Advanced differential quadrature methods
Zong, Zhi
2009-01-01
Modern Tools to Perform Numerical DifferentiationThe original direct differential quadrature (DQ) method has been known to fail for problems with strong nonlinearity and material discontinuity as well as for problems involving singularity, irregularity, and multiple scales. But now researchers in applied mathematics, computational mechanics, and engineering have developed a range of innovative DQ-based methods to overcome these shortcomings. Advanced Differential Quadrature Methods explores new DQ methods and uses these methods to solve problems beyond the capabilities of the direct DQ method.After a basic introduction to the direct DQ method, the book presents a number of DQ methods, including complex DQ, triangular DQ, multi-scale DQ, variable order DQ, multi-domain DQ, and localized DQ. It also provides a mathematical compendium that summarizes Gauss elimination, the Runge-Kutta method, complex analysis, and more. The final chapter contains three codes written in the FORTRAN language, enabling readers to q...
Differential quadrature method of nonlinear bending of functionally graded beam
Gangnian, Xu; Liansheng, Ma; Wang, Youzhi; Quan, Yuan; Weijie, You
2018-02-01
Using the third-order shear deflection beam theory (TBT), nonlinear bending of functionally graded (FG) beams composed with various amounts of ceramic and metal is analyzed utilizing the differential quadrature method (DQM). The properties of beam material are supposed to accord with the power law index along to thickness. First, according to the principle of stationary potential energy, the partial differential control formulae of the FG beams subjected to a distributed lateral force are derived. To obtain numerical results of the nonlinear bending, non-dimensional boundary conditions and control formulae are dispersed by applying the DQM. To verify the present solution, several examples are analyzed for nonlinear bending of homogeneous beams with various edges. A minute parametric research is in progress about the effect of the law index, transverse shear deformation, distributed lateral force and boundary conditions.
Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations
International Nuclear Information System (INIS)
Mokhtari, R.; Toodar, A. Samadi; Chegini, N.G.
2011-01-01
The aim of this paper is to obtain numerical solutions of the one-dimensional, two-dimensional and coupled Burgers' equations through the generalized differential quadrature method (GDQM). The polynomial-based differential quadrature (PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta (TVD-RK) method. The numerical solutions are satisfactorily coincident with the exact solutions. The method can compete against the methods applied in the literature. (general)
International Nuclear Information System (INIS)
Mozaffari, M.; Atai, A. A.; Mostafa, N.
2009-01-01
This paper presents a computationally efficient and accurate new methodology in the differential quadrature analysis of structural mechanics for flexible membranes ballooning in three dimensions under a negative air pressure differential. The differential quadrature method is employed to discretize the resulting equations in the axial direction as well as for the solution procedure. The weighting coefficients employed are not exclusive, and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the methods weighting coefficients. A second-order paraboloid of revolution is assumed to describe the ballooning shape. This study asserts the accuracy, convergency, and efficiency of the methodology by solving some typical stability, straining analysis membrane problems, and comparing the results with those of the exact solutions and/or those of physical tests
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Mozaffari, M.; Atai, A. A.; Mostafa, N. [Islamic Azad University, Karaj (Iran, Islamic Republic of)
2009-11-15
This paper presents a computationally efficient and accurate new methodology in the differential quadrature analysis of structural mechanics for flexible membranes ballooning in three dimensions under a negative air pressure differential. The differential quadrature method is employed to discretize the resulting equations in the axial direction as well as for the solution procedure. The weighting coefficients employed are not exclusive, and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the methods weighting coefficients. A second-order paraboloid of revolution is assumed to describe the ballooning shape. This study asserts the accuracy, convergency, and efficiency of the methodology by solving some typical stability, straining analysis membrane problems, and comparing the results with those of the exact solutions and/or those of physical tests
International Nuclear Information System (INIS)
Mokhtari, R.; Toodar, A. Samadi; Chegini, N. G.
2011-01-01
We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrödinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge—Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out. (general)
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Maziar Janghorban
Full Text Available Static and free vibration analysis of carbon nano wires with rectangular cross section based on Timoshenko beam theory is studied in this research. Differential quadrature method (DQM is employed to solve the governing equations. From the knowledge of author, it is the first time that free vibration of nano wires is investigated. It is also the first time that differential quadrature method is used for bending analysis of nano wires.
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Mittal, R.C.; Rohila, Rajni
2016-01-01
In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.
Optimization of convective-radiative fins by using differential quadrature element method
International Nuclear Information System (INIS)
Malekzadeh, P.; Rahideh, H.; Karami, G.
2006-01-01
A first endeavor to exploit the differential quadrature element method (DQEM) as a simple, accurate and computationally efficient numerical tool for the shape optimization of convective-radiating extended surfaces or fins is made. The formulations are general so that the spatial and spatial-temperature dependent geometrical and thermal parameters can easily be implemented. The thermal conductivity of the fin is assumed to vary as a linear function of the temperature. The effects of a convective-radiative condition at the fin tip and effective convective condition at the fin base are considered. The optimization of fins with uniform and step cross-sections is investigated. The accuracy of the method is demonstrated by comparing its results with those generated by Adomian's decomposition technique, Taylor transformation technique and finite difference method. It is shown that, using few grid points, highly accurate results are obtained. Less computational effort of the method with respect to the finite difference method is shown
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G. H. Rahimi
2014-01-01
Full Text Available A three-dimensional elasticity theory by means of a state-space based differential quadrature method is presented for free vibration analysis of fiber metal laminate annular plate. The kinds of composite material and metal layers are considered to be S2-glass and aluminum, respectively. A semianalytical approach which uses state-space in the thickness and differential quadrature in the radial direction is implemented for evaluating the nondimensional natural frequencies of the annular plates. The influences of changes in boundary condition, plate thickness, and lay-up direction on the natural frequencies are studied. A comparison is also made with the numerical results reported by ABAQUS software which shows an excellent agreement.
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Alashti, R. Akbari, E-mail: raalashti@nit.ac.ir [Mechanical Engineering Department, Babol University of Technology, P.O. Box 484, Shariati Avenue, Babol (Iran, Islamic Republic of); Khorsand, M. [Mechanical Engineering Department, Babol University of Technology, P.O. Box 484, Shariati Avenue, Babol (Iran, Islamic Republic of)
2011-05-15
Three-dimensional thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads is carried out. Numerical results of displacement, stress and thermal fields are obtained using two versions of the differential quadrature methods, namely polynomial and Fourier quadrature methods. Material properties of the shell are assumed to be graded in the radial direction according to a power law but the Poisson's ratio is assumed to be constant. Shells are considered to be under the effect of the pressure loading in the form of cosine and ring pressure loads, electric potentials and temperature fields. Numerical results for various boundary conditions are obtained and the effects of the thickness of piezoelectric layers, grading index of material properties and the ratio of the thickness to the radius of the shell on these results is presented. - Highlights: > A numerical study of an FGM cylindrical shell with piezoelectric layers is made. > Governing equations are solved by two versions of differential quadrature methods. > The effect of layers thickness, grading index and geometrical ratios is presented.
International Nuclear Information System (INIS)
Alashti, R. Akbari; Khorsand, M.
2011-01-01
Three-dimensional thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads is carried out. Numerical results of displacement, stress and thermal fields are obtained using two versions of the differential quadrature methods, namely polynomial and Fourier quadrature methods. Material properties of the shell are assumed to be graded in the radial direction according to a power law but the Poisson's ratio is assumed to be constant. Shells are considered to be under the effect of the pressure loading in the form of cosine and ring pressure loads, electric potentials and temperature fields. Numerical results for various boundary conditions are obtained and the effects of the thickness of piezoelectric layers, grading index of material properties and the ratio of the thickness to the radius of the shell on these results is presented. - Highlights: → A numerical study of an FGM cylindrical shell with piezoelectric layers is made. → Governing equations are solved by two versions of differential quadrature methods. → The effect of layers thickness, grading index and geometrical ratios is presented.
International Nuclear Information System (INIS)
Shin, Young Jae; Hwang, Ki Sup; Yun, Jong Hak
2006-01-01
The main purpose of this paper is to apply Differential Transformation Method(DTM) and Generalized Differential Quadrature Method(GDQM) to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. In this paper the concepts of DTM and GDQM were briefly introduced. The governing equation of motion of the beam with open cracks on elastic foundation is derived. The cracks are modeled by massless substitute spring. The effects of the crack location, size and the foundation constants, on the natural frequencies of the beam, are investigated. Numerical calculations are carried out and compared with previous published results
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Ye Li
Full Text Available The use of quadrature RF magnetic fields has been demonstrated to be an efficient method to reduce transmit power and to increase the signal-to-noise (SNR in magnetic resonance (MR imaging. The goal of this project was to develop a new method using the common-mode and differential-mode (CMDM technique for compact, planar, distributed-element quadrature transmit/receive resonators for MR signal excitation and detection and to investigate its performance for MR imaging, particularly, at ultrahigh magnetic fields. A prototype resonator based on CMDM method implemented by using microstrip transmission line was designed and fabricated for 7T imaging. Both the common mode (CM and the differential mode (DM of the resonator were tuned and matched at 298MHz independently. Numerical electromagnetic simulation was performed to verify the orthogonal B1 field direction of the two modes of the CMDM resonator. Both workbench tests and MR imaging experiments were carried out to evaluate the performance. The intrinsic decoupling between the two modes of the CMDM resonator was demonstrated by the bench test, showing a better than -36 dB transmission coefficient between the two modes at resonance frequency. The MR images acquired by using each mode and the images combined in quadrature showed that the CM and DM of the proposed resonator provided similar B1 coverage and achieved SNR improvement in the entire region of interest. The simulation and experimental results demonstrate that the proposed CMDM method with distributed-element transmission line technique is a feasible and efficient technique for planar quadrature RF coil design at ultrahigh fields, providing intrinsic decoupling between two quadrature channels and high frequency capability. Due to its simple and compact geometry and easy implementation of decoupling methods, the CMDM quadrature resonator can possibly be a good candidate for design blocks in multichannel RF coil arrays.
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A. Karami Mohammadi
2015-07-01
Full Text Available : In this paper, a nonlinear model of clamped-clamped microbeam actuated by electrostatic load with stretching and thermoelastic effects is presented. Free vibration frequency is calculated by discretization based on DQ method. Frequency is a complex value due to the thermoelastic effect that dissipates the energy. By separating the real and imaginary parts of frequency, quality factor of thermoelastic damping is calculated. Both stretching and thermoelastic effects are validated against the results of the reference papers. The variations of thermoelastic damping versus elasticity modulus, coefficient of thermal expansion and geometrical parameters such as thickness, gap distance, and length are investigated and these results are compared in the linear and nonlinear models for high values of voltage. Also, this paper shows that since for high values of electrostatic voltage the linear model reveals a large error for calculating the thermoelastic damping, the nonlinear model should be used for this purpose.
Başhan, Ali; Uçar, Yusuf; Murat Yağmurlu, N.; Esen, Alaattin
2018-01-01
In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. For this purpose, first of all, the Schrödinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, L2 and L_{∞}, as well as the two lowest invariants, I1 and I2, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.
International Nuclear Information System (INIS)
Civalek, Oemer
2005-01-01
The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation
Comparison of two Galerkin quadrature methods
International Nuclear Information System (INIS)
Morel, J. E.; Warsa, J. S.; Franke, B. C.; Prinja, A. K.
2013-01-01
We compare two methods for generating Galerkin quadrature for problems with highly forward-peaked scattering. In Method 1, the standard Sn method is used to generate the moment-to-discrete matrix and the discrete-to-moment is generated by inverting the moment-to-discrete matrix. In Method 2, which we introduce here, the standard Sn method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. Method 1 has the advantage that it preserves both N eigenvalues and N eigenvectors (in a pointwise sense) of the scattering operator with an N-point quadrature. Method 2 has the advantage that it generates consistent angular moment equations from the corresponding S N equations while preserving N eigenvalues of the scattering operator with an N-point quadrature. Our computational results indicate that these two methods are quite comparable for the test problem considered. (authors)
Method of mechanical quadratures for solving singular integral equations of various types
Sahakyan, A. V.; Amirjanyan, H. A.
2018-04-01
The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.
Analysis of Differential Quadrature Method on Wind Turbine Tower Free Vibration%风电机组塔架自由振动的微分求积法分析
Institute of Scientific and Technical Information of China (English)
王清波; 陈婷
2013-01-01
塔架结构的振动，不仅会引起塔架的附加应力，影响其结构强度，而且还会影响风轮的变形和振动，从而影响其性能。因此，在风电机组的设计中，必须分析计算风力引起的塔架结构动力学问题。本文介绍了微分求积法原理，使用该方法求解了风电机组锥筒型塔架的固有频率，并与其它数值方法求解的结果进行了对比，结果表明，微分求积法原理简单，计算量小，精度较高，且易于在计算机上实现。%Te vibration of wind turbine tower structure can not only cause the additional stress of the tower, afect the structural strength, but also afect the deformation and vibration of the wind turbine rotor, which afects its performance. Terefore, the analysis and calculation of the wind turbine tower structure dynamics caused by the wind shall be taken into account in the design of the wind turbine. Te principle of the diferential quadrature method has been introduced in this paper. Te natural frequency of the taper cylinder tower has been computed by this method. Numerical results from this approach are compared with other numerical methods. It is shown that the principle of differential quadrature method is simple, and its computation efficiency is higher, accuracy, and easy to implement on computer.
International Nuclear Information System (INIS)
Aruchunan, E.
2015-01-01
In this paper, we have examined the effectiveness of the quarter-sweep iteration concept on conjugate gradient normal residual (CGNR) iterative method by using composite Simpson's (CS) and finite difference (FD) discretization schemes in solving Fredholm integro-differential equations. For comparison purposes, Gauss- Seidel (GS) and the standard or full- and half-sweep CGNR methods namely FSCGNR and HSCGNR are also presented. To validate the efficacy of the proposed method, several analyses were carried out such as computational complexity and percentage reduction on the proposed and existing methods. (author)
Effective quadrature formula in solving linear integro-differential equations of order two
Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.
2017-08-01
In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.
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Malekzadeh, P. [Department of Mechanical Engineering, Persian Gulf University, Boushehr 75168 (Iran, Islamic Republic of); Center of Excellence for Computational Mechanics in Mechanical Engineering, Shiraz University, Shiraz (Iran, Islamic Republic of)], E-mail: malekzadeh@pgu.ac.ir; Farid, M. [Center of Excellence for Computational Mechanics in Mechanical Engineering, Shiraz University, Shiraz (Iran, Islamic Republic of); Department of Mechanical Engineering, Shiraz University, Shiraz (Iran, Islamic Republic of); Zahedinejad, P. [Department of Mechanical Engineering, Shiraz University, Shiraz (Iran, Islamic Republic of)
2008-07-15
A mixed layerwise theory and differential quadrature (DQ) method (LW-DQ) for three-dimensional free vibration analysis of arbitrary laminated circular cylindrical shells is introduced. Using the layerwise theory in conjunction with the three-dimensional form of Hamilton's principle, the transversely discretized equations of motion and the related boundary conditions are obtained. Then, the DQ method is employed to discretize the resulting equations in the axial directions. The fast convergence behavior of the method is demonstrated and its accuracy is verified by comparing the results with those of other shell theories obtained using conventional methods and also with those of ANSYS software. In the case of arbitrary laminated shells with simply supported ends, the exact solution is developed for comparison purposes. It is shown that using few DQ grid points, converged accurate solutions are obtained. Less computational efforts of the proposed approach with respect to ANSYS software is shown.
