cost reduction compared to that for the orthorhombic case, especially when the symmetry planes are tilted and/or rotated. However, ellipsoidal anisotropy does not provide accurate focusing for media of orthorhombic anisotropy. Therefore, we develop effective EA models that correctly capture the kinematic behavior of the wavefield for tilted orthorhombic (TOR) media. Specifically, we compute effective source-dependent velocities for the EA model using kinematic high-frequency representation of the TOR wavefield. The effective model allows us to use the cheaper EA wavefield extrapolation operator to obtain approximate wavefield solutions for a TOR model. Despite the fact that the effective EA models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TOR media, particularly for media of low to moderate complexity. We demonstrate applicability of the proposed approach on a layered TOR model.

  3. An efficient wave extrapolation method for tilted orthorhombic media using effective ellipsoidal models

    Waheed, Umair bin

    2014-08-01

    The wavefield extrapolation operator for ellipsoidally anisotropic (EA) media offers significant cost reduction compared to that for the orthorhombic case, especially when the symmetry planes are tilted and/or rotated. However, ellipsoidal anisotropy does not provide accurate focusing for media of orthorhombic anisotropy. Therefore, we develop effective EA models that correctly capture the kinematic behavior of the wavefield for tilted orthorhombic (TOR) media. Specifically, we compute effective source-dependent velocities for the EA model using kinematic high-frequency representation of the TOR wavefield. The effective model allows us to use the cheaper EA wavefield extrapolation operator to obtain approximate wavefield solutions for a TOR model. Despite the fact that the effective EA models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TOR media, particularly for media of low to moderate complexity. We demonstrate applicability of the proposed approach on a layered TOR model.

  4. Comparison among creep rupture strength extrapolation methods with application to data for AISI 316 SS from Italy, France, U.K. and F.R.G

    Brunori, G.; Cappellato, S.; Vacchiano, S.; Guglielmi, F.

    1982-01-01

    Inside Activity 3 ''Materials'' of WGCS, the member states UK and FRG have developed a work regarding extrapolation methods for creep data. This work has been done by comparising extrapolation methods in use in their countries by applying them to creep rupture strength data on AISI 316 SS obtained in UK and FRG. This work has been issued on April 1978 and the Community has dealed it to all Activity 3 Members. Italy, in the figure of NIRA S.p.A., has received, from the European Community a contract to extend the work to Italian and French data, using extrapolation methods currently in use in Italy. The work should deal with the following points: - Collect of Italian experimental data; - Chemical analysis on Italian Specimen; - Comparison among Italian experimental data with French, FRG and UK data; - Description of extrapolation methods in use in Italy; - Application of these extrapolation methods to Italian, French, British and Germany data; - Extensions of a Final Report

  5. Comparative studies of parameters based on the most probable versus an approximate linear extrapolation distance estimates for circular cylindrical absorbing rod

    Wassef, W.A.

    1982-01-01

    Estimates and techniques that are valid to calculate the linear extrapolation distance for an infinitely long circular cylindrical absorbing region are reviewed. Two estimates, in particular, are put into consideration, that is the most probable and the value resulting from an approximate technique based on matching the integral transport equation inside the absorber with the diffusion approximation in the surrounding infinite scattering medium. Consequently, the effective diffusion parameters and the blackness of the cylinder are derived and subjected to comparative studies. A computer code is set up to calculate and compare the different parameters, which is useful in reactor analysis and serves to establish a beneficial estimates that are amenable to direct application to reactor design codes

  6. COMPARISON OF CORONAL EXTRAPOLATION METHODS FOR CYCLE 24 USING HMI DATA

    Arden, William M. [University of Southern Queensland, Toowoomba, Queensland (Australia); Norton, Aimee A.; Sun, Xudong; Zhao, Xuepu [Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305 (United States)

    2016-05-20

    Two extrapolation models of the solar coronal magnetic field are compared using magnetogram data from the Solar Dynamics Observatory /Helioseismic and Magnetic Imager instrument. The two models, a horizontal current–current sheet–source surface (HCCSSS) model and a potential field–source surface (PFSS) model, differ in their treatment of coronal currents. Each model has its own critical variable, respectively, the radius of a cusp surface and a source surface, and it is found that adjusting these heights over the period studied allows for a better fit between the models and the solar open flux at 1 au as calculated from the Interplanetary Magnetic Field (IMF). The HCCSSS model provides the better fit for the overall period from 2010 November to 2015 May as well as for two subsets of the period: the minimum/rising part of the solar cycle and the recently identified peak in the IMF from mid-2014 to mid-2015 just after solar maximum. It is found that an HCCSSS cusp surface height of 1.7 R {sub ⊙} provides the best fit to the IMF for the overall period, while 1.7 and 1.9 R {sub ⊙} give the best fits for the two subsets. The corresponding values for the PFSS source surface height are 2.1, 2.2, and 2.0 R {sub ⊙} respectively. This means that the HCCSSS cusp surface rises as the solar cycle progresses while the PFSS source surface falls.

  7. A new technique for extracting the red edge position from hyperspectral data : the linear extrapolation method

    Cho, M.A.; Skidmore, A.K.

    2006-01-01

    There is increasing interest in using hyperspectral data for quantitative characterization of vegetation in spatial and temporal scopes. Many spectral indices are being developed to improve vegetation sensitivity by minimizing the background influence. The chlorophyll absorption continuum index

  8. Statistical Analysis of a Class: Monte Carlo and Multiple Imputation Spreadsheet Methods for Estimation and Extrapolation

    Fish, Laurel J.; Halcoussis, Dennis; Phillips, G. Michael

    2017-01-01

    The Monte Carlo method and related multiple imputation methods are traditionally used in math, physics and science to estimate and analyze data and are now becoming standard tools in analyzing business and financial problems. However, few sources explain the application of the Monte Carlo method for individuals and business professionals who are…

  9. Simulation-extrapolation method to address errors in atomic bomb survivor dosimetry on solid cancer and leukaemia mortality risk estimates, 1950-2003

    Allodji, Rodrigue S.; Schwartz, Boris; Diallo, Ibrahima; Vathaire, Florent de [Gustave Roussy B2M, Radiation Epidemiology Group/CESP - Unit 1018 INSERM, Villejuif Cedex (France); Univ. Paris-Sud, Villejuif (France); Agbovon, Cesaire [Pierre and Vacances - Center Parcs Group, L' artois - Espace Pont de Flandre, Paris Cedex 19 (France); Laurier, Dominique [Institut de Radioprotection et de Surete Nucleaire (IRSN), DRPH, SRBE, Laboratoire d' epidemiologie, BP17, Fontenay-aux-Roses Cedex (France)

    2015-08-15

    Analyses of the Life Span Study (LSS) of Japanese atomic bombing survivors have routinely incorporated corrections for additive classical measurement errors using regression calibration. Recently, several studies reported that the efficiency of the simulation-extrapolation method (SIMEX) is slightly more accurate than the simple regression calibration method (RCAL). In the present paper, the SIMEX and RCAL methods have been used to address errors in atomic bomb survivor dosimetry on solid cancer and leukaemia mortality risk estimates. For instance, it is shown that using the SIMEX method, the ERR/Gy is increased by an amount of about 29 % for all solid cancer deaths using a linear model compared to the RCAL method, and the corrected EAR 10{sup -4} person-years at 1 Gy (the linear terms) is decreased by about 8 %, while the corrected quadratic term (EAR 10{sup -4} person-years/Gy{sup 2}) is increased by about 65 % for leukaemia deaths based on a linear-quadratic model. The results with SIMEX method are slightly higher than published values. The observed differences were probably due to the fact that with the RCAL method the dosimetric data were partially corrected, while all doses were considered with the SIMEX method. Therefore, one should be careful when comparing the estimated risks and it may be useful to use several correction techniques in order to obtain a range of corrected estimates, rather than to rely on a single technique. This work will enable to improve the risk estimates derived from LSS data, and help to make more reliable the development of radiation protection standards. (orig.)

  10. Creep behavior of bone cement: a method for time extrapolation using time-temperature equivalence.

    Morgan, R L; Farrar, D F; Rose, J; Forster, H; Morgan, I

    2003-04-01

    The clinical lifetime of poly(methyl methacrylate) (PMMA) bone cement is considerably longer than the time over which it is convenient to perform creep testing. Consequently, it is desirable to be able to predict the long term creep behavior of bone cement from the results of short term testing. A simple method is described for prediction of long term creep using the principle of time-temperature equivalence in polymers. The use of the method is illustrated using a commercial acrylic bone cement. A creep strain of approximately 0.6% is predicted after 400 days under a constant flexural stress of 2 MPa. The temperature range and stress levels over which it is appropriate to perform testing are described. Finally, the effects of physical aging on the accuracy of the method are discussed and creep data from aged cement are reported.

  11. Standardization of low energy beta and beta-gamma complex emitters by the tracer and the efficiency extrapolation methods

    Sahagia, M.

    1978-01-01

    The absolute standardization of radioactive solutions of low energy beta emitters and beta-gamma emitters with a high probability of disintegration to the ground state is described; the tracer and the efficiency extrapolation methods were used. Both types of radionuclides were mathematically and physically treated in an unified manner. The theoretical relations between different beta spectra were calculated according to Williams' model and experimentally verified for: 35 S + 60 Co, 35 S + 95 Nb, 147 Pm + 60 Co, 14 C + 95 Nb and two beta branches of 99 Mo. The optimum range of beta efficiency variation was indicated. The basic supposition that all beta efficieny tend to unity in the same time was experimentally verified, using two 192 Ir beta branches. Four computer programs, written in the FORTRAN IV language, were elaborated, for the adequate processing of the experimental data. Good precision coefficients according to international standards were obtained in the absolute standardization of 35 S, 147 Pm, 99 Mo solutions. (author)

  12. Determination of the most appropriate method for extrapolating overall survival data from a placebo-controlled clinical trial of lenvatinib for progressive, radioiodine-refractory differentiated thyroid cancer.

    Tremblay, Gabriel; Livings, Christopher; Crowe, Lydia; Kapetanakis, Venediktos; Briggs, Andrew

    2016-01-01

    Cost-effectiveness models for the treatment of long-term conditions often require information on survival beyond the period of available data. This paper aims to identify a robust and reliable method for the extrapolation of overall survival (OS) in patients with radioiodine-refractory differentiated thyroid cancer receiving lenvatinib or placebo. Data from 392 patients (lenvatinib: 261, placebo: 131) from the SELECT trial are used over a 34-month period of follow-up. A previously published criterion-based approach is employed to ascertain credible estimates of OS beyond the trial data. Parametric models with and without a treatment covariate and piecewise models are used to extrapolate OS, and a holistic approach, where a series of statistical and visual tests are considered collectively, is taken in determining the most appropriate extrapolation model. A piecewise model, in which the Kaplan-Meier survivor function is used over the trial period and an extrapolated tail is based on the Exponential distribution, is identified as the optimal model. In the absence of long-term survival estimates from clinical trials, survival estimates often need to be extrapolated from the available data. The use of a systematic method based on a priori determined selection criteria provides a transparent approach and reduces the risk of bias. The extrapolated OS estimates will be used to investigate the potential long-term benefits of lenvatinib in the treatment of radioiodine-refractory differentiated thyroid cancer patients and populate future cost-effectiveness analyses.

  13. Two linearization methods for atmospheric remote sensing

    Doicu, A.; Trautmann, T.

    2009-01-01

    We present two linearization methods for a pseudo-spherical atmosphere and general viewing geometries. The first approach is based on an analytical linearization of the discrete ordinate method with matrix exponential and incorporates two models for matrix exponential calculation: the matrix eigenvalue method and the Pade approximation. The second method referred to as the forward-adjoint approach is based on the adjoint radiative transfer for a pseudo-spherical atmosphere. We provide a compact description of the proposed methods as well as a numerical analysis of their accuracy and efficiency.

  14. Statistical modeling and extrapolation of carcinogenesis data

    Krewski, D.; Murdoch, D.; Dewanji, A.

    1986-01-01

    Mathematical models of carcinogenesis are reviewed, including pharmacokinetic models for metabolic activation of carcinogenic substances. Maximum likelihood procedures for fitting these models to epidemiological data are discussed, including situations where the time to tumor occurrence is unobservable. The plausibility of different possible shapes of the dose response curve at low doses is examined, and a robust method for linear extrapolation to low doses is proposed and applied to epidemiological data on radiation carcinogenesis

  15. Application of the EXtrapolated Efficiency Method (EXEM) to infer the gamma-cascade detection efficiency in the actinide region

    Ducasse, Q.; Jurado, B.; Mathieu, L.; Marini, P.; Morillon, B.; Aiche, M.; Tsekhanovich, I.

    2016-01-01

    The study of transfer-induced gamma-decay probabilities is very useful for understanding the surrogate-reaction method and, more generally, for constraining statistical-model calculations. One of the main difficulties in the measurement of gamma-decay probabilities is the determination of the gamma-cascade detection efficiency. In Boutoux et al. (2013) [10] we developed the EXtrapolated Efficiency Method (EXEM), a new method to measure this quantity. In this work, we have applied, for the first time, the EXEM to infer the gamma-cascade detection efficiency in the actinide region. In particular, we have considered the "2"3"8U(d,p)"2"3"9U and "2"3"8U("3He,d)"2"3"9Np reactions. We have performed Hauser–Feshbach calculations to interpret our results and to verify the hypothesis on which the EXEM is based. The determination of fission and gamma-decay probabilities of "2"3"9Np below the neutron separation energy allowed us to validate the EXEM.

  16. Application of the EXtrapolated Efficiency Method (EXEM) to infer the gamma-cascade detection efficiency in the actinide region

    Ducasse, Q. [CENBG, CNRS/IN2P3-Université de Bordeaux, Chemin du Solarium B.P. 120, 33175 Gradignan (France); CEA-Cadarache, DEN/DER/SPRC/LEPh, 13108 Saint Paul lez Durance (France); Jurado, B., E-mail: jurado@cenbg.in2p3.fr [CENBG, CNRS/IN2P3-Université de Bordeaux, Chemin du Solarium B.P. 120, 33175 Gradignan (France); Mathieu, L.; Marini, P. [CENBG, CNRS/IN2P3-Université de Bordeaux, Chemin du Solarium B.P. 120, 33175 Gradignan (France); Morillon, B. [CEA DAM DIF, 91297 Arpajon (France); Aiche, M.; Tsekhanovich, I. [CENBG, CNRS/IN2P3-Université de Bordeaux, Chemin du Solarium B.P. 120, 33175 Gradignan (France)

    2016-08-01

    The study of transfer-induced gamma-decay probabilities is very useful for understanding the surrogate-reaction method and, more generally, for constraining statistical-model calculations. One of the main difficulties in the measurement of gamma-decay probabilities is the determination of the gamma-cascade detection efficiency. In Boutoux et al. (2013) [10] we developed the EXtrapolated Efficiency Method (EXEM), a new method to measure this quantity. In this work, we have applied, for the first time, the EXEM to infer the gamma-cascade detection efficiency in the actinide region. In particular, we have considered the {sup 238}U(d,p){sup 239}U and {sup 238}U({sup 3}He,d){sup 239}Np reactions. We have performed Hauser–Feshbach calculations to interpret our results and to verify the hypothesis on which the EXEM is based. The determination of fission and gamma-decay probabilities of {sup 239}Np below the neutron separation energy allowed us to validate the EXEM.

  17. Sparsity Prevention Pivoting Method for Linear Programming

    Li, Peiqiang; Li, Qiyuan; Li, Canbing

    2018-01-01

    When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper....... The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

  18. Sparsity Prevention Pivoting Method for Linear Programming

    Li, Peiqiang; Li, Qiyuan; Li, Canbing

    2018-01-01

    . The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following......When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

  19. Determination of the most appropriate method for extrapolating overall survival data from a placebo-controlled clinical trial of lenvatinib for progressive, radioiodine-refractory differentiated thyroid cancer

    Tremblay G

    2016-06-01

    Full Text Available Gabriel Tremblay,1 Christopher Livings,2 Lydia Crowe,2 Venediktos Kapetanakis,2 Andrew Briggs3 1Global Health Economics and Health Technology Assessment, Eisai Inc., Woodcliff Lake, NJ, USA; 2Health Economics, Decision Resources Group, Bicester, Oxfordshire, 3Health Economics and Health Technology Assessment, Institute of Health and Wellbeing, University of Glasgow, Glasgow, UK Background: Cost-effectiveness models for the treatment of long-term conditions often require information on survival beyond the period of available data. Objectives: This paper aims to identify a robust and reliable method for the extrapolation of overall survival (OS in patients with radioiodine-refractory differentiated thyroid cancer receiving lenvatinib or placebo. Methods: Data from 392 patients (lenvatinib: 261, placebo: 131 from the SELECT trial are used over a 34-month period of follow-up. A previously published criterion-based approach is employed to ascertain credible estimates of OS beyond the trial data. Parametric models with and without a treatment covariate and piecewise models are used to extrapolate OS, and a holistic approach, where a series of statistical and visual tests are considered collectively, is taken in determining the most appropriate extrapolation model. Results: A piecewise model, in which the Kaplan–Meier survivor function is used over the trial period and an extrapolated tail is based on the Exponential distribution, is identified as the optimal model. Conclusion: In the absence of long-term survival estimates from clinical trials, survival estimates often need to be extrapolated from the available data. The use of a systematic method based on a priori determined selection criteria provides a transparent approach and reduces the risk of bias. The extrapolated OS estimates will be used to investigate the potential long-term benefits of lenvatinib in the treatment of radioiodine-refractory differentiated thyroid cancer patients and

  20. The linearization method in hydrodynamical stability theory

    Yudovich, V I

    1989-01-01

    This book presents the theory of the linearization method as applied to the problem of steady-state and periodic motions of continuous media. The author proves infinite-dimensional analogues of Lyapunov's theorems on stability, instability, and conditional stability for a large class of continuous media. In addition, semigroup properties for the linearized Navier-Stokes equations in the case of an incompressible fluid are studied, and coercivity inequalities and completeness of a system of small oscillations are proved.

  1. Non-linear M -sequences Generation Method

    Z. R. Garifullina

    2011-06-01

    Full Text Available The article deals with a new method for modeling a pseudorandom number generator based on R-blocks. The gist of the method is the replacement of a multi digit XOR element by a stochastic adder in a parallel binary linear feedback shift register scheme.

  2. Uzawa method for fuzzy linear system

    Ke Wang

    2013-01-01

    An Uzawa method is presented for solving fuzzy linear systems whose coefficient matrix is crisp and the right-hand side column is arbitrary fuzzy number vector. The explicit iterative scheme is given. The convergence is analyzed with convergence theorems and the optimal parameter is obtained. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

  3. The simplex method of linear programming

    Ficken, Frederick A

    1961-01-01

    This concise but detailed and thorough treatment discusses the rudiments of the well-known simplex method for solving optimization problems in linear programming. Geared toward undergraduate students, the approach offers sufficient material for readers without a strong background in linear algebra. Many different kinds of problems further enrich the presentation. The text begins with examinations of the allocation problem, matrix notation for dual problems, feasibility, and theorems on duality and existence. Subsequent chapters address convex sets and boundedness, the prepared problem and boun

  4. Propagation of internal errors in explicit Runge–Kutta methods and internal stability of SSP and extrapolation methods

    Ketcheson, David I.; Loczi, Lajos; Parsani, Matteo

    2014-01-01

    of internal stability polynomials can be obtained by modifying the implementation details. We provide bounds on the internal error amplification constants for some classes of methods with many stages, including strong stability preserving methods

  5. Preface: Introductory Remarks: Linear Scaling Methods

    Bowler, D. R.; Fattebert, J.-L.; Gillan, M. J.; Haynes, P. D.; Skylaris, C.-K.

    2008-07-01

    It has been just over twenty years since the publication of the seminal paper on molecular dynamics with ab initio methods by Car and Parrinello [1], and the contribution of density functional theory (DFT) and the related techniques to physics, chemistry, materials science, earth science and biochemistry has been huge. Nevertheless, significant improvements are still being made to the performance of these standard techniques; recent work suggests that speed improvements of one or even two orders of magnitude are possible [2]. One of the areas where major progress has long been expected is in O(N), or linear scaling, DFT, in which the computer effort is proportional to the number of atoms. Linear scaling DFT methods have been in development for over ten years [3] but we are now in an exciting period where more and more research groups are working on these methods. Naturally there is a strong and continuing effort to improve the efficiency of the methods and to make them more robust. But there is also a growing ambition to apply them to challenging real-life problems. This special issue contains papers submitted following the CECAM Workshop 'Linear-scaling ab initio calculations: applications and future directions', held in Lyon from 3-6 September 2007. A noteworthy feature of the workshop is that it included a significant number of presentations involving real applications of O(N) methods, as well as work to extend O(N) methods into areas of greater accuracy (correlated wavefunction methods, quantum Monte Carlo, TDDFT) and large scale computer architectures. As well as explicitly linear scaling methods, the conference included presentations on techniques designed to accelerate and improve the efficiency of standard (that is non-linear-scaling) methods; this highlights the important question of crossover—that is, at what size of system does it become more efficient to use a linear-scaling method? As well as fundamental algorithmic questions, this brings up

  6. Polarized atomic orbitals for linear scaling methods

    Berghold, Gerd; Parrinello, Michele; Hutter, Jürg

    2002-02-01

    We present a modified version of the polarized atomic orbital (PAO) method [M. S. Lee and M. Head-Gordon, J. Chem. Phys. 107, 9085 (1997)] to construct minimal basis sets optimized in the molecular environment. The minimal basis set derives its flexibility from the fact that it is formed as a linear combination of a larger set of atomic orbitals. This approach significantly reduces the number of independent variables to be determined during a calculation, while retaining most of the essential chemistry resulting from the admixture of higher angular momentum functions. Furthermore, we combine the PAO method with linear scaling algorithms. We use the Chebyshev polynomial expansion method, the conjugate gradient density matrix search, and the canonical purification of the density matrix. The combined scheme overcomes one of the major drawbacks of standard approaches for large nonorthogonal basis sets, namely numerical instabilities resulting from ill-conditioned overlap matrices. We find that the condition number of the PAO overlap matrix is independent from the condition number of the underlying extended basis set, and consequently no numerical instabilities are encountered. Various applications are shown to confirm this conclusion and to compare the performance of the PAO method with extended basis-set calculations.

  7. Beam Based Measurements of Field Multipoles in the RHIC Low Beta Insertions and Extrapolation of the Method to the LHC

    Koutchouk, Jean-Pierre; Ptitsyn, V I

    2001-01-01

    The multipolar content of the dipoles and quadrupoles is known to limit the stability of the beam dynamics in super-conducting machines like RHIC and even more in LHC. The low-beta quadrupoles are thus equipped with correcting coils up to the dodecapole order. The correction is planned to rely on magnetic measurements. We show that a relatively simple method allows an accurate measurement of the multipolar field aberrations using the beam. The principle is to displace the beam in the non-linear fields by local closed orbit bumps and to measure the variation of sensitive beam observable. The resolution and robustness of the method are found appropriate. Experimentation at RHIC showed clearly the presence of normal and skew sextupolar field components in addition to a skew quadrupolar component in the interaction regions. Higher-order components up to decapole order appear as well.

  8. New nonlinear methods for linear transport calculations

    Adams, M.L.

    1993-01-01

    We present a new family of methods for the numerical solution of the linear transport equation. With these methods an iteration consists of an 'S N sweep' followed by an 'S 2 -like' calculation. We show, by analysis as well as numerical results, that iterative convergence is always rapid. We show that this rapid convergence does not depend on a consistent discretization of the S 2 -like equations - they can be discretized independently from the S N equations. We show further that independent discretizations can offer significant advantages over consistent ones. In particular, we find that in a wide range of problems, an accurate discretization of the S 2 -like equation can be combined with a crude discretization of the S N equations to produce an accurate S N answer. We demonstrate this by analysis as well as numerical results. (orig.)

  9. Principles of animal extrapolation

    Calabrese, E.J.

    1991-01-01

    Animal Extrapolation presents a comprehensive examination of the scientific issues involved in extrapolating results of animal experiments to human response. This text attempts to present a comprehensive synthesis and analysis of the host of biomedical and toxicological studies of interspecies extrapolation. Calabrese's work presents not only the conceptual basis of interspecies extrapolation, but also illustrates how these principles may be better used in selection of animal experimentation models and in the interpretation of animal experimental results. The book's theme centers around four types of extrapolation: (1) from average animal model to the average human; (2) from small animals to large ones; (3) from high-risk animal to the high risk human; and (4) from high doses of exposure to lower, more realistic, doses. Calabrese attacks the issues of interspecies extrapolation by dealing individually with the factors which contribute to interspecies variability: differences in absorption, intestinal flora, tissue distribution, metabolism, repair mechanisms, and excretion. From this foundation, Calabrese then discusses the heterogeneticity of these same factors in the human population in an attempt to evaluate the representativeness of various animal models in light of interindividual variations. In addition to discussing the question of suitable animal models for specific high-risk groups and specific toxicological endpoints, the author also examines extrapolation questions related to the use of short-term tests to predict long-term human carcinogenicity and birth defects. The book is comprehensive in scope and specific in detail; for those environmental health professions seeking to understand the toxicological models which underlay health risk assessments, Animal Extrapolation is a valuable information source.

  10. Studying the method of linearization of exponential calibration curves

    Bunzh, Z.A.

    1989-01-01

    The results of study of the method for linearization of exponential calibration curves are given. The calibration technique and comparison of the proposed method with piecewise-linear approximation and power series expansion, are given

  11. A logic circuit for solving linear function by digital method

    Ma Yonghe

    1986-01-01

    A mathematical method for determining the linear relation of physical quantity with rediation intensity is described. A logic circuit has been designed for solving linear function by digital method. Some applications and the circuit function are discussed

  12. NLT and extrapolated DLT:3-D cinematography alternatives for enlarging the volume of calibration.

    Hinrichs, R N; McLean, S P

    1995-10-01

    This study investigated the accuracy of the direct linear transformation (DLT) and non-linear transformation (NLT) methods of 3-D cinematography/videography. A comparison of standard DLT, extrapolated DLT, and NLT calibrations showed the standard (non-extrapolated) DLT to be the most accurate, especially when a large number of control points (40-60) were used. The NLT was more accurate than the extrapolated DLT when the level of extrapolation exceeded 100%. The results indicated that when possible one should use the DLT with a control object, sufficiently large as to encompass the entire activity being studied. However, in situations where the activity volume exceeds the size of one's DLT control object, the NLT method should be considered.

  13. Methods in half-linear asymptotic theory

    Řehák, Pavel

    2016-01-01

    Roč. 2016, Č. 267 (2016), s. 1-27 ISSN 1072-6691 Institutional support: RVO:67985840 Keywords : half-linear differential equation * nonoscillatory solution * regular variation Subject RIV: BA - General Mathematics Impact factor: 0.954, year: 2016 http://ejde.math.txstate.edu/Volumes/2016/267/abstr.html

  14. Methods in half-linear asymptotic theory

    Pavel Rehak

    2016-10-01

    Full Text Available We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $$ (r(t|y'|^{\\alpha-1}\\hbox{sgn} y''=p(t|y|^{\\alpha-1}\\hbox{sgn} y, $$ where r(t and p(t are positive continuous functions on $[a,\\infty$, $\\alpha\\in(1,\\infty$. The aim of this article is twofold. On the one hand, we show applications of a wide variety of tools, like the Karamata theory of regular variation, the de Haan theory, the Riccati technique, comparison theorems, the reciprocity principle, a certain transformation of dependent variable, and principal solutions. On the other hand, we solve open problems posed in the literature and generalize existing results. Most of our observations are new also in the linear case.

  15. Finite lattice extrapolation algorithms

    Henkel, M.; Schuetz, G.

    1987-08-01

    Two algorithms for sequence extrapolation, due to von den Broeck and Schwartz and Bulirsch and Stoer are reviewed and critically compared. Applications to three states and six states quantum chains and to the (2+1)D Ising model show that the algorithm of Bulirsch and Stoer is superior, in particular if only very few finite lattice data are available. (orig.)

  16. Convergence of hybrid methods for solving non-linear partial ...

    This paper is concerned with the numerical solution and convergence analysis of non-linear partial differential equations using a hybrid method. The solution technique involves discretizing the non-linear system of PDE to obtain a corresponding non-linear system of algebraic difference equations to be solved at each time ...

  17. Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function

    Yi-hua Zhong

    2013-01-01

    Full Text Available Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems.

  18. A Proposed Method for Solving Fuzzy System of Linear Equations

    Reza Kargar

    2014-01-01

    Full Text Available This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m×n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.

  19. Efficient Wavefield Extrapolation In Anisotropic Media

    Alkhalifah, Tariq; Ma, Xuxin; Waheed, Umair bin; Zuberi, Mohammad Akbar Hosain

    2014-01-01

    Various examples are provided for wavefield extrapolation in anisotropic media. In one example, among others, a method includes determining an effective isotropic velocity model and extrapolating an equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. The effective isotropic velocity model can be based upon a kinematic geometrical representation of an anisotropic, poroelastic or viscoelastic wavefield. Extrapolating the equivalent propagation can use isotopic, acoustic or elastic operators based upon the determined effective isotropic velocity model. In another example, non-transitory computer readable medium stores an application that, when executed by processing circuitry, causes the processing circuitry to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. In another example, a system includes processing circuitry and an application configured to cause the system to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield.

  20. Efficient Wavefield Extrapolation In Anisotropic Media

    Alkhalifah, Tariq

    2014-07-03

    Various examples are provided for wavefield extrapolation in anisotropic media. In one example, among others, a method includes determining an effective isotropic velocity model and extrapolating an equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. The effective isotropic velocity model can be based upon a kinematic geometrical representation of an anisotropic, poroelastic or viscoelastic wavefield. Extrapolating the equivalent propagation can use isotopic, acoustic or elastic operators based upon the determined effective isotropic velocity model. In another example, non-transitory computer readable medium stores an application that, when executed by processing circuitry, causes the processing circuitry to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. In another example, a system includes processing circuitry and an application configured to cause the system to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield.

  1. Builtin vs. auxiliary detection of extrapolation risk.

    Munson, Miles Arthur; Kegelmeyer, W. Philip,

    2013-02-01

    A key assumption in supervised machine learning is that future data will be similar to historical data. This assumption is often false in real world applications, and as a result, prediction models often return predictions that are extrapolations. We compare four approaches to estimating extrapolation risk for machine learning predictions. Two builtin methods use information available from the classification model to decide if the model would be extrapolating for an input data point. The other two build auxiliary models to supplement the classification model and explicitly model extrapolation risk. Experiments with synthetic and real data sets show that the auxiliary models are more reliable risk detectors. To best safeguard against extrapolating predictions, however, we recommend combining builtin and auxiliary diagnostics.

  2. Mathematical methods linear algebra normed spaces distributions integration

    Korevaar, Jacob

    1968-01-01

    Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions.The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector

  3. Ecotoxicological effects extrapolation models

    Suter, G.W. II

    1996-09-01

    One of the central problems of ecological risk assessment is modeling the relationship between test endpoints (numerical summaries of the results of toxicity tests) and assessment endpoints (formal expressions of the properties of the environment that are to be protected). For example, one may wish to estimate the reduction in species richness of fishes in a stream reach exposed to an effluent and have only a fathead minnow 96 hr LC50 as an effects metric. The problem is to extrapolate from what is known (the fathead minnow LC50) to what matters to the decision maker, the loss of fish species. Models used for this purpose may be termed Effects Extrapolation Models (EEMs) or Activity-Activity Relationships (AARs), by analogy to Structure-Activity Relationships (SARs). These models have been previously reviewed in Ch. 7 and 9 of and by an OECD workshop. This paper updates those reviews and attempts to further clarify the issues involved in the development and use of EEMs. Although there is some overlap, this paper does not repeat those reviews and the reader is referred to the previous reviews for a more complete historical perspective, and for treatment of additional extrapolation issues.

  4. A feasible DY conjugate gradient method for linear equality constraints

    LI, Can

    2017-09-01

    In this paper, we propose a feasible conjugate gradient method for solving linear equality constrained optimization problem. The method is an extension of the Dai-Yuan conjugate gradient method proposed by Dai and Yuan to linear equality constrained optimization problem. It can be applied to solve large linear equality constrained problem due to lower storage requirement. An attractive property of the method is that the generated direction is always feasible and descent direction. Under mild conditions, the global convergence of the proposed method with exact line search is established. Numerical experiments are also given which show the efficiency of the method.

  5. Fast linear method of illumination classification

    Cooper, Ted J.; Baqai, Farhan A.

    2003-01-01

    We present a simple method for estimating the scene illuminant for images obtained by a Digital Still Camera (DSC). The proposed method utilizes basis vectors obtained from known memory color reflectance to identify the memory color objects in the image. Once the memory color pixels are identified, we use the ratios of the red/green and blue/green to determine the most likely illuminant in the image. The critical part of the method is to estimate the smallest set of basis vectors that closely represent the memory color reflectances. Basis vectors obtained from both Principal Component Analysis (PCA) and Independent Component Analysis (ICA) are used. We will show that only two ICA basis vectors are needed to get an acceptable estimate.

  6. Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

    Amini Afshar, Mostafa; Bingham, Harry B.

    2017-01-01

    . Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...

  7. One-step lowrank wave extrapolation

    Sindi, Ghada Atif; Alkhalifah, Tariq Ali

    2014-01-01

    Wavefield extrapolation is at the heart of modeling, imaging, and Full waveform inversion. Spectral methods gained well deserved attention due to their dispersion free solutions and their natural handling of anisotropic media. We propose a scheme a

  8. Interior-Point Methods for Linear Programming: A Review

    Singh, J. N.; Singh, D.

    2002-01-01

    The paper reviews some recent advances in interior-point methods for linear programming and indicates directions in which future progress can be made. Most of the interior-point methods belong to any of three categories: affine-scaling methods, potential reduction methods and central path methods. These methods are discussed together with…

  9. Strong-stability-preserving additive linear multistep methods

    Hadjimichael, Yiannis

    2018-02-20

    The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain larger monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding nonadditive SSP linear multistep methods.

  10. Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

    S. Narayanamoorthy

    2015-01-01

    Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

  11. One-step lowrank wave extrapolation

    Sindi, Ghada Atif

    2014-01-01

    Wavefield extrapolation is at the heart of modeling, imaging, and Full waveform inversion. Spectral methods gained well deserved attention due to their dispersion free solutions and their natural handling of anisotropic media. We propose a scheme a modified one-step lowrank wave extrapolation using Shanks transform in isotropic, and anisotropic media. Specifically, we utilize a velocity gradient term to add to the accuracy of the phase approximation function in the spectral implementation. With the higher accuracy, we can utilize larger time steps and make the extrapolation more efficient. Applications to models with strong inhomogeneity and considerable anisotropy demonstrates the utility of the approach.

  12. Non-linear programming method in optimization of fast reactors

    Pavelesku, M.; Dumitresku, Kh.; Adam, S.

    1975-01-01

    Application of the non-linear programming methods on optimization of nuclear materials distribution in fast reactor is discussed. The programming task composition is made on the basis of the reactor calculation dependent on the fuel distribution strategy. As an illustration of this method application the solution of simple example is given. Solution of the non-linear program is done on the basis of the numerical method SUMT. (I.T.)

  13. Two-dimensional differential transform method for solving linear and non-linear Schroedinger equations

    Ravi Kanth, A.S.V.; Aruna, K.

    2009-01-01

    In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.

  14. Application of the simplex method of linear programming model to ...

    This work discussed how the simplex method of linear programming could be used to maximize the profit of any business firm using Saclux Paint Company as a case study. It equally elucidated the effect variation in the optimal result obtained from linear programming model, will have on any given firm. It was demonstrated ...

  15. Ground-state inversion method applied to calculation of molecular photoionization cross-sections by atomic extrapolation: Interference effects at low energies

    Hilton, P.R.; Nordholm, S.; Hush, N.S.

    1980-01-01

    The ground-state inversion method, which we have previously developed for the calculation of atomic cross-sections, is applied to the calculation of molecular photoionization cross-sections. These are obtained as a weighted sum of atomic subshell cross-sections plus multi-centre interference terms. The atomic cross-sections are calculated directly for the atomic functions which when summed over centre and symmetry yield the molecular orbital wave function. The use of the ground-state inversion method for this allows the effect of the molecular environment on the atomic cross-sections to be calculated. Multi-centre terms are estimated on the basis of an effective plane-wave expression for this contribution to the total cross-section. Finally the method is applied to the range of photon energies from 0 to 44 eV where atomic extrapolation procedures have not previously been tested. Results obtained for H 2 , N 2 and CO show good agreement with experiment, particularly when interference effects and effects of the molecular environment on the atomic cross-sections are included. The accuracy is very much better than that of previous plane-wave and orthogonalized plane-wave methods, and can stand comparison with that of recent more sophisticated approaches. It is a feature of the method that calculation of cross-sections either of atoms or of large molecules requires very little computer time, provided that good quality wave functions are available, and it is then of considerable potential practical interest for photoelectorn spectroscopy. (orig.)

  16. Strong-stability-preserving additive linear multistep methods

    Hadjimichael, Yiannis; Ketcheson, David I.

    2018-01-01

    The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal perturbed

  17. Direct Linear Transformation Method for Three-Dimensional Cinematography

    Shapiro, Robert

    1978-01-01

    The ability of Direct Linear Transformation Method for three-dimensional cinematography to locate points in space was shown to meet the accuracy requirements associated with research on human movement. (JD)

  18. Computation of Optimal Monotonicity Preserving General Linear Methods

    Ketcheson, David I.

    2009-07-01

    Monotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal methods even among classes involving very high order accuracy and that use many steps and/or stages. The optimality of some recently proposed methods is verified, and many more efficient methods are found. We use similar algorithms to find optimal strong stability preserving linear multistep methods of both explicit and implicit type, including methods for hyperbolic PDEs that use downwind-biased operators.

  19. Linear regression methods a ccording to objective functions

    Yasemin Sisman; Sebahattin Bektas

    2012-01-01

    The aim of the study is to explain the parameter estimation methods and the regression analysis. The simple linear regressionmethods grouped according to the objective function are introduced. The numerical solution is achieved for the simple linear regressionmethods according to objective function of Least Squares and theLeast Absolute Value adjustment methods. The success of the appliedmethods is analyzed using their objective function values.

  20. Efficient decomposition and linearization methods for the stochastic transportation problem

    Holmberg, K.

    1993-01-01

    The stochastic transportation problem can be formulated as a convex transportation problem with nonlinear objective function and linear constraints. We compare several different methods based on decomposition techniques and linearization techniques for this problem, trying to find the most efficient method or combination of methods. We discuss and test a separable programming approach, the Frank-Wolfe method with and without modifications, the new technique of mean value cross decomposition and the more well known Lagrangian relaxation with subgradient optimization, as well as combinations of these approaches. Computational tests are presented, indicating that some new combination methods are quite efficient for large scale problems. (authors) (27 refs.)

  1. A method for evaluating dynamical friction in linear ball bearings.

    Fujii, Yusaku; Maru, Koichi; Jin, Tao; Yupapin, Preecha P; Mitatha, Somsak

    2010-01-01

    A method is proposed for evaluating the dynamical friction of linear bearings, whose motion is not perfectly linear due to some play in its internal mechanism. In this method, the moving part of a linear bearing is made to move freely, and the force acting on the moving part is measured as the inertial force given by the product of its mass and the acceleration of its centre of gravity. To evaluate the acceleration of its centre of gravity, the acceleration of two different points on it is measured using a dual-axis optical interferometer.

  2. Hybrid Method for Solving Inventory Problems with a Linear ...

    Osagiede and Omosigho (2004) proposed a direct search method for identifying the number of replenishment when the demand pattern is linearly increasing. The main computational task in this direct search method was associated with finding the optimal number of replenishments. To accelerate the use of this method, the ...