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Xinwei Wang
2016-11-01
Full Text Available Sandwich structures are widely used in practice and thus various engineering theories adopting simplifying assumptions are available. However, most engineering theories of beams, plates and shells cannot recover all stresses accurately through their constitutive equations. Therefore, the soft-core is directly modeled by two-dimensional (2D elasticity theory without any pre-assumption on the displacement field. The top and bottom faces act like the elastic supports on the top and bottom edges of the core. The differential equations of the 2D core are then solved by the harmonic differential quadrature method (HDQM. To circumvent the difficulties in dealing with the locally distributed load by point discrete methods such as the HDQM, a general and rigorous way is proposed to treat the locally distributed load. Detailed formulations are provided. The static behavior of sandwich panels under different locally distributed loads is investigated. For verification, results are compared with data obtained by ABAQUS with very fine meshes. A high degree of accuracy on both displacement and stress has been observed.
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S. A. Eftekhari
Full Text Available AbstractThe differential quadrature method (DQM is one of the most elegant and efficient methods for the numerical solution of partial differential equations arising in engineering and applied sciences. It is simple to use and also straightforward to implement. However, the DQM is well-known to have some difficulty when applied to partial differential equations involving singular functions like the Dirac-delta function. This is caused by the fact that the Dirac-delta function cannot be directly discretized by the DQM. To overcome this difficulty, this paper presents a simple differential quadrature procedure in which the Dirac-delta function is replaced by regularized smooth functions. By regularizing the Dirac-delta function, such singular function is treated as non-singular functions and can be easily and directly discretized using the DQM. To demonstrate the applicability and reliability of the proposed method, it is applied here to solve some moving load problems of beams and rectangular plates, where the location of the moving load is described by a time-dependent Dirac-delta function. The results generated by the proposed method are compared with analytical and numerical results available in the literature. Numerical results reveal that the proposed method can be used as an efficient tool for dynamic analysis of beam- and plate-type structures traversed by moving dynamic loads.
On optimal quadrature formulae
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Lanzara Flavia
2000-01-01
Full Text Available A procedure to construct quadrature formulae which are exact for solutions of linear differential equations and are optimal in the sense of Sard is discussed. We give necessary and sufficient conditions under which such formulae do exist. Several formulae obtained by applying this method are considered and compared with well known formulae.
Optimization and Experimentation of Dual-Mass MEMS Gyroscope Quadrature Error Correction Methods.
Cao, Huiliang; Li, Hongsheng; Kou, Zhiwei; Shi, Yunbo; Tang, Jun; Ma, Zongmin; Shen, Chong; Liu, Jun
2016-01-07
This paper focuses on an optimal quadrature error correction method for the dual-mass MEMS gyroscope, in order to reduce the long term bias drift. It is known that the coupling stiffness and demodulation error are important elements causing bias drift. The coupling stiffness in dual-mass structures is analyzed. The experiment proves that the left and right masses' quadrature errors are different, and the quadrature correction system should be arranged independently. The process leading to quadrature error is proposed, and the Charge Injecting Correction (CIC), Quadrature Force Correction (QFC) and Coupling Stiffness Correction (CSC) methods are introduced. The correction objects of these three methods are the quadrature error signal, force and the coupling stiffness, respectively. The three methods are investigated through control theory analysis, model simulation and circuit experiments, and the results support the theoretical analysis. The bias stability results based on CIC, QFC and CSC are 48 °/h, 9.9 °/h and 3.7 °/h, respectively, and this value is 38 °/h before quadrature error correction. The CSC method is proved to be the better method for quadrature correction, and it improves the Angle Random Walking (ARW) value, increasing it from 0.66 °/√h to 0.21 °/√h. The CSC system general test results show that it works well across the full temperature range, and the bias stabilities of the six groups' output data are 3.8 °/h, 3.6 °/h, 3.4 °/h, 3.1 °/h, 3.0 °/h and 4.2 °/h, respectively, which proves the system has excellent repeatability.
Optimization and Experimentation of Dual-Mass MEMS Gyroscope Quadrature Error Correction Methods
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Huiliang Cao
2016-01-01
Full Text Available This paper focuses on an optimal quadrature error correction method for the dual-mass MEMS gyroscope, in order to reduce the long term bias drift. It is known that the coupling stiffness and demodulation error are important elements causing bias drift. The coupling stiffness in dual-mass structures is analyzed. The experiment proves that the left and right masses’ quadrature errors are different, and the quadrature correction system should be arranged independently. The process leading to quadrature error is proposed, and the Charge Injecting Correction (CIC, Quadrature Force Correction (QFC and Coupling Stiffness Correction (CSC methods are introduced. The correction objects of these three methods are the quadrature error signal, force and the coupling stiffness, respectively. The three methods are investigated through control theory analysis, model simulation and circuit experiments, and the results support the theoretical analysis. The bias stability results based on CIC, QFC and CSC are 48 °/h, 9.9 °/h and 3.7 °/h, respectively, and this value is 38 °/h before quadrature error correction. The CSC method is proved to be the better method for quadrature correction, and it improves the Angle Random Walking (ARW value, increasing it from 0.66 °/√h to 0.21 °/√h. The CSC system general test results show that it works well across the full temperature range, and the bias stabilities of the six groups’ output data are 3.8 °/h, 3.6 °/h, 3.4 °/h, 3.1 °/h, 3.0 °/h and 4.2 °/h, respectively, which proves the system has excellent repeatability.
Optimization and Experimentation of Dual-Mass MEMS Gyroscope Quadrature Error Correction Methods
Cao, Huiliang; Li, Hongsheng; Kou, Zhiwei; Shi, Yunbo; Tang, Jun; Ma, Zongmin; Shen, Chong; Liu, Jun
2016-01-01
This paper focuses on an optimal quadrature error correction method for the dual-mass MEMS gyroscope, in order to reduce the long term bias drift. It is known that the coupling stiffness and demodulation error are important elements causing bias drift. The coupling stiffness in dual-mass structures is analyzed. The experiment proves that the left and right masses’ quadrature errors are different, and the quadrature correction system should be arranged independently. The process leading to quadrature error is proposed, and the Charge Injecting Correction (CIC), Quadrature Force Correction (QFC) and Coupling Stiffness Correction (CSC) methods are introduced. The correction objects of these three methods are the quadrature error signal, force and the coupling stiffness, respectively. The three methods are investigated through control theory analysis, model simulation and circuit experiments, and the results support the theoretical analysis. The bias stability results based on CIC, QFC and CSC are 48 °/h, 9.9 °/h and 3.7 °/h, respectively, and this value is 38 °/h before quadrature error correction. The CSC method is proved to be the better method for quadrature correction, and it improves the Angle Random Walking (ARW) value, increasing it from 0.66 °/√h to 0.21 °/√h. The CSC system general test results show that it works well across the full temperature range, and the bias stabilities of the six groups’ output data are 3.8 °/h, 3.6 °/h, 3.4 °/h, 3.1 °/h, 3.0 °/h and 4.2 °/h, respectively, which proves the system has excellent repeatability. PMID:26751455
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Zhiqiang Shen
2012-01-01
Full Text Available Deformation of partially composite beams under distributed loading and free vibrations of partially composite beams under various boundary conditions are examined in this paper. The weak-form quadrature element method, which is characterized by direct evaluation of the integrals involved in the variational description of a problem, is used. One quadrature element is normally sufficient for a partially composite beam regardless of the magnitude of the shear connection stiffness. The number of integration points in a quadrature element is adjustable in accordance with convergence requirement. Results are compared with those of various finite element formulations. It is shown that the weak form quadrature element solution for partially composite beams is free of slip locking, and high computational accuracy is achieved with smaller number of degrees of freedom. Besides, it is found that longitudinal inertia of motion cannot be simply neglected in assessment of dynamic behavior of partially composite beams.
International Nuclear Information System (INIS)
Amin, Najam Muhammad; Wang Zhigong; Li Zhiqun
2015-01-01
A down-conversion in-phase/quadrature (I/Q) mixer employing a folded-type topology, integrated with a passive differential quadrature all-pass filter (D-QAF), in order to realize the final down-conversion stage of a 60 GHz receiver architecture is presented in this work. Instead of employing conventional quadrature generation techniques such as a polyphase filter or a frequency divider for the local oscillator (LO) of the mixer, a passive D-QAF structure is employed. Fabricated in a 65 nm CMOS process, the mixer exhibits a voltage gain of 7–8 dB in an intermediate frequency (IF) band ranging from 10 MHz–1.75 GHz. A fixed LO frequency of 12 GHz is used to down-convert a radio frequency (RF) band of 10.25–13.75 GHz. The mixer displays a third order input referred intercept point (IIP 3 ) ranging from −8.75 to −7.37 dBm for a fixed IF frequency of 10 MHz and a minimum single-sideband noise figure (SSB-NF) of 11.3 dB. The mixer draws a current of 6 mA from a 1.2 V supply voltage dissipating a power of 7.2 mW. (paper)
LC Quadrature Generation in Integrated Circuits
DEFF Research Database (Denmark)
Christensen, Kåre Tais
2001-01-01
Today quadrature signals for IQ demodulation are provided through RC polyphase networks, quadrature oscillators or double frequency VCOs. This paper presents a new method for generating quadrature signals in integrated circuits using only inductors and capacitors. This LC quadrature generation...
Goldstein, M; Haussmann, W; Hayman, W; Rogge, L
1992-01-01
This volume consists of the proceedings of the NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics, which was held at Hanstholm, Denmark. These proceedings include the main invited talks and contributed papers given during the workshop. The aim of these lectures was to present a selection of results of the latest research in the field. In addition to covering topics in approximation by solutions of partial differential equations and quadrature formulae, this volume is also concerned with related areas, such as Gaussian quadratures, the Pompelu problem, rational approximation to the Fresnel integral, boundary correspondence of univalent harmonic mappings, the application of the Hilbert transform in two dimensional aerodynamics, finely open sets in the limit set of a finitely generated Kleinian group, scattering theory, harmonic and maximal measures for rational functions and the solution of the classical Dirichlet problem. In ...
Nonlinear Fredholm Integral Equation of the Second Kind with Quadrature Methods
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M. Jafari Emamzadeh
2010-06-01
Full Text Available In this paper, a numerical method for solving the nonlinear Fredholm integral equation is presented. We intend to approximate the solution of this equation by quadrature methods and by doing so, we solve the nonlinear Fredholm integral equation more accurately. Several examples are given at the end of this paper
A multivariate quadrature based moment method for LES based modeling of supersonic combustion
Donde, Pratik; Koo, Heeseok; Raman, Venkat
2012-07-01
The transported probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of scramjet combustors. In this approach, a high-dimensional transport equation for the joint composition-enthalpy PDF needs to be solved. Quadrature based approaches provide deterministic Eulerian methods for solving the joint-PDF transport equation. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach.
Diamond difference method with hybrid angular quadrature applied to neutron transport problems
International Nuclear Information System (INIS)
Zani, Jose H.; Barros, Ricardo C.; Alves Filho, Hermes
2005-01-01
In this work we presents the results for the calculations of the disadvantage factor in thermal nuclear reactor physics. We use the one-group discrete ordinates (S N ) equations to mathematically model the flux distributions in slab lattices. We apply the diamond difference method with source iteration iterative scheme to numerically solve the discretized systems equations. We used special interface conditions to describe the method with hybrid angular quadrature. We show numerical results to illustrate the accuracy of the hybrid method. (author)
Solution of stochastic media transport problems using a numerical quadrature-based method
International Nuclear Information System (INIS)
Pautz, S. D.; Franke, B. C.; Prinja, A. K.; Olson, A. J.
2013-01-01
We present a new conceptual framework for analyzing transport problems in random media. We decompose such problems into stratified subproblems according to the number of material pseudo-interfaces within realizations. For a given subproblem we assign pseudo-interface locations in each realization according to product quadrature rules, which allows us to deterministically generate a fixed number of realizations. Quadrature integration of the solutions of these realizations thus approximately solves each subproblem; the weighted superposition of solutions of the subproblems approximately solves the general stochastic media transport problem. We revisit some benchmark problems to determine the accuracy and efficiency of this approach in comparison to randomly generated realizations. We find that this method is very accurate and fast when the number of pseudo-interfaces in a problem is generally low, but that these advantages quickly degrade as the number of pseudo-interfaces increases. (authors)
A Gaussian quadrature method for total energy analysis in electronic state calculations
Fukushima, Kimichika
This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article showed that, for diatomic molecules such as CO and FeO, elliptic coordinates efficiently achieved high numerical integral accuracy even with a numerical basis set including transition metal atomic orbitals. This article will generalize straightforward details for multiatomic systems with direct integrals in each decomposed elliptic coordinate determined from the nuclear positions of picked-up atom pairs. Sample calculations were performed for the molecules O3 and H2O. This article will also try to present, in another coordinate, a numerical integral by partially using the Becke's decomposition published in 1988, but without the Becke's fuzzy cell generated by the polynomials of internuclear distance between the pair atoms. Instead, simple nuclear weights comprising exponential functions around nuclei are used. The one-center integral is performed with a Gaussian quadrature pack in a spherical coordinate, included in the author's original program in around 1980. As for this decomposition into one-center integrals, sample calculations are carried out for Li2.
Angular quadrature sets for the streaming ray method in x-y geometry
International Nuclear Information System (INIS)
England, R.; Filippone, W.L.
1983-01-01
Steaming ray (SR) computations normally employ a set of specially selected ray directions. For x-y geometry, these directions are not uniformly spaced in the azimuthal angle, nor do they conform to any of the standard quadrature sets in current use. For simplicity in all previous SR computations, uniform angular weights were used. This note investigates two methods--a bisection scheme and a Fourier scheme--for selecting more appropriate azimuthal angular weights. In the bisection scheme, the azimuthal weight assigned to an SR direction is half the angular spread (in the x-y plane) between its two adjacent ray directions. In the Fourier method, the weights are chosen such that the number of terms in a Fourier series exactly integrable on the interval (0, 2π) is maximized. Several sample calculations have been performed. While both the Fourier and bisection weights showed significant advantage over the uniform weights used previously, the Fourier scheme appears to be the best method. Lists of bisection and Fourier weights are given for quadrature sets containing 4, 8, 12, ..., 60 azimuthal SR directions
Directory of Open Access Journals (Sweden)
B. Kuldeep
2015-06-01
Full Text Available Fractional calculus has recently been identified as a very important mathematical tool in the field of signal processing. Digital filters designed by fractional derivatives give more accurate frequency response in the prescribed frequency region. Digital filters are most important part of multi-rate filter bank systems. In this paper, an improved method based on fractional derivative constraints is presented for the design of two-channel quadrature mirror filter (QMF bank. The design problem is formulated as minimization of L2 error of filter bank transfer function in passband, stopband interval and at quadrature frequency, and then Lagrange multiplier method with fractional derivative constraints is applied to solve it. The proposed method is then successfully applied for the design of two-channel QMF bank with higher order filter taps. Performance of the QMF bank design is then examined through study of various parameters such as passband error, stopband error, transition band error, peak reconstruction error (PRE, stopband attenuation (As. It is found that, the good design can be obtained with the change of number and value of fractional derivative constraint coefficients.
Contributions to multidimensional quadrature formulas
International Nuclear Information System (INIS)
Guenther, C.
1976-11-01
The general objective of this paper is to construct multidimensional quadrature formulas similar to the Gaussian Quadrature Formulas in one dimension. The correspondence between these formulas and orthogonal and nonnegative polynomials is established. One part of the paper considers the construction of multidimensional quadrature formulas using only methods of algebraic geometry, on the other part it is tried to obtain results on quadrature formulas with real nodes and, if possible, with positive weights. The results include the existence of quadrature formulas, information on the number resp. on the maximum possible number of points in the formulas for given polynomial degree N and the construction of formulas. (orig.) [de
International Nuclear Information System (INIS)
Pal, T.K.; Bajpai, R.K.; Datta, D.