  3. Runge-Kutta Methods for Linear Ordinary Differential Equations

    Zingg, David W.; Chisholm, Todd T.

    1997-01-01

    Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

  4. Generalization of the linear algebraic method to three dimensions

    Lynch, D.L.; Schneider, B.I.

    1991-01-01

    We present a numerical method for the solution of the Lippmann-Schwinger equation for electron-molecule collisions. By performing a three-dimensional numerical quadrature, this approach avoids both a basis-set representation of the wave function and a partial-wave expansion of the scattering potential. The resulting linear equations, analogous in form to the one-dimensional linear algebraic method, are solved with the direct iteration-variation method. Several numerical examples are presented. The prospect for using this numerical quadrature scheme for electron-polyatomic molecules is discussed

  5. Comments on new iterative methods for solving linear systems

    Wang Ke

    2017-06-01

    Full Text Available Some new iterative methods were presented by Du, Zheng and Wang for solving linear systems in [3], where it is shown that the new methods, comparing to the classical Jacobi or Gauss-Seidel method, can be applied to more systems and have faster convergence. This note shows that their methods are suitable for more matrices than positive matrices which the authors suggested through further analysis and numerical examples.

  6. Load Extrapolation During Operation for Wind Turbines

    Toft, Henrik Stensgaard; Sørensen, John Dalsgaard

    2008-01-01

    In the recent years load extrapolation for wind turbines has been widely considered in the wind turbine industry. Loads on wind turbines during operations are normally dependent on the mean wind speed, the turbulence intensity and the type and settings of the control system. All these parameters...... must be taken into account when characteristic load effects during operation are determined. In the wind turbine standard IEC 61400-1 a method for load extrapolation using the peak over threshold method is recommended. In this paper this method is considered and some of the assumptions are examined...

  7. New Implicit General Linear Method | Ibrahim | Journal of the ...

    A New implicit general linear method is designed for the numerical olution of stiff differential Equations. The coefficients matrix is derived from the stability function. The method combines the single-implicitness or diagonal implicitness with property that the first two rows are implicit and third and fourth row are explicit.

  8. Linearly convergent stochastic heavy ball method for minimizing generalization error

    Loizou, Nicolas; Richtarik, Peter

    2017-01-01

    In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss

  9. Sodium flow rate measurement method of annular linear induction pump

    Araseki, Hideo

    2011-01-01

    This report describes a method for measuring sodium flow rate of annular linear induction pumps arranged in parallel and its verification result obtained through an experiment and a numerical analysis. In the method, the leaked magnetic field is measured with measuring coils at the stator end on the outlet side and is correlated with the sodium flow rate. The experimental data and the numerical result indicate that the leaked magnetic field at the stator edge keeps almost constant when the sodium flow rate changes and that the leaked magnetic field change arising from the flow rate change is small compared with the overall leaked magnetic field. It is shown that the correlation between the leaked magnetic field and the sodium flow rate is almost linear due to this feature of the leaked magnetic field, which indicates the applicability of the method to small-scale annular linear induction pumps. (author)

  10. EPMLR: sequence-based linear B-cell epitope prediction method using multiple linear regression.

    Lian, Yao; Ge, Meng; Pan, Xian-Ming

    2014-12-19

    B-cell epitopes have been studied extensively due to their immunological applications, such as peptide-based vaccine development, antibody production, and disease diagnosis and therapy. Despite several decades of research, the accurate prediction of linear B-cell epitopes has remained a challenging task. In this work, based on the antigen's primary sequence information, a novel linear B-cell epitope prediction model was developed using the multiple linear regression (MLR). A 10-fold cross-validation test on a large non-redundant dataset was performed to evaluate the performance of our model. To alleviate the problem caused by the noise of negative dataset, 300 experiments utilizing 300 sub-datasets were performed. We achieved overall sensitivity of 81.8%, precision of 64.1% and area under the receiver operating characteristic curve (AUC) of 0.728. We have presented a reliable method for the identification of linear B cell epitope using antigen's primary sequence information. Moreover, a web server EPMLR has been developed for linear B-cell epitope prediction: http://www.bioinfo.tsinghua.edu.cn/epitope/EPMLR/ .

  11. Comparison of linear, mixed integer and non-linear programming methods in energy system dispatch modelling

    Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian

    2014-01-01

    In the paper, three frequently used operation optimisation methods are examined with respect to their impact on operation management of the combined utility technologies for electric power and DH (district heating) of eastern Denmark. The investigation focusses on individual plant operation...... differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... as a benchmark, as this type is frequently used, and has the lowest amount of constraints of the three. A comparison of the optimised operation of a number of units shows significant differences between the three methods. Compared to the reference, the use of binary integer variables, increases operation...

  12. On a linear method in bootstrap confidence intervals

    Andrea Pallini

    2007-10-01

    Full Text Available A linear method for the construction of asymptotic bootstrap confidence intervals is proposed. We approximate asymptotically pivotal and non-pivotal quantities, which are smooth functions of means of n independent and identically distributed random variables, by using a sum of n independent smooth functions of the same analytical form. Errors are of order Op(n-3/2 and Op(n-2, respectively. The linear method allows a straightforward approximation of bootstrap cumulants, by considering the set of n independent smooth functions as an original random sample to be resampled with replacement.

  13. Relaxation Methods for Strictly Convex Regularizations of Piecewise Linear Programs

    Kiwiel, K. C.

    1998-01-01

    We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of B -functions (generalized Bregman functions)

  14. Lattice Boltzmann methods for global linear instability analysis

    Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis

    2017-12-01

    Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.

  15. The Embedding Method for Linear Partial Differential Equations

    The recently suggested embedding method to solve linear boundary value problems is here extended to cover situations where the domain of interest is unbounded or multiply connected. The extensions involve the use of complete sets of exterior and interior eigenfunctions on canonical domains. Applications to typical ...

  16. Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

    Bru, R.; Marín, J.; Mas, J.; Tůma, Miroslav

    2014-01-01

    Roč. 36, č. 4 (2014), A2002-A2022 ISSN 1064-8275 Institutional support: RVO:67985807 Keywords : preconditioned iterative methods * incomplete decompositions * approximate inverses * linear least squares Subject RIV: BA - General Mathematics Impact factor: 1.854, year: 2014

  17. A General Linear Method for Equating with Small Samples

    Albano, Anthony D.

    2015-01-01

    Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…

  18. Sodium flow rate measurement method of annular linear induction pumps

    Araseki, Hideo; Kirillov, Igor R.; Preslitsky, Gennady V.

    2012-01-01

    Highlights: ► We found a new method of flow rate monitoring of electromagnetic pump. ► The method is very simple and does not require a large space. ► The method was verified with an experiment and a numerical analysis. ► The experimental data and the numerical results are in good agreement. - Abstract: The present paper proposes a method for measuring sodium flow rate of annular linear induction pumps. The feature of the method lies in measuring the leaked magnetic field with measuring coils near the stator end on the outlet side and in correlating it with the sodium flow rate. This method is verified through an experiment and a numerical analysis. The data obtained in the experiment reveals that the correlation between the leaked magnetic field and the sodium flow rate is almost linear. The result of the numerical analysis agrees with the experimental data. The present method will be particularly effective to sodium flow rate monitoring of each one of plural annular linear induction pumps arranged in parallel in a vessel which forms a large-scale pump unit.

  19. Estimation of low-level neutron dose-equivalent rate by using extrapolation method for a curie level Am–Be neutron source

    Li, Gang; Xu, Jiayun; Zhang, Jie

    2015-01-01

    Neutron radiation protection is an important research area because of the strong radiation biological effect of neutron field. The radiation dose of neutron is closely related to the neutron energy, and the connected relationship is a complex function of energy. For the low-level neutron radiation field (e.g. the Am–Be source), the commonly used commercial neutron dosimeter cannot always reflect the low-level dose rate, which is restricted by its own sensitivity limit and measuring range. In this paper, the intensity distribution of neutron field caused by a curie level Am–Be neutron source was investigated by measuring the count rates obtained through a 3 He proportional counter at different locations around the source. The results indicate that the count rates outside of the source room are negligible compared with the count rates measured in the source room. In the source room, 3 He proportional counter and neutron dosimeter were used to measure the count rates and dose rates respectively at different distances to the source. The results indicate that both the count rates and dose rates decrease exponentially with the increasing distance, and the dose rates measured by a commercial dosimeter are in good agreement with the results calculated by the Geant4 simulation within the inherent errors recommended by ICRP and IEC. Further studies presented in this paper indicate that the low-level neutron dose equivalent rates in the source room increase exponentially with the increasing low-energy neutron count rates when the source is lifted from the shield with different radiation intensities. Based on this relationship as well as the count rates measured at larger distance to the source, the dose rates can be calculated approximately by the extrapolation method. This principle can be used to estimate the low level neutron dose values in the source room which cannot be measured directly by a commercial dosimeter. - Highlights: • The scope of the affected area for

  20. Linearly convergent stochastic heavy ball method for minimizing generalization error

    Loizou, Nicolas

    2017-10-30

    In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss and not on finite-sum minimization, which is typically a much harder problem. While in the analysis we constrain ourselves to quadratic loss, the overall objective is not necessarily strongly convex.

  1. Linear algebraic methods applied to intensity modulated radiation therapy.

    Crooks, S M; Xing, L

    2001-10-01

    Methods of linear algebra are applied to the choice of beam weights for intensity modulated radiation therapy (IMRT). It is shown that the physical interpretation of the beam weights, target homogeneity and ratios of deposited energy can be given in terms of matrix equations and quadratic forms. The methodology of fitting using linear algebra as applied to IMRT is examined. Results are compared with IMRT plans that had been prepared using a commercially available IMRT treatment planning system and previously delivered to cancer patients.

  2. Linear density response function in the projector augmented wave method

    Yan, Jun; Mortensen, Jens Jørgen; Jacobsen, Karsten Wedel

    2011-01-01

    We present an implementation of the linear density response function within the projector-augmented wave method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single...... functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001...

  3. An extended GS method for dense linear systems

    Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

    2009-09-01

    Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

  4. Wavefield extrapolation in pseudodepth domain

    Ma, Xuxin

    2013-02-01

    Wavefields are commonly computed in the Cartesian coordinate frame. Its efficiency is inherently limited due to spatial oversampling in deep layers, where the velocity is high and wavelengths are long. To alleviate this computational waste due to uneven wavelength sampling, we convert the vertical axis of the conventional domain from depth to vertical time or pseudodepth. This creates a nonorthognal Riemannian coordinate system. Isotropic and anisotropic wavefields can be extrapolated in the new coordinate frame with improved efficiency and good consistency with Cartesian domain extrapolation results. Prestack depth migrations are also evaluated based on the wavefield extrapolation in the pseudodepth domain.© 2013 Society of Exploration Geophysicists. All rights reserved.

  5. Solution methods for large systems of linear equations in BACCHUS

    Homann, C.; Dorr, B.

    1993-05-01

    The computer programme BACCHUS is used to describe steady state and transient thermal-hydraulic behaviour of a coolant in a fuel element with intact geometry in a fast breeder reactor. In such computer programmes generally large systems of linear equations with sparse matrices of coefficients, resulting from discretization of coolant conservation equations, must be solved thousands of times giving rise to large demands of main storage and CPU time. Direct and iterative solution methods of the systems of linear equations, available in BACCHUS, are described, giving theoretical details and experience with their use in the programme. Besides use of a method of lines, a Runge-Kutta-method, for solution of the partial differential equation is outlined. (orig.) [de

  6. Linear finite element method for one-dimensional diffusion problems

    Brandao, Michele A.; Dominguez, Dany S.; Iglesias, Susana M., E-mail: micheleabrandao@gmail.com, E-mail: dany@labbi.uesc.br, E-mail: smiglesias@uesc.br [Universidade Estadual de Santa Cruz (LCC/DCET/UESC), Ilheus, BA (Brazil). Departamento de Ciencias Exatas e Tecnologicas. Laboratorio de Computacao Cientifica

    2011-07-01

    We describe in this paper the fundamentals of Linear Finite Element Method (LFEM) applied to one-speed diffusion problems in slab geometry. We present the mathematical formulation to solve eigenvalue and fixed source problems. First, we discretized a calculus domain using a finite set of elements. At this point, we obtain the spatial balance equations for zero order and first order spatial moments inside each element. Then, we introduce the linear auxiliary equations to approximate neutron flux and current inside the element and architect a numerical scheme to obtain the solution. We offer numerical results for fixed source typical model problems to illustrate the method's accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains. Also, we compare the accuracy and computational performance of LFEM formulation with conventional Finite Difference Method (FDM). (author)

  7. Linear-scaling quantum mechanical methods for excited states.

    Yam, ChiYung; Zhang, Qing; Wang, Fan; Chen, GuanHua

    2012-05-21

    The poor scaling of many existing quantum mechanical methods with respect to the system size hinders their applications to large systems. In this tutorial review, we focus on latest research on linear-scaling or O(N) quantum mechanical methods for excited states. Based on the locality of quantum mechanical systems, O(N) quantum mechanical methods for excited states are comprised of two categories, the time-domain and frequency-domain methods. The former solves the dynamics of the electronic systems in real time while the latter involves direct evaluation of electronic response in the frequency-domain. The localized density matrix (LDM) method is the first and most mature linear-scaling quantum mechanical method for excited states. It has been implemented in time- and frequency-domains. The O(N) time-domain methods also include the approach that solves the time-dependent Kohn-Sham (TDKS) equation using the non-orthogonal localized molecular orbitals (NOLMOs). Besides the frequency-domain LDM method, other O(N) frequency-domain methods have been proposed and implemented at the first-principles level. Except one-dimensional or quasi-one-dimensional systems, the O(N) frequency-domain methods are often not applicable to resonant responses because of the convergence problem. For linear response, the most efficient O(N) first-principles method is found to be the LDM method with Chebyshev expansion for time integration. For off-resonant response (including nonlinear properties) at a specific frequency, the frequency-domain methods with iterative solvers are quite efficient and thus practical. For nonlinear response, both on-resonance and off-resonance, the time-domain methods can be used, however, as the time-domain first-principles methods are quite expensive, time-domain O(N) semi-empirical methods are often the practical choice. Compared to the O(N) frequency-domain methods, the O(N) time-domain methods for excited states are much more mature and numerically stable, and

  8. Galerkin projection methods for solving multiple related linear systems

    Chan, T.F.; Ng, M.; Wan, W.L.

    1996-12-31

    We consider using Galerkin projection methods for solving multiple related linear systems A{sup (i)}x{sup (i)} = b{sup (i)} for 1 {le} i {le} s, where A{sup (i)} and b{sup (i)} are different in general. We start with the special case where A{sup (i)} = A and A is symmetric positive definite. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a super-convergence behaviour of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this talk, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method. The above procedure can actually be modified for solving multiple linear systems A{sup (i)}x{sup (i)} = b{sup (i)}, where A{sup (i)} are now different. We can also extend the previous analytical results to this more general case. Applications of this method to multiple related linear systems arising from image restoration and recursive least squares computations are considered as examples.

  9. Seismic analysis of equipment system with non-linearities such as gap and friction using equivalent linearization method

    Murakami, H.; Hirai, T.; Nakata, M.; Kobori, T.; Mizukoshi, K.; Takenaka, Y.; Miyagawa, N.

    1989-01-01

    Many of the equipment systems of nuclear power plants contain a number of non-linearities, such as gap and friction, due to their mechanical functions. It is desirable to take such non-linearities into account appropriately for the evaluation of the aseismic soundness. However, in usual design works, linear analysis method with rough assumptions is applied from engineering point of view. An equivalent linearization method is considered to be one of the effective analytical techniques to evaluate non-linear responses, provided that errors to a certain extent are tolerated, because it has greater simplicity in analysis and economization in computing time than non-linear analysis. The objective of this paper is to investigate the applicability of the equivalent linearization method to evaluate the maximum earthquake response of equipment systems such as the CANDU Fuelling Machine which has multiple non- linearities

  10. Deterministic operations research models and methods in linear optimization

    Rader, David J

    2013-01-01

    Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations resear

  11. Efficient and stable extrapolation of prestack wavefields

    Wu, Zedong

    2013-09-22

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers and the image point, or in other words, prestack wavefields. Extrapolating such wavefields in time, nevertheless, is a big challenge because the radicand can be negative, thus reduce to a complex phase velocity, which will make the rank of the mixed domain matrix very high. Using the vertical offset between the sources and receivers, we introduce a method for deriving the DSR formulation, which gives us the opportunity to derive approximations for the mixed domain operator. The method extrapolates prestack wavefields by combining all data into one wave extrapolation procedure, allowing both upgoing and downgoing wavefields since the extrapolation is done in time, and doesn’t have the v(z) assumption in the offset axis of the media. Thus, the imaging condition is imposed by taking the zero-time and zero-offset slice from the multi-dimensional prestack wavefield. Unlike reverse time migration (RTM), no crosscorrelation is needed and we also have access to the subsurface offset information, which is important for migration velocity analysis. Numerical examples show the capability of this approach in dealing with complex velocity models and can provide a better quality image compared to RTM more efficiently.

  12. Efficient and stable extrapolation of prestack wavefields

    Wu, Zedong; Alkhalifah, Tariq Ali

    2013-01-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers and the image point, or in other words, prestack wavefields. Extrapolating such wavefields in time, nevertheless, is a big challenge because the radicand can be negative, thus reduce to a complex phase velocity, which will make the rank of the mixed domain matrix very high. Using the vertical offset between the sources and receivers, we introduce a method for deriving the DSR formulation, which gives us the opportunity to derive approximations for the mixed domain operator. The method extrapolates prestack wavefields by combining all data into one wave extrapolation procedure, allowing both upgoing and downgoing wavefields since the extrapolation is done in time, and doesn’t have the v(z) assumption in the offset axis of the media. Thus, the imaging condition is imposed by taking the zero-time and zero-offset slice from the multi-dimensional prestack wavefield. Unlike reverse time migration (RTM), no crosscorrelation is needed and we also have access to the subsurface offset information, which is important for migration velocity analysis. Numerical examples show the capability of this approach in dealing with complex velocity models and can provide a better quality image compared to RTM more efficiently.

  13. Optimal overlapping of waveform relaxation method for linear differential equations

    Yamada, Susumu; Ozawa, Kazufumi

    2000-01-01

    Waveform relaxation (WR) method is extremely suitable for solving large systems of ordinary differential equations (ODEs) on parallel computers, but the convergence of the method is generally slow. In order to accelerate the convergence, the methods which decouple the system into many subsystems with overlaps some of the components between the adjacent subsystems have been proposed. The methods, in general, converge much faster than the ones without overlapping, but the computational cost per iteration becomes larger due to the increase of the dimension of each subsystem. In this research, the convergence of the WR method for solving constant coefficients linear ODEs is investigated and the strategy to determine the number of overlapped components which minimizes the cost of the parallel computations is proposed. Numerical experiments on an SR2201 parallel computer show that the estimated number of the overlapped components by the proposed strategy is reasonable. (author)

  14. A Lagrangian meshfree method applied to linear and nonlinear elasticity.

    Walker, Wade A

    2017-01-01

    The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

  15. Exact solution of some linear matrix equations using algebraic methods

    Djaferis, T. E.; Mitter, S. K.

    1977-01-01

    A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

  16. Comparison of equivalent linear and non linear methods on ground response analysis: case study at West Bangka site

    Eko Rudi Iswanto; Eric Yee

    2016-01-01

    Within the framework of identifying NPP sites, site surveys are performed in West Bangka (WB), Bangka-Belitung Island Province. Ground response analysis of a potential site has been carried out using peak strain profiles and peak ground acceleration. The objective of this research is to compare Equivalent Linear (EQL) and Non Linear (NL) methods of ground response analysis on the selected NPP site (West Bangka) using Deep Soil software. Equivalent linear method is widely used because requires soil data in simple way and short time of computational process. On the other hand, non linear method is capable of representing the actual soil behaviour by considering non linear soil parameter. The results showed that EQL method has similar trends to NL method. At surface layer, the acceleration values for EQL and NL methods are resulted as 0.425 g and 0.375 g respectively. NL method is more reliable in capturing higher frequencies of spectral acceleration compared to EQL method. (author)

  17. Linear augmented plane wave method for self-consistent calculations

    Takeda, T.; Kuebler, J.

    1979-01-01

    O.K. Andersen has recently introduced a linear augmented plane wave method (LAPW) for the calculation of electronic structure that was shown to be computationally fast. A more general formulation of an LAPW method is presented here. It makes use of a freely disposable number of eigenfunctions of the radial Schroedinger equation. These eigenfunctions can be selected in a self-consistent way. The present formulation also results in a computationally fast method. It is shown that Andersen's LAPW is obtained in a special limit from the present formulation. Self-consistent test calculations for copper show the present method to be remarkably accurate. As an application, scalar-relativistic self-consistent calculations are presented for the band structure of FCC lanthanum. (author)

  18. A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE

    M. ZANGIABADI; H. R. MALEKI

    2007-01-01

    In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, w...

  19. An improved partial bundle method for linearly constrained minimax problems

    Chunming Tang

    2016-02-01

    Full Text Available In this paper, we propose an improved partial bundle method for solving linearly constrained minimax problems. In order to reduce the number of component function evaluations, we utilize a partial cutting-planes model to substitute for the traditional one. At each iteration, only one quadratic programming subproblem needs to be solved to obtain a new trial point. An improved descent test criterion is introduced to simplify the algorithm. The method produces a sequence of feasible trial points, and ensures that the objective function is monotonically decreasing on the sequence of stability centers. Global convergence of the algorithm is established. Moreover, we utilize the subgradient aggregation strategy to control the size of the bundle and therefore overcome the difficulty of computation and storage. Finally, some preliminary numerical results show that the proposed method is effective.

  20. Electrostatic Discharge Current Linear Approach and Circuit Design Method

    Pavlos K. Katsivelis

    2010-11-01

    Full Text Available The Electrostatic Discharge phenomenon is a great threat to all electronic devices and ICs. An electric charge passing rapidly from a charged body to another can seriously harm the last one. However, there is a lack in a linear mathematical approach which will make it possible to design a circuit capable of producing such a sophisticated current waveform. The commonly accepted Electrostatic Discharge current waveform is the one set by the IEC 61000-4-2. However, the over-simplified circuit included in the same standard is incapable of producing such a waveform. Treating the Electrostatic Discharge current waveform of the IEC 61000-4-2 as reference, an approximation method, based on Prony’s method, is developed and applied in order to obtain a linear system’s response. Considering a known input, a method to design a circuit, able to generate this ESD current waveform in presented. The circuit synthesis assumes ideal active elements. A simulation is carried out using the PSpice software.

  1. Discrete linear canonical transform computation by adaptive method.

    Zhang, Feng; Tao, Ran; Wang, Yue

    2013-07-29

    The linear canonical transform (LCT) describes the effect of quadratic phase systems on a wavefield and generalizes many optical transforms. In this paper, the computation method for the discrete LCT using the adaptive least-mean-square (LMS) algorithm is presented. The computation approaches of the block-based discrete LCT and the stream-based discrete LCT using the LMS algorithm are derived, and the implementation structures of these approaches by the adaptive filter system are considered. The proposed computation approaches have the inherent parallel structures which make them suitable for efficient VLSI implementations, and are robust to the propagation of possible errors in the computation process.

  2. Alternating direction transport sweeps for linear discontinuous SN method

    Yavuz, M.; Aykanat, C.

    1993-01-01

    The performance of Alternating Direction Transport Sweep (ADTS) method is investigated for spatially differenced Linear Discontinuous S N (LD-S N ) problems on a MIMD multicomputer, Intel IPSC/2. The method consists of dividing a transport problem spatially into sub-problems, assigning each sub-problem to a separate processor. Then, the problem is solved by performing transport sweeps iterating on the scattering source and interface fluxes between the sub-problems. In each processor, the order of transport sweeps is scheduled such that a processor completing its computation in a quadrant of a transport sweep is able to use the most recent information (exiting fluxes of neighboring processor) as its incoming fluxes to start the next quadrant calculation. Implementation of this method on the Intel IPSC/2 multicomputer displays significant speedups over the one-processor method. Also, the performance of the method is compared with those reported previously for the Diamond Differenced S N (DD-S N ) method. Our experimental experience illustrates that the parallel performance of both the ADTS LD- and DD-S N methods is the same. (orig.)

  3. Deep Learning Methods for Improved Decoding of Linear Codes

    Nachmani, Eliya; Marciano, Elad; Lugosch, Loren; Gross, Warren J.; Burshtein, David; Be'ery, Yair

    2018-02-01

    The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder, despite the large example space. Similar improvements are obtained for the min-sum algorithm. It is also shown that tying the parameters of the decoders across iterations, so as to form a recurrent neural network architecture, can be implemented with comparable results. The advantage is that significantly less parameters are required. We also introduce a recurrent neural decoder architecture based on the method of successive relaxation. Improvements over standard belief propagation are also observed on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the neural belief propagation decoder can be used to improve the performance, or alternatively reduce the computational complexity, of a close to optimal decoder of short BCH codes.

  4. Linear source approximation scheme for method of characteristics

    Tang Chuntao

    2011-01-01

    Method of characteristics (MOC) for solving neutron transport equation based on unstructured mesh has already become one of the fundamental methods for lattice calculation of nuclear design code system. However, most of MOC codes are developed with flat source approximation called step characteristics (SC) scheme, which is another basic assumption for MOC. A linear source (LS) characteristics scheme and its corresponding modification for negative source distribution were proposed. The OECD/NEA C5G7-MOX 2D benchmark and a self-defined BWR mini-core problem were employed to validate the new LS module of PEACH code. Numerical results indicate that the proposed LS scheme employs less memory and computational time compared with SC scheme at the same accuracy. (authors)

  5. Adaptive discontinuous Galerkin methods for non-linear reactive flows

    Uzunca, Murat

    2016-01-01

    The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way. After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence. As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.

  6. On Richardson extrapolation for low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes

    Havasi, Ágnes; Kazemi, Ehsan

    2018-04-01

    In the modeling of wave propagation phenomena it is necessary to use time integration methods which are not only sufficiently accurate, but also properly describe the amplitude and phase of the propagating waves. It is not clear if amending the developed schemes by extrapolation methods to obtain a high order of accuracy preserves the qualitative properties of these schemes in the perspective of dissipation, dispersion and stability analysis. It is illustrated that the combination of various optimized schemes with Richardson extrapolation is not optimal for minimal dissipation and dispersion errors. Optimized third-order and fourth-order methods are obtained, and it is shown that the proposed methods combined with Richardson extrapolation result in fourth and fifth orders of accuracy correspondingly, while preserving optimality and stability. The numerical applications include the linear wave equation, a stiff system of reaction-diffusion equations and the nonlinear Euler equations with oscillatory initial conditions. It is demonstrated that the extrapolated third-order scheme outperforms the recently developed fourth-order diagonally implicit Runge-Kutta scheme in terms of accuracy and stability.

  7. Non linear permanent magnets modelling with the finite element method

    Chavanne, J.; Meunier, G.; Sabonnadiere, J.C.

    1989-01-01

    In order to perform the calculation of permanent magnets with the finite element method, it is necessary to take into account the anisotropic behaviour of hard magnetic materials (Ferrites, NdFeB, SmCo5). In linear cases, the permeability of permanent magnets is a tensor. This one is fully described with the permeabilities parallel and perpendicular to the easy axis of the magnet. In non linear cases, the model uses a texture function which represents the distribution of the local easy axis of the cristallytes of the magnet. This function allows a good representation of the angular dependance of the coercitive field of the magnet. As a result, it is possible to express the magnetic induction B and the tensor as functions of the field and the texture parameter. This model has been implemented in the software FLUX3D where the tensor is used for the Newton-Raphson procedure. 3D demagnetization of a ferrite magnet by a NdFeB magnet is a suitable representative example. They analyze the results obtained for an ideally oriented ferrite magnet and a real one using a measured texture parameter

  8. Linear Strength Vortex Panel Method for NACA 4412 Airfoil

    Liu, Han

    2018-03-01

    The objective of this article is to formulate numerical models for two-dimensional potential flow over the NACA 4412 Airfoil using linear vortex panel methods. By satisfying the no penetration boundary condition and Kutta condition, the circulation density on each boundary points (end point of every panel) are obtained and according to which, surface pressure distribution and lift coefficients of the airfoil are predicted and validated by Xfoil, an interactive program for the design and analysis of airfoil. The sensitivity of results to the number of panels is also investigated in the end, which shows that the results are sensitive to the number of panels when panel number ranges from 10 to 160. With the increasing panel number (N>160), the results become relatively insensitive to it.

  9. Seismic wave extrapolation using lowrank symbol approximation

    Fomel, Sergey

    2012-04-30

    We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.

  10. Residual extrapolation operators for efficient wavefield construction

    Alkhalifah, Tariq Ali

    2013-02-27

    Solving the wave equation using finite-difference approximations allows for fast extrapolation of the wavefield for modelling, imaging and inversion in complex media. It, however, suffers from dispersion and stability-related limitations that might hamper its efficient or proper application to high frequencies. Spectral-based time extrapolation methods tend to mitigate these problems, but at an additional cost to the extrapolation. I investigate the prospective of using a residual formulation of the spectral approach, along with utilizing Shanks transform-based expansions, that adheres to the residual requirements, to improve accuracy and reduce the cost. Utilizing the fact that spectral methods excel (time steps are allowed to be large) in homogeneous and smooth media, the residual implementation based on velocity perturbation optimizes the use of this feature. Most of the other implementations based on the spectral approach are focussed on reducing cost by reducing the number of inverse Fourier transforms required in every step of the spectral-based implementation. The approach here fixes that by improving the accuracy of each, potentially longer, time step.

  11. The ATLAS Track Extrapolation Package

    Salzburger, A

    2007-01-01

    The extrapolation of track parameters and their associated covariances to destination surfaces of different types is a very frequent process in the event reconstruction of high energy physics experiments. This is amongst other reasons due to the fact that most track and vertex fitting techniques are based on the first and second momentum of the underlying probability density distribution. The correct stochastic or deterministic treatment of interactions with the traversed detector material is hereby crucial for high quality track reconstruction throughout the entire momentum range of final state particles that are produced in high energy physics collision experiments. This document presents the main concepts, the algorithms and the implementation of the newly developed, powerful ATLAS track extrapolation engine. It also emphasises on validation procedures, timing measurements and the integration into the ATLAS offline reconstruction software.

  12. UFOs: Observations, Studies and Extrapolations

    Baer, T; Barnes, M J; Bartmann, W; Bracco, C; Carlier, E; Cerutti, F; Dehning, B; Ducimetière, L; Ferrari, A; Ferro-Luzzi, M; Garrel, N; Gerardin, A; Goddard, B; Holzer, E B; Jackson, S; Jimenez, J M; Kain, V; Zimmermann, F; Lechner, A; Mertens, V; Misiowiec, M; Nebot Del Busto, E; Morón Ballester, R; Norderhaug Drosdal, L; Nordt, A; Papotti, G; Redaelli, S; Uythoven, J; Velghe, B; Vlachoudis, V; Wenninger, J; Zamantzas, C; Zerlauth, M; Fuster Martinez, N

    2012-01-01

    UFOs (“ Unidentified Falling Objects”) could be one of the major performance limitations for nominal LHC operation. Therefore, in 2011, the diagnostics for UFO events were significantly improved, dedicated experiments and measurements in the LHC and in the laboratory were made and complemented by FLUKA simulations and theoretical studies. The state of knowledge is summarized and extrapolations for LHC operation in 2012 and beyond are presented. Mitigation strategies are proposed and related tests and measures for 2012 are specified.

  13. Effective orthorhombic anisotropic models for wavefield extrapolation

    Ibanez-Jacome, W.

    2014-07-18

    Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models to reproduce wave propagation phenomena in the Earth\\'s subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, we generate effective isotropic inhomogeneous models that are capable of reproducing the firstarrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, we develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic ones, is represented by a sixth order polynomial equation with the fastest solution corresponding to outgoing P waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, and using them to explicitly evaluate the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. We extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the more expensive anisotropic extrapolator.

  14. Effective orthorhombic anisotropic models for wavefield extrapolation

    Ibanez-Jacome, W.; Alkhalifah, Tariq Ali; Waheed, Umair bin

    2014-01-01

    Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models to reproduce wave propagation phenomena in the Earth's subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, we generate effective isotropic inhomogeneous models that are capable of reproducing the firstarrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, we develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic ones, is represented by a sixth order polynomial equation with the fastest solution corresponding to outgoing P waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, and using them to explicitly evaluate the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. We extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the more expensive anisotropic extrapolator.

  15. Irradiated food: validity of extrapolating wholesomeness data

    Taub, I.A.; Angelini, P.; Merritt, C. Jr.

    1976-01-01

    Criteria are considered for validly extrapolating the conclusions reached on the wholesomeness of an irradiated food receiving high doses to the same food receiving a lower dose. A consideration first is made of the possible chemical mechanisms that could give rise to different functional dependences of radiolytic products on dose. It is shown that such products should increase linearly with dose and the ratio of products should be constant throughout the dose range considered. The assumption, generally accepted in pharmacology, then is made that if any adverse effects related to the food are discerned in the test animals, then the intensity of these effects would increase with the concentration of radiolytic products in the food. Lastly, the need to compare data from animal studies with foods irradiated to several doses against chemical evidence obtained over a comparable dose range is considered. It is concluded that if the products depend linearly on dose and if feeding studies indicate no adverse effects, then an extrapolation to lower doses is clearly valid. This approach is illustrated for irradiated codfish. The formation of selected volatile products in samples receiving between 0.1 and 3 Mrads was examined, and their concentrations were found to increase linearly at least up to 1 Mrad. These data were compared with results from animal feeding studies establishing the wholesomeness of codfish and haddock irradiated to 0.2, 0.6 and 2.8 Mrads. It is stated, therefore, that if ocean fish, currently under consideration for onboard processing, were irradiated to 0.1 Mrad, it would be correspondingly wholesome

  16. Lithographic linear motor, lithographic apparatus, and device manufacturing method

    2006-01-01

    A linear motor having a high driving force, high efficiency and low normal force comprises two opposed magnet tracks and an armature comprising three open coil sets. The linear motor may be used to drive a stage, such as, for example, a mask or wafer stage, in a lithographic apparatus.

  17. Mathematical and Numerical Methods for Non-linear Beam Dynamics

    Herr, W

    2014-01-01

    Non-linear effects in accelerator physics are important for both successful operation of accelerators and during the design stage. Since both of these aspects are closely related, they will be treated together in this overview. Some of the most important aspects are well described by methods established in other areas of physics and mathematics. The treatment will be focused on the problems in accelerators used for particle physics experiments. Although the main emphasis will be on accelerator physics issues, some of the aspects of more general interest will be discussed. In particular, we demonstrate that in recent years a framework has been built to handle the complex problems in a consistent form, technically superior and conceptually simpler than the traditional techniques. The need to understand the stability of particle beams has substantially contributed to the development of new techniques and is an important source of examples which can be verified experimentally. Unfortunately, the documentation of these developments is often poor or even unpublished, in many cases only available as lectures or conference proceedings

  18. Linearized versus non-linear inverse methods for seismic localization of underground sources

    Oh, Geok Lian; Jacobsen, Finn

    2013-01-01

    The problem of localization of underground sources from seismic measurements detected by several geophones located on the ground surface is addressed. Two main approaches to the solution of the problem are considered: a beamforming approach that is derived from the linearized inversion problem, a...

  19. Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

    Ho, Yuh-Shan

    2006-01-01

    A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

  20. Extension of the linear nodal method to large concrete building calculations

    Childs, R.L.; Rhoades, W.A.

    1985-01-01

    The implementation of the linear nodal method in the TORT code is described, and the results of a mesh refinement study to test the effectiveness of the linear nodal and weighted diamond difference methods available in TORT are presented

  1. Method and apparatus of highly linear optical modulation

    DeRose, Christopher; Watts, Michael R.

    2016-05-03

    In a new optical intensity modulator, a nonlinear change in refractive index is used to balance the nonlinearities in the optical transfer function in a way that leads to highly linear optical intensity modulation.

  2. A Cost-effective Method for Resolution Increase of the Twostage Piecewise Linear ADC Used for Sensor Linearization

    Jovanović Jelena

    2016-02-01

    Full Text Available A cost-effective method for resolution increase of a two-stage piecewise linear analog-to-digital converter used for sensor linearization is proposed in this paper. In both conversion stages flash analog-to-digital converters are employed. Resolution increase by one bit per conversion stage is performed by introducing one additional comparator in front of each of two flash analog-to-digital converters, while the converters’ resolutions remain the same. As a result, the number of employed comparators, as well as the circuit complexity and the power consumption originating from employed comparators are for almost 50 % lower in comparison to the same parameters referring to the linearization circuit of the conventional design and of the same resolution. Since the number of employed comparators is significantly reduced according to the proposed method, special modifications of the linearization circuit are needed in order to properly adjust reference voltages of employed comparators.

  3. Extrapolating Satellite Winds to Turbine Operating Heights

    Badger, Merete; Pena Diaz, Alfredo; Hahmann, Andrea N.

    2016-01-01

    Ocean wind retrievals from satellite sensors are typically performed for the standard level of 10 m. This restricts their full exploitation for wind energy planning, which requires wind information at much higher levels where wind turbines operate. A new method is presented for the vertical...... extrapolation of satellitebased wind maps. Winds near the sea surface are obtained from satellite data and used together with an adaptation of the Monin–Obukhov similarity theory to estimate the wind speed at higher levels. The thermal stratification of the atmosphere is taken into account through a long...

  4. Lowrank seismic-wave extrapolation on a staggered grid

    Fang, Gang; Fomel, Sergey; Du, Qizhen; Hu, Jingwei

    2014-01-01

    © 2014 Society of Exploration Geophysicists. We evaluated a new spectral method and a new finite-difference (FD) method for seismic-wave extrapolation in time. Using staggered temporal and spatial grids, we derived a wave-extrapolation operator using a lowrank decomposition for a first-order system of wave equations and designed the corresponding FD scheme. The proposed methods extend previously proposed lowrank and lowrank FD wave extrapolation methods from the cases of constant density to those of variable density. Dispersion analysis demonstrated that the proposed methods have high accuracy for a wide wavenumber range and significantly reduce the numerical dispersion. The method of manufactured solutions coupled with mesh refinement was used to verify each method and to compare numerical errors. Tests on 2D synthetic examples demonstrated that the proposed method is highly accurate and stable. The proposed methods can be used for seismic modeling or reverse-time migration.

  5. Lowrank seismic-wave extrapolation on a staggered grid

    Fang, Gang

    2014-05-01

    © 2014 Society of Exploration Geophysicists. We evaluated a new spectral method and a new finite-difference (FD) method for seismic-wave extrapolation in time. Using staggered temporal and spatial grids, we derived a wave-extrapolation operator using a lowrank decomposition for a first-order system of wave equations and designed the corresponding FD scheme. The proposed methods extend previously proposed lowrank and lowrank FD wave extrapolation methods from the cases of constant density to those of variable density. Dispersion analysis demonstrated that the proposed methods have high accuracy for a wide wavenumber range and significantly reduce the numerical dispersion. The method of manufactured solutions coupled with mesh refinement was used to verify each method and to compare numerical errors. Tests on 2D synthetic examples demonstrated that the proposed method is highly accurate and stable. The proposed methods can be used for seismic modeling or reverse-time migration.

  6. Algebraic coarsening methods for linear and nonlinear PDE and systems

    McWilliams, J C

    2000-01-01

    In [l] Brandt describes a general approach for algebraic coarsening. Given fine-grid equations and a prescribed relaxation method, an approach is presented for defining both the coarse-grid variables and the coarse-grid equations corresponding to these variables. Although, these two tasks are not necessarily related (and, indeed, are often performed independently and with distinct techniques) in the approaches of [1] both revolve around the same underlying observation. To determine whether a given set of coarse-grid variables is appropriate it is suggested that one should employ compatible relaxation. This is a generalization of so-called F-relaxation (e.g., [2]). Suppose that the coarse-grid variables are defined as a subset of the fine-grid variables. Then, F-relaxation simply means relaxing only the F-variables (i.e., fine-grid variables that do not correspond to coarse-grid variables), while leaving the remaining fine-grid variables (C-variables) unchanged. The generalization of compatible relaxation is in allowing the coarse-grid variables to be defined differently, say as linear combinations of fine-grid variables, or even nondeterministically (see examples in [1]). For the present summary it suffices to consider the simple case. The central observation regarding the set of coarse-grid variables is the following [1]: Observation 1--A general measure for the quality of the set of coarse-grid variables is the convergence rate of compatible relaxation. The conclusion is that a necessary condition for efficient multigrid solution (e.g., with convergence rates independent of problem size) is that the compatible-relaxation convergence be bounded away from 1, independently of the number of variables. This is often a sufficient condition, provided that the coarse-grid equations are sufficiently accurate. Therefore, it is suggested in [1] that the convergence rate of compatible relaxation should be used as a criterion for choosing and evaluating the set of coarse

  7. Functional differential equations with unbounded delay in extrapolation spaces

    Mostafa Adimy

    2014-08-01

    Full Text Available We study the existence, regularity and stability of solutions for nonlinear partial neutral functional differential equations with unbounded delay and a Hille-Yosida operator on a Banach space X. We consider two nonlinear perturbations: the first one is a function taking its values in X and the second one is a function belonging to a space larger than X, an extrapolated space. We use the extrapolation techniques to prove the existence and regularity of solutions and we establish a linearization principle for the stability of the equilibria of our equation.

  8. An implementation analysis of the linear discontinuous finite element method

    Becker, T. L.

    2013-01-01

    This paper provides an implementation analysis of the linear discontinuous finite element method (LD-FEM) that spans the space of (l, x, y, z). A practical implementation of LD includes 1) selecting a computationally efficient algorithm to solve the 4 x 4 matrix system Ax = b that describes the angular flux in a mesh element, and 2) choosing how to store the data used to construct the matrix A and the vector b to either reduce memory consumption or increase computational speed. To analyze the first of these, three algorithms were selected to solve the 4 x 4 matrix equation: Cramer's rule, a streamlined implementation of Gaussian elimination, and LAPACK's Gaussian elimination subroutine dgesv. The results indicate that Cramer's rule and the streamlined Gaussian elimination algorithm perform nearly equivalently and outperform LAPACK's implementation of Gaussian elimination by a factor of 2. To analyze the second implementation detail, three formulations of the discretized LD-FEM equations were provided for implementation in a transport solver: 1) a low-memory formulation, which relies heavily on 'on-the-fly' calculations and less on the storage of pre-computed data, 2) a high-memory formulation, which pre-computes much of the data used to construct A and b, and 3) a reduced-memory formulation, which lies between the low - and high-memory formulations. These three formulations were assessed in the Jaguar transport solver based on relative memory footprint and computational speed for increasing mesh size and quadrature order. The results indicated that the memory savings of the low-memory formulation were not sufficient to warrant its implementation. The high-memory formulation resulted in a significant speed advantage over the reduced-memory option (10-50%), but also resulted in a proportional increase in memory consumption (5-45%) for increasing quadrature order and mesh count; therefore, the practitioner should weigh the system memory constraints against any

  9. An implementation analysis of the linear discontinuous finite element method

    Becker, T. L. [Bechtel Marine Propulsion Corporation, Knolls Atomic Power Laboratory, P.O. Box 1072, Schenectady, NY 12301-1072 (United States)

    2013-07-01

    This paper provides an implementation analysis of the linear discontinuous finite element method (LD-FEM) that spans the space of (l, x, y, z). A practical implementation of LD includes 1) selecting a computationally efficient algorithm to solve the 4 x 4 matrix system Ax = b that describes the angular flux in a mesh element, and 2) choosing how to store the data used to construct the matrix A and the vector b to either reduce memory consumption or increase computational speed. To analyze the first of these, three algorithms were selected to solve the 4 x 4 matrix equation: Cramer's rule, a streamlined implementation of Gaussian elimination, and LAPACK's Gaussian elimination subroutine dgesv. The results indicate that Cramer's rule and the streamlined Gaussian elimination algorithm perform nearly equivalently and outperform LAPACK's implementation of Gaussian elimination by a factor of 2. To analyze the second implementation detail, three formulations of the discretized LD-FEM equations were provided for implementation in a transport solver: 1) a low-memory formulation, which relies heavily on 'on-the-fly' calculations and less on the storage of pre-computed data, 2) a high-memory formulation, which pre-computes much of the data used to construct A and b, and 3) a reduced-memory formulation, which lies between the low - and high-memory formulations. These three formulations were assessed in the Jaguar transport solver based on relative memory footprint and computational speed for increasing mesh size and quadrature order. The results indicated that the memory savings of the low-memory formulation were not sufficient to warrant its implementation. The high-memory formulation resulted in a significant speed advantage over the reduced-memory option (10-50%), but also resulted in a proportional increase in memory consumption (5-45%) for increasing quadrature order and mesh count; therefore, the practitioner should weigh the system memory

  10. Proposal of Realization Restricted Quantum Game with Linear Optic Method

    Zhao Haijun; Fang Ximing

    2006-01-01

    We present a quantum game with the restricted strategic space and its realization with linear optical system, which can be played by two players who are separated remotely. This game can also be realized on any other quantum computers. We find that the constraint brings some interesting properties that are useful for making game models.

  11. Improved Methods for Pitch Synchronous Linear Prediction Analysis of Speech

    劉, 麗清

    2015-01-01

    Linear prediction (LP) analysis has been applied to speech system over the last few decades. LP technique is well-suited for speech analysis due to its ability to model speech production process approximately. Hence LP analysis has been widely used for speech enhancement, low-bit-rate speech coding in cellular telephony, speech recognition, characteristic parameter extraction (vocal tract resonances frequencies, fundamental frequency called pitch) and so on. However, the performance of the co...

  12. A general method for enclosing solutions of interval linear equations

    Rohn, Jiří

    2012-01-01

    Roč. 6, č. 4 (2012), s. 709-717 ISSN 1862-4472 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * enclosure * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 1.654, year: 2012

  13. Locally linear approximation for Kernel methods : the Railway Kernel

    Muñoz, Alberto; González, Javier

    2008-01-01

    In this paper we present a new kernel, the Railway Kernel, that works properly for general (nonlinear) classification problems, with the interesting property that acts locally as a linear kernel. In this way, we avoid potential problems due to the use of a general purpose kernel, like the RBF kernel, as the high dimension of the induced feature space. As a consequence, following our methodology the number of support vectors is much lower and, therefore, the generalization capab...

  14. Second derivative continuous linear multistep methods for the ...

    step methods (LMM), with properties that embed the characteristics of LMM and hybrid methods. This paper gives a continuous reformulation of the Enright [5] second derivative methods. The motivation lies in the fact that the new formulation ...

  15. A novel evaluation method for extrapolated retention factor in determination of n-octanol/water partition coefficient of halogenated organic pollutants by reversed-phase high performance liquid chromatography.

    Han, Shu-ying; Liang, Chao; Qiao, Jun-qin; Lian, Hong-zhen; Ge, Xin; Chen, Hong-yuan

    2012-02-03

    The retention factor corresponding to pure water in reversed-phase high performance liquid chromatography (RP-HPLC), k(w), was commonly obtained by extrapolation of retention factor (k) in a mixture of organic modifier and water as mobile phase in tedious experiments. In this paper, a relationship between logk(w) and logk for directly determining k(w) has been proposed for the first time. With a satisfactory validation, the approach was confirmed to enable easy and accurate evaluation of k(w) for compounds in question with similar structure to model compounds. Eight PCB congeners with different degree of chlorination were selected as a training set for modeling the logk(w)-logk correlation on both silica-based C(8) and C(18) stationary phases to evaluate logk(w) of sample compounds including seven PCB, six PBB and eight PBDE congeners. These eight model PCBs were subsequently combined with seven structure-similar benzene derivatives possessing reliable experimental K(ow) values as a whole training set for logK(ow)-logk(w) regressions on the two stationary phases. Consequently, the evaluated logk(w) values of sample compounds were used to determine their logK(ow) by the derived logK(ow)-logk(w) models. The logK(ow) values obtained by these evaluated logk(w) were well comparable with those obtained by experimental-extrapolated logk(w), demonstrating that the proposed method for logk(w) evaluation in this present study could be an effective means in lipophilicity study of environmental contaminants with numerous congeners. As a result, logK(ow) data of many PCBs, PBBs and PBDEs could be offered. These contaminants are considered to widely exist in the environment, but there have been no reliable experimental K(ow) data available yet. Copyright © 2011 Elsevier B.V. All rights reserved.

  16. SU-F-T-579: Extrapolation Techniques for Small Field Dosimetry Using Gafchromic EBT3 Film

    Morales, J [Chris OBrien Lifehouse, Camperdown, NSW (Australia)

    2016-06-15

    Purpose: The purpose of this project is to test an experimental approach using an extrapolation technique for Gafchromic EBT3 film for small field x-ray dosimetry. Methods: Small fields from a Novalis Tx linear accelerator with HD Multileaf Collimators with 6 MV was used. The field sizes ranged from 5 × 5 to 50 × 50 mm2 MLC fields and a range of circular cones of 4 to 30 mm2 diameters. All measurements were performed in water at an SSD of 100 cm and at a depth of 10 cm. The relative output factors (ROFs) were determined from an extrapolation technique developed to eliminate the effects of partial volume averaging in film scan by scanning films with high resolution (1200 DPI). The size of the regions of interest (ROI) was varied to produce a plot of ROFs versus ROI which was then extrapolated to zero ROI to determine the relative output factor. The results were compared with other solid state detectors with proper correction, namely, IBA SFD diode, PTW 60008 and PTW 60012 diode. Results: For the 4 mm cone, the extrapolated ROF had a value of 0.658 ± 0.014 as compared to 0.642 and 0.636 for 0.5 mm and 1 mm2 ROI analysis, respectively. This showed a change in output factor of 2.4% and 3.3% at this comparative ROI sizes. In comparison, the 25 mm cone had a difference in measured output factor of 0.3% and 0.5% between 0.5 and 1.0 mm, respectively compared to zero volume. For the fields defined by MLCs a difference of up to 2% for 5×5 mm2 was observed. Conclusion: A measureable difference can be seen in ROF based on the ROI when radiochromic film is used. Using extrapolation technique from high resolution scanning a good agreement can be achieved.

  17. The magnetic field of active region 11158 during the 2011 February 12-17 flares: Differences between photospheric extrapolation and coronal forward-fitting methods

    Aschwanden, Markus J.; Sun, Xudong; Liu, Yang

    2014-01-01

    We developed a coronal nonlinear force-free field (COR-NLFFF) forward-fitting code that fits an approximate nonlinear force-free field (NLFFF) solution to the observed geometry of automatically traced coronal loops. In contrast to photospheric NLFFF codes, which calculate a magnetic field solution from the constraints of the transverse photospheric field, this new code uses coronal constraints instead, and this way provides important information on systematic errors of each magnetic field calculation method, as well as on the non-force-freeness in the lower chromosphere. In this study we applied the COR-NLFFF code to NOAA Active Region 11158, during the time interval of 2011 February 12-17, which includes an X2.2 GOES-class flare plus 35 M- and C-class flares. We calculated the free magnetic energy with a 6 minute cadence over 5 days. We find good agreement between the two types of codes for the total nonpotential E N and potential energy E P but find up to a factor of 4 discrepancy in the free energy E free = E N – E P and up to a factor of 10 discrepancy in the decrease of the free energy ΔE free during flares. The coronal NLFFF code exhibits a larger time variability and yields a decrease of free energy during the flare that is sufficient to satisfy the flare energy budget, while the photospheric NLFFF code shows much less time variability and an order of magnitude less free-energy decrease during flares. The discrepancy may partly be due to the preprocessing of photospheric vector data but more likely is due to the non-force-freeness in the lower chromosphere. We conclude that the coronal field cannot be correctly calculated on the basis of photospheric data alone and requires additional information on coronal loop geometries.

  18. Leapfrog variants of iterative methods for linear algebra equations

    Saylor, Paul E.

    1988-01-01

    Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial approximation, a variant of the iteration called the grand-leap method. In the case of the grand-leap variant, a set of parameters is required. An algorithm is presented to compute these parameters that is related to algorithms to compute the weights and abscissas for Gaussian quadrature. General algorithms to implement the leapfrog and grand-leap methods are presented. Algorithms for the important special case of the Chebyshev method are also given.

  19. Generalized linear mixed models modern concepts, methods and applications

    Stroup, Walter W

    2012-01-01

    PART I The Big PictureModeling BasicsWhat Is a Model?Two Model Forms: Model Equation and Probability DistributionTypes of Model EffectsWriting Models in Matrix FormSummary: Essential Elements for a Complete Statement of the ModelDesign MattersIntroductory Ideas for Translating Design and Objectives into ModelsDescribing ""Data Architecture"" to Facilitate Model SpecificationFrom Plot Plan to Linear PredictorDistribution MattersMore Complex Example: Multiple Factors with Different Units of ReplicationSetting the StageGoals for Inference with Models: OverviewBasic Tools of InferenceIssue I: Data

  20. Free magnetic energy and relative magnetic helicity diagnostics for the quality of NLFF field extrapolations

    Moraitis, Kostas; Archontis, Vasilis; Tziotziou, Konstantinos; Georgoulis, Manolis K.

    We calculate the instantaneous free magnetic energy and relative magnetic helicity of solar active regions using two independent approaches: a) a non-linear force-free (NLFF) method that requires only a single photospheric vector magnetogram, and b) well known semi-analytical formulas that require the full three-dimensional (3D) magnetic field structure. The 3D field is obtained either from MHD simulations, or from observed magnetograms via respective NLFF field extrapolations. We find qualitative agreement between the two methods and, quantitatively, a discrepancy not exceeding a factor of 4. The comparison of the two methods reveals, as a byproduct, two independent tests for the quality of a given force-free field extrapolation. We find that not all extrapolations manage to achieve the force-free condition in a valid, divergence-free, magnetic configuration. This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: Thales. Investing in knowledge society through the European Social Fund.

  1. Flavor extrapolation in lattice QCD

    Duffy, W.C.

    1984-01-01

    Explicit calculation of the effect of virtual quark-antiquark pairs in lattice QCD has eluded researchers. To include their effect explicitly one must calculate the determinant of the fermion-fermion coupling matrix. Owing to the large number of sites in a continuum limit size lattice, direct evaluation of this term requires an unrealistic amount of computer time. The effect of the virtual pairs can be approximated by ignoring this term and adjusting lattice couplings to reproduce experimental results. This procedure is called the valence approximation since it ignores all but the minimal number of quarks needed to describe hadrons. In this work the effect of the quark-antiquark pairs has been incorporated in a theory with an effective negative number of quark flavors contributing to the closed loops. Various particle masses and decay constants have been calculated for this theory and for one with no virtual pairs. The author attempts to extrapolate results towards positive numbers of quark flavors. The results show approximate agreement with experimental measurements and demonstrate the smoothness of lattice expectations in the number of quark flavors

  2. One testing method of dynamic linearity of an accelerometer

    Lei Jing-Yu

    2015-01-01

    Full Text Available To effectively test dynamic linearity of an accelerometer over a wide rang of 104 g to about 20 × 104g, one published patent technology is first experimentally verified and analysed, and its deficient is presented, then based on stress wave propagation theory on the thin long bar, the relation between the strain signal and the corresponding acceleration signal is obtained, one special link of two coaxial projectile is developed. These two coaxial metal cylinders (inner cylinder and circular tube are used as projectiles, to prevent their mutual slip inside the gun barrel during movement, the one end of two projectiles is always fastened by small screws. Ti6-AL4-V bar with diameter of 30 mm is used to propagate loading stress pulse. The resultant compression wave can be measured by the strain gauges on the bar, and a half –sine strain pulse is obtained. The measuring accelerometer is attached on the other end of the bar by a vacuum clamp. In this clamp, the accelerometer only bear compression wave, the reflected tension pulse make the accelerometer off the bar. Using this system, dynamic linearity measurement of accelerometer can be easily tested in wider range of acceleration values. And a really measuring results are presented.

  3. Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems

    Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)

    1996-12-31

    A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.

  4. A simple finite element method for linear hyperbolic problems

    Mu, Lin; Ye, Xiu

    2017-01-01

    Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

  5. Linear and kernel methods for multi- and hypervariate change detection

    Nielsen, Allan Aasbjerg; Canty, Morton J.

    2010-01-01

    . Principal component analysis (PCA) as well as maximum autocorrelation factor (MAF) and minimum noise fraction (MNF) analyses of IR-MAD images, both linear and kernel-based (which are nonlinear), may further enhance change signals relative to no-change background. The kernel versions are based on a dual...... formulation, also termed Q-mode analysis, in which the data enter into the analysis via inner products in the Gram matrix only. In the kernel version the inner products of the original data are replaced by inner products between nonlinear mappings into higher dimensional feature space. Via kernel substitution......, also known as the kernel trick, these inner products between the mappings are in turn replaced by a kernel function and all quantities needed in the analysis are expressed in terms of the kernel function. This means that we need not know the nonlinear mappings explicitly. Kernel principal component...

  6. Linear and kernel methods for multivariate change detection

    Canty, Morton J.; Nielsen, Allan Aasbjerg

    2012-01-01

    ), as well as maximum autocorrelation factor (MAF) and minimum noise fraction (MNF) analyses of IR-MAD images, both linear and kernel-based (nonlinear), may further enhance change signals relative to no-change background. IDL (Interactive Data Language) implementations of IR-MAD, automatic radiometric...... normalization, and kernel PCA/MAF/MNF transformations are presented that function as transparent and fully integrated extensions of the ENVI remote sensing image analysis environment. The train/test approach to kernel PCA is evaluated against a Hebbian learning procedure. Matlab code is also available...... that allows fast data exploration and experimentation with smaller datasets. New, multiresolution versions of IR-MAD that accelerate convergence and that further reduce no-change background noise are introduced. Computationally expensive matrix diagonalization and kernel image projections are programmed...

  7. On some properties of the block linear multi-step methods | Chollom ...

    The convergence, stability and order of Block linear Multistep methods have been determined in the past based on individual members of the block. In this paper, methods are proposed to examine the properties of the entire block. Some Block Linear Multistep methods have been considered, their convergence, stability and ...

  8. Krylov subspace methods for solving large unsymmetric linear systems

    Saad, Y.

    1981-01-01

    Some algorithms based upon a projection process onto the Krylov subspace K/sub m/ = Span(r 0 , Ar 0 ,...,A/sup m/-1r 0 ) are developed, generalizing the method of conjugate gradients to unsymmetric systems. These methods are extensions of Arnoldi's algorithm for solving eigenvalue problems. The convergence is analyzed in terms of the distance of the solution to the subspace K/sub m/ and some error bounds are established showing, in particular, a similarity with the conjugate gradient method (for symmetric matrices) when the eigenvalues are real. Several numerical experiments are described and discussed

  9. Method for validating radiobiological samples using a linear accelerator

    Brengues, Muriel; Liu, David; Korn, Ronald; Zenhausern, Frederic

    2014-01-01

    There is an immediate need for rapid triage of the population in case of a large scale exposure to ionizing radiation. Knowing the dose absorbed by the body will allow clinicians to administer medical treatment for the best chance of recovery for the victim. In addition, today's radiotherapy treatment could benefit from additional information regarding the patient's sensitivity to radiation before starting the treatment. As of today, there is no system in place to respond to this demand. This paper will describe specific procedures to mimic the effects of human exposure to ionizing radiation creating the tools for optimization of administered radiation dosimetry for radiotherapy and/or to estimate the doses of radiation received accidentally during a radiation event that could pose a danger to the public. In order to obtain irradiated biological samples to study ionizing radiation absorbed by the body, we performed ex-vivo irradiation of human blood samples using the linear accelerator (LINAC). The LINAC was implemented and calibrated for irradiating human whole blood samples. To test the calibration, a 2 Gy test run was successfully performed on a tube filled with water with an accuracy of 3% in dose distribution. To validate our technique the blood samples were ex-vivo irradiated and the results were analyzed using a gene expression assay to follow the effect of the ionizing irradiation by characterizing dose responsive biomarkers from radiobiological assays. The response of 5 genes was monitored resulting in expression increase with the dose of radiation received. The blood samples treated with the LINAC can provide effective irradiated blood samples suitable for molecular profiling to validate radiobiological measurements via the gene-expression based biodosimetry tools. (orig.)

  10. Method for validating radiobiological samples using a linear accelerator.

    Brengues, Muriel; Liu, David; Korn, Ronald; Zenhausern, Frederic

    2014-04-29

    There is an immediate need for rapid triage of the population in case of a large scale exposure to ionizing radiation. Knowing the dose absorbed by the body will allow clinicians to administer medical treatment for the best chance of recovery for the victim. In addition, today's radiotherapy treatment could benefit from additional information regarding the patient's sensitivity to radiation before starting the treatment. As of today, there is no system in place to respond to this demand. This paper will describe specific procedures to mimic the effects of human exposure to ionizing radiation creating the tools for optimization of administered radiation dosimetry for radiotherapy and/or to estimate the doses of radiation received accidentally during a radiation event that could pose a danger to the public. In order to obtain irradiated biological samples to study ionizing radiation absorbed by the body, we performed ex-vivo irradiation of human blood samples using the linear accelerator (LINAC). The LINAC was implemented and calibrated for irradiating human whole blood samples. To test the calibration, a 2 Gy test run was successfully performed on a tube filled with water with an accuracy of 3% in dose distribution. To validate our technique the blood samples were ex-vivo irradiated and the results were analyzed using a gene expression assay to follow the effect of the ionizing irradiation by characterizing dose responsive biomarkers from radiobiological assays. The response of 5 genes was monitored resulting in expression increase with the dose of radiation received. The blood samples treated with the LINAC can provide effective irradiated blood samples suitable for molecular profiling to validate radiobiological measurements via the gene-expression based biodosimetry tools.

  11. Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model

    Oluwaseun Egbelowo

    2017-05-01

    Full Text Available We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK models are commonly used to predict drug concentrations that drive controlled intravenous (I.V. transfers (or infusion and oral transfers while pharmacokinetic and pharmacodynamic (PD interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.

  12. Interpolation from Grid Lines: Linear, Transfinite and Weighted Method

    Lindberg, Anne-Sofie Wessel; Jørgensen, Thomas Martini; Dahl, Vedrana Andersen

    2017-01-01

    When two sets of line scans are acquired orthogonal to each other, intensity values are known along the lines of a grid. To view these values as an image, intensities need to be interpolated at regularly spaced pixel positions. In this paper we evaluate three methods for interpolation from grid l...

  13. Huffman and linear scanning methods with statistical language models.

    Roark, Brian; Fried-Oken, Melanie; Gibbons, Chris

    2015-03-01

    Current scanning access methods for text generation in AAC devices are limited to relatively few options, most notably row/column variations within a matrix. We present Huffman scanning, a new method for applying statistical language models to binary-switch, static-grid typing AAC interfaces, and compare it to other scanning options under a variety of conditions. We present results for 16 adults without disabilities and one 36-year-old man with locked-in syndrome who presents with complex communication needs and uses AAC scanning devices for writing. Huffman scanning with a statistical language model yielded significant typing speedups for the 16 participants without disabilities versus any of the other methods tested, including two row/column scanning methods. A similar pattern of results was found with the individual with locked-in syndrome. Interestingly, faster typing speeds were obtained with Huffman scanning using a more leisurely scan rate than relatively fast individually calibrated scan rates. Overall, the results reported here demonstrate great promise for the usability of Huffman scanning as a faster alternative to row/column scanning.

  14. Construction of extended exponential general linear methods 524 ...

    This paper introduces a new approach for constructing higher order of EEGLM which have become very popular and novel due to its enviable stability properties. This paper also shows that methods 524 is stable with its characteristics root lies in a unit circle. Numerical experiments indicate that Extended Exponential ...

  15. A fast method for linear waves based on geometrical optics

    Stolk, C.C.

    2009-01-01

    We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the

  16. Numerical method for solving linear Fredholm fuzzy integral equations of the second kind

    Abbasbandy, S. [Department of Mathematics, Imam Khomeini International University, P.O. Box 288, Ghazvin 34194 (Iran, Islamic Republic of)]. E-mail: saeid@abbasbandy.com; Babolian, E. [Faculty of Mathematical Sciences and Computer Engineering, Teacher Training University, Tehran 15618 (Iran, Islamic Republic of); Alavi, M. [Department of Mathematics, Arak Branch, Islamic Azad University, Arak 38135 (Iran, Islamic Republic of)

    2007-01-15

    In this paper we use parametric form of fuzzy number and convert a linear fuzzy Fredholm integral equation to two linear system of integral equation of the second kind in crisp case. We can use one of the numerical method such as Nystrom and find the approximation solution of the system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equations of the second kind. The proposed method is illustrated by solving some numerical examples.

  17. The intelligence of dual simplex method to solve linear fractional fuzzy transportation problem.

    Narayanamoorthy, S; Kalyani, S

    2015-01-01

    An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

  18. The Intelligence of Dual Simplex Method to Solve Linear Fractional Fuzzy Transportation Problem

    S. Narayanamoorthy

    2015-01-01

    Full Text Available An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

  19. Linear electron accelerator body and method of its manufacture

    Landa, V.; Maresova, V.; Lucek, J.; Prusa, F.

    1988-01-01

    The accelerator body consists of a hollow casing made of a high electric conductivity metal. The inside is partitioned with a system of resonators. The resonator body is made of one piece of the same metal as the casing or a related one (e.g., copper -coper, silver-copper, copper-copper alloy). The accelerator body is manufactured using the cathodic process on the periphery of a system of metal partitions and negative models of resonator cavities fitted to a metal pin. The pin is then removed from the system and the soluble models of the cavities are dissolved in a solvent. The advantage of the design and the method of manufacture is that the result is a compact, perfectly tight body with a perfectly lustre surface. The casing wall can be very thin, which improves accelerator performance. The claimed method can also be used in manufacturing miniature accelerators. (E.J.). 1 fig

  20. Non-linear methods for the quantification of cyclic motion

    Quintana Duque, Juan Carlos

    2016-01-01

    Traditional methods of human motion analysis assume that fluctuations in cycles (e.g. gait motion) and repetitions (e.g. tennis shots) arise solely from noise. However, the fluctuations may have enough information to describe the properties of motion. Recently, the fluctuations in motion have been analysed based on the concepts of variability and stability, but they are not used uniformly. On the one hand, these concepts are often mixed in the existing literature, while on the other hand, the...

  1. Linear facility location in three dimensions - Models and solution methods

    Brimberg, Jack; Juel, Henrik; Schöbel, Anita

    2002-01-01

    We consider the problem of locating a line or a line segment in three-dimensional space, such that the sum of distances from the facility represented by the line (segment) to a given set of points is minimized. An example is planning the drilling of a mine shaft, with access to ore deposits through...... horizontal tunnels connecting the deposits and the shaft. Various models of the problem are developed and analyzed, and efficient solution methods are given....

  2. Analysis of blood pressure signal in patients with different ventricular ejection fraction using linear and non-linear methods.

    Arcentales, Andres; Rivera, Patricio; Caminal, Pere; Voss, Andreas; Bayes-Genis, Antonio; Giraldo, Beatriz F

    2016-08-01

    Changes in the left ventricle function produce alternans in the hemodynamic and electric behavior of the cardiovascular system. A total of 49 cardiomyopathy patients have been studied based on the blood pressure signal (BP), and were classified according to the left ventricular ejection fraction (LVEF) in low risk (LR: LVEF>35%, 17 patients) and high risk (HR: LVEF≤35, 32 patients) groups. We propose to characterize these patients using a linear and a nonlinear methods, based on the spectral estimation and the recurrence plot, respectively. From BP signal, we extracted each systolic time interval (STI), upward systolic slope (BPsl), and the difference between systolic and diastolic BP, defined as pulse pressure (PP). After, the best subset of parameters were obtained through the sequential feature selection (SFS) method. According to the results, the best classification was obtained using a combination of linear and nonlinear features from STI and PP parameters. For STI, the best combination was obtained considering the frequency peak and the diagonal structures of RP, with an area under the curve (AUC) of 79%. The same results were obtained when comparing PP values. Consequently, the use of combined linear and nonlinear parameters could improve the risk stratification of cardiomyopathy patients.

  3. Fundamental solution of the problem of linear programming and method of its determination

    Petrunin, S. V.

    1978-01-01

    The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.

  4. Linear feature selection in texture analysis - A PLS based method

    Marques, Joselene; Igel, Christian; Lillholm, Martin

    2013-01-01

    We present a texture analysis methodology that combined uncommitted machine-learning techniques and partial least square (PLS) in a fully automatic framework. Our approach introduces a robust PLS-based dimensionality reduction (DR) step to specifically address outliers and high-dimensional feature...... and considering all CV groups, the methods selected 36 % of the original features available. The diagnosis evaluation reached a generalization area-under-the-ROC curve of 0.92, which was higher than established cartilage-based markers known to relate to OA diagnosis....

  5. Excited-state lifetime measurements: Linearization of the Foerster equation by the phase-plane method

    Love, J.C.; Demas, J.N.

    1983-01-01

    The Foerster equation describes excited-state decay curves involving resonance intermolecular energy transfer. A linearized solution based on the phase-plane method has been developed. The new method is quick, insensitive to the fitting region, accurate, and precise

  6. Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size

    Hadjimichael, Yiannis; Ketcheson, David I.; Loczi, Lajos; Né meth, Adriá n

    2016-01-01

    Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order

  7. Optimal Homotopy Asymptotic Method for Solving the Linear Fredholm Integral Equations of the First Kind

    Mohammad Almousa

    2013-01-01

    Full Text Available The aim of this study is to present the use of a semi analytical method called the optimal homotopy asymptotic method (OHAM for solving the linear Fredholm integral equations of the first kind. Three examples are discussed to show the ability of the method to solve the linear Fredholm integral equations of the first kind. The results indicated that the method is very effective and simple.

  8. Solution of linear ordinary differential equations by means of the method of variation of arbitrary constants

    Mejlbro, Leif

    1997-01-01

    An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians.......An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians....

  9. The separation-combination method of linear structures in remote sensing image interpretation and its application

    Liu Linqin

    1991-01-01

    The separation-combination method a new kind of analysis method of linear structures in remote sensing image interpretation is introduced taking northwestern Fujian as the example, its practical application is examined. The practice shows that application results not only reflect intensities of linear structures in overall directions at different locations, but also contribute to the zonation of linear structures and display their space distribution laws. Based on analyses of linear structures, it can provide more information concerning remote sensing on studies of regional mineralization laws and the guide to ore-finding combining with mineralization

  10. Effect of chamber enclosure time on soil respiration flux: A comparison of linear and non-linear flux calculation methods

    Kandel, Tanka P; Lærke, Poul Erik; Elsgaard, Lars

    2016-01-01

    One of the shortcomings of closed chamber methods for soil respiration (SR) measurements is the decreased CO2 diffusion rate from soil to chamber headspace that may occur due to increased chamber CO2 concentrations. This feedback on diffusion rate may lead to underestimation of pre-deployment flu......One of the shortcomings of closed chamber methods for soil respiration (SR) measurements is the decreased CO2 diffusion rate from soil to chamber headspace that may occur due to increased chamber CO2 concentrations. This feedback on diffusion rate may lead to underestimation of pre...... was placed on fixed collars, and CO2 concentration in the chamber headspace were recorded at 1-s intervals for 45 min. Fluxes were measured in different soil types (sandy, sandy loam and organic soils), and for various manipulations (tillage, rain and drought) and soil conditions (temperature and moisture......) to obtain a range of fluxes with different shapes of flux curves. The linear method provided more stable flux results during short enclosure times (few min) but underestimated initial fluxes by 15–300% after 45 min deployment time. Non-linear models reduced the underestimation as average underestimation...

  11. Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

    Freund, Roland

    1989-01-01

    We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

  12. Solution of systems of linear algebraic equations by the method of summation of divergent series

    Kirichenko, G.A.; Korovin, Ya.S.; Khisamutdinov, M.V.; Shmojlov, V.I.

    2015-01-01

    A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated [ru

  13. Environmental impact assessment methods of the radiation generated by the runing medical linear accelerator

    Yin haihua; Yao Zhigang

    2014-01-01

    This article describes the environmental impact assessment methods of the radiation generated by the runing. medical linear accelerator. The material and thickness of shielding wall and protective doors of the linear accelerator were already knew, therefore we can evaluate the radiation by the runing. medical linear accelerator whether or not in the normal range of national standard by calculating the annual effective radiation dose of the surrounding personnel suffered. (authors)

  14. Chosen interval methods for solving linear interval systems with special type of matrix

    Szyszka, Barbara

    2013-10-01

    The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

  15. Outlier robustness for wind turbine extrapolated extreme loads

    Natarajan, Anand; Verelst, David Robert

    2012-01-01

    . Stochastic identification of numerical artifacts in simulated loads is demonstrated using the method of principal component analysis. The extrapolation methodology is made robust to outliers through a weighted loads approach, whereby the eigenvalues of the correlation matrix obtained using the loads with its...

  16. A Linear Birefringence Measurement Method for an Optical Fiber Current Sensor.

    Xu, Shaoyi; Shao, Haiming; Li, Chuansheng; Xing, Fangfang; Wang, Yuqiao; Li, Wei

    2017-07-03

    In this work, a linear birefringence measurement method is proposed for an optical fiber current sensor (OFCS). First, the optical configuration of the measurement system is presented. Then, the elimination method of the effect of the azimuth angles between the sensing fiber and the two polarizers is demonstrated. Moreover, the relationship of the linear birefringence, the Faraday rotation angle and the final output is determined. On these bases, the multi-valued problem on the linear birefringence is simulated and its solution is illustrated when the linear birefringence is unknown. Finally, the experiments are conducted to prove the feasibility of the proposed method. When the numbers of turns of the sensing fiber in the OFCS are about 15, 19, 23, 27, 31, 35, and 39, the measured linear birefringence obtained by the proposed method are about 1.3577, 1.8425, 2.0983, 2.5914, 2.7891, 3.2003 and 3.5198 rad. Two typical methods provide the references for the proposed method. The proposed method is proven to be suitable for the linear birefringence measurement in the full range without the limitation that the linear birefringence must be smaller than π/2.

  17. Hierarchical and Non-Hierarchical Linear and Non-Linear Clustering Methods to “Shakespeare Authorship Question”

    Refat Aljumily

    2015-09-01

    Full Text Available A few literary scholars have long claimed that Shakespeare did not write some of his best plays (history plays and tragedies and proposed at one time or another various suspect authorship candidates. Most modern-day scholars of Shakespeare have rejected this claim, arguing that strong evidence that Shakespeare wrote the plays and poems being his name appears on them as the author. This has caused and led to an ongoing scholarly academic debate for quite some long time. Stylometry is a fast-growing field often used to attribute authorship to anonymous or disputed texts. Stylometric attempts to resolve this literary puzzle have raised interesting questions over the past few years. The following paper contributes to “the Shakespeare authorship question” by using a mathematically-based methodology to examine the hypothesis that Shakespeare wrote all the disputed plays traditionally attributed to him. More specifically, the mathematically based methodology used here is based on Mean Proximity, as a linear hierarchical clustering method, and on Principal Components Analysis, as a non-hierarchical linear clustering method. It is also based, for the first time in the domain, on Self-Organizing Map U-Matrix and Voronoi Map, as non-linear clustering methods to cover the possibility that our data contains significant non-linearities. Vector Space Model (VSM is used to convert texts into vectors in a high dimensional space. The aim of which is to compare the degrees of similarity within and between limited samples of text (the disputed plays. The various works and plays assumed to have been written by Shakespeare and possible authors notably, Sir Francis Bacon, Christopher Marlowe, John Fletcher, and Thomas Kyd, where “similarity” is defined in terms of correlation/distance coefficient measure based on the frequency of usage profiles of function words, word bi-grams, and character triple-grams. The claim that Shakespeare authored all the disputed

  18. Statistically extrapolated nowcasting of summertime precipitation over the Eastern Alps

    Chen, Min; Bica, Benedikt; Tüchler, Lukas; Kann, Alexander; Wang, Yong

    2017-07-01

    This paper presents a new multiple linear regression (MLR) approach to updating the hourly, extrapolated precipitation forecasts generated by the INCA (Integrated Nowcasting through Comprehensive Analysis) system for the Eastern Alps. The generalized form of the model approximates the updated precipitation forecast as a linear response to combinations of predictors selected through a backward elimination algorithm from a pool of predictors. The predictors comprise the raw output of the extrapolated precipitation forecast, the latest radar observations, the convective analysis, and the precipitation analysis. For every MLR model, bias and distribution correction procedures are designed to further correct the systematic regression errors. Applications of the MLR models to a verification dataset containing two months of qualified samples, and to one-month gridded data, are performed and evaluated. Generally, MLR yields slight, but definite, improvements in the intensity accuracy of forecasts during the late evening to morning period, and significantly improves the forecasts for large thresholds. The structure-amplitude-location scores, used to evaluate the performance of the MLR approach, based on its simulation of morphological features, indicate that MLR typically reduces the overestimation of amplitudes and generates similar horizontal structures in precipitation patterns and slightly degraded location forecasts, when compared with the extrapolated nowcasting.

  19. Endangered species toxicity extrapolation using ICE models

    The National Research Council’s (NRC) report on assessing pesticide risks to threatened and endangered species (T&E) included the recommendation of using interspecies correlation models (ICE) as an alternative to general safety factors for extrapolating across species. ...

  20. Libraries for spectrum identification: Method of normalized coordinates versus linear correlation

    Ferrero, A.; Lucena, P.; Herrera, R.G.; Dona, A.; Fernandez-Reyes, R.; Laserna, J.J.

    2008-01-01

    In this work it is proposed that an easy solution based directly on linear algebra in order to obtain the relation between a spectrum and a spectrum base. This solution is based on the algebraic determination of an unknown spectrum coordinates with respect to a spectral library base. The identification capacity comparison between this algebraic method and the linear correlation method has been shown using experimental spectra of polymers. Unlike the linear correlation (where the presence of impurities may decrease the discrimination capacity), this method allows to detect quantitatively the existence of a mixture of several substances in a sample and, consequently, to beer in mind impurities for improving the identification

  1. Infeasible Interior-Point Methods for Linear Optimization Based on Large Neighborhood

    Asadi, A.R.; Roos, C.

    2015-01-01

    In this paper, we design a class of infeasible interior-point methods for linear optimization based on large neighborhood. The algorithm is inspired by a full-Newton step infeasible algorithm with a linear convergence rate in problem dimension that was recently proposed by the second author.

  2. A Comparison of Traditional Worksheet and Linear Programming Methods for Teaching Manure Application Planning.

    Schmitt, M. A.; And Others

    1994-01-01

    Compares traditional manure application planning techniques calculated to meet agronomic nutrient needs on a field-by-field basis with plans developed using computer-assisted linear programming optimization methods. Linear programming provided the most economical and environmentally sound manure application strategy. (Contains 15 references.) (MDH)

  3. Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

    Camporesi, Roberto

    2011-01-01

    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

  4. An Evaluation of Five Linear Equating Methods for the NEAT Design

    Mroch, Andrew A.; Suh, Youngsuk; Kane, Michael T.; Ripkey, Douglas R.

    2009-01-01

    This study uses the results of two previous papers (Kane, Mroch, Suh, & Ripkey, this issue; Suh, Mroch, Kane, & Ripkey, this issue) and the literature on linear equating to evaluate five linear equating methods along several dimensions, including the plausibility of their assumptions and their levels of bias and root mean squared difference…

  5. Genomic prediction based on data from three layer lines: a comparison between linear methods

    Calus, M.P.L.; Huang, H.; Vereijken, J.; Visscher, J.; Napel, ten J.; Windig, J.J.