2016-01-01
Differential Quadrature Method (DQM) based computational scheme is developed to solve diffusion equation in cylindrical coordinate. In this scheme, time derivative is approximated using forward difference and the spatial derivatives using polynomial based DQM. This developed scheme is applied to simulate test problem on radionuclide leaching from radioactive waste form. Leach rate is calculated after simulating the leaching process. DQM based results are compared with the analytical solutions and good agreements between the two results are established. The developed tool is used as a numerical tool for computationally intensive calculations, such as regression analysis and correlation analysis etc. Multivariate regression analysis is carried out to establish a linear relationship between leach rate and model parameters e.g., diffusion coefficient, porosity and linear sorption coefficient. Study of correlation analysis carried out in this study shows that diffusion coefficient is positively more correlated with leach rate compared to porosity whereas, K_d is negatively correlated with leach rate. (author)
Increasing reliability of Gauss-Kronrod quadrature by Eratosthenes' sieve method
Adam, Gh.; Adam, S.
2001-04-01
The reliability of the local error estimates returned by the Gauss-Kronrod quadrature rules can be raised up to the theoretical 100% rate of success, under error estimate sharpening, provided a number of natural validating conditions are required. The self-validating scheme of the local error estimates, which is easy to implement and adds little supplementary computing effort, strengthens considerably the correctness of the decisions within the automatic adaptive quadrature.
Chang, Chun; Huang, Benxiong; Xu, Zhengguang; Li, Bin; Zhao, Nan
2018-02-01
Three soft-input-soft-output (SISO) detection methods for dual-polarized quadrature duobinary (DP-QDB), including maximum-logarithmic-maximum-a-posteriori-probability-algorithm (Max-log-MAP)-based detection, soft-output-Viterbi-algorithm (SOVA)-based detection, and a proposed SISO detection, which can all be combined with SISO decoding, are presented. The three detection methods are investigated at 128 Gb/s in five-channel wavelength-division-multiplexing uncoded and low-density-parity-check (LDPC) coded DP-QDB systems by simulations. Max-log-MAP-based detection needs the returning-to-initial-states (RTIS) process despite having the best performance. When the LDPC code with a code rate of 0.83 is used, the detecting-and-decoding scheme with the SISO detection does not need RTIS and has better bit error rate (BER) performance than the scheme with SOVA-based detection. The former can reduce the optical signal-to-noise ratio (OSNR) requirement (at BER=10-5) by 2.56 dB relative to the latter. The application of the SISO iterative detection in LDPC-coded DP-QDB systems makes a good trade-off between requirements on transmission efficiency, OSNR requirement, and transmission distance, compared with the other two SISO methods.
Continuous multistep methods for volterra integro-differential ...
African Journals Online (AJOL)
A new class of numerical methods for Volterra integro-differential equations of the second order is developed. The methods are based on interpolation and collocation of the shifted Legendre polynomial as basis function with Trapezoidal quadrature rules. The convergence analysis revealed that the methods are consistent ...
Wang, Wei; Shen, Jianqi
2018-06-01
The use of a shaped beam for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively. Numerical techniques for evaluating the BSCs of a shaped beam, such as the quadrature, the localized approximation (LA), the integral localized approximation (ILA) methods, have been developed within the framework of generalized Lorenz-Mie theory (GLMT). The quadrature methods usually employ the 2-/3-dimensional integrations. In this work, the expressions of the BSCs for an elliptical Gaussian beam (EGB) are simplified into the 1-dimensional integral so as to speed up the numerical computation. Numerical results of BSCs are used to reconstruct the beam field and the fidelity of the reconstructed field to the given beam field is estimated. It is demonstrated that the proposed method is much faster than the 2-dimensional integrations and it can acquire more accurate results than the LA method. Limitations of the quadrature method and also the LA method in the numerical calculation are analyzed in detail.
Chebfun and numerical quadrature
Hale, Nicholas; Trefethen, Lloyd N.
2012-01-01
Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators. We begin by describing Chebfun's fast capabilities for Clenshaw-Curtis and also Gauss-Legendre, -Jacobi, -Hermite, and -Laguerre quadrature, based on algorithms of Waldvogel and Glaser, Liu and Rokhlin. Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles, fractional derivatives and integrals, functions defined on unbounded intervals, and the fast computation of weights for barycentric interpolation. © 2012 Science China Press and Springer-Verlag Berlin Heidelberg.
Chebfun and numerical quadrature
Hale, Nicholas
2012-07-24
Chebfun is a Matlab-based software system that overloads Matlab\\'s discrete operations for vectors and matrices to analogous continuous operations for functions and operators. We begin by describing Chebfun\\'s fast capabilities for Clenshaw-Curtis and also Gauss-Legendre, -Jacobi, -Hermite, and -Laguerre quadrature, based on algorithms of Waldvogel and Glaser, Liu and Rokhlin. Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles, fractional derivatives and integrals, functions defined on unbounded intervals, and the fast computation of weights for barycentric interpolation. © 2012 Science China Press and Springer-Verlag Berlin Heidelberg.
International Nuclear Information System (INIS)
Fox, R.O.; Laurent, F.; Massot, M.
2008-01-01
The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v,u;x,t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. [F. Laurent, M. Massot, P. Villedieu, Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays, J. Comput. Phys. 194 (2004) 505-543]. The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox [D.L. Marchisio, R.O. Fox, Solution of population balance equations using the direct quadrature method of moments, J. Aerosol Sci. 36 (2005) 43-73] to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to focus on the difficulties associated with treating size-dependent coalescence and to avoid numerical uncertainty issues associated with two-way coupling, only one-way coupling between the droplets and a given gas velocity field is considered. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver. The third key point of the study is a detailed description of the limitations associated with each method, thus giving criteria for
Large eddy simulations of coal jet flame ignition using the direct quadrature method of moments
Pedel, Julien
The Direct Quadrature Method of Moments (DQMOM) was implemented in the Large Eddy Simulation (LES) tool ARCHES to model coal particles. LES coupled with DQMOM was first applied to nonreacting particle-laden turbulent jets. Simulation results were compared to experimental data and accurately modeled a wide range of particle behaviors, such as particle jet waviness, spreading, break up, particle clustering and segregation, in different configurations. Simulations also accurately predicted the mean axial velocity along the centerline for both the gas phase and the solid phase, thus demonstrating the validity of the approach to model particles in turbulent flows. LES was then applied to the prediction of pulverized coal flame ignition. The stability of an oxy-coal flame as a function of changing primary gas composition (CO2 and O2) was first investigated. Flame stability was measured using optical measurements of the flame standoff distance in a 40 kW pilot facility. Large Eddy Simulations (LES) of the facility provided valuable insight into the experimentally observed data and the importance of factors such as heterogeneous reactions, radiation or wall temperature. The effects of three parameters on the flame stand-off distance were studied and simulation predictions were compared to experimental data using the data collaboration method. An additional validation study of the ARCHES LES tool was then performed on an air-fired pulverized coal jet flame ignited by a preheated gas flow. The simulation results were compared qualitatively and quantitatively to experimental observations for different inlet stoichiometric ratios. LES simulations were able to capture the various combustion regimes observed during flame ignition and to accurately model the flame stand-off distance sensitivity to the stoichiometric ratio. Gas temperature and coal burnout predictions were also examined and showed good agreement with experimental data. Overall, this research shows that high
Energy Technology Data Exchange (ETDEWEB)
Gaillard, J.P.; Lalleman, S.; Bertrand, M. [CEA, Centre de Marcoule, Nuclear Energy Division, RadioChemistry and Process Department, F-30207 Bagnols sur Ceze (France); Plasari, E. [Ecole Nationale Superieure des Industries Chimiques, Laboratoire Reactions et Genie des Procedes, Universite de Lorraine - CNRS,1 rue Grandville, BP 20451, 54001, Nancy Cedex (France)
2016-07-01
Oxalic precipitation is generally used in the nuclear industry to deal with radioactive waste and recover the actinides from a multicomponent solution. To facilitate the development of experimental methods and data acquisitions, actinides are often simulated using lanthanides, gaining experience more easily. The purpose of this article is to compare the results achieved by two methods for solving the population balance during neodymium oxalate precipitation in a continuous MSMPR (Mixed Suspension Mixed Product Removal). The method of classes, also called discretized population balance, used in this study is based on the method of Litster. Whereas, the Quadrature Method of Moment (QMOM) is written in terms of the transport equations of the moments of the number density function. All the integrals are solved through a quadrature approximation thanks to the product-difference algorithm or the Chebyshev algorithm. Primary nucleation, crystal growth and agglomeration are taken into account. Agglomeration phenomena have been found to be represented by a loose agglomerates model. Thermodynamic effects are modeled by activity coefficients which are calculated using the Bromley model. The sizes of particles predicted by the two methods are in good agreement with experimental measurements. (authors)
Directory of Open Access Journals (Sweden)
Thomas Acher
2014-12-01
Full Text Available A simulation model for 3D polydisperse bubble column flows in an Eulerian/Eulerian framework is presented. A computationally efficient and numerically stable algorithm is created by making use of quadrature method of moments (QMOM functionalities, in conjunction with appropriate breakup and coalescence models. To account for size dependent bubble motion, the constituent moments of the bubble size distribution function are transported with individual velocities. Validation of the simulation results against experimental and numerical data of Hansen [1] show the capability of the present model to accurately predict complex gas-liquid flows.
Suryanarayana, Phanish; Pratapa, Phanisri P.; Sharma, Abhiraj; Pask, John E.
2018-03-01
We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method for O(N) Kohn-Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw-Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw-Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. We further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect O(N) scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.
Sun, Dan; Garmory, Andrew; Page, Gary J.
2017-02-01
For flows where the particle number density is low and the Stokes number is relatively high, as found when sand or ice is ingested into aircraft gas turbine engines, streams of particles can cross each other's path or bounce from a solid surface without being influenced by inter-particle collisions. The aim of this work is to develop an Eulerian method to simulate these types of flow. To this end, a two-node quadrature-based moment method using 13 moments is proposed. In the proposed algorithm thirteen moments of particle velocity, including cross-moments of second order, are used to determine the weights and abscissas of the two nodes and to set up the association between the velocity components in each node. Previous Quadrature Method of Moments (QMOM) algorithms either use more than two nodes, leading to increased computational expense, or are shown here to give incorrect results under some circumstances. This method gives the computational efficiency advantages of only needing two particle phase velocity fields whilst ensuring that a correct combination of weights and abscissas is returned for any arbitrary combination of particle trajectories without the need for any further assumptions. Particle crossing and wall bouncing with arbitrary combinations of angles are demonstrated using the method in a two-dimensional scheme. The ability of the scheme to include the presence of drag from a carrier phase is also demonstrated, as is bouncing off surfaces with inelastic collisions. The method is also applied to the Taylor-Green vortex flow test case and is found to give results superior to the existing two-node QMOM method and is in good agreement with results from Lagrangian modelling of this case.
Longoni, Gianluca
In the nuclear science and engineering field, radiation transport calculations play a key-role in the design and optimization of nuclear devices. The linear Boltzmann equation describes the angular, energy and spatial variations of the particle or radiation distribution. The discrete ordinates method (S N) is the most widely used technique for solving the linear Boltzmann equation. However, for realistic problems, the memory and computing time require the use of supercomputers. This research is devoted to the development of new formulations for the SN method, especially for highly angular dependent problems, in parallel environments. The present research work addresses two main issues affecting the accuracy and performance of SN transport theory methods: quadrature sets and acceleration techniques. New advanced quadrature techniques which allow for large numbers of angles with a capability for local angular refinement have been developed. These techniques have been integrated into the 3-D SN PENTRAN (Parallel Environment Neutral-particle TRANsport) code and applied to highly angular dependent problems, such as CT-Scan devices, that are widely used to obtain detailed 3-D images for industrial/medical applications. In addition, the accurate simulation of core physics and shielding problems with strong heterogeneities and transport effects requires the numerical solution of the transport equation. In general, the convergence rate of the solution methods for the transport equation is reduced for large problems with optically thick regions and scattering ratios approaching unity. To remedy this situation, new acceleration algorithms based on the Even-Parity Simplified SN (EP-SSN) method have been developed. A new stand-alone code system, PENSSn (Parallel Environment Neutral-particle Simplified SN), has been developed based on the EP-SSN method. The code is designed for parallel computing environments with spatial, angular and hybrid (spatial/angular) domain
Stuebner, Michael; Haider, Mansoor A
2010-06-18
A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage. Copyright (c) 2010 Elsevier Ltd. All rights reserved.
Kalra, Tarandeep S.; Aretxabaleta, Alfredo; Seshadri, Pranay; Ganju, Neil K.; Beudin, Alexis
2017-12-01
Coastal hydrodynamics can be greatly affected by the presence of submerged aquatic vegetation. The effect of vegetation has been incorporated into the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) modeling system. The vegetation implementation includes the plant-induced three-dimensional drag, in-canopy wave-induced streaming, and the production of turbulent kinetic energy by the presence of vegetation. In this study, we evaluate the sensitivity of the flow and wave dynamics to vegetation parameters using Sobol' indices and a least squares polynomial approach referred to as the Effective Quadratures method. This method reduces the number of simulations needed for evaluating Sobol' indices and provides a robust, practical, and efficient approach for the parameter sensitivity analysis. The evaluation of Sobol' indices shows that kinetic energy, turbulent kinetic energy, and water level changes are affected by plant stem density, height, and, to a lesser degree, diameter. Wave dissipation is mostly dependent on the variation in plant stem density. Performing sensitivity analyses for the vegetation module in COAWST provides guidance to optimize efforts and reduce exploration of parameter space for future observational and modeling work.
Directory of Open Access Journals (Sweden)
T. S. Kalra
2017-12-01
Full Text Available Coastal hydrodynamics can be greatly affected by the presence of submerged aquatic vegetation. The effect of vegetation has been incorporated into the Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST modeling system. The vegetation implementation includes the plant-induced three-dimensional drag, in-canopy wave-induced streaming, and the production of turbulent kinetic energy by the presence of vegetation. In this study, we evaluate the sensitivity of the flow and wave dynamics to vegetation parameters using Sobol' indices and a least squares polynomial approach referred to as the Effective Quadratures method. This method reduces the number of simulations needed for evaluating Sobol' indices and provides a robust, practical, and efficient approach for the parameter sensitivity analysis. The evaluation of Sobol' indices shows that kinetic energy, turbulent kinetic energy, and water level changes are affected by plant stem density, height, and, to a lesser degree, diameter. Wave dissipation is mostly dependent on the variation in plant stem density. Performing sensitivity analyses for the vegetation module in COAWST provides guidance to optimize efforts and reduce exploration of parameter space for future observational and modeling work.
International Nuclear Information System (INIS)
Peña-Monferrer, C.; Passalacqua, A.; Chiva, S.; Muñoz-Cobo, J.L.