    2014-01-01

    Background The prediction accuracy of several linear genomic prediction models, which have previously been used for within-line genomic prediction, was evaluated for multi-line genomic prediction. Methods Compared to a conventional BLUP (best linear unbiased prediction) model using pedigree data, we

  6. An introduction to fuzzy linear programming problems theory, methods and applications

    Kaur, Jagdeep

    2016-01-01

    The book presents a snapshot of the state of the art in the field of fully fuzzy linear programming. The main focus is on showing current methods for finding the fuzzy optimal solution of fully fuzzy linear programming problems in which all the parameters and decision variables are represented by non-negative fuzzy numbers. It presents new methods developed by the authors, as well as existing methods developed by others, and their application to real-world problems, including fuzzy transportation problems. Moreover, it compares the outcomes of the different methods and discusses their advantages/disadvantages. As the first work to collect at one place the most important methods for solving fuzzy linear programming problems, the book represents a useful reference guide for students and researchers, providing them with the necessary theoretical and practical knowledge to deal with linear programming problems under uncertainty.

  7. Medical extrapolation chamber dosimeter model XW6012A

    Jin Tao; Wang Mi; Wu Jinzheng; Guo Qi

    1992-01-01

    An extrapolation chamber dosimeter has been developed for clinical dosimetry of electron beams and X-rays from medical linear accelerators. It consists of a new type extrapolation chamber, a water phantom and an intelligent portable instrument. With a thin entrance window and a φ20 mm collecting electrode made of polystyrene, the electrode spacing can be varied from 0.2 to 6 mm. The dosimeter can accomplish dose measurement automatically, and has functions of error self-diagnosis and dose self-recording. The energy range applicable is 0.5-20 MeV, and the dose-rate range 0.02-40 Gy/min. The total uncertainty is 2.7%

  8. Improvement of linear reactivity methods and application to long range fuel management

    Woehlke, R.A.; Quan, B.L.

    1982-01-01

    The original development of the linear reactivity theory assumes flat burnup, batch by batch. The validity of this assumption is explored using multicycle burnup data generated with a detailed 3-D SIMULATE model. The results show that the linear reactivity method can be improved by correcting for batchwise power sharing. The application of linear reactivity to long range fuel management is demonstrated in several examples. Correcting for batchwise power sharing improves the accuracy of the analysis. However, with regard to the sensitivity of fuel cost to changes in various parameters, the corrected and uncorrected linear reactivity theories give remarkably similar results

  9. On Extended Exponential General Linear Methods PSQ with S>Q ...

    This paper is concerned with the construction and Numerical Analysis of Extended Exponential General Linear Methods. These methods, in contrast to other methods in literatures, consider methods with the step greater than the stage order (S>Q).Numerical experiments in this study, indicate that Extended Exponential ...

  10. Electric field control methods for foil coils in high-voltage linear actuators

    Beek, van T.A.; Jansen, J.W.; Lomonova, E.A.

    2015-01-01

    This paper describes multiple electric field control methods for foil coils in high-voltage coreless linear actuators. The field control methods are evaluated using 2-D and 3-D boundary element methods. A comparison is presented between the field control methods and their ability to mitigate

  11. A simple linear regression method for quantitative trait loci linkage analysis with censored observations.

    Anderson, Carl A; McRae, Allan F; Visscher, Peter M

    2006-07-01

    Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using simulation we compare this method to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods and is significantly better than the standard linear regression method when censored observations are present. The method is also robust to the proportion of censored individuals and the underlying distribution of the trait. On the basis of linear regression methodology, the grouped linear regression model is computationally simple and fast and can be implemented readily in freely available statistical software.

  12. Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods

    Mozartova, A.; Savostianov, I.; Hundsdorfer, W.

    2015-01-01

    © 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.

  13. Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods

    Mozartova, A.

    2015-05-01

    © 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.

  14. SU-E-J-145: Geometric Uncertainty in CBCT Extrapolation for Head and Neck Adaptive Radiotherapy

    Liu, C; Kumarasiri, A; Chetvertkov, M; Gordon, J; Chetty, I; Siddiqui, F; Kim, J [Henry Ford Health System, Detroit, MI (United States)

    2014-06-01

    Purpose: One primary limitation of using CBCT images for H'N adaptive radiotherapy (ART) is the limited field of view (FOV) range. We propose a method to extrapolate the CBCT by using a deformed planning CT for the dose of the day calculations. The aim was to estimate the geometric uncertainty of our extrapolation method. Methods: Ten H'N patients, each with a planning CT (CT1) and a subsequent CT (CT2) taken, were selected. Furthermore, a small FOV CBCT (CT2short) was synthetically created by cropping CT2 to the size of a CBCT image. Then, an extrapolated CBCT (CBCTextrp) was generated by deformably registering CT1 to CT2short and resampling with a wider FOV (42mm more from the CT2short borders), where CT1 is deformed through translation, rigid, affine, and b-spline transformations in order. The geometric error is measured as the distance map ||DVF|| produced by a deformable registration between CBCTextrp and CT2. Mean errors were calculated as a function of the distance away from the CBCT borders. The quality of all the registrations was visually verified. Results: Results were collected based on the average numbers from 10 patients. The extrapolation error increased linearly as a function of the distance (at a rate of 0.7mm per 1 cm) away from the CBCT borders in the S/I direction. The errors (μ±σ) at the superior and inferior boarders were 0.8 ± 0.5mm and 3.0 ± 1.5mm respectively, and increased to 2.7 ± 2.2mm and 5.9 ± 1.9mm at 4.2cm away. The mean error within CBCT borders was 1.16 ± 0.54mm . The overall errors within 4.2cm error expansion were 2.0 ± 1.2mm (sup) and 4.5 ± 1.6mm (inf). Conclusion: The overall error in inf direction is larger due to more large unpredictable deformations in the chest. The error introduced by extrapolation is plan dependent. The mean error in the expanded region can be large, and must be considered during implementation. This work is supported in part by Varian Medical Systems, Palo Alto, CA.

  15. Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

    Jeffrey, Alan

    1971-01-01

    The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

  16. A method for computing the stationary points of a function subject to linear equality constraints

    Uko, U.L.

    1989-09-01

    We give a new method for the numerical calculation of stationary points of a function when it is subject to equality constraints. An application to the solution of linear equations is given, together with a numerical example. (author). 5 refs

  17. Contractivity properties of a class of linear multistep methods for nonlinear neutral delay differential equations

    Wang Wansheng; Li Shoufu; Wang Wenqiang

    2009-01-01

    In this paper, we show that under identical conditions which guarantee the contractivity of the theoretical solutions of general nonlinear NDDEs, the numerical solutions obtained by a class of linear multistep methods are also contractive.

  18. Linearized method: A new approach for kinetic analysis of central dopamine D2 receptor specific binding

    Watabe, Hiroshi; Hatazawa, Jun; Ishiwata, Kiichi; Ido, Tatsuo; Itoh, Masatoshi; Iwata, Ren; Nakamura, Takashi; Takahashi, Toshihiro; Hatano, Kentaro

    1995-01-01

    The authors proposed a new method (Linearized method) to analyze neuroleptic ligand-receptor specific binding in a human brain using positron emission tomography (PET). They derived the linear equation to solve four rate constants, k 3 , k 4 , k 5 , k 6 from PET data. This method does not demand radioactivity curve in plasma as an input function to brain, and can do fast calculations in order to determine rate constants. They also tested Nonlinearized method including nonlinear equations which is conventional analysis using plasma radioactivity corrected for ligand metabolites as an input function. The authors applied these methods to evaluate dopamine D 2 receptor specific binding of [ 11 C] YM-09151-2. The value of B max /K d = k 3 k 4 obtained by Linearized method was 5.72 ± 3.1 which was consistent with the value of 5.78 ± 3.4 obtained by Nonlinearized method

  19. Linear, Transfinite and Weighted Method for Interpolation from Grid Lines Applied to OCT Images

    Lindberg, Anne-Sofie Wessel; Jørgensen, Thomas Martini; Dahl, Vedrana Andersen

    2018-01-01

    of a square grid, but are unknown inside each square. To view these values as an image, intensities need to be interpolated at regularly spaced pixel positions. In this paper we evaluate three methods for interpolation from grid lines: linear, transfinite and weighted. The linear method does not preserve...... and the stability of the linear method further away. An important parameter influencing the performance of the interpolation methods is the upsampling rate. We perform an extensive evaluation of the three interpolation methods across a range of upsampling rates. Our statistical analysis shows significant difference...... in the performance of the three methods. We find that the transfinite interpolation works well for small upsampling rates and the proposed weighted interpolation method performs very well for all upsampling rates typically used in practice. On the basis of these findings we propose an approach for combining two OCT...

  20. Proposal for an alignment method of the CLIC linear accelerator - From geodesic networks to the active pre-alignment

    Touze, T.

    2011-01-01

    The compact linear collider (CLIC) is the particle accelerator project proposed by the european organization for nuclear research (CERN) for high energy physics after the large hadron collider (LHC). Because of the nano-metric scale of the CLIC leptons beams, the emittance growth budget is very tight. It induces alignment tolerances on the positions of the CLIC components that have never been achieved before. The last step of the CLIC alignment will be done according to the beam itself. It falls within the competence of the physicists. However, in order to implement the beam-based feedback, a challenging pre-alignment is required: 10 μm at 3σ along a 200 m sliding window. For such a precision, the proposed solution must be compatible with a feedback between the measurement and repositioning systems. The CLIC pre-alignment will have to be active. This thesis does not demonstrate the feasibility of the CLIC active pre-alignment but shows the way to the last developments that have to be done for that purpose. A method is proposed. Based on the management of the Helmert transformations between Euclidean coordinate systems, from the geodetic networks to the metrological measurements, this method is likely to solve the CLIC pre-alignment problem. Large scale facilities have been built and Monte-Carlo simulations have been made in order to validate the mathematical modeling of the measurement systems and of the alignment references. When this is done, it will be possible to extrapolate the modeling to the entire CLIC length. It will be the last step towards the demonstration of the CLIC pre-alignment feasibility. (author)

  1. Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

    Ai-Min Yang

    2014-01-01

    Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

  2. Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems

    Wang, Xue-Zhong; Huang, Ting-Zhu; Fu, Ying-Ding

    2007-09-01

    In this paper, we present some comparison theorems on preconditioned iterative method for solving Z-matrices linear systems, Comparison results show that the rate of convergence of the Gauss-Seidel-type method is faster than the rate of convergence of the SOR-type iterative method.

  3. A Fifth Order Hybrid Linear Multistep method For the Direct Solution ...

    A linear multistep hybrid method (LMHM)with continuous coefficients isconsidered and directly applied to solve third order initial and boundary value problems (IBVPs). The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) (each of order 5) which are combined as simultaneous numerical ...

  4. Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

    Freund, Roland W.

    1991-01-01

    We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

  5. Motion extrapolation in the central fovea.

    Zhuanghua Shi

    Full Text Available Neural transmission latency would introduce a spatial lag when an object moves across the visual field, if the latency was not compensated. A visual predictive mechanism has been proposed, which overcomes such spatial lag by extrapolating the position of the moving object forward. However, a forward position shift is often absent if the object abruptly stops moving (motion-termination. A recent "correction-for-extrapolation" hypothesis suggests that the absence of forward shifts is caused by sensory signals representing 'failed' predictions. Thus far, this hypothesis has been tested only for extra-foveal retinal locations. We tested this hypothesis using two foveal scotomas: scotoma to dim light and scotoma to blue light. We found that the perceived position of a dim dot is extrapolated into the fovea during motion-termination. Next, we compared the perceived position shifts of a blue versus a green moving dot. As predicted the extrapolation at motion-termination was only found with the blue moving dot. The results provide new evidence for the correction-for-extrapolation hypothesis for the region with highest spatial acuity, the fovea.

  6. Development of pre-critical excore detector linear subchannel calibration method

    Choi, Yoo Sun; Goo, Bon Seung; Cha, Kyun Ho; Lee, Chang Seop; Kim, Yong Hee; Ahn, Chul Soo; Kim, Man Soo

    2001-01-01

    The improved pre-critical excore detector linear subchannel calibration method has been developed to improve the applicability of pre-critical calibration method. The existing calibration method does not always guarantee the accuracy of pre-critical calibration because the calibration results of the previous cycle are not reflected into the current cycle calibration. The developed method has a desirable feature that calibration error would not be propagated in the following cycles since the calibration data determined in previous cycle is incorporated in the current cycle calibration. The pre-critical excore detector linear calibration is tested for YGN unit 3 and UCN unit 3 to evaluate its characteristics and accuracy

  7. Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

    Guo, Sangang

    2017-09-01

    There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

  8. Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem

    Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States)

    1996-12-31

    Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.

  9. An introduction to linear ordinary differential equations using the impulsive response method and factorization

    Camporesi, Roberto

    2016-01-01

    This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.

  10. Effective wavefield extrapolation in anisotropic media: Accounting for resolvable anisotropy

    Alkhalifah, Tariq Ali

    2014-01-01

    Spectral methods provide artefact-free and generally dispersion-free wavefield extrapolation in anisotropic media. Their apparent weakness is in accessing the medium-inhomogeneity information in an efficient manner. This is usually handled through a velocity-weighted summation (interpolation) of representative constant-velocity extrapolated wavefields, with the number of these extrapolations controlled by the effective rank of the original mixed-domain operator or, more specifically, by the complexity of the velocity model. Conversely, with pseudo-spectral methods, because only the space derivatives are handled in the wavenumber domain, we obtain relatively efficient access to the inhomogeneity in isotropic media, but we often resort to weak approximations to handle the anisotropy efficiently. Utilizing perturbation theory, I isolate the contribution of anisotropy to the wavefield extrapolation process. This allows us to factorize as much of the inhomogeneity in the anisotropic parameters as possible out of the spectral implementation, yielding effectively a pseudo-spectral formulation. This is particularly true if the inhomogeneity of the dimensionless anisotropic parameters are mild compared with the velocity (i.e., factorized anisotropic media). I improve on the accuracy by using the Shanks transformation to incorporate a denominator in the expansion that predicts the higher-order omitted terms; thus, we deal with fewer terms for a high level of accuracy. In fact, when we use this new separation-based implementation, the anisotropy correction to the extrapolation can be applied separately as a residual operation, which provides a tool for anisotropic parameter sensitivity analysis. The accuracy of the approximation is high, as demonstrated in a complex tilted transversely isotropic model. © 2014 European Association of Geoscientists & Engineers.

  11. Effective wavefield extrapolation in anisotropic media: Accounting for resolvable anisotropy

    Alkhalifah, Tariq Ali

    2014-04-30

    Spectral methods provide artefact-free and generally dispersion-free wavefield extrapolation in anisotropic media. Their apparent weakness is in accessing the medium-inhomogeneity information in an efficient manner. This is usually handled through a velocity-weighted summation (interpolation) of representative constant-velocity extrapolated wavefields, with the number of these extrapolations controlled by the effective rank of the original mixed-domain operator or, more specifically, by the complexity of the velocity model. Conversely, with pseudo-spectral methods, because only the space derivatives are handled in the wavenumber domain, we obtain relatively efficient access to the inhomogeneity in isotropic media, but we often resort to weak approximations to handle the anisotropy efficiently. Utilizing perturbation theory, I isolate the contribution of anisotropy to the wavefield extrapolation process. This allows us to factorize as much of the inhomogeneity in the anisotropic parameters as possible out of the spectral implementation, yielding effectively a pseudo-spectral formulation. This is particularly true if the inhomogeneity of the dimensionless anisotropic parameters are mild compared with the velocity (i.e., factorized anisotropic media). I improve on the accuracy by using the Shanks transformation to incorporate a denominator in the expansion that predicts the higher-order omitted terms; thus, we deal with fewer terms for a high level of accuracy. In fact, when we use this new separation-based implementation, the anisotropy correction to the extrapolation can be applied separately as a residual operation, which provides a tool for anisotropic parameter sensitivity analysis. The accuracy of the approximation is high, as demonstrated in a complex tilted transversely isotropic model. © 2014 European Association of Geoscientists & Engineers.

  12. An explicit method in non-linear soil-structure interaction

    Kunar, R.R.

    1981-01-01

    The explicit method of analysis in the time domain is ideally suited for the solution of transient dynamic non-linear problems. Though the method is not new, its application to seismic soil-structure interaction is relatively new and deserving of public discussion. This paper describes the principles of the explicit approach in soil-structure interaction and it presents a simple algorithm that can be used in the development of explicit computer codes. The paper also discusses some of the practical considerations like non-reflecting boundaries and time steps. The practicality of the method is demonstrated using a computer code, PRESS, which is used to compare the treatment of strain-dependent properties using average strain levels over the whole time history (the equivalent linear method) and using the actual strain levels at every time step to modify the soil properties (non-linear method). (orig.)

  13. Uniform irradiation using rotational-linear scanning method for narrow synchrotron radiation beam

    Nariyama, N.; Ohnishi, S.; Odano, N.

    2004-01-01

    At SPring-8, photon intensity monitors for synchrotron radiation have been developed. Using these monitors, the responses of radiation detectors and dosimeters to monoenergetic photons can be measured. In most cases, uniform irradiation to the sample is necessary. Here, two scanning methods are proposed. One is an XZ-linear scanning method, which moves the sample simultaneously in both the X and Z direction, that is, in zigzag fashion. The other is a rotational-linear scanning method, which rotates the sample moving in the X direction. To investigate the validity of the two methods, thermoluminescent dosimeters were irradiated with a broad synchrotron-radiation beam, and the readings from the two methods were compared with that of the dosimeters fixed in the beam. The results for both scanning methods virtually agreed with that of the fixed method. The advantages of the rotational-linear scanning method are that low- and medium-dose irradiation is possible, uniformity is excellent and the load to the scanning equipment is light: hence, this method is superior to the XZ-linear scanning method for most applications. (author)

  14. Wavefield extrapolation in pseudo-depth domain

    Ma, Xuxin; Alkhalifah, Tariq Ali

    2012-01-01

    Extrapolating seismic waves in Cartesian coordinate is prone to uneven spatial sampling, because the seismic wavelength tends to grow with depth, as velocity increase. We transform the vertical depth axis to a pseudo one using a velocity weighted mapping, which can effectively mitigate this wavelength variation. We derive acoustic wave equations in this new domain based on the direct transformation of the Laplacian derivatives, which admits solutions that are more accurate and stable than those derived from the kinematic transformation. The anisotropic versions of these equations allow us to isolate the vertical velocity influence and reduce its impact on modeling and imaging. The major benefit of extrapolating wavefields in pseudo-depth space is its near uniform wavelength as opposed to the normally dramatic change of wavelength with the conventional approach. Time wavefield extrapolation on a complex velocity shows some of the features of this approach.

  15. Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

    Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

    2012-01-01

    In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

  16. Equivalent linearization method for limit cycle flutter analysis of plate-type structure in axial flow

    Lu Li; Yang Yiren

    2009-01-01

    The responses and limit cycle flutter of a plate-type structure with cubic stiffness in viscous flow were studied. The continuous system was dispersed by utilizing Galerkin Method. The equivalent linearization concept was performed to predict the ranges of limit cycle flutter velocities. The coupled map of flutter amplitude-equivalent linear stiffness-critical velocity was used to analyze the stability of limit cycle flutter. The theoretical results agree well with the results of numerical integration, which indicates that the equivalent linearization concept is available to the analysis of limit cycle flutter of plate-type structure. (authors)

  17. A complex linear least-squares method to derive relative and absolute orientations of seismic sensors

    F. Grigoli; Simone Cesca; Torsten Dahm; L. Krieger

    2012-01-01

    Determining the relative orientation of the horizontal components of seismic sensors is a common problem that limits data analysis and interpretation for several acquisition setups, including linear arrays of geophones deployed in borehole installations or ocean bottom seismometers deployed at the seafloor. To solve this problem we propose a new inversion method based on a complex linear algebra approach. Relative orientation angles are retrieved by minimizing, in a least-squares sense, the l...

  18. General methods for determining the linear stability of coronal magnetic fields

    Craig, I. J. D.; Sneyd, A. D.; Mcclymont, A. N.

    1988-01-01

    A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak.

  19. Non-linear shape functions over time in the space-time finite element method

    Kacprzyk Zbigniew

    2017-01-01

    Full Text Available This work presents a generalisation of the space-time finite element method proposed by Kączkowski in his seminal of 1970’s and early 1980’s works. Kączkowski used linear shape functions in time. The recurrence formula obtained by Kączkowski was conditionally stable. In this paper, non-linear shape functions in time are proposed.

  20. Treating experimental data of inverse kinetic method by unitary linear regression analysis

    Zhao Yusen; Chen Xiaoliang

    2009-01-01

    The theory of treating experimental data of inverse kinetic method by unitary linear regression analysis was described. Not only the reactivity, but also the effective neutron source intensity could be calculated by this method. Computer code was compiled base on the inverse kinetic method and unitary linear regression analysis. The data of zero power facility BFS-1 in Russia were processed and the results were compared. The results show that the reactivity and the effective neutron source intensity can be obtained correctly by treating experimental data of inverse kinetic method using unitary linear regression analysis and the precision of reactivity measurement is improved. The central element efficiency can be calculated by using the reactivity. The result also shows that the effect to reactivity measurement caused by external neutron source should be considered when the reactor power is low and the intensity of external neutron source is strong. (authors)

  1. A Method of Calculating Motion Error in a Linear Motion Bearing Stage

    Gyungho Khim

    2015-01-01

    Full Text Available We report a method of calculating the motion error of a linear motion bearing stage. The transfer function method, which exploits reaction forces of individual bearings, is effective for estimating motion errors; however, it requires the rail-form errors. This is not suitable for a linear motion bearing stage because obtaining the rail-form errors is not straightforward. In the method described here, we use the straightness errors of a bearing block to calculate the reaction forces on the bearing block. The reaction forces were compared with those of the transfer function method. Parallelism errors between two rails were considered, and the motion errors of the linear motion bearing stage were measured and compared with the results of the calculations, revealing good agreement.

  2. A Method of Calculating Motion Error in a Linear Motion Bearing Stage

    Khim, Gyungho; Park, Chun Hong; Oh, Jeong Seok

    2015-01-01

    We report a method of calculating the motion error of a linear motion bearing stage. The transfer function method, which exploits reaction forces of individual bearings, is effective for estimating motion errors; however, it requires the rail-form errors. This is not suitable for a linear motion bearing stage because obtaining the rail-form errors is not straightforward. In the method described here, we use the straightness errors of a bearing block to calculate the reaction forces on the bearing block. The reaction forces were compared with those of the transfer function method. Parallelism errors between two rails were considered, and the motion errors of the linear motion bearing stage were measured and compared with the results of the calculations, revealing good agreement. PMID:25705715

  3. On a new iterative method for solving linear systems and comparison results

    Jing, Yan-Fei; Huang, Ting-Zhu

    2008-10-01

    In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a different approach is established, which is both theoretically and numerically proven to be better than (at least the same as) Ujevic's. As the presented numerical examples show, in most cases, the convergence rate is more than one and a half that of Ujevic.

  4. Shifted Legendre method with residual error estimation for delay linear Fredholm integro-differential equations

    Şuayip Yüzbaşı

    2017-03-01

    Full Text Available In this paper, we suggest a matrix method for obtaining the approximate solutions of the delay linear Fredholm integro-differential equations with constant coefficients using the shifted Legendre polynomials. The problem is considered with mixed conditions. Using the required matrix operations, the delay linear Fredholm integro-differential equation is transformed into a matrix equation. Additionally, error analysis for the method is presented using the residual function. Illustrative examples are given to demonstrate the efficiency of the method. The results obtained in this study are compared with the known results.

  5. Methods of measurement of integral and differential linearity distortions of spectrometry sets

    Fuan, Jacques; Grimont, Bernard; Marin, Roland; Richard, Jean-Pierre

    1969-05-01

    The objective of this document is to describe different measurement methods, and more particularly to present a software for the processing of obtained results in order to avoid interpretation by the investigator. In a first part, the authors define the parameters of integral and differential linearity, outlines their importance in measurements performed by spectrometry, and describe the use of these parameters. In the second part, they propose various methods of measurement of these linearity parameters, report experimental applications of these methods and compare the obtained results

  6. Proposition of Improved Methodology in Creep Life Extrapolation

    Kim, Woo Gon; Park, Jae Young; Jang, Jin Sung [KAERI, Daejeon (Korea, Republic of)

    2016-05-15

    To design SFRs for a 60-year operation, it is desirable to have the experimental creep-rupture data for Gr. 91 steel close to 20 y, or at least rupture lives significantly higher than 10{sup 5} h. This requirement arises from the fact that, for the creep design, a factor of 3 times for extrapolation is considered to be appropriate. However, obtaining experimental data close to 20 y would be expensive and also take considerable time. Therefore, reliable creep life extrapolation techniques become necessary for a safe design life of 60 y. In addition, it is appropriate to obtain experimental longterm creep-rupture data in the range 10{sup 5} ∼ 2x10{sup 5} h to improve the reliability of extrapolation. In the present investigation, a new function of a hyperbolic sine ('sinh') form for a master curve in time-temperature parameter (TTP) methods, was proposed to accurately extrapolate the long-term creep rupture stress of Gr. 91 steel. Constant values used for each parametric equation were optimized on the basis of the creep rupture data. Average stress values predicted for up to 60 y were evaluated and compared with those of French Nuclear Design Code, RCC-MRx. The results showed that the master curve of the 'sinh' function was a wider acceptance with good flexibility in the low stress ranges beyond the experimental data. It was clarified clarified that the 'sinh' function was reasonable in creep life extrapolation compared with polynomial forms, which have been used conventionally until now.

  7. Proposition of Improved Methodology in Creep Life Extrapolation

    Kim, Woo Gon; Park, Jae Young; Jang, Jin Sung

    2016-01-01

    To design SFRs for a 60-year operation, it is desirable to have the experimental creep-rupture data for Gr. 91 steel close to 20 y, or at least rupture lives significantly higher than 10"5 h. This requirement arises from the fact that, for the creep design, a factor of 3 times for extrapolation is considered to be appropriate. However, obtaining experimental data close to 20 y would be expensive and also take considerable time. Therefore, reliable creep life extrapolation techniques become necessary for a safe design life of 60 y. In addition, it is appropriate to obtain experimental longterm creep-rupture data in the range 10"5 ∼ 2x10"5 h to improve the reliability of extrapolation. In the present investigation, a new function of a hyperbolic sine ('sinh') form for a master curve in time-temperature parameter (TTP) methods, was proposed to accurately extrapolate the long-term creep rupture stress of Gr. 91 steel. Constant values used for each parametric equation were optimized on the basis of the creep rupture data. Average stress values predicted for up to 60 y were evaluated and compared with those of French Nuclear Design Code, RCC-MRx. The results showed that the master curve of the 'sinh' function was a wider acceptance with good flexibility in the low stress ranges beyond the experimental data. It was clarified clarified that the 'sinh' function was reasonable in creep life extrapolation compared with polynomial forms, which have been used conventionally until now.

  8. More on Generalizations and Modifications of Iterative Methods for Solving Large Sparse Indefinite Linear Systems

    Jen-Yuan Chen

    2014-01-01

    Full Text Available Continuing from the works of Li et al. (2014, Li (2007, and Kincaid et al. (2000, we present more generalizations and modifications of iterative methods for solving large sparse symmetric and nonsymmetric indefinite systems of linear equations. We discuss a variety of iterative methods such as GMRES, MGMRES, MINRES, LQ-MINRES, QR MINRES, MMINRES, MGRES, and others.

  9. An Introduction to Graphical and Mathematical Methods for Detecting Heteroscedasticity in Linear Regression.

    Thompson, Russel L.

    Homoscedasticity is an important assumption of linear regression. This paper explains what it is and why it is important to the researcher. Graphical and mathematical methods for testing the homoscedasticity assumption are demonstrated. Sources of homoscedasticity and types of homoscedasticity are discussed, and methods for correction are…

  10. Experimental validation for calcul methods of structures having shock non-linearity

    Brochard, D.; Buland, P.

    1987-01-01

    For the seismic analysis of non-linear structures, numerical methods have been developed which need to be validated on experimental results. The aim of this paper is to present the design method of a test program which results will be used for this purpose. Some applications to nuclear components will illustrate this presentation [fr

  11. Calculation of U, Ra, Th and K contents in uranium ore by multiple linear regression method

    Lin Chao; Chen Yingqiang; Zhang Qingwen; Tan Fuwen; Peng Guanghui

    1991-01-01

    A multiple linear regression method was used to compute γ spectra of uranium ore samples and to calculate contents of U, Ra, Th, and K. In comparison with the inverse matrix method, its advantage is that no standard samples of pure U, Ra, Th and K are needed for obtaining response coefficients

  12. Effective linear two-body method for many-body problems in atomic and nuclear physics

    Kim, Y.E.; Zubarev, A.L.

    2000-01-01

    We present an equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schroedinger equation by the use of a variational principle. The method is applied to several problems in atomic and nuclear physics. (author)

  13. Engineered high expansion glass-ceramics having near linear thermal strain and methods thereof

    Dai, Steve Xunhu; Rodriguez, Mark A.; Lyon, Nathanael L.

    2018-01-30

    The present invention relates to glass-ceramic compositions, as well as methods for forming such composition. In particular, the compositions include various polymorphs of silica that provide beneficial thermal expansion characteristics (e.g., a near linear thermal strain). Also described are methods of forming such compositions, as well as connectors including hermetic seals containing such compositions.

  14. A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

    Bochev, Mikhail A.

    2013-01-01

    We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of

  15. A study on linear and nonlinear Schrodinger equations by the variational iteration method

    Wazwaz, Abdul-Majid

    2008-01-01

    In this work, we introduce a framework to obtain exact solutions to linear and nonlinear Schrodinger equations. The He's variational iteration method (VIM) is used for analytic treatment of these equations. Numerical examples are tested to show the pertinent features of this method

  16. Linear Discontinuous Expansion Method using the Subcell Balances for Unstructured Geometry SN Transport

    Hong, Ser Gi; Kim, Jong Woon; Lee, Young Ouk; Kim, Kyo Youn

    2010-01-01

    The subcell balance methods have been developed for one- and two-dimensional SN transport calculations. In this paper, a linear discontinuous expansion method using sub-cell balances (LDEM-SCB) is developed for neutral particle S N transport calculations in 3D unstructured geometrical problems. At present, this method is applied to the tetrahedral meshes. As the name means, this method assumes the linear distribution of the particle flux in each tetrahedral mesh and uses the balance equations for four sub-cells of each tetrahedral mesh to obtain the equations for the four sub-cell average fluxes which are unknowns. This method was implemented in the computer code MUST (Multi-group Unstructured geometry S N Transport). The numerical tests show that this method gives more robust solution than DFEM (Discontinuous Finite Element Method)

  17. Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size

    Hadjimichael, Yiannis

    2016-09-08

    Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and three) with variable step size, and prove their optimality, stability, and convergence. The choice of step size for multistep SSP methods is an interesting problem because the allowable step size depends on the SSP coefficient, which in turn depends on the chosen step sizes. The description of the methods includes an optimal step-size strategy. We prove sharp upper bounds on the allowable step size for explicit SSP linear multistep methods and show the existence of methods with arbitrarily high order of accuracy. The effectiveness of the methods is demonstrated through numerical examples.

  18. Cosmogony as an extrapolation of magnetospheric research

    Alfven, H.

    1984-03-01

    A theory of the origin and evolution of the Solar System (Alfven and Arrhenius, 1975: 1976) which considered electromagnetic forces and plasma effects is revised in the light of new information supplied by space research. In situ measurements in the magnetospheres and solar wind have changed our views of basic properties of cosmic plasmas. These results can be extrapolated both outwards in space, to interstellar clouds, backwards in time, to the formation of the solar system. The first extrapolation leads to a revision of some cloud properties which are essential for the early phases in the formation of stars and solar nebule. The latter extrapolation makes possible to approach the cosmogonic processes by extrapolation of (rather) well-known magnetospheric phenomena. Pioneer-Voyager observations of the Saturnian rings indicate that essential parts of their structure are fossils from cosmogonic times. By using detailed information from these space missions, it seems possible to reconstruct certain events 4-5 billion years ago with an accuracy of a few percent. This will cause a change in our views of the evolution of the solar system.(author)

  19. A discrete homotopy perturbation method for non-linear Schrodinger equation

    H. A. Wahab

    2015-12-01

    Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.

  20. Analytical study of dynamic aperture for storage ring by using successive linearization method

    Yang Jiancheng; Xia Jiawen; Wu Junxia; Xia Guoxing; Liu Wei; Yin Xuejun

    2004-01-01

    The determination of dynamic aperture is a critical issue in circular accelerator. In this paper, authors solved the equation of motion including non-linear forces by using successive linearization method and got a criterion for the determining of the dynamic aperture of the machine. Applying this criterion, a storage ring with FODO lattice has been studied. The results are agree well with the tracking results in a large range of linear turn (Q). The purpose is to improve our understanding of the mechanisms driving the particle motion in the presence of non-linear forces and got another mechanism driving instability of particle in storage ring-parametric resonance caused by 'fluctuating transfer matrices' at small amplification

  1. A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

    S. S. Motsa

    2013-01-01

    Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

  2. A penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography.

    Shang, Shang; Bai, Jing; Song, Xiaolei; Wang, Hongkai; Lau, Jaclyn

    2007-01-01

    Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

  3. Performance study of Active Queue Management methods: Adaptive GRED, REDD, and GRED-Linear analytical model

    Hussein Abdel-jaber

    2015-10-01

    Full Text Available Congestion control is one of the hot research topics that helps maintain the performance of computer networks. This paper compares three Active Queue Management (AQM methods, namely, Adaptive Gentle Random Early Detection (Adaptive GRED, Random Early Dynamic Detection (REDD, and GRED Linear analytical model with respect to different performance measures. Adaptive GRED and REDD are implemented based on simulation, whereas GRED Linear is implemented as a discrete-time analytical model. Several performance measures are used to evaluate the effectiveness of the compared methods mainly mean queue length, throughput, average queueing delay, overflow packet loss probability, and packet dropping probability. The ultimate aim is to identify the method that offers the highest satisfactory performance in non-congestion or congestion scenarios. The first comparison results that are based on different packet arrival probability values show that GRED Linear provides better mean queue length; average queueing delay and packet overflow probability than Adaptive GRED and REDD methods in the presence of congestion. Further and using the same evaluation measures, Adaptive GRED offers a more satisfactory performance than REDD when heavy congestion is present. When the finite capacity of queue values varies the GRED Linear model provides the highest satisfactory performance with reference to mean queue length and average queueing delay and all the compared methods provide similar throughput performance. However, when the finite capacity value is large, the compared methods have similar results in regard to probabilities of both packet overflowing and packet dropping.

  4. Method for linearizing the potentiometric curves of precipitation titration in nonaqueous and aqueous-organic solutions

    Bykova, L.N.; Chesnokova, O.Ya.; Orlova, M.V.

    1995-01-01

    The method for linearizing the potentiometric curves of precipitation titration is studied for its application in the determination of halide ions (Cl - , Br - , I - ) in dimethylacetamide, dimethylformamide, in which titration is complicated by additional equilibrium processes. It is found that the method of linearization permits the determination of the titrant volume at the end point of titration to high accuracy in the case of titration curves without a potential jump in the proximity of the equivalent point (5 x 10 -5 M). 3 refs., 2 figs., 3 tabs

  5. First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

    Heinz Toparkus

    2014-04-01

    Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

  6. Krylov subspace method with communication avoiding technique for linear system obtained from electromagnetic analysis

    Ikuno, Soichiro; Chen, Gong; Yamamoto, Susumu; Itoh, Taku; Abe, Kuniyoshi; Nakamura, Hiroaki

    2016-01-01

    Krylov subspace method and the variable preconditioned Krylov subspace method with communication avoiding technique for a linear system obtained from electromagnetic analysis are numerically investigated. In the k−skip Krylov method, the inner product calculations are expanded by Krylov basis, and the inner product calculations are transformed to the scholar operations. k−skip CG method is applied for the inner-loop solver of Variable Preconditioned Krylov subspace methods, and the converged solution of electromagnetic problem is obtained using the method. (author)

  7. Linear regression based on Minimum Covariance Determinant (MCD) and TELBS methods on the productivity of phytoplankton

    Gusriani, N.; Firdaniza

    2018-03-01

    The existence of outliers on multiple linear regression analysis causes the Gaussian assumption to be unfulfilled. If the Least Square method is forcedly used on these data, it will produce a model that cannot represent most data. For that, we need a robust regression method against outliers. This paper will compare the Minimum Covariance Determinant (MCD) method and the TELBS method on secondary data on the productivity of phytoplankton, which contains outliers. Based on the robust determinant coefficient value, MCD method produces a better model compared to TELBS method.

  8. Fibonacci collocation method with a residual error Function to solve linear Volterra integro differential equations

    Salih Yalcinbas

    2016-01-01

    Full Text Available In this paper, a new collocation method based on the Fibonacci polynomials is introduced to solve the high-order linear Volterra integro-differential equations under the conditions. Numerical examples are included to demonstrate the applicability and validity of the proposed method and comparisons are made with the existing results. In addition, an error estimation based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation.

  9. Measurements of linear attenuation coefficients of irregular shaped samples by two media method

    Singh, Sukhpal; Kumar, Ashok; Thind, Kulwant Singh; Mudahar, Gurmel S.

    2008-01-01

    The linear attenuation coefficient values of regular and irregular shaped flyash materials have been measured without knowing the thickness of a sample using a new technique namely 'two media method'. These values have also been measured with a standard gamma ray transmission method and obtained theoretically with winXCOM computer code. From the comparison it is reported that the two media method has given accurate results of attenuation coefficients of flyash materials

  10. A simple method for identifying parameter correlations in partially observed linear dynamic models.

    Li, Pu; Vu, Quoc Dong

    2015-12-14

    Parameter estimation represents one of the most significant challenges in systems biology. This is because biological models commonly contain a large number of parameters among which there may be functional interrelationships, thus leading to the problem of non-identifiability. Although identifiability analysis has been extensively studied by analytical as well as numerical approaches, systematic methods for remedying practically non-identifiable models have rarely been investigated. We propose a simple method for identifying pairwise correlations and higher order interrelationships of parameters in partially observed linear dynamic models. This is made by derivation of the output sensitivity matrix and analysis of the linear dependencies of its columns. Consequently, analytical relations between the identifiability of the model parameters and the initial conditions as well as the input functions can be achieved. In the case of structural non-identifiability, identifiable combinations can be obtained by solving the resulting homogenous linear equations. In the case of practical non-identifiability, experiment conditions (i.e. initial condition and constant control signals) can be provided which are necessary for remedying the non-identifiability and unique parameter estimation. It is noted that the approach does not consider noisy data. In this way, the practical non-identifiability issue, which is popular for linear biological models, can be remedied. Several linear compartment models including an insulin receptor dynamics model are taken to illustrate the application of the proposed approach. Both structural and practical identifiability of partially observed linear dynamic models can be clarified by the proposed method. The result of this method provides important information for experimental design to remedy the practical non-identifiability if applicable. The derivation of the method is straightforward and thus the algorithm can be easily implemented into a

  11. An Extrapolation of a Radical Equation More Accurately Predicts Shelf Life of Frozen Biological Matrices.

    De Vore, Karl W; Fatahi, Nadia M; Sass, John E

    2016-08-01

    Arrhenius modeling of analyte recovery at increased temperatures to predict long-term colder storage stability of biological raw materials, reagents, calibrators, and controls is standard practice in the diagnostics industry. Predicting subzero temperature stability using the same practice is frequently criticized but nevertheless heavily relied upon. We compared the ability to predict analyte recovery during frozen storage using 3 separate strategies: traditional accelerated studies with Arrhenius modeling, and extrapolation of recovery at 20% of shelf life using either ordinary least squares or a radical equation y = B1x(0.5) + B0. Computer simulations were performed to establish equivalence of statistical power to discern the expected changes during frozen storage or accelerated stress. This was followed by actual predictive and follow-up confirmatory testing of 12 chemistry and immunoassay analytes. Linear extrapolations tended to be the most conservative in the predicted percent recovery, reducing customer and patient risk. However, the majority of analytes followed a rate of change that slowed over time, which was fit best to a radical equation of the form y = B1x(0.5) + B0. Other evidence strongly suggested that the slowing of the rate was not due to higher-order kinetics, but to changes in the matrix during storage. Predicting shelf life of frozen products through extrapolation of early initial real-time storage analyte recovery should be considered the most accurate method. Although in this study the time required for a prediction was longer than a typical accelerated testing protocol, there are less potential sources of error, reduced costs, and a lower expenditure of resources. © 2016 American Association for Clinical Chemistry.