2016-01-01
Highlights: • A population balance equation solved with QMOM approximation is implemented in OpenFOAM. • Available models for interfacial forces and bubble induced turbulence are analyzed. • A vertical pipe flow is simulated for different bubbly flow conditions. • Two-phase flow characteristics in vertical pipes are properly predicted. - Abstract: An Eulerian–Eulerian approach was investigated to model adiabatic bubbly flow with CFD techniques. In the framework of the OpenFOAM"® software, a two-fluid model solver was modified to include a population balance equation, solved with the quadrature method of moments approximation to predict upward bubbly flow in vertical pipes considering the polydisperse nature of two-phase flow. Some progress have been made recently solving population balance equations in OpenFOAM"® and this research aims to extend its application to the case of vertical pipes under different conditions of liquid and gas velocities. In order to test the solver for nuclear applications, interfacial forces and bubble induced turbulence models were included to provide to this solver the capability to correctly predict the behavior of the continuous and disperse phases. Two-phase flow experiments with different superficial velocities of gas and liquid are used to validate the model and its implementation. Radial profiles of void fraction, gas and liquid velocities, Sauter mean diameter and turbulence intensity are compared to the computational results. These results are in satisfactory agreement with the experiments, showing the capability of the solver to predict two-phase flow characteristics.
Durant, Bradford; Hackl, Jason; Balachandar, Sivaramakrishnan
2017-11-01
Nodal discontinuous Galerkin schemes present an attractive approach to robust high-order solution of the equations of fluid mechanics, but remain accompanied by subtle challenges in their consistent stabilization. The effect of quadrature choices (full mass matrix vs spectral elements), over-integration to manage aliasing errors, and explicit artificial viscosity on the numerical solution of a steady homentropic vortex are assessed over a wide range of resolutions and polynomial orders using quadrilateral elements. In both stagnant and advected vortices in periodic and non-periodic domains the need arises for explicit stabilization beyond the numerical surface fluxes of discontinuous Galerkin spectral elements. Artificial viscosity via the entropy viscosity method is assessed as a stabilizing mechanism. It is shown that the regularity of the artificial viscosity field is essential to its use for long-time stabilization of small-scale features in nodal discontinuous Galerkin solutions of the Euler equations of gas dynamics. Supported by the Department of Energy Predictive Science Academic Alliance Program Contract DE-NA0002378.
Goto, Nobuo; Miyazaki, Yasumitsu
2014-06-01
Optical switching of high-bit-rate quadrature-phase-shift-keying (QPSK) pulse trains using collinear acousto-optic (AO) devices is theoretically discussed. Since the collinear AO devices have wavelength selectivity, the switched optical pulse trains suffer from distortion when the bandwidth of the pulse train is comparable to the pass bandwidth of the AO device. As the AO device, a sidelobe-suppressed device with a tapered surface-acoustic-wave (SAW) waveguide and a Butterworth-type filter device with a lossy SAW directional coupler are considered. Phase distortion of optical pulse trains at 40 to 100 Gsymbols/s in QPSK format is numerically analyzed. Bit-error-rate performance with additive Gaussian noise is also evaluated by the Monte Carlo method.
Energy Technology Data Exchange (ETDEWEB)
Peña-Monferrer, C., E-mail: cmonfer@upv.es [Institute for Energy Engineering, Universitat Politècnica de València, 46022 València (Spain); Passalacqua, A., E-mail: albertop@iastate.edu [Department of Mechanical Engineering, Iowa State University, Ames, IA 50011 (United States); Chiva, S., E-mail: schiva@emc.uji.es [Department of Mechanical Engineering and Construction, Universitat Jaume I, 12080 Castelló de la Plana (Spain); Muñoz-Cobo, J.L., E-mail: jlcobos@iqn.upv.es [Institute for Energy Engineering, Universitat Politècnica de València, 46022 València (Spain)
2016-05-15
Highlights: • A population balance equation solved with QMOM approximation is implemented in OpenFOAM. • Available models for interfacial forces and bubble induced turbulence are analyzed. • A vertical pipe flow is simulated for different bubbly flow conditions. • Two-phase flow characteristics in vertical pipes are properly predicted. - Abstract: An Eulerian–Eulerian approach was investigated to model adiabatic bubbly flow with CFD techniques. In the framework of the OpenFOAM{sup ®} software, a two-fluid model solver was modified to include a population balance equation, solved with the quadrature method of moments approximation to predict upward bubbly flow in vertical pipes considering the polydisperse nature of two-phase flow. Some progress have been made recently solving population balance equations in OpenFOAM{sup ®} and this research aims to extend its application to the case of vertical pipes under different conditions of liquid and gas velocities. In order to test the solver for nuclear applications, interfacial forces and bubble induced turbulence models were included to provide to this solver the capability to correctly predict the behavior of the continuous and disperse phases. Two-phase flow experiments with different superficial velocities of gas and liquid are used to validate the model and its implementation. Radial profiles of void fraction, gas and liquid velocities, Sauter mean diameter and turbulence intensity are compared to the computational results. These results are in satisfactory agreement with the experiments, showing the capability of the solver to predict two-phase flow characteristics.
Directory of Open Access Journals (Sweden)
Haiyan Yuan
2013-01-01
Full Text Available This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of (k,l-algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a (k,l-algebraically stable two-step Runge-Kutta method with 0
Dekkers, A L M; Slob, W
2012-10-01
In dietary exposure assessment, statistical methods exist for estimating the usual intake distribution from daily intake data. These methods transform the dietary intake data to normal observations, eliminate the within-person variance, and then back-transform the data to the original scale. We propose Gaussian Quadrature (GQ), a numerical integration method, as an efficient way of back-transformation. We compare GQ with six published methods. One method uses a log-transformation, while the other methods, including GQ, use a Box-Cox transformation. This study shows that, for various parameter choices, the methods with a Box-Cox transformation estimate the theoretical usual intake distributions quite well, although one method, a Taylor approximation, is less accurate. Two applications--on folate intake and fruit consumption--confirmed these results. In one extreme case, some methods, including GQ, could not be applied for low percentiles. We solved this problem by modifying GQ. One method is based on the assumption that the daily intakes are log-normally distributed. Even if this condition is not fulfilled, the log-transformation performs well as long as the within-individual variance is small compared to the mean. We conclude that the modified GQ is an efficient, fast and accurate method for estimating the usual intake distribution. Copyright © 2012 Elsevier Ltd. All rights reserved.
Four New Applications of Second-Order Generalized Integrator Quadrature Signal Generator
DEFF Research Database (Denmark)
Xin, Zhen; Zhao, Rende; Wang, Xiongfei
2016-01-01
The Second-Order Generalized Integrator (SOGI) was used as a building block for the SOGI-Quadrature-Signal Generator (SOGI-QSG) which has been widely used for grid synchronization, frequency estimation, and harmonic extraction over the past decade. This paper further investigates its integration...... and differentiation characteristics, with four new integrators and differentiators proposed. Theoretical analysis shows that the proposed SOGI-QSG based integration and differentiation methods can effectively overcome the drawbacks of the pure integrator and differentiator. The proposed four new methods...
International Nuclear Information System (INIS)
Kotikov, A.V.
1993-01-01
A new method of massive Feynman diagrams calculation is presented. It provides a fairly simple procedure to obtain the result without the D-space integral calculation (for the dimensional regularization). Some diagrams are calculated as an illustration of this method capacities. (author). 7 refs
Digital quadrature phase detection
Smith, J.A.; Johnson, J.A.
1992-05-26
A system for detecting the phase of a frequency or phase modulated signal that includes digital quadrature sampling of the frequency or phase modulated signal at two times that are one quarter of a cycle of a reference signal apart, determination of the arctangent of the ratio of a first sampling of the frequency or phase modulated signal to the second sampling of the frequency or phase modulated signal, and a determination of quadrant in which the phase determination is increased by 2[pi] when the quadrant changes from the first quadrant to the fourth quadrant and decreased by 2[pi] when the quadrant changes from the fourth quadrant to the first quadrant whereby the absolute phase of the frequency or phase modulated signal can be determined using an arbitrary reference convention. 6 figs.
Load Insensitive, Low Voltage Quadrature Oscillator Using Single Active Element
Directory of Open Access Journals (Sweden)
Jitendra Mohan
2017-01-01
Full Text Available In this paper, a load insensitive quadrature oscillator using single differential voltage dual-X second generation current conveyor operated at low voltage is proposed. The proposed circuit employs single active element, three grounded resistors and two grounded capacitors. The proposed oscillator offers two load insensitive quadrature current outputs and three quadrature voltage outputs simultaneously. Effects of non-idealities along with the effects of parasitic are further studied. The proposed circuit enjoys the feature of low active and passive sensitivities. Additionally, a resistorless realization of the proposed quadrature oscillator is also explored. Simulation results using PSPICE program on cadence tool using 90 nm Complementary Metal Oxide Semiconductor (CMOS process parameters confirm the validity and practical utility of the proposed circuit.
Multilevel quadrature of elliptic PDEs with log-normal diffusion
Harbrecht, Helmut
2015-01-07
We apply multilevel quadrature methods for the moment computation of the solution of elliptic PDEs with lognormally distributed diffusion coefficients. The computation of the moments is a difficult task since they appear as high dimensional Bochner integrals over an unbounded domain. Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number of quadrature points times the complexity for a single elliptic PDE solve. The multilevel idea is to reduce this complexity by combining quadrature methods with different accuracies with several spatial discretization levels in a sparse grid like fashion.
Quadrature formulas for Fourier coefficients
Bojanov, Borislav; Petrova, Guergana
2009-01-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node
Robust structural optimization using Gauss-type quadrature formula
International Nuclear Information System (INIS)
Lee, Sang Hoon; Seo, Ki Seog; Chen, Shikui; Chen, Wei
2009-01-01
In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the Tensor Product Quadrature (TPQ) formula and the Univariate Dimension Reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.
Robust structural optimization using Gauss-type quadrature formula
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Hoon; Seo, Ki Seog [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Chen, Shikui; Chen, Wei [Northwestern University, Illinois (United States)
2009-07-01
In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the Tensor Product Quadrature (TPQ) formula and the Univariate Dimension Reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.
Robust Structural Optimization Using Gauss-type Quadrature Formula
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Hoon; Seo, Ki Seog; Chen, Shikui; Chen, Wei [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2009-08-15
In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the tensor product quadrature (TPQ) formula and the univariate dimension reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.
Robust Structural Optimization Using Gauss-type Quadrature Formula
International Nuclear Information System (INIS)
Lee, Sang Hoon; Seo, Ki Seog; Chen, Shikui; Chen, Wei
2009-01-01
In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the tensor product quadrature (TPQ) formula and the univariate dimension reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty
Differential equations methods and applications
Said-Houari, Belkacem
2015-01-01
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .
DEFF Research Database (Denmark)
Jalaal, M.; Soleimani, Soheil; Domairry, G.
2011-01-01
In this paper the meshless Local Multi Quadrics-based Differential Quadrature (MQ-DQ) method is applied to obtain the electric field distribution for different applicable irregular geometries. This method is the combination of Differential Quadrature approximation of derivatives and function...
Directory of Open Access Journals (Sweden)
Ali H. Bhrawy
2014-01-01
Full Text Available The modified generalized Laguerre-Gauss collocation (MGLC method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.
A multi-domain spectral method for time-fractional differential equations
Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.
2015-07-01
This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.
Pseudospectral collocation methods for fourth order differential equations
Malek, Alaeddin; Phillips, Timothy N.
1994-01-01
Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.
Generalized differential transform method to differential-difference equation
International Nuclear Information System (INIS)
Zou Li; Wang Zhen; Zong Zhi
2009-01-01
In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Pade technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation.
Comparison of two methods for customer differentiation
A.F. Gabor (Adriana); Y. Guang (Yang); S. Axsäter (Sven)
2014-01-01
textabstractIn response to customer specific time guarantee requirements, service providers can offer differentiated ser- vices. However, conventional customer differentiation methods often lead to high holding costs and may have some practical drawbacks. We compare two customer differentiation
Length Scales in Bayesian Automatic Adaptive Quadrature
Directory of Open Access Journals (Sweden)
Adam Gh.
2016-01-01
Full Text Available Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1–16 (2012] are reported. First, it is shown that the numerical quadrature which avoids the overcomputing and minimizes the hidden floating point loss of precision asks for the consideration of three classes of integration domain lengths endowed with specific quadrature sums: microscopic (trapezoidal rule, mesoscopic (Simpson rule, and macroscopic (quadrature sums of high algebraic degrees of precision. Second, sensitive diagnostic tools for the Bayesian inference on macroscopic ranges, coming from the use of Clenshaw-Curtis quadrature, are derived.
DOQDP ADOQ, Discrete Ordinate Quadrature Generator for Programs DOT and ANISN
International Nuclear Information System (INIS)
1978-01-01
1 - Description of problem or function: DOQDP is used to generate direction sets (quadratures used as input to ANISN, DOT, and other related codes). If a fully symmetric quadrature is desired, DOQDP can generate the direction cosines to be used. If other than a fully quadrature is to be generated, the user must supply the appropriate direction cosines. Once the direction cosines are specified, the code will generate the quadrature weights. 2 - Method of solution: To determine point weights, DOQDP solves a set of simultaneous linear equations by Gaussian elimination with error improvement iterations. 3 - Restrictions on the complexity of the problem: None noted
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
General n-dimensional quadrature transform and its application to interferogram demodulation.
Servin, Manuel; Quiroga, Juan Antonio; Marroquin, Jose Luis
2003-05-01
Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward.
Abstract methods in partial differential equations
Carroll, Robert W
2012-01-01
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
Maximum entropy estimation via Gauss-LP quadratures
Thély, Maxime; Sutter, Tobias; Mohajerin Esfahani, P.; Lygeros, John; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
2017-01-01
We present an approximation method to a class of parametric integration problems that naturally appear when solving the dual of the maximum entropy estimation problem. Our method builds up on a recent generalization of Gauss quadratures via an infinite-dimensional linear program, and utilizes a
Iterative Splitting Methods for Differential Equations
Geiser, Juergen
2011-01-01
Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential
Power flow control using quadrature boosters
Sadanandan, Sandeep N.
A power system that can be controlled within security constraints would be an advantage to power planners and real-time operators. Controlling flows can lessen reliability issues such as thermal limit violations, power stability problems, and/or voltage stability conditions. Control of flows can also mitigate market issues by reducing congestion on some lines and rerouting power to less loaded lines or onto preferable paths. In the traditional control of power flows, phase shifters are often used. More advanced methods include using Flexible AC Transmission System (FACTS) Controllers. Some examples include Thyristor Controlled Series Capacitors, Synchronous Series Static Compensators, and Unified Power Flow Controllers. Quadrature Boosters (QBs) have similar structures to phase-shifters, but allow for higher voltage magnitude during real power flow control. In comparison with other FACTS controllers QBs are not as complex and not as expensive. The present study proposes to use QBs to control power flows on a power system. With the inclusion of QBs, real power flows can be controlled to desired scheduled values. In this thesis, the linearized power flow equations used for power flow analysis were modified for the control problem. This included modifying the Jacobian matrix, the power error vector, and calculating the voltage injected by the quadrature booster for the scheduled real power flow. Two scenarios were examined using the proposed power flow control method. First, the power flow in a line in a 5-bus system was modified with a QB using the method developed in this thesis. Simulation was carried out using Matlab. Second, the method was applied to a 30-bus system and then to a 118-bus system using several QBs. In all the cases, the calculated values of the QB voltages led to desired power flows in the designated line.
Nonclassical Orthogonal Polynomials and Corresponding Quadratures
Fukuda, H; Alt, E O; Matveenko, A V
2004-01-01
We construct nonclassical orthogonal polynomials and calculate abscissas and weights of Gaussian quadrature for arbitrary weight and interval. The program is written by Mathematica and it works if moment integrals are given analytically. The result is a FORTRAN subroutine ready to utilize the quadrature.