  12. Two new modified Gauss-Seidel methods for linear system with M-matrices

    Zheng, Bing; Miao, Shu-Xin

    2009-12-01

    In 2002, H. Kotakemori et al. proposed the modified Gauss-Seidel (MGS) method for solving the linear system with the preconditioner [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner () J. Comput. Appl. Math. 145 (2002) 373-378]. Since this preconditioner is constructed by only the largest element on each row of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the nth row. In the present paper, to deal with this drawback, we propose two new preconditioners. The convergence and comparison theorems of the modified Gauss-Seidel methods with these two preconditioners for solving the linear system are established. The convergence rates of the new proposed preconditioned methods are compared. In addition, numerical experiments are used to show the effectiveness of the new MGS methods.

  13. Local linearization methods for the numerical integration of ordinary differential equations: An overview

    Jimenez, J.C.

    2009-06-01

    Local Linearization (LL) methods conform a class of one-step explicit integrators for ODEs derived from the following primary and common strategy: the vector field of the differential equation is locally (piecewise) approximated through a first-order Taylor expansion at each time step, thus obtaining successive linear equations that are explicitly integrated. Hereafter, the LL approach may include some additional strategies to improve that basic affine approximation. Theoretical and practical results have shown that the LL integrators have a number of convenient properties. These include arbitrary order of convergence, A-stability, linearization preserving, regularity under quite general conditions, preservation of the dynamics of the exact solution around hyperbolic equilibrium points and periodic orbits, integration of stiff and high-dimensional equations, low computational cost, and others. In this paper, a review of the LL methods and their properties is presented. (author)

  14. Comparison of different methods for the solution of sets of linear equations

    Bilfinger, T.; Schmidt, F.

    1978-06-01

    The application of the conjugate-gradient methods as novel general iterative methods for the solution of sets of linear equations with symmetrical systems matrices led to this paper, where a comparison of these methods with the conventional differently accelerated Gauss-Seidel iteration was carried out. In additon, the direct Cholesky method was also included in the comparison. The studies referred mainly to memory requirement, computing time, speed of convergence, and accuracy of different conditions of the systems matrices, by which also the sensibility of the methods with respect to the influence of truncation errors may be recognized. (orig.) 891 RW [de

  15. Robust fault detection of linear systems using a computationally efficient set-membership method

    Tabatabaeipour, Mojtaba; Bak, Thomas

    2014-01-01

    In this paper, a computationally efficient set-membership method for robust fault detection of linear systems is proposed. The method computes an interval outer-approximation of the output of the system that is consistent with the model, the bounds on noise and disturbance, and the past measureme...... is trivially parallelizable. The method is demonstrated for fault detection of a hydraulic pitch actuator of a wind turbine. We show the effectiveness of the proposed method by comparing our results with two zonotope-based set-membership methods....

  16. An overview of solution methods for multi-objective mixed integer linear programming programs

    Andersen, Kim Allan; Stidsen, Thomas Riis

    Multiple objective mixed integer linear programming (MOMIP) problems are notoriously hard to solve to optimality, i.e. finding the complete set of non-dominated solutions. We will give an overview of existing methods. Among those are interactive methods, the two phases method and enumeration...... methods. In particular we will discuss the existing branch and bound approaches for solving multiple objective integer programming problems. Despite the fact that branch and bound methods has been applied successfully to integer programming problems with one criterion only a few attempts has been made...

  17. Extrapolated HPGe efficiency estimates based on a single calibration measurement

    Winn, W.G.

    1994-01-01

    Gamma spectroscopists often must analyze samples with geometries for which their detectors are not calibrated. The effort to experimentally recalibrate a detector for a new geometry can be quite time consuming, causing delay in reporting useful results. Such concerns have motivated development of a method for extrapolating HPGe efficiency estimates from an existing single measured efficiency. Overall, the method provides useful preliminary results for analyses that do not require exceptional accuracy, while reliably bracketing the credible range. The estimated efficiency element-of for a uniform sample in a geometry with volume V is extrapolated from the measured element-of 0 of the base sample of volume V 0 . Assuming all samples are centered atop the detector for maximum efficiency, element-of decreases monotonically as V increases about V 0 , and vice versa. Extrapolation of high and low efficiency estimates element-of h and element-of L provides an average estimate of element-of = 1/2 [element-of h + element-of L ] ± 1/2 [element-of h - element-of L ] (general) where an uncertainty D element-of = 1/2 (element-of h - element-of L ] brackets limits for a maximum possible error. The element-of h and element-of L both diverge from element-of 0 as V deviates from V 0 , causing D element-of to increase accordingly. The above concepts guided development of both conservative and refined estimates for element-of

  18. A Simple and Convenient Method of Multiple Linear Regression to Calculate Iodine Molecular Constants

    Cooper, Paul D.

    2010-01-01

    A new procedure using a student-friendly least-squares multiple linear-regression technique utilizing a function within Microsoft Excel is described that enables students to calculate molecular constants from the vibronic spectrum of iodine. This method is advantageous pedagogically as it calculates molecular constants for ground and excited…

  19. Linear shrinkage test: justification for its reintroduction as a standard South African test method

    Sampson, LR

    2009-06-04

    Full Text Available Several problems with the linear shrinkage test specified in Method A4 of the THM 1 1979 were addressed as part of this investigation in an effort to improve the alleged poor reproducibility of the test and justify its reintroduction into THM 1. A...

  20. Asymptotic method for non-linear magnetosonic waves in an isothermal plasma with a finite conductivity

    Fusco, D [Messina Univ. (Italy). Instituto de Matematica

    1979-01-01

    The paper is concerned with a three-dimensional theory of non-linear magnetosonic waves in a turbulent plasma. A perturbation method is used that allows a transport equation, like Burgers equation but with a variable coefficient to be obtained.

  1. Engineering method of calculation and choice of main parameters of the linear induction accelerator inductors

    В.Т. Чемерис

    2006-04-01

    Full Text Available  There is a method of simplified calculation and design parameters choice elaborated in this article with corresponding basing for the induction system of electron-beam sterilizer on the base of linear induction accelerator taking into account the parameters of magnetic material for production of cores and parameters of pulsed voltage.

  2. The H-N method for solving linear transport equation: theory and application

    Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

    2002-01-01

    The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

  3. Slab albedo for linearly and quadratically anisotropic scattering kernel with modified F{sub N} method

    Tuereci, R. Goekhan [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School

    2017-11-15

    One speed, time independent and homogeneous medium neutron transport equation is solved with the anisotropic scattering which includes both the linearly and the quadratically anisotropic scattering kernel. Having written Case's eigenfunctions and the orthogonality relations among of these eigenfunctions, slab albedo problem is investigated as numerically by using Modified F{sub N} method. Selected numerical results are presented in tables.

  4. An Empirical Comparison of Five Linear Equating Methods for the NEAT Design

    Suh, Youngsuk; Mroch, Andrew A.; Kane, Michael T.; Ripkey, Douglas R.

    2009-01-01

    In this study, a data base containing the responses of 40,000 candidates to 90 multiple-choice questions was used to mimic data sets for 50-item tests under the "nonequivalent groups with anchor test" (NEAT) design. Using these smaller data sets, we evaluated the performance of five linear equating methods for the NEAT design with five levels of…

  5. National pattern for the realization of the unit of the dose speed absorbed in air for beta radiation. (Method: Ionometer, cavity of Bragg-Gray implemented in an extrapolation chamber with electrodes of variable separation, exposed to a field of beta radiation of 90Sr/90Y)

    Alvarez R, M. T.; Morales P, J. R.

    2001-01-01

    From the year of 1987 the Department of Metrology of the ININ, in their Secondary Laboratory of Calibration Dosimetric, has a patron group of sources of radiation beta and an extrapolation chamber of electrodes of variable separation.Their objective is to carry out of the unit of the dose speed absorbed in air for radiation beta. It uses the ionometric method, cavity Bragg-Gray in the extrapolation chamber with which it counts. The services that offers are: i) it Calibration : Radioactive Fuentes of radiation beta, isotopes: 90 Sr/ 90 Y; Ophthalmic applicators 9 0 S r/ 90 Y; Instruments for detection of beta radiation with to the radiological protection: Ionization chambers, Geiger-Muller, etc.; Personal Dosemeters. ii) Irradiation with beta radiation of materials to the investigation. (Author)

  6. A Revised Piecewise Linear Recursive Convolution FDTD Method for Magnetized Plasmas

    Liu Song; Zhong Shuangying; Liu Shaobin

    2005-01-01

    The piecewise linear recursive convolution (PLRC) finite-different time-domain (FDTD) method improves accuracy over the original recursive convolution (RC) FDTD approach and current density convolution (JEC) but retains their advantages in speed and efficiency. This paper describes a revised piecewise linear recursive convolution PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations of the reflection and transmission coefficients through a magnetized plasma layer. The results show that the revised PLRC-FDTD method has improved the accuracy over the original RC FDTD method and JEC FDTD method

  7. A Simple Linear Regression Method for Quantitative Trait Loci Linkage Analysis With Censored Observations

    Anderson, Carl A.; McRae, Allan F.; Visscher, Peter M.

    2006-01-01

    Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using...

  8. Interior-Point Method for Non-Linear Non-Convex Optimization

    Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan

    2004-01-01

    Roč. 11, č. 5-6 (2004), s. 431-453 ISSN 1070-5325 R&D Projects: GA AV ČR IAA1030103 Institutional research plan: CEZ:AV0Z1030915 Keywords : non-linear programming * interior point methods * indefinite systems * indefinite preconditioners * preconditioned conjugate gradient method * merit functions * algorithms * computational experiments Subject RIV: BA - General Mathematics Impact factor: 0.727, year: 2004

  9. Method for solving fully fuzzy linear programming problems using deviation degree measure

    Haifang Cheng; Weilai Huang; Jianhu Cai

    2013-01-01

    A new ful y fuzzy linear programming (FFLP) prob-lem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crispδ-parametric linear programming (LP) problem. Giving the value of deviation degree in each constraint, the δ-fuzzy optimal so-lution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict: to improve the va-lues of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to il ustrate the proposed method.

  10. Study on non-linear bistable dynamics model based EEG signal discrimination analysis method.

    Ying, Xiaoguo; Lin, Han; Hui, Guohua

    2015-01-01

    Electroencephalogram (EEG) is the recording of electrical activity along the scalp. EEG measures voltage fluctuations generating from ionic current flows within the neurons of the brain. EEG signal is looked as one of the most important factors that will be focused in the next 20 years. In this paper, EEG signal discrimination based on non-linear bistable dynamical model was proposed. EEG signals were processed by non-linear bistable dynamical model, and features of EEG signals were characterized by coherence index. Experimental results showed that the proposed method could properly extract the features of different EEG signals.

  11. Radiographic film: surface dose extrapolation techniques

    Cheung, T.; Yu, P.K.N.; Butson, M.J.; Cancer Services, Wollongong, NSW; Currie, M.

    2004-01-01

    Full text: Assessment of surface dose delivered from radiotherapy x-ray beams for optimal results should be performed both inside and outside the prescribed treatment fields An extrapolation technique can be used with radiographic film to perform surface dose assessment for open field high energy x-ray beams. This can produce an accurate 2 dimensional map of surface dose if required. Results have shown that surface % dose can be estimated within ±3% of parallel plate ionisation chamber results with radiographic film using a series of film layers to produce an extrapolated result. Extrapolated percentage dose assessment for 10cm, 20cmand 30cm square fields was estimated to be 15% ± 2%, 29% ± 3% and 38% ± 3% at the central axis and relatively uniform across the treatment field. Corresponding parallel plate ionisation chamber measurement are 16%, 27% and 37% respectively. Surface doses are also measured outside the treatment field which are mainly due to scattered electron contamination. To achieve this result, film calibration curves must be irradiated to similar x-ray field sizes as the experimental film to minimize quantitative variations in film optical density caused by varying x-ray spectrum with field size. Copyright (2004) Australasian College of Physical Scientists and Engineers in Medicine

  12. Surface dose extrapolation measurements with radiographic film

    Butson, Martin J; Cheung Tsang; Yu, Peter K N; Currie, Michael

    2004-01-01

    Assessment of surface dose delivered from radiotherapy x-ray beams for optimal results should be performed both inside and outside the prescribed treatment fields. An extrapolation technique can be used with radiographic film to perform surface dose assessment for open field high energy x-ray beams. This can produce an accurate two-dimensional map of surface dose if required. Results have shown that the surface percentage dose can be estimated within ±3% of parallel plate ionization chamber results with radiographic film using a series of film layers to produce an extrapolated result. Extrapolated percentage dose assessment for 10 cm, 20 cm and 30 cm square fields was estimated to be 15% ± 2%, 29% ± 3% and 38% ± 3% at the central axis and relatively uniform across the treatment field. The corresponding parallel plate ionization chamber measurements are 16%, 27% and 37%, respectively. Surface doses are also measured outside the treatment field which are mainly due to scattered electron contamination. To achieve this result, film calibration curves must be irradiated to similar x-ray field sizes as the experimental film to minimize quantitative variations in film optical density caused by varying x-ray spectrum with field size. (note)

  13. Restoring the missing features of the corrupted speech using linear interpolation methods

    Rassem, Taha H.; Makbol, Nasrin M.; Hasan, Ali Muttaleb; Zaki, Siti Syazni Mohd; Girija, P. N.

    2017-10-01

    One of the main challenges in the Automatic Speech Recognition (ASR) is the noise. The performance of the ASR system reduces significantly if the speech is corrupted by noise. In spectrogram representation of a speech signal, after deleting low Signal to Noise Ratio (SNR) elements, the incomplete spectrogram is obtained. In this case, the speech recognizer should make modifications to the spectrogram in order to restore the missing elements, which is one direction. In another direction, speech recognizer should be able to restore the missing elements due to deleting low SNR elements before performing the recognition. This is can be done using different spectrogram reconstruction methods. In this paper, the geometrical spectrogram reconstruction methods suggested by some researchers are implemented as a toolbox. In these geometrical reconstruction methods, the linear interpolation along time or frequency methods are used to predict the missing elements between adjacent observed elements in the spectrogram. Moreover, a new linear interpolation method using time and frequency together is presented. The CMU Sphinx III software is used in the experiments to test the performance of the linear interpolation reconstruction method. The experiments are done under different conditions such as different lengths of the window and different lengths of utterances. Speech corpus consists of 20 males and 20 females; each one has two different utterances are used in the experiments. As a result, 80% recognition accuracy is achieved with 25% SNR ratio.

  14. Generalization of Asaoka method to linearly anisotropic scattering: benchmark data in cylindrical geometry

    Sanchez, Richard.

    1975-11-01

    The Integral Transform Method for the neutron transport equation has been developed in last years by Asaoka and others. The method uses Fourier transform techniques in solving isotropic one-dimensional transport problems in homogeneous media. The method has been extended to linearly anisotropic transport in one-dimensional homogeneous media. Series expansions were also obtained using Hembd techniques for the new anisotropic matrix elements in cylindrical geometry. Carlvik spatial-spherical harmonics method was generalized to solve the same problem. By applying a relation between the isotropic and anisotropic one-dimensional kernels, it was demonstrated that anisotropic matrix elements can be calculated by a linear combination of a few isotropic matrix elements. This means in practice that the anisotropic problem of order N with the N+2 isotropic matrix for the plane and spherical geometries, and N+1 isotropic matrix for cylindrical geometries can be solved. A method of solving linearly anisotropic one-dimensional transport problems in homogeneous media was defined by applying Mika and Stankiewicz observations: isotropic matrix elements were computed by Hembd series and anisotropic matrix elements then calculated from recursive relations. The method has been applied to albedo and critical problems in cylindrical geometries. Finally, a number of results were computed with 12-digit accuracy for use as benchmarks [fr

  15. Response Load Extrapolation for Wind Turbines during Operation Based on Average Conditional Exceedance Rates

    Toft, Henrik Stensgaard; Naess, Arvid; Saha, Nilanjan

    2011-01-01

    to cases where the Gumbel distribution is the appropriate asymptotic extreme value distribution. However, two extra parameters are introduced by which a more general and flexible class of extreme value distributions is obtained with the Gumbel distribution as a subclass. The general method is implemented...... within a hierarchical model where the variables that influence the loading are divided into ergodic variables and time-invariant non-ergodic variables. The presented method for statistical response load extrapolation was compared with the existing methods based on peak extrapolation for the blade out......The paper explores a recently developed method for statistical response load (load effect) extrapolation for application to extreme response of wind turbines during operation. The extrapolation method is based on average conditional exceedance rates and is in the present implementation restricted...

  16. Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method

    Seçil YALAZ

    2016-10-01

    Full Text Available Our work on regression and classification provides a new contribution to the analysis of time series used in many areas for years. Owing to the fact that convergence could not obtained with the methods used in autocorrelation fixing process faced with time series regression application, success is not met or fall into obligation of changing the models’ degree. Changing the models’ degree may not be desirable in every situation. In our study, recommended for these situations, time series data was fuzzified by using the simple membership function and fuzzy rule generation technique (SMRGT and to estimate future an equation has created by applying fuzzy least square regression (FLSR method which is a simple linear regression method to this data. Although SMRGT has success in determining the flow discharge in open channels and can be used confidently for flow discharge modeling in open canals, as well as in pipe flow with some modifications, there is no clue about that this technique is successful in fuzzy linear regression modeling. Therefore, in order to address the luck of such a modeling, a new hybrid model has been described within this study. In conclusion, to demonstrate our methods’ efficiency, classical linear regression for time series data and linear regression for fuzzy time series data were applied to two different data sets, and these two approaches performances were compared by using different measures.

  17. A linear multiple balance method for discrete ordinates neutron transport equations

    Park, Chang Je; Cho, Nam Zin

    2000-01-01

    A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

  18. Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method

    Olumuyiwa A. Agbolade

    2017-01-01

    Full Text Available The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.

  19. Exact solution to the Coulomb wave using the linearized phase-amplitude method

    Shuji Kiyokawa

    2015-08-01

    Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

  20. A spectral analysis of the domain decomposed Monte Carlo method for linear systems

    Slattery, S. R.; Wilson, P. P. H. [Engineering Physics Department, University of Wisconsin - Madison, 1500 Engineering Dr., Madison, WI 53706 (United States); Evans, T. M. [Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37830 (United States)

    2013-07-01

    The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

  1. A spectral analysis of the domain decomposed Monte Carlo method for linear systems

    Slattery, S. R.; Wilson, P. P. H.; Evans, T. M.

    2013-01-01

    The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

  2. Linear least-squares method for global luminescent oil film skin friction field analysis

    Lee, Taekjin; Nonomura, Taku; Asai, Keisuke; Liu, Tianshu

    2018-06-01

    A data analysis method based on the linear least-squares (LLS) method was developed for the extraction of high-resolution skin friction fields from global luminescent oil film (GLOF) visualization images of a surface in an aerodynamic flow. In this method, the oil film thickness distribution and its spatiotemporal development are measured by detecting the luminescence intensity of the thin oil film. From the resulting set of GLOF images, the thin oil film equation is solved to obtain an ensemble-averaged (steady) skin friction field as an inverse problem. In this paper, the formulation of a discrete linear system of equations for the LLS method is described, and an error analysis is given to identify the main error sources and the relevant parameters. Simulations were conducted to evaluate the accuracy of the LLS method and the effects of the image patterns, image noise, and sample numbers on the results in comparison with the previous snapshot-solution-averaging (SSA) method. An experimental case is shown to enable the comparison of the results obtained using conventional oil flow visualization and those obtained using both the LLS and SSA methods. The overall results show that the LLS method is more reliable than the SSA method and the LLS method can yield a more detailed skin friction topology in an objective way.

  3. A simple extrapolation of thermodynamic perturbation theory to infinite order

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2015-01-01

    Recent analyses of the third and fourth order perturbation contributions to the equations of state for square well spheres and Lennard-Jones chains show trends that persist across orders and molecular models. In particular, the ratio between orders (e.g., A 3 /A 2 , where A i is the ith order perturbation contribution) exhibits a peak when plotted with respect to density. The trend resembles a Gaussian curve with the peak near the critical density. This observation can form the basis for a simple recursion and extrapolation from the highest available order to infinite order. The resulting extrapolation is analytic and therefore cannot fully characterize the critical region, but it remarkably improves accuracy, especially for the binodal curve. Whereas a second order theory is typically accurate for the binodal at temperatures within 90% of the critical temperature, the extrapolated result is accurate to within 99% of the critical temperature. In addition to square well spheres and Lennard-Jones chains, we demonstrate how the method can be applied semi-empirically to the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT)

  4. Predicting structural properties of fluids by thermodynamic extrapolation

    Mahynski, Nathan A.; Jiao, Sally; Hatch, Harold W.; Blanco, Marco A.; Shen, Vincent K.

    2018-05-01

    We describe a methodology for extrapolating the structural properties of multicomponent fluids from one thermodynamic state to another. These properties generally include features of a system that may be computed from an individual configuration such as radial distribution functions, cluster size distributions, or a polymer's radius of gyration. This approach is based on the principle of using fluctuations in a system's extensive thermodynamic variables, such as energy, to construct an appropriate Taylor series expansion for these structural properties in terms of intensive conjugate variables, such as temperature. Thus, one may extrapolate these properties from one state to another when the series is truncated to some finite order. We demonstrate this extrapolation for simple and coarse-grained fluids in both the canonical and grand canonical ensembles, in terms of both temperatures and the chemical potentials of different components. The results show that this method is able to reasonably approximate structural properties of such fluids over a broad range of conditions. Consequently, this methodology may be employed to increase the computational efficiency of molecular simulations used to measure the structural properties of certain fluid systems, especially those used in high-throughput or data-driven investigations.

  5. Line-of-sight extrapolation noise in dust polarization

    Poh, Jason; Dodelson, Scott

    2017-05-19

    The B-modes of polarization at frequencies ranging from 50-1000 GHz are produced by Galactic dust, lensing of primordial E-modes in the cosmic microwave background (CMB) by intervening large scale structure, and possibly by primordial B-modes in the CMB imprinted by gravitational waves produced during inflation. The conventional method used to separate the dust component of the signal is to assume that the signal at high frequencies (e.g., 350 GHz) is due solely to dust and then extrapolate the signal down to lower frequency (e.g., 150 GHz) using the measured scaling of the polarized dust signal amplitude with frequency. For typical Galactic thermal dust temperatures of about 20K, these frequencies are not fully in the Rayleigh-Jeans limit. Therefore, deviations in the dust cloud temperatures from cloud to cloud will lead to different scaling factors for clouds of different temperatures. Hence, when multiple clouds of different temperatures and polarization angles contribute to the integrated line-of-sight polarization signal, the relative contribution of individual clouds to the integrated signal can change between frequencies. This can cause the integrated signal to be decorrelated in both amplitude and direction when extrapolating in frequency. Here we carry out a Monte Carlo analysis on the impact of this line-of-sight extrapolation noise, enabling us to quantify its effect. Using results from the Planck experiment, we find that this effect is small, more than an order of magnitude smaller than the current uncertainties. However, line-of-sight extrapolation noise may be a significant source of uncertainty in future low-noise primordial B-mode experiments. Scaling from Planck results, we find that accounting for this uncertainty becomes potentially important when experiments are sensitive to primordial B-mode signals with amplitude r < 0.0015 .

  6. Effective Orthorhombic Anisotropic Models for Wave field Extrapolation

    Ibanez Jacome, Wilson

    2013-05-01

    Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models, to reproduce wave propagation phenomena in the Earth\\'s subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, I generate effective isotropic inhomogeneous models that are capable of reproducing the first-arrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, I develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic one, is represented by a sixth order polynomial equation that includes the fastest solution corresponding to outgoing P-waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, which is done by explicitly solving the isotropic eikonal equation for the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. I extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the

  7. Linearly decoupled energy-stable numerical methods for multi-component two-phase compressible flow

    Kou, Jisheng

    2017-12-06

    In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are constructed based on the scalar auxiliary variable (SAV) approaches for Helmholtz free energy and the intermediate velocities that are designed to decouple the tight relationship between velocity and molar densities. The intermediate velocities are also involved in the discrete momentum equation to ensure a consistency relationship with the mass balance equations. Moreover, we propose a component-wise SAV approach for a multi-component fluid, which requires solving a sequence of linear, separate mass balance equations. We prove that the methods have the unconditional energy-dissipation feature. Numerical results are presented to verify the effectiveness of the proposed methods.

  8. An Online Method for Interpolating Linear Parametric Reduced-Order Models

    Amsallem, David; Farhat, Charbel

    2011-01-01

    A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon. © 2011 Society for Industrial and Applied Mathematics.

  9. Two media method for linear attenuation coefficient determination of irregular soil samples

    Vici, Carlos Henrique Georges

    2004-01-01

    In several situations of nuclear applications, the knowledge of gamma-ray linear attenuation coefficient for irregular samples is necessary, such as in soil physics and geology. This work presents the validation of a methodology for the determination of the linear attenuation coefficient (μ) of irregular shape samples, in such a way that it is not necessary to know the thickness of the considered sample. With this methodology irregular soil samples (undeformed field samples) from Londrina region, north of Parana were studied. It was employed the two media method for the μ determination. It consists of the μ determination through the measurement of a gamma-ray beam attenuation by the sample sequentially immersed in two different media, with known and appropriately chosen attenuation coefficients. For comparison, the theoretical value of μ was calculated by the product of the mass attenuation coefficient, obtained by the WinXcom code, and the measured value of the density sample. This software employs the chemical composition of the samples and supplies a table of the mass attenuation coefficients versus the photon energy. To verify the validity of the two media method, compared with the simple gamma ray transmission method, regular pome stone samples were used. With these results for the attenuation coefficients and their respective deviations, it was possible to compare the two methods. In this way we concluded that the two media method is a good tool for the determination of the linear attenuation coefficient of irregular materials, particularly in the study of soils samples. (author)

  10. The linear characteristic method for spatially discretizing the discrete ordinates equations in (x,y)-geometry

    Larsen, E.W.; Alcouffe, R.E.

    1981-01-01

    In this article a new linear characteristic (LC) spatial differencing scheme for the discrete ordinates equations in (x,y)-geometry is described and numerical comparisons are given with the diamond difference (DD) method. The LC method is more stable with mesh size and is generally much more accurate than the DD method on both fine and coarse meshes, for eigenvalue and deep penetration problems. The LC method is based on computations involving the exact solution of a cell problem which has spatially linear boundary conditions and interior source. The LC method is coupled to the diffusion synthetic acceleration (DSA) algorithm in that the linear variations of the source are determined in part by the results of the DSA calculation from the previous inner iteration. An inexpensive negative-flux fixup is used which has very little effect on the accuracy of the solution. The storage requirements for LC are essentially the same as that for DD, while the computational times for LC are generally less than twice the DD computational times for the same mesh. This increase in computational cost is offset if one computes LC solutions on somewhat coarser meshes than DD; the resulting LC solutions are still generally much more accurate than the DD solutions. (orig.) [de

  11. Non-linear analysis of skew thin plate by finite difference method

    Kim, Chi Kyung; Hwang, Myung Hwan

    2012-01-01

    This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed

  12. A method for fitting regression splines with varying polynomial order in the linear mixed model.

    Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

    2006-02-15

    The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

  13. Linear and nonlinear methods in modeling the aqueous solubility of organic compounds.

    Catana, Cornel; Gao, Hua; Orrenius, Christian; Stouten, Pieter F W

    2005-01-01

    Solubility data for 930 diverse compounds have been analyzed using linear Partial Least Square (PLS) and nonlinear PLS methods, Continuum Regression (CR), and Neural Networks (NN). 1D and 2D descriptors from MOE package in combination with E-state or ISIS keys have been used. The best model was obtained using linear PLS for a combination between 22 MOE descriptors and 65 ISIS keys. It has a correlation coefficient (r2) of 0.935 and a root-mean-square error (RMSE) of 0.468 log molar solubility (log S(w)). The model validated on a test set of 177 compounds not included in the training set has r2 0.911 and RMSE 0.475 log S(w). The descriptors were ranked according to their importance, and at the top of the list have been found the 22 MOE descriptors. The CR model produced results as good as PLS, and because of the way in which cross-validation has been done it is expected to be a valuable tool in prediction besides PLS model. The statistics obtained using nonlinear methods did not surpass those got with linear ones. The good statistic obtained for linear PLS and CR recommends these models to be used in prediction when it is difficult or impossible to make experimental measurements, for virtual screening, combinatorial library design, and efficient leads optimization.

  14. Alpins and thibos vectorial astigmatism analyses: proposal of a linear regression model between methods

    Giuliano de Oliveira Freitas

    2013-10-01

    Full Text Available PURPOSE: To determine linear regression models between Alpins descriptive indices and Thibos astigmatic power vectors (APV, assessing the validity and strength of such correlations. METHODS: This case series prospectively assessed 62 eyes of 31 consecutive cataract patients with preoperative corneal astigmatism between 0.75 and 2.50 diopters in both eyes. Patients were randomly assorted among two phacoemulsification groups: one assigned to receive AcrySof®Toric intraocular lens (IOL in both eyes and another assigned to have AcrySof Natural IOL associated with limbal relaxing incisions, also in both eyes. All patients were reevaluated postoperatively at 6 months, when refractive astigmatism analysis was performed using both Alpins and Thibos methods. The ratio between Thibos postoperative APV and preoperative APV (APVratio and its linear regression to Alpins percentage of success of astigmatic surgery, percentage of astigmatism corrected and percentage of astigmatism reduction at the intended axis were assessed. RESULTS: Significant negative correlation between the ratio of post- and preoperative Thibos APVratio and Alpins percentage of success (%Success was found (Spearman's ρ=-0.93; linear regression is given by the following equation: %Success = (-APVratio + 1.00x100. CONCLUSION: The linear regression we found between APVratio and %Success permits a validated mathematical inference concerning the overall success of astigmatic surgery.

  15. A Novel Method of Robust Trajectory Linearization Control Based on Disturbance Rejection

    Xingling Shao

    2014-01-01

    Full Text Available A novel method of robust trajectory linearization control for a class of nonlinear systems with uncertainties based on disturbance rejection is proposed. Firstly, on the basis of trajectory linearization control (TLC method, a feedback linearization based control law is designed to transform the original tracking error dynamics to the canonical integral-chain form. To address the issue of reducing the influence made by uncertainties, with tracking error as input, linear extended state observer (LESO is constructed to estimate the tracking error vector, as well as the uncertainties in an integrated manner. Meanwhile, the boundedness of the estimated error is investigated by theoretical analysis. In addition, decoupled controller (which has the characteristic of well-tuning and simple form based on LESO is synthesized to realize the output tracking for closed-loop system. The closed-loop stability of the system under the proposed LESO-based control structure is established. Also, simulation results are presented to illustrate the effectiveness of the control strategy.

  16. A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate

    Min Sun

    2014-01-01

    Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.

  17. A simple method for HPLC retention time prediction: linear calibration using two reference substances.

    Sun, Lei; Jin, Hong-Yu; Tian, Run-Tao; Wang, Ming-Juan; Liu, Li-Na; Ye, Liu-Ping; Zuo, Tian-Tian; Ma, Shuang-Cheng

    2017-01-01

    Analysis of related substances in pharmaceutical chemicals and multi-components in traditional Chinese medicines needs bulk of reference substances to identify the chromatographic peaks accurately. But the reference substances are costly. Thus, the relative retention (RR) method has been widely adopted in pharmacopoeias and literatures for characterizing HPLC behaviors of those reference substances unavailable. The problem is it is difficult to reproduce the RR on different columns due to the error between measured retention time (t R ) and predicted t R in some cases. Therefore, it is useful to develop an alternative and simple method for prediction of t R accurately. In the present study, based on the thermodynamic theory of HPLC, a method named linear calibration using two reference substances (LCTRS) was proposed. The method includes three steps, procedure of two points prediction, procedure of validation by multiple points regression and sequential matching. The t R of compounds on a HPLC column can be calculated by standard retention time and linear relationship. The method was validated in two medicines on 30 columns. It was demonstrated that, LCTRS method is simple, but more accurate and more robust on different HPLC columns than RR method. Hence quality standards using LCTRS method are easy to reproduce in different laboratories with lower cost of reference substances.

  18. Direct integral linear least square regression method for kinetic evaluation of hepatobiliary scintigraphy

    Shuke, Noriyuki

    1991-01-01

    In hepatobiliary scintigraphy, kinetic model analysis, which provides kinetic parameters like hepatic extraction or excretion rate, have been done for quantitative evaluation of liver function. In this analysis, unknown model parameters are usually determined using nonlinear least square regression method (NLS method) where iterative calculation and initial estimate for unknown parameters are required. As a simple alternative to NLS method, direct integral linear least square regression method (DILS method), which can determine model parameters by a simple calculation without initial estimate, is proposed, and tested the applicability to analysis of hepatobiliary scintigraphy. In order to see whether DILS method could determine model parameters as good as NLS method, or to determine appropriate weight for DILS method, simulated theoretical data based on prefixed parameters were fitted to 1 compartment model using both DILS method with various weightings and NLS method. The parameter values obtained were then compared with prefixed values which were used for data generation. The effect of various weights on the error of parameter estimate was examined, and inverse of time was found to be the best weight to make the error minimum. When using this weight, DILS method could give parameter values close to those obtained by NLS method and both parameter values were very close to prefixed values. With appropriate weighting, the DILS method could provide reliable parameter estimate which is relatively insensitive to the data noise. In conclusion, the DILS method could be used as a simple alternative to NLS method, providing reliable parameter estimate. (author)

  19. Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method

    Desmal, Abdulla

    2014-07-01

    A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.

  20. A Projected Non-linear Conjugate Gradient Method for Interactive Inverse Kinematics

    Engell-Nørregård, Morten; Erleben, Kenny

    2009-01-01

    Inverse kinematics is the problem of posing an articulated figure to obtain a wanted goal, without regarding inertia and forces. Joint limits are modeled as bounds on individual degrees of freedom, leading to a box-constrained optimization problem. We present A projected Non-linear Conjugate...... Gradient optimization method suitable for box-constrained optimization problems for inverse kinematics. We show application on inverse kinematics positioning of a human figure. Performance is measured and compared to a traditional Jacobian Transpose method. Visual quality of the developed method...

  1. Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method

    Desmal, Abdulla; Bagci, Hakan

    2014-01-01

    A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.

  2. Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems

    Oskar Cahueñas

    2013-05-01

    Full Text Available We address the issue of approximating the pseudoinverse of the coefficient matrix for dynamically building preconditioning strategies for the numerical solution of large dense linear least-squares problems. The new preconditioning strategies are embedded into simple and well-known iterative schemes that avoid the use of the, usually ill-conditioned, normal equations. We analyze a scheme to approximate the pseudoinverse, based on Schulz iterative method, and also different iterative schemes, based on extensions of Richardson's method, and the conjugate gradient method, that are suitable for preconditioning strategies. We present preliminary numerical results to illustrate the advantages of the proposed schemes.

  3. Linearized self-consistent quasiparticle GW method: Application to semiconductors and simple metals

    Kutepov, A. L.

    2017-01-01

    We present a code implementing the linearized self-consistent quasiparticle GW method (QSGW) in the LAPW basis. Our approach is based on the linearization of the self-energy around zero frequency which differs it from the existing implementations of the QSGW method. The linearization allows us to use Matsubara frequencies instead of working on the real axis. This results in efficiency gains by switching to the imaginary time representation in the same way as in the space time method. The all electron LAPW basis set eliminates the need for pseudopotentials. We discuss the advantages of our approach, such as its N 3 scaling with the system size N, as well as its shortcomings. We apply our approach to study the electronic properties of selected semiconductors, insulators, and simple metals and show that our code produces the results very close to the previously published QSGW data. Our implementation is a good platform for further many body diagrammatic resummations such as the vertex-corrected GW approach and the GW+DMFT method.

  4. Linearized image reconstruction method for ultrasound modulated electrical impedance tomography based on power density distribution

    Song, Xizi; Xu, Yanbin; Dong, Feng

    2017-01-01

    Electrical resistance tomography (ERT) is a promising measurement technique with important industrial and clinical applications. However, with limited effective measurements, it suffers from poor spatial resolution due to the ill-posedness of the inverse problem. Recently, there has been an increasing research interest in hybrid imaging techniques, utilizing couplings of physical modalities, because these techniques obtain much more effective measurement information and promise high resolution. Ultrasound modulated electrical impedance tomography (UMEIT) is one of the newly developed hybrid imaging techniques, which combines electric and acoustic modalities. A linearized image reconstruction method based on power density is proposed for UMEIT. The interior data, power density distribution, is adopted to reconstruct the conductivity distribution with the proposed image reconstruction method. At the same time, relating the power density change to the change in conductivity, the Jacobian matrix is employed to make the nonlinear problem into a linear one. The analytic formulation of this Jacobian matrix is derived and its effectiveness is also verified. In addition, different excitation patterns are tested and analyzed, and opposite excitation provides the best performance with the proposed method. Also, multiple power density distributions are combined to implement image reconstruction. Finally, image reconstruction is implemented with the linear back-projection (LBP) algorithm. Compared with ERT, with the proposed image reconstruction method, UMEIT can produce reconstructed images with higher quality and better quantitative evaluation results. (paper)

  5. Modifications of Steepest Descent Method and Conjugate Gradient Method Against Noise for Ill-posed Linear Systems

    Chein-Shan Liu

    2012-04-01

    Full Text Available It is well known that the numerical algorithms of the steepest descent method (SDM, and the conjugate gradient method (CGM are effective for solving well-posed linear systems. However, they are vulnerable to noisy disturbance for solving ill-posed linear systems. We propose the modifications of SDM and CGM, namely the modified steepest descent method (MSDM, and the modified conjugate gradient method (MCGM. The starting point is an invariant manifold defined in terms of a minimum functional and a fictitious time-like variable; however, in the final stage we can derive a purely iterative algorithm including an acceleration parameter. Through the Hopf bifurcation, this parameter indeed plays a major role to switch the situation of slow convergence to a new situation that the functional is stepwisely decreased very fast. Several numerical examples are examined and compared with exact solutions, revealing that the new algorithms of MSDM and MCGM have good computational efficiency and accuracy, even for the highly ill-conditioned linear equations system with a large noise being imposed on the given data.

  6. Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers

    Li, Deng-Feng

    2016-01-01

    This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .

  7. Simple estimating method of damages of concrete gravity dam based on linear dynamic analysis

    Sasaki, T.; Kanenawa, K.; Yamaguchi, Y. [Public Works Research Institute, Tsukuba, Ibaraki (Japan). Hydraulic Engineering Research Group

    2004-07-01

    Due to the occurrence of large earthquakes like the Kobe Earthquake in 1995, there is a strong need to verify seismic resistance of dams against much larger earthquake motions than those considered in the present design standard in Japan. Problems exist in using nonlinear analysis to evaluate the safety of dams including: that the influence which the set material properties have on the results of nonlinear analysis is large, and that the results of nonlinear analysis differ greatly according to the damage estimation models or analysis programs. This paper reports the evaluation indices based on a linear dynamic analysis method and the characteristics of the progress of cracks in concrete gravity dams with different shapes using a nonlinear dynamic analysis method. The study concludes that if simple linear dynamic analysis is appropriately conducted to estimate tensile stress at potential locations of initiating cracks, the damage due to cracks would be predicted roughly. 4 refs., 1 tab., 13 figs.

  8. A Low-Complexity ESPRIT-Based DOA Estimation Method for Co-Prime Linear Arrays.

    Sun, Fenggang; Gao, Bin; Chen, Lizhen; Lan, Peng

    2016-08-25

    The problem of direction-of-arrival (DOA) estimation is investigated for co-prime array, where the co-prime array consists of two uniform sparse linear subarrays with extended inter-element spacing. For each sparse subarray, true DOAs are mapped into several equivalent angles impinging on the traditional uniform linear array with half-wavelength spacing. Then, by applying the estimation of signal parameters via rotational invariance technique (ESPRIT), the equivalent DOAs are estimated, and the candidate DOAs are recovered according to the relationship among equivalent and true DOAs. Finally, the true DOAs are estimated by combining the results of the two subarrays. The proposed method achieves a better complexity-performance tradeoff as compared to other existing methods.

  9. Acceleration of step and linear discontinuous schemes for the method of characteristics in DRAGON5

    Alain Hébert

    2017-09-01

    Full Text Available The applicability of the algebraic collapsing acceleration (ACA technique to the method of characteristics (MOC in cases with scattering anisotropy and/or linear sources was investigated. Previously, the ACA was proven successful in cases with isotropic scattering and uniform (step sources. A presentation is first made of the MOC implementation, available in the DRAGON5 code. Two categories of schemes are available for integrating the propagation equations: (1 the first category is based on exact integration and leads to the classical step characteristics (SC and linear discontinuous characteristics (LDC schemes and (2 the second category leads to diamond differencing schemes of various orders in space. The acceleration of these MOC schemes using a combination of the generalized minimal residual [GMRES(m] method preconditioned with the ACA technique was focused on. Numerical results are provided for a two-dimensional (2D eight-symmetry pressurized water reactor (PWR assembly mockup in the context of the DRAGON5 code.

  10. Stability of numerical method for semi-linear stochastic pantograph differential equations

    Yu Zhang

    2016-01-01

    Full Text Available Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations. Some suitable conditions for the mean-square stability of an analytical solution are obtained. Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution is stable, then the exponential Euler method applied to the system is mean-square stable for arbitrary step-size h > 0 $h>0$ . Numerical examples further illustrate the obtained theoretical results.

  11. Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

    Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

    2018-02-01

    In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

  12. Direct observations of the viscosity of Earth's outer core and extrapolation of measurements of the viscosity of liquid iron

    Smylie, D E; Brazhkin, Vadim V; Palmer, Andrew

    2009-01-01

    Estimates vary widely as to the viscosity of Earth's outer fluid core. Directly observed viscosity is usually orders of magnitude higher than the values extrapolated from high-pressure high-temperature laboratory experiments, which are close to those for liquid iron at atmospheric pressure. It turned out that this discrepancy can be removed by extrapolating via the widely known Arrhenius activation model modified by lifting the commonly used assumption of pressure-independent activation volume (which is possible due to the discovery that at high pressures the activation volume increases strongly with pressure, resulting in 10 2 Pa s at the top of the fluid core, and in 10 11 Pa s at its bottom). There are of course many uncertainties affecting this extrapolation process. This paper reviews two viscosity determination methods, one for the top and the other for the bottom of the outer core, the former of which relies on the decay of free core nutations and yields 2371 ± 1530 Pa s, while the other relies on the reduction in the rotational splitting of the two equatorial translational modes of the solid inner core oscillations and yields an average of 1.247 ± 0.035 Pa s. Encouraged by the good performance of the Arrhenius extrapolation, a differential form of the Arrhenius activation model is used to interpolate along the melting temperature curve and to find the viscosity profile across the entire outer core. The viscosity variation is found to be nearly log-linear between the measured boundary values. (methodological notes)

  13. Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

    Lee, Kookjin [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science; Carlberg, Kevin [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Elman, Howard C. [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science and Inst. for Advanced Computer Studies

    2018-03-29

    Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weighted $\\ell^2$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $\\ell^2$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.

  14. Biosimilars: From Extrapolation into Off Label Use.

    Zhao, Sizheng; Nair, Jagdish R; Moots, Robert J

    2017-01-01

    Biologic drugs have revolutionised the management of many inflammatory conditions. Patent expirations have stimulated development of highly similar but non-identical molecules, the biosimilars. Extrapolation of indications is a key concept in the development of biosimilars. However, this has been met with concerns around mechanisms of action, equivalence in efficacy and immunogenicity, which are reviewed in this article. Narrative overview composed from literature search and the authors' experience. Literature search included Pubmed, Web of Science, and online document archives of the Food and Drug Administration and European Medicines Agency. The concepts of biosimilarity and extrapolation of indications are revisited. Concerns around extrapolation are exemplified using the biosimilar infliximab, CT-P13, focusing on mechanisms of action, immunogenicity and trial design. The opportunities and cautions for using biologics and biosimilars in unlicensed inflammatory conditions are reviewed. Biosimilars offer many potential opportunities in improving treatment access and increasing treatment options. The high cost associated with marketing approval means that many bio-originators may never become licenced for rarer inflammatory conditions, despite clinical efficacy. Biosimilars, with lower acquisition cost, may improve access for off-label use of biologics in the management of these patients. They may also provide opportunities to explore off-label treatment of conditions where biologic therapy is less established. However, this potential advantage must be balanced with the awareness that off-label prescribing can potentially expose patients to risky and ineffective treatments. Post-marketing surveillance is critical to developing long-term evidence to provide assurances on efficacy as well as safety. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

  15. Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization

    2016-11-22

    structure of the graph, we replace the ℓ1- norm by the nonconvex Capped -ℓ1 norm , and obtain the Generalized Capped -ℓ1 regularized logistic regression...X. M. Yuan. Linearized augmented lagrangian and alternating direction methods for nuclear norm minimization. Mathematics of Computation, 82(281):301...better approximations of ℓ0- norm theoretically and computationally beyond ℓ1- norm , for example, the compressive sensing (Xiao et al., 2011). The

  16. The regression-calibration method for fitting generalized linear models with additive measurement error

    James W. Hardin; Henrik Schmeidiche; Raymond J. Carroll

    2003-01-01

    This paper discusses and illustrates the method of regression calibration. This is a straightforward technique for fitting models with additive measurement error. We present this discussion in terms of generalized linear models (GLMs) following the notation defined in Hardin and Carroll (2003). Discussion will include specified measurement error, measurement error estimated by replicate error-prone proxies, and measurement error estimated by instrumental variables. The discussion focuses on s...

  17. An enhanced finite volume method to model 2D linear elastic structures

    Suliman, Ridhwaan

    2014-04-01

    Full Text Available . Suliman) Preprint submitted to Applied Mathematical Modelling July 22, 2013 Keywords: finite volume, finite element, locking, error analysis 1. Introduction Since the 1960s, the finite element method has mainly been used for modelling the mechanics... formulation provides higher accuracy 2 for displacement solutions. It is well known that the linear finite element formulation suffers from sensitivity to element aspect ratio or shear locking when subjected to bend- ing [16]. Fallah [8] and Wheel [6] present...

  18. Solution of second order linear fuzzy difference equation by Lagrange's multiplier method

    Sankar Prasad Mondal

    2016-06-01

    Full Text Available In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.

  19. Linear motion device and method for inserting and withdrawing control rods

    Smith, J.E.

    Disclosed is a linear motion device and more specifically a control rod drive mechanism (CRDM) for inserting and withdrawing control rods into a reactor core. The CRDM and method disclosed is capable of independently and sequentially positioning two sets of control rods with a single motor stator and rotor. The CRDM disclosed can control more than one control rod lead screw without incurring a substantial increase in the size of the mechanism.

  20. Linearized self-consistent quasiparticle GW method: Application to semiconductors and simple metals

    Kutepov, A. L.; Oudovenko, V. S.; Kotliar, G.

    2017-10-01

    We present a code implementing the linearized quasiparticle self-consistent GW method (LQSGW) in the LAPW basis. Our approach is based on the linearization of the self-energy around zero frequency which differs it from the existing implementations of the QSGW method. The linearization allows us to use Matsubara frequencies instead of working on the real axis. This results in efficiency gains by switching to the imaginary time representation in the same way as in the space time method. The all electron LAPW basis set eliminates the need for pseudopotentials. We discuss the advantages of our approach, such as its N3 scaling with the system size N, as well as its shortcomings. We apply our approach to study the electronic properties of selected semiconductors, insulators, and simple metals and show that our code produces the results very close to the previously published QSGW data. Our implementation is a good platform for further many body diagrammatic resummations such as the vertex-corrected GW approach and the GW+DMFT method. Program Files doi:http://dx.doi.org/10.17632/cpchkfty4w.1 Licensing provisions: GNU General Public License Programming language: Fortran 90 External routines/libraries: BLAS, LAPACK, MPI (optional) Nature of problem: Direct implementation of the GW method scales as N4 with the system size, which quickly becomes prohibitively time consuming even in the modern computers. Solution method: We implemented the GW approach using a method that switches between real space and momentum space representations. Some operations are faster in real space, whereas others are more computationally efficient in the reciprocal space. This makes our approach scale as N3. Restrictions: The limiting factor is usually the memory available in a computer. Using 10 GB/core of memory allows us to study the systems up to 15 atoms per unit cell.

  1. On the economical solution method for a system of linear algebraic equations

    Jan Awrejcewicz

    2004-01-01

    Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O(hx12+hx22. The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.

  2. Linear time delay methods and stability analyses of the human spine. Effects of neuromuscular reflex response.

    Franklin, Timothy C; Granata, Kevin P; Madigan, Michael L; Hendricks, Scott L

    2008-08-01

    Linear stability methods were applied to a biomechanical model of the human musculoskeletal spine to investigate effects of reflex gain and reflex delay on stability. Equations of motion represented a dynamic 18 degrees-of-freedom rigid-body model with time-delayed reflexes. Optimal muscle activation levels were identified by minimizing metabolic power with the constraints of equilibrium and stability with zero reflex time delay. Muscle activation levels and associated muscle forces were used to find the delay margin, i.e., the maximum reflex delay for which the system was stable. Results demonstrated that stiffness due to antagonistic co-contraction necessary for stability declined with increased proportional reflex gain. Reflex delay limited the maximum acceptable proportional reflex gain, i.e., long reflex delay required smaller maximum reflex gain to avoid instability. As differential reflex gain increased, there was a small increase in acceptable reflex delay. However, differential reflex gain with values near intrinsic damping caused the delay margin to approach zero. Forward-dynamic simulations of the fully nonlinear time-delayed system verified the linear results. The linear methods accurately found the delay margin below which the nonlinear system was asymptotically stable. These methods may aid future investigations in the role of reflexes in musculoskeletal stability.

  3. An Improved Method for Solving Multiobjective Integer Linear Fractional Programming Problem

    Meriem Ait Mehdi

    2014-01-01

    Full Text Available We describe an improvement of Chergui and Moulaï’s method (2008 that generates the whole efficient set of a multiobjective integer linear fractional program based on the branch and cut concept. The general step of this method consists in optimizing (maximizing without loss of generality one of the fractional objective functions over a subset of the original continuous feasible set; then if necessary, a branching process is carried out until obtaining an integer feasible solution. At this stage, an efficient cut is built from the criteria’s growth directions in order to discard a part of the feasible domain containing only nonefficient solutions. Our contribution concerns firstly the optimization process where a linear program that we define later will be solved at each step rather than a fractional linear program. Secondly, local ideal and nadir points will be used as bounds to prune some branches leading to nonefficient solutions. The computational experiments show that the new method outperforms the old one in all the treated instances.

  4. Standard test method for linear thermal expansion of glaze frits and ceramic whiteware materials by the interferometric method

    American Society for Testing and Materials. Philadelphia

    1995-01-01

    1.1 This test method covers the interferometric determination of linear thermal expansion of premelted glaze frits and fired ceramic whiteware materials at temperatures lower than 1000°C (1830°F). 1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

  5. Base Isolation for Seismic Retrofitting of a Multiple Building Structure: Evaluation of Equivalent Linearization Method

    Massimiliano Ferraioli

    2016-01-01

    Full Text Available Although the most commonly used isolation systems exhibit nonlinear inelastic behaviour, the equivalent linear elastic analysis is commonly used in the design and assessment of seismic-isolated structures. The paper investigates if the linear elastic model is suitable for the analysis of a seismically isolated multiple building structure. To this aim, its computed responses were compared with those calculated by nonlinear dynamic analysis. A common base isolation plane connects the isolation bearings supporting the adjacent structures. In this situation, the conventional equivalent linear elastic analysis may have some problems of accuracy because this method is calibrated on single base-isolated structures. Moreover, the torsional characteristics of the combined system are significantly different from those of separate isolated buildings. A number of numerical simulations and parametric studies under earthquake excitations were performed. The accuracy of the dynamic response obtained by the equivalent linear elastic model was calculated by the magnitude of the error with respect to the corresponding response considering the nonlinear behaviour of the isolation system. The maximum displacements at the isolation level, the maximum interstorey drifts, and the peak absolute acceleration were selected as the most important response measures. The influence of mass eccentricity, torsion, and high-modes effects was finally investigated.

  6. An Improved Isotropic Periodic Sum Method That Uses Linear Combinations of Basis Potentials

    Takahashi, Kazuaki Z.

    2012-11-13

    Isotropic periodic sum (IPS) is a technique that calculates long-range interactions differently than conventional lattice sum methods. The difference between IPS and lattice sum methods lies in the shape and distribution of remote images for long-range interaction calculations. The images used in lattice sum calculations are identical to those generated from periodic boundary conditions and are discretely positioned at lattice points in space. The images for IPS calculations are "imaginary", which means they do not explicitly exist in a simulation system and are distributed isotropically and periodically around each particle. Two different versions of the original IPS method exist. The IPSn method is applied to calculations for point charges, whereas the IPSp method calculates polar molecules. However, both IPSn and IPSp have their advantages and disadvantages in simulating bulk water or water-vapor interfacial systems. In bulk water systems, the cutoff radius effect of IPSn strongly affects the configuration, whereas IPSp does not provide adequate estimations of water-vapor interfacial systems unless very long cutoff radii are used. To extend the applicability of the IPS technique, an improved IPS method, which has better accuracy in both homogeneous and heterogeneous systems has been developed and named the linear-combination-based isotropic periodic sum (LIPS) method. This improved IPS method uses linear combinations of basis potentials. We performed molecular dynamics (MD) simulations of bulk water and water-vapor interfacial systems to evaluate the accuracy of the LIPS method. For bulk water systems, the LIPS method has better accuracy than IPSn in estimating thermodynamic and configurational properties without the countercharge assumption, which is used for IPSp. For water-vapor interfacial systems, LIPS has better accuracy than IPSp and properly estimates thermodynamic and configurational properties. In conclusion, the LIPS method can successfully estimate

  7. An Improved Isotropic Periodic Sum Method That Uses Linear Combinations of Basis Potentials

    Takahashi, Kazuaki Z.; Narumi, Tetsu; Suh, Donguk; Yasuoka, Kenji

    2012-01-01

    Isotropic periodic sum (IPS) is a technique that calculates long-range interactions differently than conventional lattice sum methods. The difference between IPS and lattice sum methods lies in the shape and distribution of remote images for long-range interaction calculations. The images used in lattice sum calculations are identical to those generated from periodic boundary conditions and are discretely positioned at lattice points in space. The images for IPS calculations are "imaginary", which means they do not explicitly exist in a simulation system and are distributed isotropically and periodically around each particle. Two different versions of the original IPS method exist. The IPSn method is applied to calculations for point charges, whereas the IPSp method calculates polar molecules. However, both IPSn and IPSp have their advantages and disadvantages in simulating bulk water or water-vapor interfacial systems. In bulk water systems, the cutoff radius effect of IPSn strongly affects the configuration, whereas IPSp does not provide adequate estimations of water-vapor interfacial systems unless very long cutoff radii are used. To extend the applicability of the IPS technique, an improved IPS method, which has better accuracy in both homogeneous and heterogeneous systems has been developed and named the linear-combination-based isotropic periodic sum (LIPS) method. This improved IPS method uses linear combinations of basis potentials. We performed molecular dynamics (MD) simulations of bulk water and water-vapor interfacial systems to evaluate the accuracy of the LIPS method. For bulk water systems, the LIPS method has better accuracy than IPSn in estimating thermodynamic and configurational properties without the countercharge assumption, which is used for IPSp. For water-vapor interfacial systems, LIPS has better accuracy than IPSp and properly estimates thermodynamic and configurational properties. In conclusion, the LIPS method can successfully estimate

  8. One step linear reconstruction method for continuous wave diffuse optical tomography

    Ukhrowiyah, N.; Yasin, M.

    2017-09-01

    The method one step linear reconstruction method for continuous wave diffuse optical tomography is proposed and demonstrated for polyvinyl chloride based material and breast phantom. Approximation which used in this method is selecting regulation coefficient and evaluating the difference between two states that corresponding to the data acquired without and with a change in optical properties. This method is used to recovery of optical parameters from measured boundary data of light propagation in the object. The research is demonstrated by simulation and experimental data. Numerical object is used to produce simulation data. Chloride based material and breast phantom sample is used to produce experimental data. Comparisons of results between experiment and simulation data are conducted to validate the proposed method. The results of the reconstruction image which is produced by the one step linear reconstruction method show that the image reconstruction almost same as the original object. This approach provides a means of imaging that is sensitive to changes in optical properties, which may be particularly useful for functional imaging used continuous wave diffuse optical tomography of early diagnosis of breast cancer.

  9. A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers

    Melboe, Hallgeir

    2001-10-01

    This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)

  10. A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

    Elias D. Nino-Ruiz

    2018-03-01

    Full Text Available In this paper, we propose an efficient EnKF implementation for non-Gaussian data assimilation based on Gaussian Mixture Models and Markov-Chain-Monte-Carlo (MCMC methods. The proposed method works as follows: based on an ensemble of model realizations, prior errors are estimated via a Gaussian Mixture density whose parameters are approximated by means of an Expectation Maximization method. Then, by using an iterative method, observation operators are linearized about current solutions and posterior modes are estimated via a MCMC implementation. The acceptance/rejection criterion is similar to that of the Metropolis-Hastings rule. Experimental tests are performed on the Lorenz 96 model. The results show that the proposed method can decrease prior errors by several order of magnitudes in a root-mean-square-error sense for nearly sparse or dense observational networks.

  11. Efficient anisotropic wavefield extrapolation using effective isotropic models

    Alkhalifah, Tariq Ali; Ma, X.; Waheed, Umair bin; Zuberi, Mohammad

    2013-01-01

    Isotropic wavefield extrapolation is more efficient than anisotropic extrapolation, and this is especially true when the anisotropy of the medium is tilted (from the vertical). We use the kinematics of the wavefield, appropriately represented

  12. Variance analysis of the Monte-Carlo perturbation source method in inhomogeneous linear particle transport problems

    Noack, K.

    1982-01-01

    The perturbation source method may be a powerful Monte-Carlo means to calculate small effects in a particle field. In a preceding paper we have formulated this methos in inhomogeneous linear particle transport problems describing the particle fields by solutions of Fredholm integral equations and have derived formulae for the second moment of the difference event point estimator. In the present paper we analyse the general structure of its variance, point out the variance peculiarities, discuss the dependence on certain transport games and on generation procedures of the auxiliary particles and draw conclusions to improve this method

  13. Method for the mechanical axis alignment of the linear induction accelerator

    Li Hong; China Academy of Engineering Physics, Mianyang; Yao Jin; Liu Yunlong; Zhang Linwen; Deng Jianjun

    2004-01-01

    Accurate mechanical axis alignment is a basic requirement for assembling a linear induction accelerator (LIA). The total length of an LIA is usually over thirty or fifty meters, and it consists of many induction cells. By using a laser tracker a new method of mechanical axis alignment for LIA is established to achieve the high accuracy. This paper introduces the method and gives implementation step and point position measure errors of the mechanical axis alignment. During the alignment process a 55 m-long alignment control survey net is built, and the theoretic revision of the coordinate of the control survey net is presented. (authors)

  14. Reproducing kernel method with Taylor expansion for linear Volterra integro-differential equations

    Azizallah Alvandi

    2017-06-01

    Full Text Available This research aims of the present a new and single algorithm for linear integro-differential equations (LIDE. To apply the reproducing Hilbert kernel method, there is made an equivalent transformation by using Taylor series for solving LIDEs. Shown in series form is the analytical solution in the reproducing kernel space and the approximate solution $ u_{N} $ is constructed by truncating the series to $ N $ terms. It is easy to prove the convergence of $ u_{N} $ to the analytical solution. The numerical solutions from the proposed method indicate that this approach can be implemented easily which shows attractive features.

  15. Model-independent separation of poorly resolved hypperfine split spectra by a linear combination method

    Nagy, D.L.; Dengler, J.; Ritter, G.

    1988-01-01

    A model-independent evaluation of the components of poorly resolved Moessbauer spectra based on a linear combination method is possible if there is a parameter as a function of which the shape of the individual components do not but their intensities do change and the dependence of the intensities on this parameter is known. The efficiency of the method is demonstrated on the example of low temperature magnetically split spectra of the high-T c superconductor YBa 2 (Cu 0.9 Fe 0 .1 ) 3 O 7-y . (author)

  16. Linear dynamic analysis of arbitrary thin shells modal superposition by using finite element method

    Goncalves Filho, O.J.A.

    1978-11-01

    The linear dynamic behaviour of arbitrary thin shells by the Finite Element Method is studied. Plane triangular elements with eighteen degrees of freedom each are used. The general equations of movement are obtained from the Hamilton Principle and solved by the Modal Superposition Method. The presence of a viscous type damping can be considered by means of percentages of the critical damping. An automatic computer program was developed to provide the vibratory properties and the dynamic response to several types of deterministic loadings, including temperature effects. The program was written in FORTRAN IV for the Burroughs B-6700 computer. (author)

  17. Experiences and extrapolations from Hiroshima and Nagasaki

    Harwell, C.C.

    1985-01-01

    This paper examines the events following the atomic bombings of Hiroshima and Nagasaki in 1945 and extrapolates from these experiences to further understand the possible consequences of detonations on a local area from weapons in the current world nuclear arsenal. The first section deals with a report of the events that occurred in Hiroshima and Nagasaki just after the 1945 bombings with respect to the physical conditions of the affected areas, the immediate effects on humans, the psychological response of the victims, and the nature of outside assistance. Because there can be no experimental data to validate the effects on cities and their populations of detonations from current weapons, the data from the actual explosions on Hiroshima and Nagasaki provide a point of departure. The second section examines possible extrapolations from and comparisons with the Hiroshima and Nagasaki experiences. The limitations of drawing upon the Hiroshima and Nagasaki experiences are discussed. A comparison is made of the scale of effects from other major disasters for urban systems, such as damages from the conventional bombings of cities during World War II, the consequences of major earthquakes, the historical effects of the Black Plague and widespread famines, and other extreme natural events. The potential effects of detonating a modern 1 MT warhead on the city of Hiroshima as it exists today are simulated. This is extended to the local effects on a targeted city from a global nuclear war, and attention is directed to problems of estimating the societal effects from such a war

  18. Chiral and continuum extrapolation of partially-quenched hadron masses

    Chris Allton; Wes Armour; Derek Leinweber; Anthony Thomas; Ross Young

    2005-01-01

    Using the finite-range regularization (FRR) of chiral effective field theory, the chiral extrapolation formula for the vector meson mass is derived for the case of partially-quenched QCD. We re-analyze the dynamical fermion QCD data for the vector meson mass from the CP-PACS collaboration. A global fit, including finite lattice spacing effects, of all 16 of their ensembles is performed. We study the FRR method together with a naive polynomial approach and find excellent agreement (∼1%) with the experimental value of M ρ from the former approach. These results are extended to the case of the nucleon mass

  19. Chiral and continuum extrapolation of partially-quenched hadron masses

    Chris Allton; Wes Armour; Derek Leinweber; Anthony Thomas; Ross Young

    2005-09-29

    Using the finite-range regularization (FRR) of chiral effective field theory, the chiral extrapolation formula for the vector meson mass is derived for the case of partially-quenched QCD. We re-analyze the dynamical fermion QCD data for the vector meson mass from the CP-PACS collaboration. A global fit, including finite lattice spacing effects, of all 16 of their ensembles is performed. We study the FRR method together with a naive polynomial approach and find excellent agreement ({approx}1%) with the experimental value of M{sub {rho}} from the former approach. These results are extended to the case of the nucleon mass.

  20. A Bayes linear Bayes method for estimation of correlated event rates.

    Quigley, John; Wilson, Kevin J; Walls, Lesley; Bedford, Tim

    2013-12-01

    Typically, full Bayesian estimation of correlated event rates can be computationally challenging since estimators are intractable. When estimation of event rates represents one activity within a larger modeling process, there is an incentive to develop more efficient inference than provided by a full Bayesian model. We develop a new subjective inference method for correlated event rates based on a Bayes linear Bayes model under the assumption that events are generated from a homogeneous Poisson process. To reduce the elicitation burden we introduce homogenization factors to the model and, as an alternative to a subjective prior, an empirical method using the method of moments is developed. Inference under the new method is compared against estimates obtained under a full Bayesian model, which takes a multivariate gamma prior, where the predictive and posterior distributions are derived in terms of well-known functions. The mathematical properties of both models are presented. A simulation study shows that the Bayes linear Bayes inference method and the full Bayesian model provide equally reliable estimates. An illustrative example, motivated by a problem of estimating correlated event rates across different users in a simple supply chain, shows how ignoring the correlation leads to biased estimation of event rates. © 2013 Society for Risk Analysis.

  1. Thin Cloud Detection Method by Linear Combination Model of Cloud Image

    Liu, L.; Li, J.; Wang, Y.; Xiao, Y.; Zhang, W.; Zhang, S.

    2018-04-01

    The existing cloud detection methods in photogrammetry often extract the image features from remote sensing images directly, and then use them to classify images into cloud or other things. But when the cloud is thin and small, these methods will be inaccurate. In this paper, a linear combination model of cloud images is proposed, by using this model, the underlying surface information of remote sensing images can be removed. So the cloud detection result can become more accurate. Firstly, the automatic cloud detection program in this paper uses the linear combination model to split the cloud information and surface information in the transparent cloud images, then uses different image features to recognize the cloud parts. In consideration of the computational efficiency, AdaBoost Classifier was introduced to combine the different features to establish a cloud classifier. AdaBoost Classifier can select the most effective features from many normal features, so the calculation time is largely reduced. Finally, we selected a cloud detection method based on tree structure and a multiple feature detection method using SVM classifier to compare with the proposed method, the experimental data shows that the proposed cloud detection program in this paper has high accuracy and fast calculation speed.

  2. A linear complementarity method for the solution of vertical vehicle-track interaction

    Zhang, Jian; Gao, Qiang; Wu, Feng; Zhong, Wan-Xie

    2018-02-01

    A new method is proposed for the solution of the vertical vehicle-track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel-rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel-rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel-rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle-track interaction including a separation between wheel and rail.

  3. An Optimal DEM Reconstruction Method for Linear Array Synthetic Aperture Radar Based on Variational Model

    Shi Jun

    2015-02-01

    Full Text Available Downward-looking Linear Array Synthetic Aperture Radar (LASAR has many potential applications in the topographic mapping, disaster monitoring and reconnaissance applications, especially in the mountainous area. However, limited by the sizes of platforms, its resolution in the linear array direction is always far lower than those in the range and azimuth directions. This disadvantage leads to the blurring of Three-Dimensional (3D images in the linear array direction, and restricts the application of LASAR. To date, the research on 3D SAR image enhancement has focused on the sparse recovery technique. In this case, the one-to-one mapping of Digital Elevation Model (DEM brakes down. To overcome this, an optimal DEM reconstruction method for LASAR based on the variational model is discussed in an effort to optimize the DEM and the associated scattering coefficient map, and to minimize the Mean Square Error (MSE. Using simulation experiments, it is found that the variational model is more suitable for DEM enhancement applications to all kinds of terrains compared with the Orthogonal Matching Pursuit (OMPand Least Absolute Shrinkage and Selection Operator (LASSO methods.

  4. A METHOD FOR SELF-CALIBRATION IN SATELLITE WITH HIGH PRECISION OF SPACE LINEAR ARRAY CAMERA

    W. Liu

    2016-06-01

    Full Text Available At present, the on-orbit calibration of the geometric parameters of a space surveying camera is usually processed by data from a ground calibration field after capturing the images. The entire process is very complicated and lengthy and cannot monitor and calibrate the geometric parameters in real time. On the basis of a large number of on-orbit calibrations, we found that owing to the influence of many factors, e.g., weather, it is often difficult to capture images of the ground calibration field. Thus, regular calibration using field data cannot be ensured. This article proposes a real time self-calibration method for a space linear array camera on a satellite using the optical auto collimation principle. A collimating light source and small matrix array CCD devices are installed inside the load system of the satellite; these use the same light path as the linear array camera. We can extract the location changes of the cross marks in the matrix array CCD to determine the real-time variations in the focal length and angle parameters of the linear array camera. The on-orbit status of the camera is rapidly obtained using this method. On one hand, the camera’s change regulation can be mastered accurately and the camera’s attitude can be adjusted in a timely manner to ensure optimal photography; in contrast, self-calibration of the camera aboard the satellite can be realized quickly, which improves the efficiency and reliability of photogrammetric processing.

  5. Comments on the comparison of global methods for linear two-point boundary value problems

    de Boor, C.; Swartz, B.

    1977-01-01

    A more careful count of the operations involved in solving the linear system associated with collocation of a two-point boundary value problem using a rough splines reverses results recently reported by others in this journal. In addition, it is observed that the use of the technique of ''condensation of parameters'' can decrease the computer storage required. Furthermore, the use of a particular highly localized basis can also reduce the setup time when the mesh is irregular. Finally, operation counts are roughly estimated for the solution of certain linear system associated with two competing collocation methods; namely, collocation with smooth splines and collocation of the equivalent first order system with continuous piecewise polynomials

  6. Sparse linear systems: Theory of decomposition, methods, technology, applications and implementation in Wolfram Mathematica

    Pilipchuk, L. A.; Pilipchuk, A. S.

    2015-01-01

    In this paper we propose the theory of decomposition, methods, technologies, applications and implementation in Wol-fram Mathematica for the constructing the solutions of the sparse linear systems. One of the applications is the Sensor Location Problem for the symmetric graph in the case when split ratios of some arc flows can be zeros. The objective of that application is to minimize the number of sensors that are assigned to the nodes. We obtain a sparse system of linear algebraic equations and research its matrix rank. Sparse systems of these types appear in generalized network flow programming problems in the form of restrictions and can be characterized as systems with a large sparse sub-matrix representing the embedded network structure

  7. A Fast Condensing Method for Solution of Linear-Quadratic Control Problems

    Frison, Gianluca; Jørgensen, John Bagterp

    2013-01-01

    consider a condensing (or state elimination) method to solve an extended version of the LQ control problem, and we show how to exploit the structure of this problem to both factorize the dense Hessian matrix and solve the system. Furthermore, we present two efficient implementations. The first......In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper we...... implementation is formally identical to the Riccati recursion based solver and has a computational complexity that is linear in the control horizon length and cubic in the number of states. The second implementation has a computational complexity that is quadratic in the control horizon length as well...

  8. Sparse linear systems: Theory of decomposition, methods, technology, applications and implementation in Wolfram Mathematica

    Pilipchuk, L. A., E-mail: pilipchik@bsu.by [Belarussian State University, 220030 Minsk, 4, Nezavisimosti avenue, Republic of Belarus (Belarus); Pilipchuk, A. S., E-mail: an.pilipchuk@gmail.com [The Natural Resources and Environmental Protestion Ministry of the Republic of Belarus, 220004 Minsk, 10 Kollektornaya Street, Republic of Belarus (Belarus)

    2015-11-30

    In this paper we propose the theory of decomposition, methods, technologies, applications and implementation in Wol-fram Mathematica for the constructing the solutions of the sparse linear systems. One of the applications is the Sensor Location Problem for the symmetric graph in the case when split ratios of some arc flows can be zeros. The objective of that application is to minimize the number of sensors that are assigned to the nodes. We obtain a sparse system of linear algebraic equations and research its matrix rank. Sparse systems of these types appear in generalized network flow programming problems in the form of restrictions and can be characterized as systems with a large sparse sub-matrix representing the embedded network structure.

  9. KEELE, Minimization of Nonlinear Function with Linear Constraints, Variable Metric Method

    Westley, G.W.

    1975-01-01

    1 - Description of problem or function: KEELE is a linearly constrained nonlinear programming algorithm for locating a local minimum of a function of n variables with the variables subject to linear equality and/or inequality constraints. 2 - Method of solution: A variable metric procedure is used where the direction of search at each iteration is obtained by multiplying the negative of the gradient vector by a positive definite matrix which approximates the inverse of the matrix of second partial derivatives associated with the function. 3 - Restrictions on the complexity of the problem: Array dimensions limit the number of variables to 20 and the number of constraints to 50. These can be changed by the user

  10. Sensitivity-based virtual fields for the non-linear virtual fields method

    Marek, Aleksander; Davis, Frances M.; Pierron, Fabrice

    2017-09-01

    The virtual fields method is an approach to inversely identify material parameters using full-field deformation data. In this manuscript, a new set of automatically-defined virtual fields for non-linear constitutive models has been proposed. These new sensitivity-based virtual fields reduce the influence of noise on the parameter identification. The sensitivity-based virtual fields were applied to a numerical example involving small strain plasticity; however, the general formulation derived for these virtual fields is applicable to any non-linear constitutive model. To quantify the improvement offered by these new virtual fields, they were compared with stiffness-based and manually defined virtual fields. The proposed sensitivity-based virtual fields were consistently able to identify plastic model parameters and outperform the stiffness-based and manually defined virtual fields when the data was corrupted by noise.

  11. In situ LTE exposure of the general public: Characterization and extrapolation.

    Joseph, Wout; Verloock, Leen; Goeminne, Francis; Vermeeren, Günter; Martens, Luc

    2012-09-01

    In situ radiofrequency (RF) exposure of the different RF sources is characterized in Reading, United Kingdom, and an extrapolation method to estimate worst-case long-term evolution (LTE) exposure is proposed. All electric field levels satisfy the International Commission on Non-Ionizing Radiation Protection (ICNIRP) reference levels with a maximal total electric field value of 4.5 V/m. The total values are dominated by frequency modulation (FM). Exposure levels for LTE of 0.2 V/m on average and 0.5 V/m maximally are obtained. Contributions of LTE to the total exposure are limited to 0.4% on average. Exposure ratios from 0.8% (LTE) to 12.5% (FM) are obtained. An extrapolation method is proposed and validated to assess the worst-case LTE exposure. For this method, the reference signal (RS) and secondary synchronization signal (S-SYNC) are measured and extrapolated to the worst-case value using an extrapolation factor. The influence of the traffic load and output power of the base station on in situ RS and S-SYNC signals are lower than 1 dB for all power and traffic load settings, showing that these signals can be used for the extrapolation method. The maximal extrapolated field value for LTE exposure equals 1.9 V/m, which is 32 times below the ICNIRP reference levels for electric fields. Copyright © 2012 Wiley Periodicals, Inc.

  12. Mehar Methods for Fuzzy Optimal Solution and Sensitivity Analysis of Fuzzy Linear Programming with Symmetric Trapezoidal Fuzzy Numbers

    Sukhpreet Kaur Sidhu

    2014-01-01

    Full Text Available The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems.

  13. Dual linear structured support vector machine tracking method via scale correlation filter

    Li, Weisheng; Chen, Yanquan; Xiao, Bin; Feng, Chen

    2018-01-01

    Adaptive tracking-by-detection methods based on structured support vector machine (SVM) performed well on recent visual tracking benchmarks. However, these methods did not adopt an effective strategy of object scale estimation, which limits the overall tracking performance. We present a tracking method based on a dual linear structured support vector machine (DLSSVM) with a discriminative scale correlation filter. The collaborative tracker comprised of a DLSSVM model and a scale correlation filter obtains good results in tracking target position and scale estimation. The fast Fourier transform is applied for detection. Extensive experiments show that our tracking approach outperforms many popular top-ranking trackers. On a benchmark including 100 challenging video sequences, the average precision of the proposed method is 82.8%.

  14. The method of varying amplitudes for solving (non)linear problems involving strong parametric excitation

    Sorokin, Vladislav; Thomsen, Jon Juel

    2015-01-01

    Parametrically excited systems appear in many fields of science and technology, intrinsically or imposed purposefully; e.g. spatially periodic structures represent an important class of such systems [4]. When the parametric excitation can be considered weak, classical asymptotic methods like...... the method of averaging [2] or multiple scales [6] can be applied. However, with many practically important applications this simplification is inadequate, e.g. with spatially periodic structures it restricts the possibility to affect their effective dynamic properties by a structural parameter modulation...... of considerable magnitude. Approximate methods based on Floquet theory [4] for analyzing problems involving parametric excitation, e.g. the classical Hill’s method of infinite determinants [3,4], can be employed also in cases of strong excitation; however, with Floquet theory being applicable only for linear...

  15. Assessment of Two Analytical Methods in Solving the Linear and Nonlinear Elastic Beam Deformation Problems

    Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari

    2010-01-01

    and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However......, as with other analytical techniques, certain limitations restrict the wide application of perturbation methods, most important of which is the dependence of these methods on the existence of a small parameter in the equation. Disappointingly, the majority of nonlinear problems have no small parameter at all......Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...

  16. Comparing performance of standard and iterative linear unmixing methods for hyperspectral signatures

    Gault, Travis R.; Jansen, Melissa E.; DeCoster, Mallory E.; Jansing, E. David; Rodriguez, Benjamin M.

    2016-05-01

    Linear unmixing is a method of decomposing a mixed signature to determine the component materials that are present in sensor's field of view, along with the abundances at which they occur. Linear unmixing assumes that energy from the materials in the field of view is mixed in a linear fashion across the spectrum of interest. Traditional unmixing methods can take advantage of adjacent pixels in the decomposition algorithm, but is not the case for point sensors. This paper explores several iterative and non-iterative methods for linear unmixing, and examines their effectiveness at identifying the individual signatures that make up simulated single pixel mixed signatures, along with their corresponding abundances. The major hurdle addressed in the proposed method is that no neighboring pixel information is available for the spectral signature of interest. Testing is performed using two collections of spectral signatures from the Johns Hopkins University Applied Physics Laboratory's Signatures Database software (SigDB): a hand-selected small dataset of 25 distinct signatures from a larger dataset of approximately 1600 pure visible/near-infrared/short-wave-infrared (VIS/NIR/SWIR) spectra. Simulated spectra are created with three and four material mixtures randomly drawn from a dataset originating from SigDB, where the abundance of one material is swept in 10% increments from 10% to 90%with the abundances of the other materials equally divided amongst the remainder. For the smaller dataset of 25 signatures, all combinations of three or four materials are used to create simulated spectra, from which the accuracy of materials returned, as well as the correctness of the abundances, is compared to the inputs. The experiment is expanded to include the signatures from the larger dataset of almost 1600 signatures evaluated using a Monte Carlo scheme with 5000 draws of three or four materials to create the simulated mixed signatures. The spectral similarity of the inputs to the

  17. Method validation using weighted linear regression models for quantification of UV filters in water samples.

    da Silva, Claudia Pereira; Emídio, Elissandro Soares; de Marchi, Mary Rosa Rodrigues

    2015-01-01

    This paper describes the validation of a method consisting of solid-phase extraction followed by gas chromatography-tandem mass spectrometry for the analysis of the ultraviolet (UV) filters benzophenone-3, ethylhexyl salicylate, ethylhexyl methoxycinnamate and octocrylene. The method validation criteria included evaluation of selectivity, analytical curve, trueness, precision, limits of detection and limits of quantification. The non-weighted linear regression model has traditionally been used for calibration, but it is not necessarily the optimal model in all cases. Because the assumption of homoscedasticity was not met for the analytical data in this work, a weighted least squares linear regression was used for the calibration method. The evaluated analytical parameters were satisfactory for the analytes and showed recoveries at four fortification levels between 62% and 107%, with relative standard deviations less than 14%. The detection limits ranged from 7.6 to 24.1 ng L(-1). The proposed method was used to determine the amount of UV filters in water samples from water treatment plants in Araraquara and Jau in São Paulo, Brazil. Copyright © 2014 Elsevier B.V. All rights reserved.