Solution of fractional differential equations by using differential transform method
International Nuclear Information System (INIS)
Arikoglu, Aytac; Ozkol, Ibrahim
2007-01-01
In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply
Solution of fractional differential equations by using differential transform method
Energy Technology Data Exchange (ETDEWEB)
Arikoglu, Aytac [Istanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Maslak, TR-34469 Istanbul (Turkey); Ozkol, Ibrahim [Istanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Maslak, TR-34469 Istanbul (Turkey)]. E-mail: ozkol@itu.edu.tr
2007-12-15
In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply.
Statistical Methods for Stochastic Differential Equations
Kessler, Mathieu; Sorensen, Michael
2012-01-01
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a sp
High-Order Quadratures for the Solution of Scattering Problems in Two Dimensions
National Research Council Canada - National Science Library
Duan, Ran; Rokhlin, Vladimir
2008-01-01
.... The scheme is based on the combination of high-order quadrature formulae, fast application of integral operators in Lippmann-Schwinger equations, and the stabilized biconjugate gradient method (BI-CGSTAB...
Numerical methods for differential equations and applications
International Nuclear Information System (INIS)
Ixaru, L.G.
1984-01-01
This book is addressed to persons who, without being professionals in applied mathematics, are often faced with the problem of numerically solving differential equations. In each of the first three chapters a definite class of methods is discussed for the solution of the initial value problem for ordinary differential equations: multistep methods; one-step methods; and piecewise perturbation methods. The fourth chapter is mainly focussed on the boundary value problems for linear second-order equations, with a section devoted to the Schroedinger equation. In the fifth chapter the eigenvalue problem for the radial Schroedinger equation is solved in several ways, with computer programs included. (Auth.)
Quadrature theory the theory of numerical integration on a compact interval
Brass, Helmut
2011-01-01
Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word "theory" in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called "co-observations," which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts. While quadrature theory is often viewed as a branch of nume...
Waveform relaxation methods for implicit differential equations
P.J. van der Houwen; W.A. van der Veen
1996-01-01
textabstractWe apply a Runge-Kutta-based waveform relaxation method to initial-value problems for implicit differential equations. In the implementation of such methods, a sequence of nonlinear systems has to be solved iteratively in each step of the integration process. The size of these systems
Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
Hale, Nicholas
2013-03-06
An efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton\\'s root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100. © 2013 Society for Industrial and Applied Mathematics.
Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
Hale, Nicholas; Townsend, Alex
2013-01-01
An efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton's root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100. © 2013 Society for Industrial and Applied Mathematics.
International Nuclear Information System (INIS)
Anaf, J.; Chalhoub, E.S.
1989-01-01
A program (RESQ) based on quadratures that evaluates, from ENDF/B data, the resolved resonance contribution in group-averaged cross sections (capture, fission and scattering) was developed. Single and Multilevel Breit-Wigner parameters are accepted. Constant weighting function and zero Kelvin were considered. To assure convergence, different quadrature orders may be analysed. Results are compared with other codes' reconstruction and integration methods. (author) [pt
Numerical Methods for Partial Differential Equations
Guo, Ben-yu
1987-01-01
These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.
Past and Future SOHO-Ulysses Quadratures
Suess, Steven; Poletto, G.
2006-01-01
With the launch of SOHO, it again became possible to carry out quadrature observations. In comparison with earlier observations, the new capabilities of coronal spectroscopy with UVCS and in situ ionization state and composition with Ulysses/SWICS enabled new types of studies. Results from two studies serve as examples: (i) The acceleration profile of wind from small coronal holes. (ii) A high-coronal reconnecting current sheet as the source of high ionization state Fe in a CME at Ulysses. Generally quadrature observations last only for a few days, when Ulysses is within ca. 5 degrees of the limb. This means luck is required for the phenomenon of interest to lie along the radial direction to Ulysses. However, when Ulysses is at high southern latitude in winter 2007 and high northern latitude in winter 2008, there will be unusually favorable configurations for quadrature observations with SOHO and corresponding bracketing limb observations from STEREO A/B. Specifically, Ulysses will be within 5 degrees of the limb from December 2006 to May 2007 and within 10 degrees of the limb from December 2007 to May 2008. These long-lasting quadratures and bracketing STEREO A/B observations overcome the limitations inherent in the short observation intervals of typical quadratures. Furthermore, ionization and charge state measurements like those on Ulysses will also be made on STEREO and these will be essential for identification of CME ejecta - one of the prime objectives for STEREO.
Two integrator loop quadrature oscillators: A review
Directory of Open Access Journals (Sweden)
Ahmed M. Soliman
2013-01-01
Full Text Available A review of the two integrator loop oscillator circuits providing two quadrature sinusoidal output voltages is given. All the circuits considered employ the minimum number of capacitors namely two except one circuit which uses three capacitors. The circuits considered are classified to four different classes. The first class includes floating capacitors and floating resistors and the active building blocks realizing these circuits are the Op Amp or the OTRA. The second class employs grounded capacitors and includes floating resistors and the active building blocks realizing these circuits are the DCVC or the unity gain cells or the CFOA. The third class employs grounded capacitors and grounded resistors and the active building blocks realizing these circuits are the CCII. The fourth class employs grounded capacitors and no resistors and the active building blocks realizing these circuits are the TA. Transformation methods showing the generation of different classes from each other is given in details and this is one of the main objectives of this paper.
Numerical methods for hyperbolic differential functional problems
Directory of Open Access Journals (Sweden)
Roman Ciarski
2008-01-01
Full Text Available The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.
Directory of Open Access Journals (Sweden)
Murat Osmanoglu
2013-01-01
Full Text Available We have considered linear partial differential algebraic equations (LPDAEs of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.
Composite Gauss-Legendre Quadrature with Error Control
Prentice, J. S. C.
2011-01-01
We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)
Quadrature representation of finite element variational forms
DEFF Research Database (Denmark)
Ølgaard, Kristian Breum; Wells, Garth N.
2012-01-01
This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations...
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
Telescopic projective methods for parabolic differential equations
Gear, C W
2003-01-01
Projective methods were introduced in an earlier paper [C.W. Gear, I.G. Kevrekidis, Projective Methods for Stiff Differential Equations: problems with gaps in their eigenvalue spectrum, NEC Research Institute Report 2001-029, available from http://www.neci.nj.nec.com/homepages/cwg/projective.pdf Abbreviated version to appear in SISC] as having potential for the efficient integration of problems with a large gap between two clusters in their eigenvalue spectrum, one cluster containing eigenvalues corresponding to components that have already been damped in the numerical solution and one corresponding to components that are still active. In this paper we introduce iterated projective methods that allow for explicit integration of stiff problems that have a large spread of eigenvalues with no gaps in their spectrum as arise in the semi-discretization of PDEs with parabolic components.
Telescopic projective methods for parabolic differential equations
International Nuclear Information System (INIS)
Gear, C.W.; Kevrekidis, Ioannis G.
2003-01-01
Projective methods were introduced in an earlier paper [C.W. Gear, I.G. Kevrekidis, Projective Methods for Stiff Differential Equations: problems with gaps in their eigenvalue spectrum, NEC Research Institute Report 2001-029, available from http://www.neci.nj.nec.com/homepages/cwg/projective.pdf Abbreviated version to appear in SISC] as having potential for the efficient integration of problems with a large gap between two clusters in their eigenvalue spectrum, one cluster containing eigenvalues corresponding to components that have already been damped in the numerical solution and one corresponding to components that are still active. In this paper we introduce iterated projective methods that allow for explicit integration of stiff problems that have a large spread of eigenvalues with no gaps in their spectrum as arise in the semi-discretization of PDEs with parabolic components
Uniform Gauss-Weight Quadratures for Discrete Ordinate Transport Calculations
International Nuclear Information System (INIS)
Carew, John F.; Hu, Kai; Zamonsky, Gabriel
2000-01-01
Recently, a uniform equal-weight quadrature set, UE n , and a uniform Gauss-weight quadrature set, UG n , have been derived. These quadratures have the advantage over the standard level-symmetric LQ n quadrature sets in that the weights are positive for all orders,and the transport solution may be systematically converged by increasing the order of the quadrature set. As the order of the quadrature is increased,the points approach a uniform continuous distribution on the unit sphere,and the quadrature is invariant with respect to spatial rotations. The numerical integrals converge for continuous functions as the order of the quadrature is increased.The numerical characteristics of the UE n quadrature set have been investigated previously. In this paper, numerical calculations are performed to evaluate the application of the UG n quadrature set in typical transport analyses. A series of DORT transport calculations of the >1-MeV neutron flux have been performed for a set of pressure-vessel fluence benchmark problems. These calculations employed the UG n (n = 8, 12, 16, 24, and 32) quadratures and indicate that the UG n solutions have converged to within ∼0.25%. The converged UG n solutions are found to be comparable to the UE n results and are more accurate than the level-symmetric S 16 predictions
The generation of arbitrary order, non-classical, Gauss-type quadrature for transport applications
International Nuclear Information System (INIS)
Spence, Peter J.
2015-01-01
A method is presented, based upon the Stieltjes method (1884), for the determination of non-classical Gauss-type quadrature rules, and the associated sets of abscissae and weights. The method is then used to generate a number of quadrature sets, to arbitrary order, which are primarily aimed at deterministic transport calculations. The quadrature rules and sets detailed include arbitrary order reproductions of those presented by Abu-Shumays in [4,8] (known as the QR sets, but labelled QRA here), in addition to a number of new rules and associated sets; these are generated in a similar way, and we label them the QRS quadrature sets. The method presented here shifts the inherent difficulty (encountered by Abu-Shumays) associated with solving the non-linear moment equations, particular to the required quadrature rule, to one of the determination of non-classical weight functions and the subsequent calculation of various associated inner products. Once a quadrature rule has been written in a standard form, with an associated weight function having been identified, the calculation of the required inner products is achieved using specific variable transformations, in addition to the use of rapid, highly accurate quadrature suited to this purpose. The associated non-classical Gauss quadrature sets can then be determined, and this can be done to any order very rapidly. In this paper, instead of listing weights and abscissae for the different quadrature sets detailed (of which there are a number), the MATLAB code written to generate them is included as Appendix D. The accuracy and efficacy (in a transport setting) of the quadrature sets presented is not tested in this paper (although the accuracy of the QRA quadrature sets has been studied in [12,13]), but comparisons to tabulated results listed in [8] are made. When comparisons are made with one of the azimuthal QRA sets detailed in [8], the inherent difficulty in the method of generation, used there, becomes apparent
The generation of arbitrary order, non-classical, Gauss-type quadrature for transport applications
Energy Technology Data Exchange (ETDEWEB)
Spence, Peter J., E-mail: peter.spence@awe.co.uk
2015-09-01
A method is presented, based upon the Stieltjes method (1884), for the determination of non-classical Gauss-type quadrature rules, and the associated sets of abscissae and weights. The method is then used to generate a number of quadrature sets, to arbitrary order, which are primarily aimed at deterministic transport calculations. The quadrature rules and sets detailed include arbitrary order reproductions of those presented by Abu-Shumays in [4,8] (known as the QR sets, but labelled QRA here), in addition to a number of new rules and associated sets; these are generated in a similar way, and we label them the QRS quadrature sets. The method presented here shifts the inherent difficulty (encountered by Abu-Shumays) associated with solving the non-linear moment equations, particular to the required quadrature rule, to one of the determination of non-classical weight functions and the subsequent calculation of various associated inner products. Once a quadrature rule has been written in a standard form, with an associated weight function having been identified, the calculation of the required inner products is achieved using specific variable transformations, in addition to the use of rapid, highly accurate quadrature suited to this purpose. The associated non-classical Gauss quadrature sets can then be determined, and this can be done to any order very rapidly. In this paper, instead of listing weights and abscissae for the different quadrature sets detailed (of which there are a number), the MATLAB code written to generate them is included as Appendix D. The accuracy and efficacy (in a transport setting) of the quadrature sets presented is not tested in this paper (although the accuracy of the QRA quadrature sets has been studied in [12,13]), but comparisons to tabulated results listed in [8] are made. When comparisons are made with one of the azimuthal QRA sets detailed in [8], the inherent difficulty in the method of generation, used there, becomes apparent
Disentangling Complexity in Bayesian Automatic Adaptive Quadrature
Adam, Gheorghe; Adam, Sanda
2018-02-01
The paper describes a Bayesian automatic adaptive quadrature (BAAQ) solution for numerical integration which is simultaneously robust, reliable, and efficient. Detailed discussion is provided of three main factors which contribute to the enhancement of these features: (1) refinement of the m-panel automatic adaptive scheme through the use of integration-domain-length-scale-adapted quadrature sums; (2) fast early problem complexity assessment - enables the non-transitive choice among three execution paths: (i) immediate termination (exceptional cases); (ii) pessimistic - involves time and resource consuming Bayesian inference resulting in radical reformulation of the problem to be solved; (iii) optimistic - asks exclusively for subrange subdivision by bisection; (3) use of the weaker accuracy target from the two possible ones (the input accuracy specifications and the intrinsic integrand properties respectively) - results in maximum possible solution accuracy under minimum possible computing time.
Multisite EPR oximetry from multiple quadrature harmonics.
Ahmad, R; Som, S; Johnson, D H; Zweier, J L; Kuppusamy, P; Potter, L C
2012-01-01
Multisite continuous wave (CW) electron paramagnetic resonance (EPR) oximetry using multiple quadrature field modulation harmonics is presented. First, a recently developed digital receiver is used to extract multiple harmonics of field modulated projection data. Second, a forward model is presented that relates the projection data to unknown parameters, including linewidth at each site. Third, a maximum likelihood estimator of unknown parameters is reported using an iterative algorithm capable of jointly processing multiple quadrature harmonics. The data modeling and processing are applicable for parametric lineshapes under nonsaturating conditions. Joint processing of multiple harmonics leads to 2-3-fold acceleration of EPR data acquisition. For demonstration in two spatial dimensions, both simulations and phantom studies on an L-band system are reported. Copyright © 2011 Elsevier Inc. All rights reserved.
Partial differential equations with numerical methods
Larsson, Stig
2003-01-01
The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.
The circumscribed quadrature of professional ethics
Nello, Antoni
2010-01-01
The circumscribed quadrature of professional ethics aimsto show the necessary shift from deontology to professional ethics, from deontological codes to ethical codes. While deontology and the deontological codes that materialise from it set their sights on professionals’ responsibilities, professional ethics and the ethical codes that should derive from it would set their sights on the professional act, on its successful performance. In this way, the stress comes to be placed not only on the ...
Technique for comparing automatic quadrature routines
Energy Technology Data Exchange (ETDEWEB)
Lyness, J N; Kaganove, J J
1976-02-01
The present unconstrained proliferation of automatic quadrature routines is a phenomenon which is wasteful in human time and computing resources. At the root of the problem is an absence of generally acceptable standards or benchmarks for comparing or evaluating such routines. In this paper a general technique, based on the nature of the performance profile, is described which can be used for evaluation of routines.
On Sensitivity of Gauss-Christoffel Quadrature
Czech Academy of Sciences Publication Activity Database
O'Leary, D.P.; Strakoš, Zdeněk; Tichý, Petr
2007-01-01
Roč. 107, č. 1 (2007), s. 147-174 ISSN 0029-599X R&D Projects: GA AV ČR 1ET400300415 Grant - others:NSF(US) CCR -0204084; NSF(US) CCF-0514213 Institutional research plan: CEZ:AV0Z10300504 Keywords : Gauss-Christoffel quadrature * sensitivity * moments Subject RIV: BA - General Mathematics Impact factor: 1.376, year: 2007
Single quadrature duplication and transparent taps
International Nuclear Information System (INIS)
Kim, Ajung
2004-01-01
The concept of single quadrature duplication, which is the process of producing two outputs with the same homodyne detecting statistics as an input, is addressed. This device has important potential application to optical communications as a transparent optical tap in a local area network environment. The characteristics of the device are examined, and a realization scheme employing a coupler and phase-sensitive amplifiers is proposed
Stochastic sampling of quadrature grids for the evaluation of vibrational expectation values
López Ríos, Pablo; Monserrat, Bartomeu; Needs, Richard J.