  18. APPLYING ROBUST RANKING METHOD IN TWO PHASE FUZZY OPTIMIZATION LINEAR PROGRAMMING PROBLEMS (FOLPP

    Monalisha Pattnaik

    2014-12-01

    Full Text Available Background: This paper explores the solutions to the fuzzy optimization linear program problems (FOLPP where some parameters are fuzzy numbers. In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either probabilistic programming or multi-objective programming methods. Methods: In this paper, using the concept of comparison of fuzzy numbers, a very effective method is introduced for solving these problems. This paper extends linear programming based problem in fuzzy environment. With the problem assumptions, the optimal solution can still be theoretically solved using the two phase simplex based method in fuzzy environment. To handle the fuzzy decision variables can be initially generated and then solved and improved sequentially using the fuzzy decision approach by introducing robust ranking technique. Results and conclusions: The model is illustrated with an application and a post optimal analysis approach is obtained. The proposed procedure was programmed with MATLAB (R2009a version software for plotting the four dimensional slice diagram to the application. Finally, numerical example is presented to illustrate the effectiveness of the theoretical results, and to gain additional managerial insights. 

  19. The application of the fall-vector method in decomposition schemes for the solution of integer linear programming problems

    Sergienko, I.V.; Golodnikov, A.N.

    1984-01-01

    This article applies the methods of decompositions, which are used to solve continuous linear problems, to integer and partially integer problems. The fall-vector method is used to solve the obtained coordinate problems. An algorithm of the fall-vector is described. The Kornai-Liptak decomposition principle is used to reduce the integer linear programming problem to integer linear programming problems of a smaller dimension and to a discrete coordinate problem with simple constraints

  20. Non-linear triangle-based polynomial expansion nodal method for hexagonal core analysis

    Cho, Jin Young; Cho, Byung Oh; Joo, Han Gyu; Zee, Sung Qunn; Park, Sang Yong

    2000-09-01

    This report is for the implementation of triangle-based polynomial expansion nodal (TPEN) method to MASTER code in conjunction with the coarse mesh finite difference(CMFD) framework for hexagonal core design and analysis. The TPEN method is a variation of the higher order polynomial expansion nodal (HOPEN) method that solves the multi-group neutron diffusion equation in the hexagonal-z geometry. In contrast with the HOPEN method, only two-dimensional intranodal expansion is considered in the TPEN method for a triangular domain. The axial dependence of the intranodal flux is incorporated separately here and it is determined by the nodal expansion method (NEM) for a hexagonal node. For the consistency of node geometry of the MASTER code which is based on hexagon, TPEN solver is coded to solve one hexagonal node which is composed of 6 triangular nodes directly with Gauss elimination scheme. To solve the CMFD linear system efficiently, stabilized bi-conjugate gradient(BiCG) algorithm and Wielandt eigenvalue shift method are adopted. And for the construction of the efficient preconditioner of BiCG algorithm, the incomplete LU(ILU) factorization scheme which has been widely used in two-dimensional problems is used. To apply the ILU factorization scheme to three-dimensional problem, a symmetric Gauss-Seidel Factorization scheme is used. In order to examine the accuracy of the TPEN solution, several eigenvalue benchmark problems and two transient problems, i.e., a realistic VVER1000 and VVER440 rod ejection benchmark problems, were solved and compared with respective references. The results of eigenvalue benchmark problems indicate that non-linear TPEN method is very accurate showing less than 15 pcm of eigenvalue errors and 1% of maximum power errors, and fast enough to solve the three-dimensional VVER-440 problem within 5 seconds on 733MHz PENTIUM-III. In the case of the transient problems, the non-linear TPEN method also shows good results within a few minute of

  1. A consensus successive projections algorithm--multiple linear regression method for analyzing near infrared spectra.

    Liu, Ke; Chen, Xiaojing; Li, Limin; Chen, Huiling; Ruan, Xiukai; Liu, Wenbin

    2015-02-09

    The successive projections algorithm (SPA) is widely used to select variables for multiple linear regression (MLR) modeling. However, SPA used only once may not obtain all the useful information of the full spectra, because the number of selected variables cannot exceed the number of calibration samples in the SPA algorithm. Therefore, the SPA-MLR method risks the loss of useful information. To make a full use of the useful information in the spectra, a new method named "consensus SPA-MLR" (C-SPA-MLR) is proposed herein. This method is the combination of consensus strategy and SPA-MLR method. In the C-SPA-MLR method, SPA-MLR is used to construct member models with different subsets of variables, which are selected from the remaining variables iteratively. A consensus prediction is obtained by combining the predictions of the member models. The proposed method is evaluated by analyzing the near infrared (NIR) spectra of corn and diesel. The results of C-SPA-MLR method showed a better prediction performance compared with the SPA-MLR and full-spectra PLS methods. Moreover, these results could serve as a reference for combination the consensus strategy and other variable selection methods when analyzing NIR spectra and other spectroscopic techniques. Copyright © 2014 Elsevier B.V. All rights reserved.

  2. Self-Consistency Method to Evaluate a Linear Expansion Thermal Coefficient of Composite with Dispersed Inclusions

    V. S. Zarubin

    2015-01-01

    Full Text Available The rational use of composites as structural materials, while perceiving the thermal and mechanical loads, to a large extent determined by their thermoelastic properties. From the presented review of works devoted to the analysis of thermoelastic characteristics of composites, it follows that the problem of estimating these characteristics is important. Among the thermoelastic properties of composites occupies an important place its temperature coefficient of linear expansion.Along with fiber composites are widely used in the technique of dispersion hardening composites, in which the role of inclusions carry particles of high-strength and high-modulus materials, including nanostructured elements. Typically, the dispersed particles have similar dimensions in all directions, which allows the shape of the particles in the first approximation the ball.In an article for the composite with isotropic spherical inclusions of a plurality of different materials by the self-produced design formulas relating the temperature coefficient of linear expansion with volume concentration of inclusions and their thermoelastic characteristics, as well as the thermoelastic properties of the matrix of the composite. Feature of the method is the self-accountability thermomechanical interaction of a single inclusion or matrix particles with a homogeneous isotropic medium having the desired temperature coefficient of linear expansion. Averaging over the volume of the composite arising from such interaction perturbation strain and stress in the inclusions and the matrix particles and makes it possible to obtain such calculation formulas.For the validation of the results of calculations of the temperature coefficient of linear expansion of the composite of this type used two-sided estimates that are based on the dual variational formulation of linear thermoelasticity problem in an inhomogeneous solid containing two alternative functional (such as Lagrange and Castigliano

  3. On summary measure analysis of linear trend repeated measures data: performance comparison with two competing methods.

    Vossoughi, Mehrdad; Ayatollahi, S M T; Towhidi, Mina; Ketabchi, Farzaneh

    2012-03-22

    The summary measure approach (SMA) is sometimes the only applicable tool for the analysis of repeated measurements in medical research, especially when the number of measurements is relatively large. This study aimed to describe techniques based on summary measures for the analysis of linear trend repeated measures data and then to compare performances of SMA, linear mixed model (LMM), and unstructured multivariate approach (UMA). Practical guidelines based on the least squares regression slope and mean of response over time for each subject were provided to test time, group, and interaction effects. Through Monte Carlo simulation studies, the efficacy of SMA vs. LMM and traditional UMA, under different types of covariance structures, was illustrated. All the methods were also employed to analyze two real data examples. Based on the simulation and example results, it was found that the SMA completely dominated the traditional UMA and performed convincingly close to the best-fitting LMM in testing all the effects. However, the LMM was not often robust and led to non-sensible results when the covariance structure for errors was misspecified. The results emphasized discarding the UMA which often yielded extremely conservative inferences as to such data. It was shown that summary measure is a simple, safe and powerful approach in which the loss of efficiency compared to the best-fitting LMM was generally negligible. The SMA is recommended as the first choice to reliably analyze the linear trend data with a moderate to large number of measurements and/or small to moderate sample sizes.

  4. Machine learning-based methods for prediction of linear B-cell epitopes.

    Wang, Hsin-Wei; Pai, Tun-Wen

    2014-01-01

    B-cell epitope prediction facilitates immunologists in designing peptide-based vaccine, diagnostic test, disease prevention, treatment, and antibody production. In comparison with T-cell epitope prediction, the performance of variable length B-cell epitope prediction is still yet to be satisfied. Fortunately, due to increasingly available verified epitope databases, bioinformaticians could adopt machine learning-based algorithms on all curated data to design an improved prediction tool for biomedical researchers. Here, we have reviewed related epitope prediction papers, especially those for linear B-cell epitope prediction. It should be noticed that a combination of selected propensity scales and statistics of epitope residues with machine learning-based tools formulated a general way for constructing linear B-cell epitope prediction systems. It is also observed from most of the comparison results that the kernel method of support vector machine (SVM) classifier outperformed other machine learning-based approaches. Hence, in this chapter, except reviewing recently published papers, we have introduced the fundamentals of B-cell epitope and SVM techniques. In addition, an example of linear B-cell prediction system based on physicochemical features and amino acid combinations is illustrated in details.

  5. Edge database analysis for extrapolation to ITER

    Shimada, M.; Janeschitz, G.; Stambaugh, R.D.

    1999-01-01

    An edge database has been archived to facilitate cross-machine comparisons of SOL and edge pedestal characteristics, and to enable comparison with theoretical models with an aim to extrapolate to ITER. The SOL decay lengths of power, density and temperature become broader for increasing density and q 95 . The power decay length is predicted to be 1.4-3.5 cm (L-mode) and 1.4-2.7 cm (H-mode) at the midplane in ITER. Analysis of Type I ELMs suggests that each giant ELM on ITER would exceed the ablation threshold of the divertor plates. Theoretical models are proposed for the H-mode transition, for Type I and Type III ELMs and are compared with the edge pedestal database. (author)

  6. Scintillation counting: an extrapolation into the future

    Ross, H.H.

    1983-01-01

    Progress in scintillation counting is intimately related to advances in a variety of other disciplines such as photochemistry, photophysics, and instrumentation. And while there is steady progress in the understanding of luminescent phenomena, there is a virtual explosion in the application of semiconductor technology to detectors, counting systems, and data processing. The exponential growth of this technology has had, and will continue to have, a profound effect on the art of scintillation spectroscopy. This paper will review key events in technology that have had an impact on the development of scintillation science (solid and liquid) and will attempt to extrapolate future directions based on existing and projected capability in associated fields. Along the way there have been occasional pitfalls and several false starts; these too will be discussed as a reminder that if you want the future to be different than the past, study the past

  7. A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation

    Banks, J.W.; Hittinger, J.A.

    2010-01-01

    Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.

  8. An improved method to accurately calibrate the gantry angle indicators of the radiotherapy linear accelerators

    Chang Liyun; Ho, S.-Y.; Du, Y.-C.; Lin, C.-M.; Chen Tainsong

    2007-01-01

    The calibration of the gantry angle indicator is an important and basic quality assurance (QA) item for the radiotherapy linear accelerator. In this study, we propose a new and practical method, which uses only the digital level, V-film, and general solid phantoms. By taking the star shot only, we can accurately calculate the true gantry angle according to the geometry of the film setup. The results on our machine showed that the gantry angle was shifted by -0.11 deg. compared with the digital indicator, and the standard deviation was within 0.05 deg. This method can also be used for the simulator. In conclusion, this proposed method could be adopted as an annual QA item for mechanical QA of the accelerator

  9. Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

    Zhang, Ling

    2017-01-01

    The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

  10. Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations

    Ling Zhang

    2017-10-01

    Full Text Available Abstract The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs. It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order 1 2 $\\frac{1}{2}$ to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

  11. Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials

    American Society for Testing and Materials. Philadelphia

    2009-01-01

    1.1 This test method covers the determination of fracture toughness (KIc) of metallic materials under predominantly linear-elastic, plane-strain conditions using fatigue precracked specimens having a thickness of 1.6 mm (0.063 in.) or greater subjected to slowly, or in special (elective) cases rapidly, increasing crack-displacement force. Details of test apparatus, specimen configuration, and experimental procedure are given in the Annexes. Note 1—Plane-strain fracture toughness tests of thinner materials that are sufficiently brittle (see 7.1) can be made using other types of specimens (1). There is no standard test method for such thin materials. 1.2 This test method is divided into two parts. The first part gives general recommendations and requirements for KIc testing. The second part consists of Annexes that give specific information on displacement gage and loading fixture design, special requirements for individual specimen configurations, and detailed procedures for fatigue precracking. Additional a...

  12. Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action

    Kim, Jin Kyu; Kim, Dong Keon

    2016-01-01

    A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics

  13. Integrated structural analysis tool using the linear matching method part 1 – Software development

    Ure, James; Chen, Haofeng; Tipping, David

    2014-01-01

    A number of direct methods based upon the Linear Matching Method (LMM) framework have been developed to address structural integrity issues for components subjected to cyclic thermal and mechanical load conditions. This paper presents a new integrated structural analysis tool using the LMM framework for the assessment of load carrying capacity, shakedown limit, ratchet limit and steady state cyclic response of structures. First, the development of the LMM for the evaluation of design limits in plasticity is introduced. Second, preliminary considerations for the development of the LMM into a tool which can be used on a regular basis by engineers are discussed. After the re-structuring of the LMM subroutines for multiple central processing unit (CPU) solution, the LMM software tool for the assessment of design limits in plasticity is implemented by developing an Abaqus CAE plug-in with graphical user interfaces. Further demonstration of this new LMM analysis tool including practical application and verification is presented in an accompanying paper. - Highlights: • A new structural analysis tool using the Linear Matching Method (LMM) is developed. • The software tool is able to evaluate the design limits in plasticity. • Able to assess limit load, shakedown, ratchet limit and steady state cyclic response. • Re-structuring of the LMM subroutines for multiple CPU solution is conducted. • The software tool is implemented by developing an Abaqus CAE plug-in with GUI

  14. Deriving the probability of a linear opinion pooling method being superior to a set of alternatives

    Bolger, Donnacha; Houlding, Brett

    2017-01-01

    Linear opinion pools are a common method for combining a set of distinct opinions into a single succinct opinion, often to be used in a decision making task. In this paper we consider a method, termed the Plug-in approach, for determining the weights to be assigned in this linear pool, in a manner that can be deemed as rational in some sense, while incorporating multiple forms of learning over time into its process. The environment that we consider is one in which every source in the pool is herself a decision maker (DM), in contrast to the more common setting in which expert judgments are amalgamated for use by a single DM. We discuss a simulation study that was conducted to show the merits of our technique, and demonstrate how theoretical probabilistic arguments can be used to exactly quantify the probability of this technique being superior (in terms of a probability density metric) to a set of alternatives. Illustrations are given of simulated proportions converging to these true probabilities in a range of commonly used distributional cases. - Highlights: • A novel context for combination of expert opinion is provided. • A dynamic reliability assessment method is stated, justified by properties and a data study. • The theoretical grounding underlying the data-driven justification is explored. • We conclude with areas for expansion and further relevant research.

  15. Arbitrary Lagrangian-Eulerian method for non-linear problems of geomechanics

    Nazem, M; Carter, J P; Airey, D W

    2010-01-01

    In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-Eulerian (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.

  16. Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action

    Kim, Jin Kyu [School of Architecture and Architectural Engineering, Hanyang University, Ansan (Korea, Republic of); Kim, Dong Keon [Dept. of Architectural Engineering, Dong A University, Busan (Korea, Republic of)

    2016-09-15

    A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics.

  17. Reactor Network Synthesis Using Coupled Genetic Algorithm with the Quasi-linear Programming Method

    Soltani, H.; Shafiei, S.; Edraki, J.

    2016-01-01

    This research is an attempt to develop a new procedure for the synthesis of reactor networks (RNs) using a genetic algorithm (GA) coupled with the quasi-linear programming (LP) method. The GA is used to produce structural configuration, whereas continuous variables are handled using a quasi-LP formulation for finding the best objective function. Quasi-LP consists of LP together with a search loop to find the best reactor conversions (xi), as well as split and recycle ratios (yi). Quasi-LP rep...

  18. Elongation cutoff technique armed with quantum fast multipole method for linear scaling.

    Korchowiec, Jacek; Lewandowski, Jakub; Makowski, Marcin; Gu, Feng Long; Aoki, Yuriko

    2009-11-30

    A linear-scaling implementation of the elongation cutoff technique (ELG/C) that speeds up Hartree-Fock (HF) self-consistent field calculations is presented. The cutoff method avoids the known bottleneck of the conventional HF scheme, that is, diagonalization, because it operates within the low dimension subspace of the whole atomic orbital space. The efficiency of ELG/C is illustrated for two model systems. The obtained results indicate that the ELG/C is a very efficient sparse matrix algebra scheme. Copyright 2009 Wiley Periodicals, Inc.

  19. Detection methods of pulsed X-rays for transmission tomography with a linear accelerator

    Glasser, F.

    1988-07-01

    Appropriate detection methods are studied for the development of a high energy tomograph using a linear accelerator for nondestructive testing of bulky objects. The aim is the selection of detectors adapted to a pulsed X-ray source and with a good behavior under X-ray radiations of several MeV. Performance of semiconductors (HgI 2 , Cl doped CdTe, GaAs, Bi 12 Ge0 20 ) and a scintillator (Bi 4 Ge 3 0 12 ) are examined. A prototype tomograph gave images that show the validity of detectors for analysis of medium size equipment such as a concrete drum of 60 cm in diameter [fr

  20. Face Hallucination with Linear Regression Model in Semi-Orthogonal Multilinear PCA Method

    Asavaskulkiet, Krissada

    2018-04-01

    In this paper, we propose a new face hallucination technique, face images reconstruction in HSV color space with a semi-orthogonal multilinear principal component analysis method. This novel hallucination technique can perform directly from tensors via tensor-to-vector projection by imposing the orthogonality constraint in only one mode. In our experiments, we use facial images from FERET database to test our hallucination approach which is demonstrated by extensive experiments with high-quality hallucinated color faces. The experimental results assure clearly demonstrated that we can generate photorealistic color face images by using the SO-MPCA subspace with a linear regression model.

  1. The evaluation of multi-element personal dosemeters using the linear programming method

    Kragh, P.; Ambrosi, P.; Boehm, J.; Hilgers, G.

    1996-01-01

    Multi-element dosemeters are frequently used in individual monitoring. Each element can be regarded as an individual dosemeter with its own individual dose measurement value. In general, the individual dose values of one dosemeter vary according to the exposure conditions, i. e. the energy and angle of incidence of the radiation. The (final) dose measurement value of the personal dosemeter is calculated from the individual dose values by means of an evaluation algorithm. The best possible dose value, i.e. that of the smallest systematic (type B) uncertainty if the exposure conditions are changed in the dosemeter's rated range of use, is obtained by the method of linear programming. (author)

  2. Faster Simulation Methods for the Non-Stationary Random Vibrations of Non-Linear MDOF Systems

    Askar, A.; Köylüoglu, H. U.; Nielsen, Søren R. K.

    subject to nonstationary Gaussian white noise excitation, as an alternative to conventional direct simulation methods. These alternative simulation procedures rely on an assumption of local Gaussianity during each time step. This assumption is tantamount to various linearizations of the equations....... Such a treatment offers higher rates of convergence, faster speed and higher accuracy. These procedures are compared to the direct Monte Carlo simulation procedure, which uses a fourth order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process...

  3. Faster Simulation Methods for the Nonstationary Random Vibrations of Non-linear MDOF Systems

    Askar, A.; Köylüo, U.; Nielsen, Søren R.K.

    1996-01-01

    subject to nonstationary Gaussian white noise excitation, as an alternative to conventional direct simulation methods. These alternative simulation procedures rely on an assumption of local Gaussianity during each time step. This assumption is tantamount to various linearizations of the equations....... Such a treatment offers higher rates of convergence, faster speed and higher accuracy. These procedures are compared to the direct Monte Carlo simulation procedure, which uses a fourth order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process...

  4. A review of methods for experimentally determining linear optics in storage rings

    Safranek, J.

    1995-01-01

    In order to maximize the brightness and provide sufficient dynamic aperture in synchrotron radiation storage rings, one must understand and control the linear optics. Control of the horizontal beta function and dispersion is important for minimizing the horizontal beam size. Control of the skew gradient distribution is important for minimizing the vertical size. In this paper, various methods for experimentally determining the optics in a storage ring will be reviewed. Recent work at the National Synchrotron Light Source X-Ray Ring will be presented as well as work done at laboratories worldwide

  5. Smooth extrapolation of unknown anatomy via statistical shape models

    Grupp, R. B.; Chiang, H.; Otake, Y.; Murphy, R. J.; Gordon, C. R.; Armand, M.; Taylor, R. H.

    2015-03-01

    Several methods to perform extrapolation of unknown anatomy were evaluated. The primary application is to enhance surgical procedures that may use partial medical images or medical images of incomplete anatomy. Le Fort-based, face-jaw-teeth transplant is one such procedure. From CT data of 36 skulls and 21 mandibles separate Statistical Shape Models of the anatomical surfaces were created. Using the Statistical Shape Models, incomplete surfaces were projected to obtain complete surface estimates. The surface estimates exhibit non-zero error in regions where the true surface is known; it is desirable to keep the true surface and seamlessly merge the estimated unknown surface. Existing extrapolation techniques produce non-smooth transitions from the true surface to the estimated surface, resulting in additional error and a less aesthetically pleasing result. The three extrapolation techniques evaluated were: copying and pasting of the surface estimate (non-smooth baseline), a feathering between the patient surface and surface estimate, and an estimate generated via a Thin Plate Spline trained from displacements between the surface estimate and corresponding vertices of the known patient surface. Feathering and Thin Plate Spline approaches both yielded smooth transitions. However, feathering corrupted known vertex values. Leave-one-out analyses were conducted, with 5% to 50% of known anatomy removed from the left-out patient and estimated via the proposed approaches. The Thin Plate Spline approach yielded smaller errors than the other two approaches, with an average vertex error improvement of 1.46 mm and 1.38 mm for the skull and mandible respectively, over the baseline approach.

  6. Calibration of the 90Sr+90Y ophthalmic and dermatological applicators with an extrapolation ionization minichamber

    Antonio, Patrícia L.; Oliveira, Mércia L.; Caldas, Linda V.E.

    2014-01-01

    90 Sr+ 90 Y clinical applicators are used for brachytherapy in Brazilian clinics even though they are not manufactured anymore. Such sources must be calibrated periodically, and one of the calibration methods in use is ionometry with extrapolation ionization chambers. 90 Sr+ 90 Y clinical applicators were calibrated using an extrapolation minichamber developed at the Calibration Laboratory at IPEN. The obtained results agree satisfactorily with the data provided in calibration certificates of the sources. - Highlights: • 90 Sr+ 90 Y clinical applicators were calibrated using a mini-extrapolation chamber. • An extrapolation curve was obtained for each applicator during its calibration. • The results were compared with those provided by the calibration certificates. • All results of the dermatological applicators presented lower differences than 5%

  7. The extrapolation of creep rupture data by PD6605 - An independent case study

    Bolton, J., E-mail: john.bolton@uwclub.net [65 Fisher Avenue, Rugby, Warks CV22 5HW (United Kingdom)

    2011-04-15

    The worked example presented in BSI document PD6605-1:1998, to illustrate the selection, validation and extrapolation of a creep rupture model using statistical analysis, was independently examined. Alternative rupture models were formulated and analysed by the same statistical methods, and were shown to represent the test data more accurately than the original model. Median rupture lives extrapolated from the original and alternative models were found to diverge widely under some conditions of practical interest. The tests prescribed in PD6605 and employed to validate the original model were applied to the better of the alternative models. But the tests were unable to discriminate between the two, demonstrating that these tests fail to ensure reliability in extrapolation. The difficulties of determining when a model is sufficiently reliable for use in extrapolation are discussed and some proposals are made.

  8. Multidimensional radiative transfer with multilevel atoms. II. The non-linear multigrid method.

    Fabiani Bendicho, P.; Trujillo Bueno, J.; Auer, L.

    1997-08-01

    A new iterative method for solving non-LTE multilevel radiative transfer (RT) problems in 1D, 2D or 3D geometries is presented. The scheme obtains the self-consistent solution of the kinetic and RT equations at the cost of only a few (iteration (Brandt, 1977, Math. Comp. 31, 333; Hackbush, 1985, Multi-Grid Methods and Applications, springer-Verlag, Berlin), an efficient multilevel RT scheme based on Gauss-Seidel iterations (cf. Trujillo Bueno & Fabiani Bendicho, 1995ApJ...455..646T), and accurate short-characteristics formal solution techniques. By combining a valid stopping criterion with a nested-grid strategy a converged solution with the desired true error is automatically guaranteed. Contrary to the current operator splitting methods the very high convergence speed of the new RT method does not deteriorate when the grid spatial resolution is increased. With this non-linear multigrid method non-LTE problems discretized on N grid points are solved in O(N) operations. The nested multigrid RT method presented here is, thus, particularly attractive in complicated multilevel transfer problems where small grid-sizes are required. The properties of the method are analyzed both analytically and with illustrative multilevel calculations for Ca II in 1D and 2D schematic model atmospheres.

  9. Iterative methods for the solution of very large complex symmetric linear systems of equations in electrodynamics

    Clemens, M.; Weiland, T. [Technische Hochschule Darmstadt (Germany)

    1996-12-31

    In the field of computational electrodynamics the discretization of Maxwell`s equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extended to a whole class of methods for complex-symmetric algorithms SCBiCG(T, n), which only require one matrix vector multiplication per iteration step. In this class the well-known conjugate orthogonal conjugate gradient (COCG) method for complex-symmetric systems corresponds to the case n = 0. The case n = 1 yields the BiCGCR method which corresponds to the conjugate residual algorithm for the real-valued case. These methods in combination with a minimal residual smoothing process are applied separately to practical 3D electro-quasistatical and eddy-current problems in electrodynamics. The practical performance of the SCBiCG methods is compared with other methods such as QMR and TFQMR.

  10. Biochemical methane potential prediction of plant biomasses: Comparing chemical composition versus near infrared methods and linear versus non-linear models.

    Godin, Bruno; Mayer, Frédéric; Agneessens, Richard; Gerin, Patrick; Dardenne, Pierre; Delfosse, Philippe; Delcarte, Jérôme

    2015-01-01

    The reliability of different models to predict the biochemical methane potential (BMP) of various plant biomasses using a multispecies dataset was compared. The most reliable prediction models of the BMP were those based on the near infrared (NIR) spectrum compared to those based on the chemical composition. The NIR predictions of local (specific regression and non-linear) models were able to estimate quantitatively, rapidly, cheaply and easily the BMP. Such a model could be further used for biomethanation plant management and optimization. The predictions of non-linear models were more reliable compared to those of linear models. The presentation form (green-dried, silage-dried and silage-wet form) of biomasses to the NIR spectrometer did not influence the performances of the NIR prediction models. The accuracy of the BMP method should be improved to enhance further the BMP prediction models. Copyright © 2014 Elsevier Ltd. All rights reserved.

  11. Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

    Ahmad, Shahid

    1991-01-01

    An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons

  12. Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method.

    Graf, Daniel; Beuerle, Matthias; Schurkus, Henry F; Luenser, Arne; Savasci, Gökcen; Ochsenfeld, Christian

    2018-05-08

    An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.

  13. Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching Control

    Chunyan Han

    2015-01-01

    Full Text Available Based on the heteroclinic Shil’nikov theorem and switching control, a kind of multipiecewise linear chaotic system is constructed in this paper. Firstly, two fundamental linear systems are constructed via linearization of a chaotic system at its two equilibrium points. Secondly, a two-piecewise linear chaotic system which satisfies the Shil’nikov theorem is generated by constructing heteroclinic loop between equilibrium points of the two fundamental systems by switching control. Finally, another multipiecewise linear chaotic system that also satisfies the Shil’nikov theorem is obtained via alternate translation of the two fundamental linear systems and heteroclinic loop construction of adjacent equilibria for the multipiecewise linear system. Some basic dynamical characteristics, including divergence, Lyapunov exponents, and bifurcation diagrams of the constructed systems, are analyzed. Meanwhile, computer simulation and circuit design are used for the proposed chaotic systems, and they are demonstrated to be effective for the method of chaos anticontrol.

  14. Using the fuzzy linear regression method to benchmark the energy efficiency of commercial buildings

    Chung, William

    2012-01-01

    Highlights: ► Fuzzy linear regression method is used for developing benchmarking systems. ► The systems can be used to benchmark energy efficiency of commercial buildings. ► The resulting benchmarking model can be used by public users. ► The resulting benchmarking model can capture the fuzzy nature of input–output data. -- Abstract: Benchmarking systems from a sample of reference buildings need to be developed to conduct benchmarking processes for the energy efficiency of commercial buildings. However, not all benchmarking systems can be adopted by public users (i.e., other non-reference building owners) because of the different methods in developing such systems. An approach for benchmarking the energy efficiency of commercial buildings using statistical regression analysis to normalize other factors, such as management performance, was developed in a previous work. However, the field data given by experts can be regarded as a distribution of possibility. Thus, the previous work may not be adequate to handle such fuzzy input–output data. Consequently, a number of fuzzy structures cannot be fully captured by statistical regression analysis. This present paper proposes the use of fuzzy linear regression analysis to develop a benchmarking process, the resulting model of which can be used by public users. An illustrative example is given as well.

  15. Parallel supercomputing: Advanced methods, algorithms, and software for large-scale linear and nonlinear problems

    Carey, G.F.; Young, D.M.

    1993-12-31

    The program outlined here is directed to research on methods, algorithms, and software for distributed parallel supercomputers. Of particular interest are finite element methods and finite difference methods together with sparse iterative solution schemes for scientific and engineering computations of very large-scale systems. Both linear and nonlinear problems will be investigated. In the nonlinear case, applications with bifurcation to multiple solutions will be considered using continuation strategies. The parallelizable numerical methods of particular interest are a family of partitioning schemes embracing domain decomposition, element-by-element strategies, and multi-level techniques. The methods will be further developed incorporating parallel iterative solution algorithms with associated preconditioners in parallel computer software. The schemes will be implemented on distributed memory parallel architectures such as the CRAY MPP, Intel Paragon, the NCUBE3, and the Connection Machine. We will also consider other new architectures such as the Kendall-Square (KSQ) and proposed machines such as the TERA. The applications will focus on large-scale three-dimensional nonlinear flow and reservoir problems with strong convective transport contributions. These are legitimate grand challenge class computational fluid dynamics (CFD) problems of significant practical interest to DOE. The methods developed and algorithms will, however, be of wider interest.

  16. An Application of Robust Method in Multiple Linear Regression Model toward Credit Card Debt

    Amira Azmi, Nur; Saifullah Rusiman, Mohd; Khalid, Kamil; Roslan, Rozaini; Sufahani, Suliadi; Mohamad, Mahathir; Salleh, Rohayu Mohd; Hamzah, Nur Shamsidah Amir

    2018-04-01

    Credit card is a convenient alternative replaced cash or cheque, and it is essential component for electronic and internet commerce. In this study, the researchers attempt to determine the relationship and significance variables between credit card debt and demographic variables such as age, household income, education level, years with current employer, years at current address, debt to income ratio and other debt. The provided data covers 850 customers information. There are three methods that applied to the credit card debt data which are multiple linear regression (MLR) models, MLR models with least quartile difference (LQD) method and MLR models with mean absolute deviation method. After comparing among three methods, it is found that MLR model with LQD method became the best model with the lowest value of mean square error (MSE). According to the final model, it shows that the years with current employer, years at current address, household income in thousands and debt to income ratio are positively associated with the amount of credit debt. Meanwhile variables for age, level of education and other debt are negatively associated with amount of credit debt. This study may serve as a reference for the bank company by using robust methods, so that they could better understand their options and choice that is best aligned with their goals for inference regarding to the credit card debt.

  17. The linearly scaling 3D fragment method for large scale electronic structure calculations

    Zhao Zhengji [National Energy Research Scientific Computing Center (NERSC) (United States); Meza, Juan; Shan Hongzhang; Strohmaier, Erich; Bailey, David; Wang Linwang [Computational Research Division, Lawrence Berkeley National Laboratory (United States); Lee, Byounghak, E-mail: ZZhao@lbl.go [Physics Department, Texas State University (United States)

    2009-07-01

    The linearly scaling three-dimensional fragment (LS3DF) method is an O(N) ab initio electronic structure method for large-scale nano material simulations. It is a divide-and-conquer approach with a novel patching scheme that effectively cancels out the artificial boundary effects, which exist in all divide-and-conquer schemes. This method has made ab initio simulations of thousand-atom nanosystems feasible in a couple of hours, while retaining essentially the same accuracy as the direct calculation methods. The LS3DF method won the 2008 ACM Gordon Bell Prize for algorithm innovation. Our code has reached 442 Tflop/s running on 147,456 processors on the Cray XT5 (Jaguar) at OLCF, and has been run on 163,840 processors on the Blue Gene/P (Intrepid) at ALCF, and has been applied to a system containing 36,000 atoms. In this paper, we will present the recent parallel performance results of this code, and will apply the method to asymmetric CdSe/CdS core/shell nanorods, which have potential applications in electronic devices and solar cells.

  18. The Inverse System Method Applied to the Derivation of Power System Non—linear Control Laws

    DonghaiLI; XuezhiJIANG; 等

    1997-01-01

    The differential geometric method has been applied to a series of power system non-linear control problems effectively.However a set of differential equations must be solved for obtaining the required diffeomorphic transformation.Therefore the derivation of control laws is very complicated.In fact because of the specificity of power system models the required diffeomorphic transformation may be obtained directly,so it is unnecessary to solve a set of differential equations.In addition inverse system method is equivalent to differential geometric method in reality and not limited to affine nonlinear systems,Its physical meaning is able to be viewed directly and its deduction needs only algebraic operation and derivation,so control laws can be obtained easily and the application to engineering is very convenient.Authors of this paper take steam valving control of power system as a typical case to be studied.It is demonstrated that the control law deduced by inverse system method is just the same as one by differential geometric method.The conclusion will simplify the control law derivations of steam valving,excitation,converter and static var compensator by differential geometric method and may be suited to similar control problems in other areas.

  19. Yager’s ranking method for solving the trapezoidal fuzzy number linear programming

    Karyati; Wutsqa, D. U.; Insani, N.

    2018-03-01

    In the previous research, the authors have studied the fuzzy simplex method for trapezoidal fuzzy number linear programming based on the Maleki’s ranking function. We have found some theories related to the term conditions for the optimum solution of fuzzy simplex method, the fuzzy Big-M method, the fuzzy two-phase method, and the sensitivity analysis. In this research, we study about the fuzzy simplex method based on the other ranking function. It is called Yager's ranking function. In this case, we investigate the optimum term conditions. Based on the result of research, it is found that Yager’s ranking function is not like Maleki’s ranking function. Using the Yager’s function, the simplex method cannot work as well as when using the Maleki’s function. By using the Yager’s function, the value of the subtraction of two equal fuzzy numbers is not equal to zero. This condition makes the optimum table of the fuzzy simplex table is undetected. As a result, the simplified fuzzy simplex table becomes stopped and does not reach the optimum solution.

  20. Mean-Variance-CvaR Model of Multiportfolio Optimization via Linear Weighted Sum Method

    Younes Elahi

    2014-01-01

    Full Text Available We propose a new approach to optimizing portfolios to mean-variance-CVaR (MVC model. Although of several researches have studied the optimal MVC model of portfolio, the linear weighted sum method (LWSM was not implemented in the area. The aim of this paper is to investigate the optimal portfolio model based on MVC via LWSM. With this method, the solution of the MVC model of portfolio as the multiobjective problem is presented. In data analysis section, this approach in investing on two assets is investigated. An MVC model of the multiportfolio was implemented in MATLAB and tested on the presented problem. It is shown that, by using three objective functions, it helps the investors to manage their portfolio better and thereby minimize the risk and maximize the return of the portfolio. The main goal of this study is to modify the current models and simplify it by using LWSM to obtain better results.

  1. Combined slope ratio analysis and linear-subtraction: An extension of the Pearce ratio method

    De Waal, Sybrand A.

    1996-07-01

    A new technique, called combined slope ratio analysis, has been developed by extending the Pearce element ratio or conserved-denominator method (Pearce, 1968) to its logical conclusions. If two stoichiometric substances are mixed and certain chemical components are uniquely contained in either one of the two mixing substances, then by treating these unique components as conserved, the composition of the substance not containing the relevant component can be accurately calculated within the limits allowed by analytical and geological error. The calculated composition can then be subjected to rigorous statistical testing using the linear-subtraction method recently advanced by Woronow (1994). Application of combined slope ratio analysis to the rocks of the Uwekahuna Laccolith, Hawaii, USA, and the lavas of the 1959-summit eruption of Kilauea Volcano, Hawaii, USA, yields results that are consistent with field observations.

  2. A Dynamic Linear Hashing Method for Redundancy Management in Train Ethernet Consist Network

    Xiaobo Nie

    2016-01-01

    Full Text Available Massive transportation systems like trains are considered critical systems because they use the communication network to control essential subsystems on board. Critical system requires zero recovery time when a failure occurs in a communication network. The newly published IEC62439-3 defines the high-availability seamless redundancy protocol, which fulfills this requirement and ensures no frame loss in the presence of an error. This paper adopts these for train Ethernet consist network. The challenge is management of the circulating frames, capable of dealing with real-time processing requirements, fast switching times, high throughout, and deterministic behavior. The main contribution of this paper is the in-depth analysis it makes of network parameters imposed by the application of the protocols to train control and monitoring system (TCMS and the redundant circulating frames discarding method based on a dynamic linear hashing, using the fastest method in order to resolve all the issues that are dealt with.

  3. Application of the method of continued fractions for electron scattering by linear molecules

    Lee, M.-T.; Iga, I.; Fujimoto, M.M.; Lara, O.; Brasilia Univ., DF

    1995-01-01

    The method of continued fractions (MCF) of Horacek and Sasakawa is adapted for the first time to study low-energy electron scattering by linear molecules. Particularly, we have calculated the reactance K-matrices for an electron scattered by hydrogen molecule and hydrogen molecular ion as well as by a polar LiH molecule in the static-exchange level. For all the applications studied herein. the calculated physical quantities converge rapidly, even for a strongly polar molecule such as LiH, to the correct values and in most cases the convergence is monotonic. Our study suggests that the MCF could be an efficient method for studying electron-molecule scattering and also photoionization of molecules. (Author)

  4. A new formulation of the linear sampling method: spatial resolution and post-processing

    Piana, M; Aramini, R; Brignone, M; Coyle, J

    2008-01-01

    A new formulation of the linear sampling method is described, which requires the regularized solution of a single functional equation set in a direct sum of L 2 spaces. This new approach presents the following notable advantages: it is computationally more effective than the traditional implementation, since time consuming samplings of the Tikhonov minimum problem and of the generalized discrepancy equation are avoided; it allows a quantitative estimate of the spatial resolution achievable by the method; it facilitates a post-processing procedure for the optimal selection of the scatterer profile by means of edge detection techniques. The formulation is described in a two-dimensional framework and in the case of obstacle scattering, although generalizations to three dimensions and penetrable inhomogeneities are straightforward

  5. A novel method to design sparse linear arrays for ultrasonic phased array.

    Yang, Ping; Chen, Bin; Shi, Ke-Ren

    2006-12-22

    In ultrasonic phased array testing, a sparse array can increase the resolution by enlarging the aperture without adding system complexity. Designing a sparse array involves choosing the best or a better configuration from a large number of candidate arrays. We firstly designed sparse arrays by using a genetic algorithm, but found that the arrays have poor performance and poor consistency. So, a method based on the Minimum Redundancy Linear Array was then adopted. Some elements are determined by the minimum-redundancy array firstly in order to ensure spatial resolution and then a genetic algorithm is used to optimize the remaining elements. Sparse arrays designed by this method have much better performance and consistency compared to the arrays designed only by a genetic algorithm. Both simulation and experiment confirm the effectiveness.

  6. The instantaneous linear motion information measurement method based on inertial sensors for ships

    Yang, Xu; Huang, Jing; Gao, Chen; Quan, Wei; Li, Ming; Zhang, Yanshun

    2018-05-01

    Ship instantaneous line motion information is the important foundation for ship control, which needs to be measured accurately. For this purpose, an instantaneous line motion measurement method based on inertial sensors is put forward for ships. By introducing a half-fixed coordinate system to realize the separation between instantaneous line motion and ship master movement, the instantaneous line motion acceleration of ships can be obtained with higher accuracy. Then, the digital high-pass filter is applied to suppress the velocity error caused by the low frequency signal such as schuler period. Finally, the instantaneous linear motion displacement of ships can be measured accurately. Simulation experimental results show that the method is reliable and effective, and can realize the precise measurement of velocity and displacement of instantaneous line motion for ships.

  7. Method for pulse to pulse dose reproducibility applied to electron linear accelerators

    Ighigeanu, D.; Martin, D.; Oproiu, C.; Cirstea, E.; Craciun, G.

    2002-01-01

    An original method for obtaining programmed beam single shots and pulse trains with programmed pulse number, pulse repetition frequency, pulse duration and pulse dose is presented. It is particularly useful for automatic control of absorbed dose rate level, irradiation process control as well as in pulse radiolysis studies, single pulse dose measurement or for research experiments where pulse-to-pulse dose reproducibility is required. This method is applied to the electron linear accelerators, ALIN-10 of 6.23 MeV and 82 W and ALID-7, of 5.5 MeV and 670 W, built in NILPRP. In order to implement this method, the accelerator triggering system (ATS) consists of two branches: the gun branch and the magnetron branch. ATS, which synchronizes all the system units, delivers trigger pulses at a programmed repetition rate (up to 250 pulses/s) to the gun (80 kV, 10 A and 4 ms) and magnetron (45 kV, 100 A, and 4 ms).The accelerated electron beam existence is determined by the electron gun and magnetron pulses overlapping. The method consists in controlling the overlapping of pulses in order to deliver the beam in the desired sequence. This control is implemented by a discrete pulse position modulation of gun and/or magnetron pulses. The instabilities of the gun and magnetron transient regimes are avoided by operating the accelerator with no accelerated beam for a certain time. At the operator 'beam start' command, the ATS controls electron gun and magnetron pulses overlapping and the linac beam is generated. The pulse-to-pulse absorbed dose variation is thus considerably reduced. Programmed absorbed dose, irradiation time, beam pulse number or other external events may interrupt the coincidence between the gun and magnetron pulses. Slow absorbed dose variation is compensated by the control of the pulse duration and repetition frequency. Two methods are reported in the electron linear accelerators' development for obtaining the pulse to pulse dose reproducibility: the method

  8. Application of linear scheduling method (LSM) for nuclear power plant (NPP) construction

    Kim, Woojoong; Ryu, Dongsoo; Jung, Youngsoo

    2014-01-01

    Highlights: • Mixed use of linear scheduling method with traditional CPM is suggested for NPP. • A methodology for selecting promising areas for LSM application is proposed. • A case-study is conducted to validate the proposed LSM selection methodology. • A case-study of reducing NPP construction duration by using LSM is introduced. - Abstract: According to a forecast, global energy demand is expected to increase by 56% from 2010 to 2040 (EIA, 2013). The nuclear power plant construction market is also growing with sharper competition. In nuclear power plant construction, scheduling is one of the most important functions due to its large size and complexity. Therefore, it is crucial to incorporate the ‘distinct characteristics of construction commodities and the complex characteristics of scheduling techniques’ (Jung and Woo, 2004) when selecting appropriate schedule control methods for nuclear power plant construction. However, among various types of construction scheduling techniques, the traditional critical path method (CPM) has been used most frequently in real-world practice. In this context, the purpose of this paper is to examine the viability and effectiveness of linear scheduling method (LSM) applications for specific areas in nuclear power plant construction. In order to identify the criteria for selecting scheduling techniques, the characteristics of CPM and LSM were compared and analyzed first through a literature review. Distinct characteristics of nuclear power plant construction were then explored by using a case project in order to develop a methodology to select effective areas of LSM application to nuclear power plant construction. Finally, promising areas for actual LSM application are suggested based on the proposed evaluation criteria and the case project. Findings and practical implications are discussed for further implementation

  9. Application of linear scheduling method (LSM) for nuclear power plant (NPP) construction

    Kim, Woojoong, E-mail: minidung@nate.com [Central Research Institute, Korea Hydro and Nuclear Power Co., Ltd, Daejeon 305-343 (Korea, Republic of); Ryu, Dongsoo, E-mail: energyboy@khnp.co.kr [Central Research Institute, Korea Hydro and Nuclear Power Co., Ltd, Daejeon 305-343 (Korea, Republic of); Jung, Youngsoo, E-mail: yjung97@mju.ac.kr [College of Architecture, Myongji University, Yongin 449-728 (Korea, Republic of)

    2014-04-01

    Highlights: • Mixed use of linear scheduling method with traditional CPM is suggested for NPP. • A methodology for selecting promising areas for LSM application is proposed. • A case-study is conducted to validate the proposed LSM selection methodology. • A case-study of reducing NPP construction duration by using LSM is introduced. - Abstract: According to a forecast, global energy demand is expected to increase by 56% from 2010 to 2040 (EIA, 2013). The nuclear power plant construction market is also growing with sharper competition. In nuclear power plant construction, scheduling is one of the most important functions due to its large size and complexity. Therefore, it is crucial to incorporate the ‘distinct characteristics of construction commodities and the complex characteristics of scheduling techniques’ (Jung and Woo, 2004) when selecting appropriate schedule control methods for nuclear power plant construction. However, among various types of construction scheduling techniques, the traditional critical path method (CPM) has been used most frequently in real-world practice. In this context, the purpose of this paper is to examine the viability and effectiveness of linear scheduling method (LSM) applications for specific areas in nuclear power plant construction. In order to identify the criteria for selecting scheduling techniques, the characteristics of CPM and LSM were compared and analyzed first through a literature review. Distinct characteristics of nuclear power plant construction were then explored by using a case project in order to develop a methodology to select effective areas of LSM application to nuclear power plant construction. Finally, promising areas for actual LSM application are suggested based on the proposed evaluation criteria and the case project. Findings and practical implications are discussed for further implementation.

  10. SU-F-T-64: An Alternative Approach to Determining the Reference Air-Kerma Rate from Extrapolation Chamber Measurements

    Schneider, T

    2016-01-01

    Purpose: Since 2008 the Physikalisch-Technische Bundesanstalt (PTB) has been offering the calibration of "1"2"5I-brachytherapy sources in terms of the reference air-kerma rate (RAKR). The primary standard is a large air-filled parallel-plate extrapolation chamber. The measurement principle is based on the fact that the air-kerma rate is proportional to the increment of ionization per increment of chamber volume at chamber depths greater than the range of secondary electrons originating from the electrode x_0. Methods: Two methods for deriving the RAKR from the measured ionization charges are: (1) to determine the RAKR from the slope of the linear fit to the so-called ’extrapolation curve’, the measured ionization charges Q vs. plate separations x or (2) to differentiate Q(x) and to derive the RAKR by a linear extrapolation towards zero plate separation. For both methods, correcting the measured data for all known influencing effects before the evaluation method is applied is a precondition. However, the discrepancy of their results is larger than the uncertainty given for the determination of the RAKR with both methods. Results: A new approach to derive the RAKR from the measurements is investigated as an alternative. The method was developed from the ground up, based on radiation transport theory. A conversion factor C(x_1, x_2) is applied to the difference of charges measured at the two plate separations x_1 and x_2. This factor is composed of quotients of three air-kerma values calculated for different plate separations in the chamber: the air kerma Ka(0) for plate separation zero, and the mean air kermas at the plate separations x_1 and x_2, respectively. The RAKR determined with method (1) yields 4.877 µGy/h, and with method (2) 4.596 µGy/h. The application of the alternative approach results in 4.810 µGy/h. Conclusion: The alternative method shall be established in the future.

  11. Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

    Gottlieb, Sigal

    2015-04-10

    High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.

  12. Nodal methods with non linear feedback for the three dimensional resolution of the diffusion's multigroup equations

    Ferri, A.A.

    1986-01-01

    Nodal methods applied in order to calculate the power distribution in a nuclear reactor core are presented. These methods have received special attention, because they yield accurate results in short computing times. Present nodal schemes contain several unknowns per node and per group. In the methods presented here, non linear feedback of the coupling coefficients has been applied to reduce this number to only one unknown per node and per group. The resulting algorithm is a 7- points formula, and the iterative process has proved stable in the response matrix scheme. The intranodal flux shape is determined by partial integration of the diffusion equations over two of the coordinates, leading to a set of three coupled one-dimensional equations. These can be solved by using a polynomial approximation or by integration (analytic solution). The tranverse net leakage is responsible for the coupling between the spatial directions, and two alternative methods are presented to evaluate its shape: direct parabolic approximation and local model expansion. Numerical results, which include the IAEA two-dimensional benchmark problem illustrate the efficiency of the developed methods. (M.E.L.) [es

  13. Iterative linear solvers in a 2D radiation-hydrodynamics code: Methods and performance

    Baldwin, C.; Brown, P.N.; Falgout, R.; Graziani, F.; Jones, J.

    1999-01-01

    Computer codes containing both hydrodynamics and radiation play a central role in simulating both astrophysical and inertial confinement fusion (ICF) phenomena. A crucial aspect of these codes is that they require an implicit solution of the radiation diffusion equations. The authors present in this paper the results of a comparison of five different linear solvers on a range of complex radiation and radiation-hydrodynamics problems. The linear solvers used are diagonally scaled conjugate gradient, GMRES with incomplete LU preconditioning, conjugate gradient with incomplete Cholesky preconditioning, multigrid, and multigrid-preconditioned conjugate gradient. These problems involve shock propagation, opacities varying over 5--6 orders of magnitude, tabular equations of state, and dynamic ALE (Arbitrary Lagrangian Eulerian) meshes. They perform a problem size scalability study by comparing linear solver performance over a wide range of problem sizes from 1,000 to 100,000 zones. The fundamental question they address in this paper is: Is it more efficient to invert the matrix in many inexpensive steps (like diagonally scaled conjugate gradient) or in fewer expensive steps (like multigrid)? In addition, what is the answer to this question as a function of problem size and is the answer problem dependent? They find that the diagonally scaled conjugate gradient method performs poorly with the growth of problem size, increasing in both iteration count and overall CPU time with the size of the problem and also increasing for larger time steps. For all problems considered, the multigrid algorithms scale almost perfectly (i.e., the iteration count is approximately independent of problem size and problem time step). For pure radiation flow problems (i.e., no hydrodynamics), they see speedups in CPU time of factors of ∼15--30 for the largest problems, when comparing the multigrid solvers relative to diagonal scaled conjugate gradient

  14. Efficient Estimation of Extreme Non-linear Roll Motions using the First-order Reliability Method (FORM)

    Jensen, Jørgen Juncher

    2007-01-01

    In on-board decision support systems efficient procedures are needed for real-time estimation of the maximum ship responses to be expected within the next few hours, given on-line information on the sea state and user defined ranges of possible headings and speeds. For linear responses standard...... frequency domain methods can be applied. To non-linear responses like the roll motion, standard methods like direct time domain simulations are not feasible due to the required computational time. However, the statistical distribution of non-linear ship responses can be estimated very accurately using...... the first-order reliability method (FORM), well-known from structural reliability problems. To illustrate the proposed procedure, the roll motion is modelled by a simplified non-linear procedure taking into account non-linear hydrodynamic damping, time-varying restoring and wave excitation moments...

  15. A frequency domain linearized Navier-Stokes method including acoustic damping by eddy viscosity using RANS

    Holmberg, Andreas; Kierkegaard, Axel; Weng, Chenyang

    2015-06-01

    In this paper, a method for including damping of acoustic energy in regions of strong turbulence is derived for a linearized Navier-Stokes method in the frequency domain. The proposed method is validated and analyzed in 2D only, although the formulation is fully presented in 3D. The result is applied in a study of the linear interaction between the acoustic and the hydrodynamic field in a 2D T-junction, subject to grazing flow at Mach 0.1. Part of the acoustic energy at the upstream edge of the junction is shed as harmonically oscillating disturbances, which are conveyed across the shear layer over the junction, where they interact with the acoustic field. As the acoustic waves travel in regions of strong shear, there is a need to include the interaction between the background turbulence and the acoustic field. For this purpose, the oscillation of the background turbulence Reynold's stress, due to the acoustic field, is modeled using an eddy Newtonian model assumption. The time averaged flow is first solved for using RANS along with a k-ε turbulence model. The spatially varying turbulent eddy viscosity is then added to the spatially invariant kinematic viscosity in the acoustic set of equations. The response of the 2D T-junction to an incident acoustic field is analyzed via a plane wave scattering matrix model, and the result is compared to experimental data for a T-junction of rectangular ducts. A strong improvement in the agreement between calculation and experimental data is found when the modification proposed in this paper is implemented. Discrepancies remaining are likely due to inaccuracies in the selected turbulence model, which is known to produce large errors e.g. for flows with significant rotation, which the grazing flow across the T-junction certainly is. A natural next step is therefore to test the proposed methodology together with more sophisticated turbulence models.

  16. Scaling and extrapolation of hydrogen distribution experiments

    Karwat, H.

    1986-01-01

    The containment plays an important role in predicting the residual risk to the environment under severe accident conditions. Risk analyses show that massive fission product release from the reactor fuel can occur only if during a loss of coolant the core is severely damaged and a containment failure is anticipated. Large amounts of hydrogen inevitably, are formed during the core degradation and will be released into the containment. More combustible gases are produced later when the coremelt will contact the containment concrete. Thus a potential for an early containment failure exists if a massive hydrogen deflagration cannot be excluded. A more remote cause for early containment failure may be an energetic steam explosion which requires a number of independent conditions when the molten core material contacts residual coolant water. The prediction of the containment loads caused by a hydrogen combustion is dependent on the prediction of the combustion mode. In the paper an attempt is made to identify on basis of a dimensional analysis such areas for which particular care must be exercised when scale experimental evidence is interpreted and extrapolated with the aid of a computer code or a system of computer codes. The study is restricted to fluid dynamic phenomena of the gas distribution process within the containment atmosphere. The gas sources and the mechanical response of containment structures are considered as given boundary conditions under which the containment is to be analyzed

  17. Quality control methods for linear accelerator radiation and mechanical axes alignment.

    Létourneau, Daniel; Keller, Harald; Becker, Nathan; Amin, Md Nurul; Norrlinger, Bernhard; Jaffray, David A

    2018-06-01

    The delivery accuracy of highly conformal dose distributions generated using intensity modulation and collimator, gantry, and couch degrees of freedom is directly affected by the quality of the alignment between the radiation beam and the mechanical axes of a linear accelerator. For this purpose, quality control (QC) guidelines recommend a tolerance of ±1 mm for the coincidence of the radiation and mechanical isocenters. Traditional QC methods for assessment of radiation and mechanical axes alignment (based on pointer alignment) are time consuming and complex tasks that provide limited accuracy. In this work, an automated test suite based on an analytical model of the linear accelerator motions was developed to streamline the QC of radiation and mechanical axes alignment. The proposed method used the automated analysis of megavoltage images of two simple task-specific phantoms acquired at different linear accelerator settings to determine the coincidence of the radiation and mechanical isocenters. The sensitivity and accuracy of the test suite were validated by introducing actual misalignments on a linear accelerator between the radiation axis and the mechanical axes using both beam steering and mechanical adjustments of the gantry and couch. The validation demonstrated that the new QC method can detect sub-millimeter misalignment between the radiation axis and the three mechanical axes of rotation. A displacement of the radiation source of 0.2 mm using beam steering parameters was easily detectable with the proposed collimator rotation axis test. Mechanical misalignments of the gantry and couch rotation axes of the same magnitude (0.2 mm) were also detectable using the new gantry and couch rotation axis tests. For the couch rotation axis, the phantom and test design allow detection of both translational and tilt misalignments with the radiation beam axis. For the collimator rotation axis, the test can isolate the misalignment between the beam radiation axis

  18. A Riccati Based Homogeneous and Self-Dual Interior-Point Method for Linear Economic Model Predictive Control

    Sokoler, Leo Emil; Frison, Gianluca; Edlund, Kristian

    2013-01-01

    In this paper, we develop an efficient interior-point method (IPM) for the linear programs arising in economic model predictive control of linear systems. The novelty of our algorithm is that it combines a homogeneous and self-dual model, and a specialized Riccati iteration procedure. We test...

  19. A Fresh Look at Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

    Camporesi, Roberto

    2016-01-01

    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

  20. New computational method for non-LTE, the linear response matrix

    Fournier, K.B.; Grasiani, F.R.; Harte, J.A.; Libby, S.B.; More, R.M.; Zimmerman, G.B.

    1998-01-01

    My coauthors have done extensive theoretical and computational calculations that lay the ground work for a linear response matrix method to calculate non-LTE (local thermodynamic equilibrium) opacities. I will give briefly review some of their work and list references. Then I will describe what has been done to utilize this theory to create a computational package to rapidly calculate mild non-LTE emission and absorption opacities suitable for use in hydrodynamic calculations. The opacities are obtained by performing table look-ups on data that has been generated with a non-LTE package. This scheme is currently under development. We can see that it offers a significant computational speed advantage. It is suitable for mild non-LTE, quasi-steady conditions. And it offers a new insertion path for high-quality non-LTE data. Currently, the linear response matrix data file is created using XSN. These data files could be generated by more detailed and rigorous calculations without changing any part of the implementation in the hydro code. The scheme is running in Lasnex and is being tested and developed

  1. Determining mineralogical variations of aeolian deposits using thermal infrared emissivity and linear deconvolution methods

    Hubbard, Bernard E.; Hooper, Donald M.; Solano, Federico; Mars, John C.

    2018-01-01

    We apply linear deconvolution methods to derive mineral and glass proportions for eight field sample training sites at seven dune fields: (1) Algodones, California; (2) Big Dune, Nevada; (3) Bruneau, Idaho; (4) Great Kobuk Sand Dunes, Alaska; (5) Great Sand Dunes National Park and Preserve, Colorado; (6) Sunset Crater, Arizona; and (7) White Sands National Monument, New Mexico. These dune fields were chosen because they represent a wide range of mineral grain mixtures and allow us to gauge a better understanding of both compositional and sorting effects within terrestrial and extraterrestrial dune systems. We also use actual ASTER TIR emissivity imagery to map the spatial distribution of these minerals throughout the seven dune fields and evaluate the effects of degraded spectral resolution on the accuracy of mineral abundances retrieved. Our results show that hyperspectral data convolutions of our laboratory emissivity spectra outperformed multispectral data convolutions of the same data with respect to the mineral, glass and lithic abundances derived. Both the number and wavelength position of spectral bands greatly impacts the accuracy of linear deconvolution retrieval of feldspar proportions (e.g. K-feldspar vs. plagioclase) especially, as well as the detection of certain mafic and carbonate minerals. In particular, ASTER mapping results show that several of the dune sites display patterns such that less dense minerals typically have higher abundances near the center of the active and most evolved dunes in the field, while more dense minerals and glasses appear to be more abundant along the margins of the active dune fields.

  2. Determining mineralogical variations of aeolian deposits using thermal infrared emissivity and linear deconvolution methods

    Hubbard, Bernard E.; Hooper, Donald M.; Solano, Federico; Mars, John C.

    2018-02-01

    We apply linear deconvolution methods to derive mineral and glass proportions for eight field sample training sites at seven dune fields: (1) Algodones, California; (2) Big Dune, Nevada; (3) Bruneau, Idaho; (4) Great Kobuk Sand Dunes, Alaska; (5) Great Sand Dunes National Park and Preserve, Colorado; (6) Sunset Crater, Arizona; and (7) White Sands National Monument, New Mexico. These dune fields were chosen because they represent a wide range of mineral grain mixtures and allow us to gauge a better understanding of both compositional and sorting effects within terrestrial and extraterrestrial dune systems. We also use actual ASTER TIR emissivity imagery to map the spatial distribution of these minerals throughout the seven dune fields and evaluate the effects of degraded spectral resolution on the accuracy of mineral abundances retrieved. Our results show that hyperspectral data convolutions of our laboratory emissivity spectra outperformed multispectral data convolutions of the same data with respect to the mineral, glass and lithic abundances derived. Both the number and wavelength position of spectral bands greatly impacts the accuracy of linear deconvolution retrieval of feldspar proportions (e.g. K-feldspar vs. plagioclase) especially, as well as the detection of certain mafic and carbonate minerals. In particular, ASTER mapping results show that several of the dune sites display patterns such that less dense minerals typically have higher abundances near the center of the active and most evolved dunes in the field, while more dense minerals and glasses appear to be more abundant along the margins of the active dune fields.

  3. Phase-of-flight method for setting the accelerating fields in the ion linear accelerator

    Dvortsov, S.V.; Lomize, L.G.

    1983-01-01

    For setting amplitudes and phases of accelerating fields in multiresonator ion accelerators presently Δt-procedure is used. The determination and setting of two unknown parameters of RF-field (amplitude and phase) in n-resonator is made according to the two increments of particle time-of-flight, measured experimentally: according to the change of the particle time-of-flight Δt 1 in the n-resonator, during the field switching in the resonator, and according to the change of Δt 2 of the time-of-flight in (n+1) resonator without RF-field with the switching of accelerating field in the n-resonator. When approaching the accelerator exit the particle energy increases, relative energy increment decreases and the accuracy of setting decreases. To enchance the accuracy of accelerating fields setting in a linear ion accelerator a phase-of-flight method is developed, in which for the setting of accelerating fields the measured time-of-flight increment Δt only in one resonator is used (the one in which the change of amplitude and phase is performed). Results of simulation of point bunch motion in the IYaI AN USSR linear accelerator are presented

  4. Nuclear lattice simulations using symmetry-sign extrapolation

    Laehde, Timo A.; Luu, Thomas [Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik, and Juelich Center for Hadron Physics, Juelich (Germany); Lee, Dean [North Carolina State University, Department of Physics, Raleigh, NC (United States); Meissner, Ulf G. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik, and Juelich Center for Hadron Physics, Juelich (Germany); Forschungszentrum Juelich, JARA - High Performance Computing, Juelich (Germany); Epelbaum, Evgeny; Krebs, Hermann [Ruhr-Universitaet Bochum, Institut fuer Theoretische Physik II, Bochum (Germany); Rupak, Gautam [Mississippi State University, Department of Physics and Astronomy, Mississippi State, MS (United States)

    2015-07-15

    Projection Monte Carlo calculations of lattice Chiral Effective Field Theory suffer from sign oscillations to a varying degree dependent on the number of protons and neutrons. Hence, such studies have hitherto been concentrated on nuclei with equal numbers of protons and neutrons, and especially on the alpha nuclei where the sign oscillations are smallest. Here, we introduce the ''symmetry-sign extrapolation'' method, which allows us to use the approximate Wigner SU(4) symmetry of the nuclear interaction to systematically extend the Projection Monte Carlo calculations to nuclear systems where the sign problem is severe. We benchmark this method by calculating the ground-state energies of the {sup 12}C, {sup 6}He and {sup 6}Be nuclei, and discuss its potential for studies of neutron-rich halo nuclei and asymmetric nuclear matter. (orig.)

  5. A Novel Coupled State/Input/Parameter Identification Method for Linear Structural Systems

    Zhimin Wan

    2018-01-01

    Full Text Available In many engineering applications, unknown states, inputs, and parameters exist in the structures. However, most methods require one or two of these variables to be known in order to identify the other(s. Recently, the authors have proposed a method called EGDF for coupled state/input/parameter identification for nonlinear system in state space. However, the EGDF method based solely on acceleration measurements is found to be unstable, which can cause the drift of the identified inputs and displacements. Although some regularization methods can be adopted for solving the problem, they are not suitable for joint input-state identification in real time. In this paper, a strategy of data fusion of displacement and acceleration measurements is used to avoid the low-frequency drift in the identified inputs and structural displacements for linear structural systems. Two numerical examples about a plane truss and a single-stage isolation system are conducted to verify the effectiveness of the proposed modified EGDF algorithm.

  6. A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

    Camporesi, Roberto

    2016-01-01

    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.

  7. Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

    Pipkins, Daniel Scott

    Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially. linear model are compared to those

  8. Study of the reaction {pi}{sup -}p {yields} {pi}{sup -}{pi}{sup 0} p at 2.77 GeV/c for low momentum transfer of the proton. Application to the Chew-Low extrapolation method for the {pi}{sup -}{pi}{sup 0} elastic scattering; Etude de la reaction {pi}{sup -}p {yields} {pi}{sup -}{pi}{sup 0} p a 2.77 GeV/c pour de faibles impulsions du proton diffuse. Application de la methode d'extrapolation de Chew et Low a la diffusion elastiques {pi}{sup -}{pi}{sup 0}

    Baton, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1968-05-01

    Study of the reaction {pi}{sup -}p {yields} {pi}{sup -}{pi}{sup 0} p at 2.77 GeV/c carried out in the CERN 2 meter large liquid hydrogen bubble chamber at the proton synchrotron, shows that 70 per cent of this reaction goes through {pi}{sup -}p {yields} {rho}{sup -}p channel. The high statistics allow us to specify the mass and the width of the {rho}{sup -} resonance. In other hand, if the {rho}{sup -} production parameters are independent of the {rho}{sup -} width, it is not the same case for the decay parameters. In the second part, the Chew-Low extrapolation method allows us to determine the {pi}{sup -}{pi}{sup 0} elastic cross section to the pole, and the phase shifts of the P waves in the isospin 1 state and S waves in the isospin 2 state. (author) [French] L'etude de la reaction {pi}{sup -}p {yields} {pi}{sup -}{pi}{sup 0} p a 2.77 GeV/c, effectuee a l'aide de la chambre a bulles a hydrogene liquide de 2 metres du CERN, exposee aupres du synchrotron a protons, montre que 70 pour cent de cette reaction passe par la voie {pi}{sup -}p {yields} {rho}{sup -}p. L'abondance de la statistique a permis de preciser la masse et la largeur de la resonance {rho}{sup -}. D'autre part, si les parametres de la production du {rho}{sup -} sont independants de la largeur de la resonance, il n'en est pas de meme des parametres de la desintegration. Dans la deuxieme partie, la methode d'extrapolation de Chew et Low permet de determiner la section efficace de diffusion elastique {pi}{sup -}{pi}{sup 0} au pole, ainsi que les dephasages des ondes P dans l'etat d'isospin 1 et S dans l'etat d'isospin 2. (auteur)

  9. CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method

    Benzley, S.E.; Beisinger, Z.E.

    1981-01-01

    1 - Description of problem or function: CHILES is a finite element computer program that calculates the strength of singularities in linear elastic bodies. Plane stress, plane strain, and axisymmetric conditions are treated. Crack tip singularity problems are solved by this version of the code, but any type of integrable singularity may be properly modeled by modifying selected subroutines in the program. 2 - Method of solution: A generalized, quadrilateral finite element that includes a singular point at a corner node is incorporated in the code. The displacement formulation is used and inter-element compatibility is maintained so that monotone convergence is preserved. 3 - Restrictions on the complexity of the problem: CHILES allows three singular points to be modeled in the body being analyzed and each singular point may have coupled Mode I and II deformations. 1000 nodal points may be used

  10. Time dependence linear transport III convergence of the discrete ordinate method

    Wilson, D.G.

    1983-01-01

    In this paper the uniform pointwise convergence of the discrete ordinate method for weak and strong solutions of the time dependent, linear transport equation posed in a multidimensional, rectangular parallelepiped with partially reflecting walls is established. The first result is that a sequence of discrete ordinate solutions converges uniformly on the quadrature points to a solution of the continuous problem provided that the corresponding sequence of truncation errors for the solution of the continuous problem converges to zero in the same manner. The second result is that continuity of the solution with respect to the velocity variables guarantees that the truncation erros in the quadrature formula go the zero and hence that the discrete ordinate approximations converge to the solution of the continuous problem as the discrete ordinate become dense. An existence theory for strong solutions of the the continuous problem follows as a result

  11. High Order A-stable Continuous General Linear Methods for Solution of Systems of Initial Value Problems in ODEs

    Dauda GuliburYAKUBU

    2012-12-01

    Full Text Available Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods.

  12. Predicting respiratory motion signals for image-guided radiotherapy using multi-step linear methods (MULIN)

    Ernst, Floris; Schweikard, Achim

    2008-01-01

    Forecasting of respiration motion in image-guided radiotherapy requires algorithms that can accurately and efficiently predict target location. Improved methods for respiratory motion forecasting were developed and tested. MULIN, a new family of prediction algorithms based on linear expansions of the prediction error, was developed and tested. Computer-generated data with a prediction horizon of 150 ms was used for testing in simulation experiments. MULIN was compared to Least Mean Squares-based predictors (LMS; normalized LMS, nLMS; wavelet-based multiscale autoregression, wLMS) and a multi-frequency Extended Kalman Filter (EKF) approach. The in vivo performance of the algorithms was tested on data sets of patients who underwent radiotherapy. The new MULIN methods are highly competitive, outperforming the LMS and the EKF prediction algorithms in real-world settings and performing similarly to optimized nLMS and wLMS prediction algorithms. On simulated, periodic data the MULIN algorithms are outperformed only by the EKF approach due to its inherent advantage in predicting periodic signals. In the presence of noise, the MULIN methods significantly outperform all other algorithms. The MULIN family of algorithms is a feasible tool for the prediction of respiratory motion, performing as well as or better than conventional algorithms while requiring significantly lower computational complexity. The MULIN algorithms are of special importance wherever high-speed prediction is required. (orig.)

  13. The Linear Quadratic Gaussian Multistage Game with Nonclassical Information Pattern Using a Direct Solution Method

    Clemens, Joshua William

    Game theory has application across multiple fields, spanning from economic strategy to optimal control of an aircraft and missile on an intercept trajectory. The idea of game theory is fascinating in that we can actually mathematically model real-world scenarios and determine optimal decision making. It may not always be easy to mathematically model certain real-world scenarios, nonetheless, game theory gives us an appreciation for the complexity involved in decision making. This complexity is especially apparent when the players involved have access to different information upon which to base their decision making (a nonclassical information pattern). Here we will focus on the class of adversarial two-player games (sometimes referred to as pursuit-evasion games) with nonclassical information pattern. We present a two-sided (simultaneous) optimization solution method for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of each player's decision making (strategy) as compared to previously used formal solution methods. In addition to the optimal control strategies, we present a saddle point proof and we derive an expression for the optimal performance index value. We provide some numerical results in order to further interpret the optimal control strategies and to highlight real-world application of this game-theoretic optimal solution.

  14. Evaluation of mathematical methods and linear programming for optimization of the planning in radiotherapy

    Fernandes, Marco A.R.; Fernandes, David M.; Florentino, Helenice O.

    2010-01-01

    The work detaches the importance of the use of mathematical tools and computer systems for optimization of the planning in radiotherapy, seeking to the distribution of dose of appropriate radiation in the white volume that provides an ideal therapeutic rate between the tumor cells and the adjacent healthy tissues, extolled in the radiotherapy protocols. Examples of target volumes mathematically modeled are analyzed with the technique of linear programming, comparing the obtained results using the Simplex algorithm with those using the algorithm of Interior Points. The System Genesis II was used for obtaining of the isodose curves for the outline and geometry of fields idealized in the computer simulations, considering the parameters of a 10 MV photons beams. Both programming methods (Simplex and Interior Points) they resulted in a distribution of integral dose in the tumor volume and allow the adaptation of the dose in the critical organs inside of the restriction limits extolled. The choice of an or other method should take into account the facility and the need of limiting the programming time. The isodose curves, obtained with the Genesis II System, illustrate that the adjacent healthy tissues to the tumor receives larger doses than those reached in the computer simulations. More coincident values can be obtained altering the weights and some factors of minimization of the objective function. The prohibitive costs of the computer planning systems, at present available for radiotherapy, it motivates the researches to look for the implementation of simpler and so effective methods for optimization of the treatment plan. (author)

  15. Engineering Mathematical Analysis Method for Productivity Rate in Linear Arrangement Serial Structure Automated Flow Assembly Line

    Tan Chan Sin

    2015-01-01

    Full Text Available Productivity rate (Q or production rate is one of the important indicator criteria for industrial engineer to improve the system and finish good output in production or assembly line. Mathematical and statistical analysis method is required to be applied for productivity rate in industry visual overviews of the failure factors and further improvement within the production line especially for automated flow line since it is complicated. Mathematical model of productivity rate in linear arrangement serial structure automated flow line with different failure rate and bottleneck machining time parameters becomes the basic model for this productivity analysis. This paper presents the engineering mathematical analysis method which is applied in an automotive company which possesses automated flow assembly line in final assembly line to produce motorcycle in Malaysia. DCAS engineering and mathematical analysis method that consists of four stages known as data collection, calculation and comparison, analysis, and sustainable improvement is used to analyze productivity in automated flow assembly line based on particular mathematical model. Variety of failure rate that causes loss of productivity and bottleneck machining time is shown specifically in mathematic figure and presents the sustainable solution for productivity improvement for this final assembly automated flow line.

  16. Predicting respiratory motion signals for image-guided radiotherapy using multi-step linear methods (MULIN)

    Ernst, Floris; Schweikard, Achim [University of Luebeck, Institute for Robotics and Cognitive Systems, Luebeck (Germany)

    2008-06-15

    Forecasting of respiration motion in image-guided radiotherapy requires algorithms that can accurately and efficiently predict target location. Improved methods for respiratory motion forecasting were developed and tested. MULIN, a new family of prediction algorithms based on linear expansions of the prediction error, was developed and tested. Computer-generated data with a prediction horizon of 150 ms was used for testing in simulation experiments. MULIN was compared to Least Mean Squares-based predictors (LMS; normalized LMS, nLMS; wavelet-based multiscale autoregression, wLMS) and a multi-frequency Extended Kalman Filter (EKF) approach. The in vivo performance of the algorithms was tested on data sets of patients who underwent radiotherapy. The new MULIN methods are highly competitive, outperforming the LMS and the EKF prediction algorithms in real-world settings and performing similarly to optimized nLMS and wLMS prediction algorithms. On simulated, periodic data the MULIN algorithms are outperformed only by the EKF approach due to its inherent advantage in predicting periodic signals. In the presence of noise, the MULIN methods significantly outperform all other algorithms. The MULIN family of algorithms is a feasible tool for the prediction of respiratory motion, performing as well as or better than conventional algorithms while requiring significantly lower computational complexity. The MULIN algorithms are of special importance wherever high-speed prediction is required. (orig.)

  17. Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers.

    Merrikh-Bayat, Farshad

    2011-04-01

    One main approach for time-domain simulation of the linear output-feedback systems containing fractional-order controllers is to approximate the transfer function of the controller with an integer-order transfer function and then perform the simulation. In general, this approach suffers from two main disadvantages: first, the internal stability of the resulting feedback system is not guaranteed, and second, the amount of error caused by this approximation is not exactly known. The aim of this paper is to propose an efficient method for time-domain simulation of such systems without facing the above mentioned drawbacks. For this purpose, the fractional-order controller is approximated with an integer-order transfer function (possibly in combination with the delay term) such that the internal stability of the closed-loop system is guaranteed, and then the simulation is performed. It is also shown that the resulting approximate controller can effectively be realized by using the proposed method. Some formulas for estimating and correcting the simulation error, when the feedback system under consideration is subjected to the unit step command or the unit step disturbance, are also presented. Finally, three numerical examples are studied and the results are compared with the Oustaloup continuous approximation method. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

  18. A three operator split-step method covering a larger set of non-linear partial differential equations

    Zia, Haider

    2017-06-01

    This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

  19. Linear methods for reducing EMG contamination in peripheral nerve motor decodes.

    Kagan, Zachary B; Wendelken, Suzanne; Page, David M; Davis, Tyler; Hutchinson, Douglas T; Clark, Gregory A; Warren, David J

    2016-08-01

    Signals recorded from the peripheral nervous system (PNS) with high channel count penetrating microelectrode arrays, such as the Utah Slanted Electrode Array (USEA), often have electromyographic (EMG) signals contaminating the neural signal. This common-mode signal source may prevent single neural units from successfully being detected, thus hindering motor decode algorithms. Reducing this EMG contamination may lead to more accurate motor decode performance. A virtual reference (VR), created by a weighted linear combination of signals from a subset of all available channels, can be used to reduce this EMG contamination. Four methods of determining individual channel weights and six different methods of selecting subsets of channels were investigated (24 different VR types in total). The methods of determining individual channel weights were equal weighting, regression-based weighting, and two different proximity-based weightings. The subsets of channels were selected by a radius-based criteria, such that a channel was included if it was within a particular radius of inclusion from the target channel. These six radii of inclusion were 1.5, 2.9, 3.2, 5, 8.4, and 12.8 electrode-distances; the 12.8 electrode radius includes all USEA electrodes. We found that application of a VR improves the detectability of neural events via increasing the SNR, but we found no statistically meaningful difference amongst the VR types we examined. The computational complexity of implementation varies with respect to the method of determining channel weights and the number of channels in a subset, but does not correlate with VR performance. Hence, we examined the computational costs of calculating and applying the VR and based on these criteria, we recommend an equal weighting method of assigning weights with a 3.2 electrode-distance radius of inclusion. Further, we found empirically that application of the recommended VR will require less than 1 ms for 33.3 ms of data from one USEA.

  20. Reflexion on linear regression trip production modelling method for ensuring good model quality

    Suprayitno, Hitapriya; Ratnasari, Vita

    2017-11-01

    Transport Modelling is important. For certain cases, the conventional model still has to be used, in which having a good trip production model is capital. A good model can only be obtained from a good sample. Two of the basic principles of a good sampling is having a sample capable to represent the population characteristics and capable to produce an acceptable error at a certain confidence level. It seems that this principle is not yet quite understood and used in trip production modeling. Therefore, investigating the Trip Production Modelling practice in Indonesia and try to formulate a better modeling method for ensuring the Model Quality is necessary. This research result is presented as follows. Statistics knows a method to calculate span of prediction value at a certain confidence level for linear regression, which is called Confidence Interval of Predicted Value. The common modeling practice uses R2 as the principal quality measure, the sampling practice varies and not always conform to the sampling principles. An experiment indicates that small sample is already capable to give excellent R2 value and sample composition can significantly change the model. Hence, good R2 value, in fact, does not always mean good model quality. These lead to three basic ideas for ensuring good model quality, i.e. reformulating quality measure, calculation procedure, and sampling method. A quality measure is defined as having a good R2 value and a good Confidence Interval of Predicted Value. Calculation procedure must incorporate statistical calculation method and appropriate statistical tests needed. A good sampling method must incorporate random well distributed stratified sampling with a certain minimum number of samples. These three ideas need to be more developed and tested.