2018-02-01
The thermal lines method for the evaluation of vibrational expectation values of electronic observables [B. Monserrat, Phys. Rev. B 93, 014302 (2016), 10.1103/PhysRevB.93.014302] was recently proposed as a physically motivated approximation offering balance between the accuracy of direct Monte Carlo integration and the low computational cost of using local quadratic approximations. In this paper we reformulate thermal lines as a stochastic implementation of quadrature-grid integration, analyze the analytical form of its bias, and extend the method to multiple-point quadrature grids applicable to any factorizable harmonic or anharmonic nuclear wave function. The bias incurred by thermal lines is found to depend on the local form of the expectation value, and we demonstrate that the use of finer quadrature grids along selected modes can eliminate this bias, while still offering an ˜30 % lower computational cost than direct Monte Carlo integration in our tests.
Continuous Multistep Methods for Volterra Integro-Differential
African Journals Online (AJOL)
Kamoh et al.
DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 1Kamoh N.M. ... methods, Volterra integro-differential equation, Convergent, ...... Research of a Multistep Method Applied to Numerical Solution of. Volterra ... Congress on Engineering.
PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS
Directory of Open Access Journals (Sweden)
Korhan KARABULUT
1998-03-01
Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.
International Nuclear Information System (INIS)
Ibrahim, R. S.; El-Kalaawy, O. H.
2006-01-01
The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painleve expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model
Directory of Open Access Journals (Sweden)
Hossein Jafari
2016-04-01
Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.
A Line-Tau Collocation Method for Partial Differential Equations ...
African Journals Online (AJOL)
This paper deals with the numerical solution of second order linear partial differential equations with the use of the method of lines coupled with the tau collocation method. The method of lines is used to convert the partial differential equation (PDE) to a sequence of ordinary differential equations (ODEs) which is then ...
Partial differential equations methods, applications and theories
Hattori, Harumi
2013-01-01
This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied mathematics. Chapters One to Five are organized according to the equations and the basic PDE's are introduced in an easy to understand manner. They include the first-order equations and the three fundamental second-order equations, i.e. the heat, wave and Laplace equations. Through these equations we learn the types of problems, how we pose the problems, and the methods of solutions such as the separation of variables and the method of characteristics. The modeling aspects are explained as well. The methods introduced in earlier chapters are developed further in Chapters Six to Twelve. They include the Fourier series, the Fourier and the Laplace transforms, and the Green's functions. The equations in higher dimensions are also discussed in detail. This volume is application-oriented and rich in examples. Going thr...
Numerov iteration method for second order integral-differential equation
International Nuclear Information System (INIS)
Zeng Fanan; Zhang Jiaju; Zhao Xuan
1987-01-01
In this paper, Numerov iterative method for second order integral-differential equation and system of equations are constructed. Numerical examples show that this method is better than direct method (Gauss elimination method) in CPU time and memoy requireing. Therefore, this method is an efficient method for solving integral-differential equation in nuclear physics
Introduction to numerical methods for time dependent differential equations
Kreiss, Heinz-Otto
2014-01-01
Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the t
Quadrature interferometry for plasma density measurements
International Nuclear Information System (INIS)
Warthen, B.J.; Shlachter, J.S.
1995-01-01
A quadrature interferometer has been used routinely in several pulsed power experiments to measure the line-averaged electron density. The optical source is a 30 mW, continuous wave Nd-YAG laser operating at 1,300 nm. The light is coupled directly to an optical fiber and split into reference and scene beams with a fiber splitter. The scene beam is transported to and from the plasma using single mode optical fibers up to 100 m in length. To simplify alignment through the plasma, the authors have used GRIN lenses on both the launch and receive sides of the single pass transmission diagnostic where this is possible. The return beam passes through a half-wave plate which is used to compensate for polarization rotation associated with slow (hour) time scale drift in the single mode fibers. The reference beam is sent through a quarter-wave plate to produce circular polarization; mixing of the reference and scene beams is accomplished using a non-polarizing beam splitter, and the interference signals are focused into additional fibers which relay the light to fast photodiodes. The quadrature optics allow for an unambiguous determination of the slope of the density changes at inflection points. All of the beam processing optics are located on a stable optical table which is remote and protected from the experiment. Final setup of the interferometer is facilitated by looking at the Lissajous figure generated from the two quadrature components. The authors have used this interferometer to diagnose the background density in the Pegasus-II power flow channel, to study the plasma plume generated in foil implosion experiments, to measure the plasma blowoff during implosions, and to understand the plasma formation mechanism in a fusion target plasma system
Integrated source of broadband quadrature squeezed light
DEFF Research Database (Denmark)
Hoff, Ulrich Busk; Nielsen, Bo Melholt; Andersen, Ulrik Lund
2015-01-01
An integrated silicon nitride resonator is proposed as an ultracompact source of bright single-mode quadrature squeezed light at 850 nm. Optical properties of the device are investigated and tailored through numerical simulations, with particular attention paid to loss associated with interfacing...... the device. An asymmetric double layer stack waveguide geometry with inverse vertical tapers is proposed for efficient and robust fibre-chip coupling, yielding a simulated total loss of -0.75 dB/facet. We assess the feasibility of the device through a full quantum noise analysis and derive the output...
Applying homotopy analysis method for solving differential-difference equation
International Nuclear Information System (INIS)
Wang Zhen; Zou Li; Zhang Hongqing
2007-01-01
In this Letter, we apply the homotopy analysis method to solving the differential-difference equations. A simple but typical example is applied to illustrate the validity and the great potential of the generalized homotopy analysis method in solving differential-difference equation. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the differential-difference equations
Differential geometric methods in system theory.
Brockett, R. W.
1971-01-01
Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.
17th century arguments for the impossibility of the indefinite and the definite circle quadrature
DEFF Research Database (Denmark)
Lützen, Jesper
2014-01-01
The classical problem of the quadrature (or equivalently the rectification) of the circle enjoyed a renaissance in the second half of the 17th century. The new analytic methods provided the means for the discovery of infinite expressions of and for the first attempts to prove impossibility statem...
Sets of Fourier coefficients using numerical quadrature
International Nuclear Information System (INIS)
Lyness, J. N.
2001-01-01
One approach to the calculation of Fourier trigonometric coefficients f(r) of a given function f(x) is to apply the trapezoidal quadrature rule to the integral representation f(r)=(line i ntegral)(sub 0)(sup 1) f(x)e(sup -2(pi)irx)dx. Some of the difficulties in this approach are discussed. A possible way of overcoming many of these is by means of a subtraction function. Thus, one sets f(x)= h(sub p-1)(x)+ g(sub p)(x), where h(sub -1)(x) is an algebraic polynomial of degree p-1, specified in such a way that the Fourier series of g(sub p)(x) converges more rapidly than that of f(x). To obtain the Fourier coefficients of f(x), one uses an analytic expression for those of h(sub p-1)(x) and numerical quadrature to approximately those of g(sub p)(x)
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...
Single-quadrature continuous-variable quantum key distribution
DEFF Research Database (Denmark)
Gehring, Tobias; Jacobsen, Christian Scheffmann; Andersen, Ulrik Lund
2016-01-01
Most continuous-variable quantum key distribution schemes are based on the Gaussian modulation of coherent states followed by continuous quadrature detection using homodyne detectors. In all previous schemes, the Gaussian modulation has been carried out in conjugate quadratures thus requiring two...... commercialization of continuous-variable quantum key distribution, provided that the low noise requirement can be achieved....
Modified Differential Transform Method for Two Singular Boundary Values Problems
Directory of Open Access Journals (Sweden)
Yinwei Lin
2014-01-01
Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.
A time-variant analysis of the 1/f^(2) phase noise in CMOS parallel LC-Tank quadrature oscillators
DEFF Research Database (Denmark)
Andreani, Pietro
2006-01-01
This paper presents a study of 1/f2 phase noise in quadrature oscillators built by connecting two differential LC-tank oscillators in a parallel fashion. The analysis clearly demonstrates the necessity of adopting a time-variant theory of phase noise, where a more simplistic, time...
Correlated quadratures of resonance fluorescence and the generalized uncertainty relation
Arnoldus, Henk F.; George, Thomas F.; Gross, Rolf W. F.
1994-01-01
Resonance fluorescence from a two-state atom has been predicted to exhibit quadrature squeezing below the Heisenberg uncertainty limit, provided that the optical parameters (Rabi frequency, detuning, laser linewidth, etc.) are chosen carefully. When the correlation between two quadratures of the radiation field does not vanish, however, the Heisenberg limit for quantum fluctuations might be an unrealistic lower bound. A generalized uncertainty relation, due to Schroedinger, takes into account the possible correlation between the quadrature components of the radiation, and it suggests a modified definition of squeezing. We show that the coherence between the two levels of a laser-driven atom is responsible for the correlation between the quadrature components of the emitted fluorescence, and that the Schrodinger uncertainty limit increases monotonically with the coherence. On the other hand, the fluctuations in the quadrature field diminish with an increasing coherence, and can disappear completely when the coherence reaches 1/2, provided that certain phase relations hold.
Modified Chebyshev Collocation Method for Solving Differential Equations
Directory of Open Access Journals (Sweden)
M Ziaul Arif
2015-05-01
Full Text Available This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial collocation method is applied to both Ordinary Differential Equations (ODEs and Partial Differential Equations (PDEs cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.
Variable-mesh method of solving differential equations
Van Wyk, R.
1969-01-01
Multistep predictor-corrector method for numerical solution of ordinary differential equations retains high local accuracy and convergence properties. In addition, the method was developed in a form conducive to the generation of effective criteria for the selection of subsequent step sizes in step-by-step solution of differential equations.
Auxiliary equation method for solving nonlinear partial differential equations
International Nuclear Information System (INIS)
Sirendaoreji,; Jiong, Sun
2003-01-01
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation
Field Method for Integrating the First Order Differential Equation
Institute of Scientific and Technical Information of China (English)
JIA Li-qun; ZHENG Shi-wang; ZHANG Yao-yu
2007-01-01
An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.
Introduction to partial differential equations and Hilbert space methods
Gustafson, Karl E
1997-01-01
Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
Approximate Method for Solving the Linear Fuzzy Delay Differential Equations
Directory of Open Access Journals (Sweden)
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.
Quadrature measurements of a bright squeezed state via sideband swapping
DEFF Research Database (Denmark)
Schneider, J.; Glockl, O.; Leuchs, G.
2009-01-01
The measurement of an arbitrary quadrature of a bright quantum state of light is a commonly requested action in many quantum information protocols, but it is experimentally challenging with previously proposed schemes. We suggest that the quadrature be measured at a specific sideband frequency...... of a bright quantum state by transferring the sideband modes under interrogation to a vacuum state and subsequently measuring the quadrature via homodyne detection. The scheme is implemented experimentally, and it is successfully tested with a bright squeezed state of light....
An auxiliary differential equation FDTD method for anisotropic magnetized plasmas
International Nuclear Information System (INIS)
Liu Shaobin; Mo Jinjun; Yuan Naichang
2004-01-01
An auxiliary differential equation finite-difference time-domain (ADE-FDTD) methodology for anisotropic magnetized plasmas is derived. The method is based on a difference approximation of the auxiliary differential equation. A comparison with the JEC method is included. The CPU time saving by several times and accuracy of the method are confirmed by computing the reflection and transmission through a magnetized plasma layer with the direction of propagation parallel to the direction of the biasing field
On Solving the Lorenz System by Differential Transformation Method
International Nuclear Information System (INIS)
Al-Sawalha, M. Mossa; Noorani, M. S. M.
2008-01-01
The differential transformation method (DTM) is employed to solve a nonlinear differential equation, namely the Lorenz system. Numerical results are compared to those obtained by the Runge–Kutta method to illustrate the preciseness and effectiveness of the proposed method. In particular, we examine the accuracy of the (DTM) as the Lorenz system changes from a non-chaotic system to a chaotic one. It is shown that the (DTM) is robust, accurate and easy to apply
Herriott Cell Augmentation of a Quadrature Heterodyne Interferometer
National Research Council Canada - National Science Library
Antonsen, Erik
2002-01-01
A quadrature heterodyne interferometer is augmented with a Herriott Cell multi-pass reflector to increase instrument resolution and enable a separation of the phase shift due to neutral density from room vibrations...
MIMIC Methods for Assessing Differential Item Functioning in Polytomous Items
Wang, Wen-Chung; Shih, Ching-Lin
2010-01-01
Three multiple indicators-multiple causes (MIMIC) methods, namely, the standard MIMIC method (M-ST), the MIMIC method with scale purification (M-SP), and the MIMIC method with a pure anchor (M-PA), were developed to assess differential item functioning (DIF) in polytomous items. In a series of simulations, it appeared that all three methods…
Noncritical quadrature squeezing through spontaneous polarization symmetry breaking
Garcia-Ferrer, Ferran V.; Navarrete-Benlloch, Carlos; de Valcárcel, Germán J.; Roldán, Eugenio
2010-01-01
We discuss the possibility of generating noncritical quadrature squeezing by spontaneous polarization symmetry breaking. We consider first type-II frequency-degenerate optical parametric oscillators, but discard them for a number of reasons. Then we propose a four-wave mixing cavity in which the polarization of the output mode is always linear but has an arbitrary orientation. We show that in such a cavity complete noise suppression in a quadrature of the output field occurs, irrespective of ...
Noncritical quadrature squeezing through spontaneous polarization symmetry breaking.
Garcia-Ferrer, Ferran V; Navarrete-Benlloch, Carlos; de Valcárcel, Germán J; Roldán, Eugenio
2010-07-01
We discuss the possibility of generating noncritical quadrature squeezing by spontaneous polarization symmetry breaking. We first consider Type II frequency-degenerate optical parametric oscillators but discard them for a number of reasons. Then we propose a four-wave-mixing cavity, in which the polarization of the output mode is always linear but has an arbitrary orientation. We show that in such a cavity, complete noise suppression in a quadrature of the output field occurs, irrespective of the parameter values.
Quantum correlations induced by multiple scattering of quadrature squeezed light
DEFF Research Database (Denmark)
Lodahl, Peter
2006-01-01
Propagating quadrature squeezed light through a multiple scattering random medium is found to induce pronounced spatial quantum correlations that have no classical analogue. The correlations are revealed in the number of photons transported through the sample that can be measured from the intensity...... fluctuations of the total transmission or reflection. In contrast, no pronounced spatial quantum correlations appear in the quadrature amplitudes where excess noise above the shot noise level is found....
Entropy methods for diffusive partial differential equations
Jüngel, Ansgar
2016-01-01
This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.
Numerical Methods for Partial Differential Equations.
1984-01-09
iteration or the conjugate gradient method. The smoothing sweeps are used to annihilate the highly oscillatory (compared to the grid spacing) components of...53 52 "- 33 41 *32 * . 31 * 21 - 11 O- carrius plane rotacions o I ~~arr: ’.trix vrS2-0 Cf A Figure 4. QM fiitorization of a BLTE (1,2) mnitrix
Khan, Sami Ullah; Ali, Ishtiaq
2018-03-01
Explicit solutions to delay differential equation (DDE) and stochastic delay differential equation (SDDE) can rarely be obtained, therefore numerical methods are adopted to solve these DDE and SDDE. While on the other hand due to unstable nature of both DDE and SDDE numerical solutions are also not straight forward and required more attention. In this study, we derive an efficient numerical scheme for DDE and SDDE based on Legendre spectral-collocation method, which proved to be numerical methods that can significantly speed up the computation. The method transforms the given differential equation into a matrix equation by means of Legendre collocation points which correspond to a system of algebraic equations with unknown Legendre coefficients. The efficiency of the proposed method is confirmed by some numerical examples. We found that our numerical technique has a very good agreement with other methods with less computational effort.
International Nuclear Information System (INIS)
Lobanov, Yu.Yu.; Shahbagian, R.R.; Zhidkov, E.P.
1991-01-01
A new method for numerical solution of the boundary problem for Schroedinger-like partial differential equations in R n is elaborated. The method is based on representation of multidimensional Green function in the form of multiple functional integral and on the use of approximation formulas which are constructed for such integrals. The convergence of approximations to the exact value is proved, the remainder of the formulas is estimated. Method reduces the initial differential problem to quadratures. 16 refs.; 7 tabs
A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
Directory of Open Access Journals (Sweden)
Erdogan Fevzi
2010-01-01
Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.
Accurate and efficient quadrature for volterra integral equations
International Nuclear Information System (INIS)
Knirk, D.L.
1976-01-01
Four quadrature schemes were tested and compared in considerable detail to determine their usefulness in the noniterative integral equation method for single-channel quantum-mechanical calculations. They are two forms of linear approximation (trapezoidal rule) and two forms of quadratic approximation (Simpson's rule). Their implementation in this method is shown, a formal discussion of error propagation is given, and tests are performed to determine actual operating characteristics on various bound and scattering problems in different potentials. The quadratic schemes are generally superior to the linear ones in terms of accuracy and efficiency. The previous implementation of Simpson's rule is shown to possess an inherent instability which requires testing on each problem for which it is used to assure its reliability. The alternative quadratic approximation does not suffer this deficiency, but still enjoys the advantages of higher order. In addition, the new scheme obeys very well an h 4 Richardson extrapolation, whereas the old one does so rather poorly. 6 figures, 11 tables
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan
2015-02-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
An introduction to neural network methods for differential equations
Yadav, Neha; Kumar, Manoj
2015-01-01
This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks, and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed...
International Conference on Multiscale Methods and Partial Differential Equations.
Energy Technology Data Exchange (ETDEWEB)
Thomas Hou
2006-12-12
The International Conference on Multiscale Methods and Partial Differential Equations (ICMMPDE for short) was held at IPAM, UCLA on August 26-27, 2005. The conference brought together researchers, students and practitioners with interest in the theoretical, computational and practical aspects of multiscale problems and related partial differential equations. The conference provided a forum to exchange and stimulate new ideas from different disciplines, and to formulate new challenging multiscale problems that will have impact in applications.
GHM method for obtaining rationalsolutions of nonlinear differential equations.
Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo
2015-01-01
In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.
A hanging drop culture method to study terminal erythroid differentiation.
Gutiérrez, Laura; Lindeboom, Fokke; Ferreira, Rita; Drissen, Roy; Grosveld, Frank; Whyatt, David; Philipsen, Sjaak
2005-10-01
To design a culture method allowing the quantitative and qualitative analysis of terminal erythroid differentiation. Primary erythroid progenitors derived either from mouse tissues or from human umbilical cord blood were differentiated using hanging drop cultures and compared to methylcellulose cultures. Cultured cells were analyzed by FACS to assess differentiation. We describe a practical culture method by adapting the previously described hanging drop culture system to conditions allowing terminal differentiation of primary erythroid progenitors. Using minimal volumes of media and small numbers of cells, we obtained quantitative terminal erythroid differentiation within two days of culture in the case of murine cells and 4 days in the case of human cells. The established methods for ex vivo culture of primary erythroid progenitors, such as methylcellulose-based burst-forming unit-erythroid (BFU-E) and colony-forming unit-erythroid (CFU-E) assays, allow the detection of committed erythroid progenitors but are of limited value to study terminal erythroid differentiation. We show that the application of hanging drop cultures is a practical alternative that, in combination with clonogenic assays, enables a comprehensive assessment of the behavior of primary erythroid cells ex vivo in the context of genetic and drug-induced perturbations.
Application of Rational Expansion Method for Differential-Difference Equation
International Nuclear Information System (INIS)
Wang Qi
2011-01-01
In this paper, we applied the rational formal expansion method to construct a series of soliton-like and period-form solutions for nonlinear differential-difference equations. Compared with most existing methods, the proposed method not only recovers some known solutions, but also finds some new and more general solutions. The efficiency of the method can be demonstrated on Toda Lattice and Ablowitz-Ladik Lattice. (general)
Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance
Happola, Juho
2017-09-19
Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.
Discontinuous Galerkin finite element methods for hyperbolic differential equations
van der Vegt, Jacobus J.W.; van der Ven, H.; Boelens, O.J.; Boelens, O.J.; Toro, E.F.
2002-01-01
In this paper a suryey is given of the important steps in the development of discontinuous Galerkin finite element methods for hyperbolic partial differential equations. Special attention is paid to the application of the discontinuous Galerkin method to the solution of the Euler equations of gas
Multigrid methods for partial differential equations - a short introduction
International Nuclear Information System (INIS)
Linden, J.; Stueben, K.
1993-01-01
These notes summarize the multigrid methods and emphasis is laid on the algorithmic concepts of multigrid for solving linear and non-linear partial differential equations. In this paper there is brief description of the basic structure of multigrid methods. Detailed introduction is also contained with applications to VLSI process simulation. (A.B.)
Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance
Happola, Juho
2017-01-01
Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.
The Fall 2000 and Fall 2001 SOHO-Ulysses Quadratures
Suess, S. T.; Poletto, G.; Rose, M. Franklin (Technical Monitor)
2001-01-01
SOHO-Ulysses quadrature occurs when the SOHO-Sun-Ulysses included angle is 90 degrees. It is only at such times that the same plasma leaving the Sun in the direction of Ulysses can first be remotely analyzed with SOHO instruments and then later be sampled in situ by Ulysses instruments. The quadratures in December 2000 and 2001 are of special significance because Ulysses will be near the south and north heliographic poles, respectively, and the solar cycle will be near sunspot maximum. Quadrature geometry is sometimes confusing and observations are influenced by solar rotation. The Fall 2000 and 2001 quadratures are more complex than usual because Ulysses is not in a true polar orbit and the orbital speed of Ulysses about the Sun is becoming comparable to the speed of SOHO about the Sun. In 2000 Ulysses will always be slightly behind the pole but will appear to hang over the pole for over two months because it is moving around the Sun in the same direction as SOHO. In 2001 Ulysses will be slightly in front of the pole so that its footpoint will be directly observable. Detailed plots will be shown of the relative positions of SOHO and Ulysses will their relative positions. In neither case is true quadrature actually achieved, but this works to the observers advantage in 2001.
Effective potentials in nonlinear polycrystals and quadrature formulae
Michel, Jean-Claude; Suquet, Pierre
2017-08-01
This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471, 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.
Nonlinear ordinary differential equations analytical approximation and numerical methods
Hermann, Martin
2016-01-01
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...
International Nuclear Information System (INIS)
Bouferguene, Ahmed
2005-01-01
When computing multicentre integrals over Slater-type orbitals (STOs) by means of the Shavitt and Karplus Gaussian integral transforms (Shavitt and Karplus 1962 J. Chem. Phys. 36 550), one usually ends up with a multiple integral of the form ∫ 0 1 du ∫ 0 1 dv ...∫ 0 ∞ dz F(u, v, ..., z) (Shavitt and Karplus 1965 J. Chem. Phys. 43 398) in which all the integrals are inter-related. The most widely used approach for computing such an integral is to apply a product of Gauss-Legendre quadratures for the integrals over [0, 1] while the semi-infinite term is evaluated by a special procedure. Although numerous approaches have been developed to accurately perform the integration over [0, ∞) efficiently, it is the aim of this work to add a new tool that could be of some benefit in carrying out the hard task of multicentre integrals over STOs. The new approach relies on a special Gauss quadrature referred to as Gauss-Bessel to accurately evaluate the semi-infinite integral of interest. In this work, emphasis is put on accuracy rather than efficiency since its aim is essentially to bring a proof of concept showing that Gauss-Bessel quadrature can successfully be applied in the context of multicentre integrals over STOs. The obtained accuracy is comparable to that obtained with other methods available in the literature
New harmonic materials: index engineering. Thin-thick quadrature frequency conversion
International Nuclear Information System (INIS)
Eimerl, D.
1985-01-01
The quadrature conversion scheme is a method of generating the second harmonic. The scheme, which uses two crystals in series, has several advantages over single-crystal or other two crystal schemes. The most important is that it is capable of high conversion efficiency over a large dynamic range of drive intensity and detuning angle. Consider a pair of KDP crystals cut for type-II phase matching. In the quadrature scheme, the optic axes of the crystals are arranged so that the plans containing the direction of the laser beam and their optic axes (the kz planes) are mutually perpendicular. This arrangement has two important properties. First, in type-II phase matching, the incident wave is polarized at 45 deg to the kz plane of the crystal. This, in the quadrature scheme, if the incident wave is correctly polarized for efficient conversion in the first crystal, it is also correctly polarized for efficient conversion in the second crystal. Both crystals can therefore convert efficiently
All-Pass Filter Based Linear Voltage Controlled Quadrature Oscillator
Directory of Open Access Journals (Sweden)
Koushick Mathur
2017-01-01
Full Text Available A linear voltage controlled quadrature oscillator implemented from a first-order electronically tunable all-pass filter (ETAF is presented. The active element is commercially available current feedback amplifier (AD844 in conjunction with the relatively new Multiplication Mode Current Conveyor (MMCC device. Electronic tunability is obtained by the control node voltage (V of the MMCC. Effects of the device nonidealities, namely, the parasitic capacitors and the roll-off poles of the port-transfer ratios of the device, are shown to be negligible, even though the usable high-frequency ranges are constrained by these imperfections. Subsequently the filter is looped with an electronically tunable integrator (ETI to implement the quadrature oscillator (QO. Experimental responses on the voltage tunable phase of the filter and the linear-tuning law of the quadrature oscillator up to 9.9 MHz at low THD are verified by simulation and hardware tests.
Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations
Directory of Open Access Journals (Sweden)
Reza Mokhtari
2012-01-01
Full Text Available On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution , is constructed by truncating the series to terms. The convergence of , to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such differential-difference problems.
Approximate analytical methods for solving ordinary differential equations
Radhika, TSL; Rani, T Raja
2015-01-01
Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods.The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete descripti
Spectral methods for time dependent partial differential equations
Gottlieb, D.; Turkel, E.
1983-01-01
The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.
The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations
Zhao, Jianping; Tang, Bo; Kumar, Sunil; Hou, Yanren
2012-01-01
An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powe...
Self-calibrating quadrature mixing front-end for SDR
CSIR Research Space (South Africa)
De Witt, JJ
2008-01-01
Full Text Available by modeling the effect of the two lowpass filters (LPFs) of the quadrature modulator. Let HI,M (f) and HQ,M (f) denote the frequency-domain representa- tions of the I and Q channels’ LPFs, respectively. If the in- phase and quadrature components of a... to be frequency independent to a first-order approximation, for a certain LO frequency [4], [6]. We may thus write the complex oscillator signal of the modulator xM (t), with a gain imbalance of α and a phase error of φ radians, as xM (t) = α cos(2pifct + φ/2...
International Nuclear Information System (INIS)
Ibrahim, R.S.
2003-01-01
The equations of magnetohydrodynamic (MHD) equilibria for a plasma in gravitational field are investigated. For equilibria with one ignorable spatial coordinate, the MHD equations are reduced to a single nonlinear elliptic equation for the magnetic potential u-tilde, known as the Grad-Shafranov equation. Specifying the arbitrary functions in this equation, the Bullough-Dodd equation can be obtained. The truncated Painleve expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the travelling wave solutions of the Bullough-Dodd equation for the case of isothermal magnetostatic atmosphere, in which the current density J is proportional to the exponentially of the magnetic flux and moreover falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height
Numerical methods for stochastic partial differential equations with white noise
Zhang, Zhongqiang
2017-01-01
This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...
Differential and difference equations a comparison of methods of solution
Maximon, Leonard C
2016-01-01
This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green’s functions and the associat...
Electrodynamics, Differential Forms and the Method of Images
Low, Robert J.
2011-01-01
This paper gives a brief description of how Maxwell's equations are expressed in the language of differential forms and use this to provide an elegant demonstration of how the method of images (well known in electrostatics) also works for electrodynamics in the presence of an infinite plane conducting boundary. The paper should be accessible to an…
Explicit Gaussian quadrature rules for C^1 cubic splines with symmetrically stretched knot sequence
Ait-Haddou, Rachid; Barton, Michael; Calo, Victor M.
2015-01-01
We provide explicit expressions for quadrature rules on the space of C^1 cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention
Workshop on Numerical Methods for Ordinary Differential Equations
Gear, Charles; Russo, Elvira
1989-01-01
Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.
Exp-function method for solving fractional partial differential equations.
Zheng, Bin
2013-01-01
We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.
Numerical Methods for a Class of Differential Algebraic Equations
Directory of Open Access Journals (Sweden)
Lei Ren
2017-01-01
Full Text Available This paper is devoted to the study of some efficient numerical methods for the differential algebraic equations (DAEs. At first, we propose a finite algorithm to compute the Drazin inverse of the time varying DAEs. Numerical experiments are presented by Drazin inverse and Radau IIA method, which illustrate that the precision of the Drazin inverse method is higher than the Radau IIA method. Then, Drazin inverse, Radau IIA, and Padé approximation are applied to the constant coefficient DAEs, respectively. Numerical results demonstrate that the Padé approximation is powerful for solving constant coefficient DAEs.
Fully Digital Chaotic Differential Equation-based Systems And Methods
Radwan, Ahmed Gomaa Ahmed
2012-09-06
Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.
Fully Digital Chaotic Differential Equation-based Systems And Methods
Radwan, Ahmed Gomaa Ahmed; Zidan, Mohammed A.; Salama, Khaled N.
2012-01-01
Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.
New uncertainties in QCD–QED rescaling factors using quadrature ...
Indian Academy of Sciences (India)
mf ). This is true for heavier quarks ... mass scale down to the physical quark mass scale is parametrised by the QCD–. QED rescaling factors ηf ... It will be an important numerical exercise to estimate the uncertainties in ηf using the quadrature ...
A novel method to solve functional differential equations
International Nuclear Information System (INIS)
Tapia, V.
1990-01-01
A method to solve differential equations containing the variational operator as the derivation operation is presented. They are called variational differential equations (VDE). The solution to a VDE should be a function containing the derivatives, with respect to the base space coordinates, of the fields up to a generic order s: a s-th-order function. The variational operator doubles the order of the function on which it acts. Therefore, in order to make compatible the orders of the different terms appearing in a VDE, the solution should be a function containing the derivatives of the fields at all orders. But this takes us again back to the functional methods. In order to avoid this, one must restrict the considerations, in the case of second-order VDEs, to the space of s-th-order functions on which the variational operator acts transitively. These functions have been characterized for a one-dimensional base space for the first- and second-order cases. These functions turn out to be polynomial in the highest-order derivatives of the fields with functions of the lower-order derivatives as coefficients. Then VDEs reduce to a system of coupled partial differential equations for the coefficients above mentioned. The importance of the method lies on the fact that the solutions to VDEs are in a one-to-one correspondence with the solutions of functional differential equations. The previous method finds direct applications in quantum field theory, where the Schroedinger equation plays a central role. Since the Schroedinger equation is reduced to a system of coupled partial differential equations, this provides a nonperturbative scheme for quantum field theory. As an example, the massless scalar field is considered
Improved stochastic approximation methods for discretized parabolic partial differential equations
Guiaş, Flavius
2016-12-01
We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).
The differential method for grating efficiencies implemented in mathematica
Energy Technology Data Exchange (ETDEWEB)
Valdes, V.; McKinney, W. [Lawrence Berkeley Lab., CA (United States); Palmer, C. [Milton Co., Rochester, NY (United States). Roy Analytical Products Div.
1993-08-01
In order to facilitate the accurate calculation of diffraction grating efficiencies in the soft x-ray region, we have implemented the differential method of Neviere and Vincent in Mathematica [1]. This simplifies the programming to maximize the transparency of the theory for the user. We alleviate some of the overhead burden of the Mathematica program by coding the time-consuming numerical integration in C subprograms. We recall the differential method directly from Maxwell`s equations. The pseudo-periodicity of the grating profile and the electromagnetic fields allows us to use their Fourier series expansions to formulate an infinite set of coupled differential equations. A finite subset of the equations are then numerically integrated using the Numerov method for the transverse electric (TE) case and a fourth-order Runge-Kutta algorithm for the transverse magnetic (TM) case. We have tested our program by comparisons with the scalar theory and with published theoretical results for the blazed, sinusoidal and square wave profiles. The Reciprocity Theorem has also been used as a means to verify the method. We have found it to be verified for several cases to within the computational accuracy of the method.
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.
International Nuclear Information System (INIS)
Mathews, K.; Sjoden, G.; Minor, B.
1994-01-01
The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport in slab geometry is derived and compared with current methods. It is similar to the linear characteristic (or, in slab geometry, the linear nodal) quadrature but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx), whose parameters are root-solved to match the known (from the previous iteration) average and first moment of the source over the cell. Like the linear adaptive method, the exponential characteristic method is positive and nonlinear but more accurate and more readily extended to other cell shapes. The nonlinearity has not interfered with convergence. The authors introduce the ''exponential moment functions,'' a generalization of the functions used by Walters in the linear nodal method, and use them to avoid numerical ill-conditioning. The method exhibits O(Δx 4 ) truncation error on fine enough meshes; the error is insensitive to mesh size for coarse meshes. In a shielding problem, it is accurate to 10% using 16-mfp-thick cells; conventional methods err by 8 to 15 orders of magnitude. The exponential characteristic method is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Unconditionally stable difference methods for delay partial differential equations
Huang, Chengming; Vandewalle, Stefan
2012-01-01
This paper is concerned with the numerical solution of parabolic partial differential equations with time-delay. We focus in particular on the delay dependent stability analysis of difference methods that use a non-constrained mesh, i.e., the time step-size is not required to be a submultiple of the delay. We prove that the fully discrete system unconditionally preserves the delay dependent asymptotic stability of the linear test problem under consideration, when the following discretizati...
Cui, Yan; He, Yuxi; Wang, Pingshan
2014-07-01
A highly tunable and sensitive radio-frequency (RF) sensor is presented for the measurement of aqueous-solution dielectric properties. Two quadrature hybrids are utilized to achieve destructive interference that eliminates the probing signals at both measurement ports. As a result, weak signals of material-under-test (MUT) are elevated for high sensitivity detections at different frequencies. The sensor is demonstrated through measuring 2-propanol-water solution permittivity at 0.01 mole fraction concentration level from ~4 GHz to ~12 GHz. De-ionized water and methanol-water solution are used to calibrate the sensor for quantitative MUT analysis through our proposed model. Micro-meter coplanar waveguides (CPW) are fabricated as RF sensing electrodes. A polydimethylsiloxane (PDMS) microfluidic channel is employed to introduce 250 nL liquid, of which ~1 nL is effectively the MUT. The permittivity and the relaxation time of 2-propanol-water solution are obtained. Compared with our power divider based sensors, the differential reflection coefficients in this work provide additional information that complements the transmission coefficient methods.
Optimal overlapping of waveform relaxation method for linear differential equations
International Nuclear Information System (INIS)
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)
DEFF Research Database (Denmark)
Xin, Zhen; Qin, Zian; Lu, Minghui
2016-01-01
Due to the simplicity and flexibility of the structure of the Second-Order Generalized Integrator based Quadrature Signal Generator (SOGI-QSG), it has been widely used over the past decade for many applications such as frequency estimation, grid synchronization, and harmonic extraction. However......, the SOGI-QSG will produce errors when its input signal contains a dc component or harmonic components with unknown frequencies. The accuracy of the signal detection methods using it may hence be compromised. To overcome the drawback, the First-Order System (FOS) concept is first used to illustrate...
Entropy Generation Due to Natural Convection in a Partially Heated Cavity by Local RBF-DQ Method
DEFF Research Database (Denmark)
Soleimani, S.; Qajarjazi, A.; Bararnia, H.
2011-01-01
The Local Radial Basis Function-Differential Quadrature (RBF-DQ) method is applied to twodimensional incompressible Navier-Stokes equations in primitive form. Numerical results of heatlines and entropy generation due to heat transfer and fluid friction have been obtained for laminar natural...
International Nuclear Information System (INIS)
Abdel-Halim Hassan, I.H.
2008-01-01
In this paper, we will compare the differential transformation method DTM and Adomian decomposition method ADM to solve partial differential equations (PDEs). The definition and operations of differential transform method was introduced by Zhou [Zhou JK. Differential transformation and its application for electrical circuits. Wuuhahn, China: Huarjung University Press; 1986 [in Chinese
KRYSI, Ordinary Differential Equations Solver with Sdirk Krylov Method
International Nuclear Information System (INIS)
Hindmarsh, A.C.; Norsett, S.P.
2001-01-01
1 - Description of program or function: KRYSI is a set of FORTRAN subroutines for solving ordinary differential equations initial value problems. It is suitable for both stiff and non-stiff systems. When solving the implicit stage equations in the stiff case, KRYSI uses a Krylov subspace iteration method called the SPIGMR (Scaled Preconditioned Incomplete Generalized Minimum Residual) method. No explicit Jacobian storage is required, except where used in pre- conditioning. A demonstration problem is included with a description of two pre-conditioners that are natural for its solution by KRYSI. 2 - Method of solution: KRYSI uses a three-stage, third-order singly diagonally implicit Runge-Kutta (SDIRK) method. In the stiff case, a preconditioned Krylov subspace iteration within a (so-called) inexact Newton iteration is used to solve the system of nonlinear algebraic equations
Electronically Tunable Current-Mode Quadrature Oscillator Using Single MCDTA
Directory of Open Access Journals (Sweden)
Y. Li
2010-12-01
Full Text Available This paper presents a modified current differencing transconductance amlpifier (MCDTA and the MCDTA based quadrature oscillator. The oscillator is current-mode and provides current output from high output impedance terminals. The circuit uses only one MCDTA and two grounded capacitors, and is easy to be integrated. Its oscillation frequency can be tuned electronically by tuning bias currents of MCDTA. Finally, frequency error is analyzed. The results of circuit simulations are in agreement with theory.
Thin-plate spline quadrature of geodetic integrals
Vangysen, Herman
1989-01-01
Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.
Quasi-quadrature interferometer for plasma density radial profile measurements
International Nuclear Information System (INIS)
Lowenthal, D.D.; Hoffman, A.L.
1979-01-01
A cw Mach Zehnder multichannel interferometer has been developed to measure time-dependent fractional fringe shifts with an accuracy of one-fortieth fringe. The design is quasi-quadrature in that known phase shifts, introduced in the reference beam, are time multiplexed with the normal reference beam. This technique requires only one detector per interferometer channel as compared to two detectors for most quadrature designs. The quadrature information makes the sense of density changes unambiguous, it automatically calibrates the instrument during the plasma event, and it makes fringe shift measurements virtually independent of fringe contrast fluctuations caused by plasma refractive and/or absorptive effects. The interferometer optical design is novel in that the electro-optic crystal used to introduce the 90 0 phase shifts is located in the common 2-mm-diam HeNe entrance beam to the interferometer, by exploiting polarization techniques, rather than in the expanded 1--2-cm reference beam itself. This arrangement greatly reduces the size, cost, and high-voltage requirements for the phase modulating crystal
[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].
Murase, Kenya
2015-01-01
In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.
Gainetdinova, A A; Gazizov, R K
2017-01-01
We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.
Convergence of method of lines approximations to partial differential equations
International Nuclear Information System (INIS)
Verwer, J.G.; Sanz-Serna, J.M.
1984-01-01
Many existing numerical schemes for evolutionary problems in partial differential equations (PDEs) can be viewed as method of lines (MOL) schemes. This paper treats the convergence of one-step MOL schemes. The main purpose is to set up a general framework for a convergence analysis applicable to nonlinear problems. The stability materials for this framework are taken from the field of nonlinear stiff ODEs. In this connection, important concepts are the logarithmic matrix norm and C-stability. A nonlinear parabolic equation and the cubic Schroedinger equation are used for illustrating the ideas. (Auth.)
Computing complex Airy functions by numerical quadrature
A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)
2001-01-01
textabstractIntegral representations are considered of solutions of the Airydifferential equation w''-z, w=0 for computing Airy functions for complex values of z.In a first method contour integral representations of the Airyfunctions are written as non-oscillating
International Nuclear Information System (INIS)
Shoupeng, Song; Zhou, Jiang
2017-01-01
Converting ultrasonic signal to ultrasonic pulse stream is the key step of finite rate of innovation (FRI) sparse sampling. At present, ultrasonic pulse-stream-forming techniques are mainly based on digital algorithms. No hardware circuit that can achieve it has been reported. This paper proposes a new quadrature demodulation (QD) based circuit implementation method for forming an ultrasonic pulse stream. Elaborating on FRI sparse sampling theory, the process of ultrasonic signal is explained, followed by a discussion and analysis of ultrasonic pulse-stream-forming methods. In contrast to ultrasonic signal envelope extracting techniques, a quadrature demodulation method (QDM) is proposed. Simulation experiments were performed to determine its performance at various signal-to-noise ratios (SNRs). The circuit was then designed, with mixing module, oscillator, low pass filter (LPF), and root of square sum module. Finally, application experiments were carried out on pipeline sample ultrasonic flaw testing. The experimental results indicate that the QDM can accurately convert ultrasonic signal to ultrasonic pulse stream, and reverse the original signal information, such as pulse width, amplitude, and time of arrival. This technique lays the foundation for ultrasonic signal FRI sparse sampling directly with hardware circuitry. (paper)
Furihata, Daisuke
2010-01-01
Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer
Advanced quadratures and periodic boundary conditions in parallel 3D Sn transport
International Nuclear Information System (INIS)
Manalo, K.; Yi, C.; Huang, M.; Sjoden, G.
2013-01-01
Significant updates in numerical quadratures have warranted investigation with 3D Sn discrete ordinates transport. We show new applications of quadrature departing from level symmetric ( 2 o) and Pn-Tn (>S 2 o). investigating 3 recently developed quadratures: Even-Odd (EO), Linear-Discontinuous Finite Element - Surface Area (LDFE-SA), and the non-symmetric Icosahedral Quadrature (IC). We discuss implementation changes to 3D Sn codes (applied to Hybrid MOC-Sn TITAN and 3D parallel PENTRAN) that can be performed to accommodate Icosahedral Quadrature, as this quadrature is not 90-degree rotation invariant. In particular, as demonstrated using PENTRAN, the properties of Icosahedral Quadrature are suitable for trivial application using periodic BCs versus that of reflective BCs. In addition to implementing periodic BCs for 3D Sn PENTRAN, we implemented a technique termed 'angular re-sweep' which properly conditions periodic BCs for outer eigenvalue iterative loop convergence. As demonstrated by two simple transport problems (3-group fixed source and 3-group reflected/periodic eigenvalue pin cell), we remark that all of the quadratures we investigated are generally superior to level symmetric quadrature, with Icosahedral Quadrature performing the most efficiently for problems tested. (authors)
Directory of Open Access Journals (Sweden)
Xiaolin Zhu
2014-01-01
Full Text Available This paper studies the T-stability of the Heun method and balanced method for solving stochastic differential delay equations (SDDEs. Two T-stable conditions of the Heun method are obtained for two kinds of linear SDDEs. Moreover, two conditions under which the balanced method is T-stable are obtained for two kinds of linear SDDEs. Some numerical examples verify the theoretical results proposed.
[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].
Murase, Kenya
2014-01-01
Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.
A radionuclide method for differentiating renovascular from essential hypertension
International Nuclear Information System (INIS)
Simeonova, A.; Kostadinova, I.; Milanov, S.; Delijska, B.; Nikolov, D.
1995-01-01
Renovascular hypertension occurs in nearly 5 per cent of patients with high blood pressure but nevertheless its diagnosis has important practical implication insofar as a complete cure is possible by resorting to percutaneous transluminal angioplasty or surgery. It is the purpose of this work to develop a radionuclide method for differential diagnosis of the two conditions using 99m Tc-DTPA which contributes to overall functional assessment of the kidneys, and introduces an objective indicator for estimating the extent of renal response to Captopril (C). A total of thirty patients, 25 of them with essential hypertension (EH) and 5 with renovascular hypertension (RVH), are studied. From the obtained data on transit time of kidneys, T max and their perceptual contribution to total renal function in EH patients, it becomes evident that the effect of C on the listed indicators is insignificant (p>0.05). In RVH patients, following drug intake, there is prolongation of the transit time, T max as well as reduced contribution of the kidney affected to total renal function (by over 6 per cent). In conclusion it is stressed that using the noninvasive radionuclide method and quantitative indicators proposed, it is possible to differentiate RVH from EH and renoparenchymal hypertension with a high-degree certainty. 6 refs., 1 tab., 2 figs. (author)
Final Report: Symposium on Adaptive Methods for Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Pernice, M.; Johnson, C.R.; Smith, P.J.; Fogelson, A.
1998-12-10
OAK-B135 Final Report: Symposium on Adaptive Methods for Partial Differential Equations. Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.
Reduced basis methods for partial differential equations an introduction
Quarteroni, Alfio; Negri, Federico
2016-01-01
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examp...
Power decoupling method for single phase differential buck converter
DEFF Research Database (Denmark)
Yao, Wenli; Tang, Yi; Zhang, Xiaobin
2015-01-01
inverter to improve the dc link power quality, and an improved active power decoupling method is proposed to achieve ripple power reduction for both AC-DC and DC-AC conversions. The ripple energy storage is realized by the filter capacitors, which are connected between the output terminal and the negative...... generation technique is proposed to provide accurate ripple power compensation, and closed-loop controllers are also designed based on small signal models. The effectiveness of this power decoupling method is verified by detailed simulation studies as well as laboratory prototype experimental results....... dc bus. By properly controlling the differential mode voltage of the capacitors, it is possible to transfer desired energy between the DC port and AC port. The common mode voltage is controlled in such a way that the ripple power on the dc side will be reduced. Furthermore, an autonomous reference...
International Nuclear Information System (INIS)
Chepe P, M.; Xolocostli M, J. V.; Gomez T, A. M.; Del Valle G, E.
2015-09-01
The deterministic transport codes for analysis of nuclear reactors have been used for several years already, these codes have evolved in terms of the methodology used and the degree of accuracy, because at the present time has more computer power. In this paper, the transport code used considers the classical technique of multi-group for discretization energy, for space discretization uses the nodal methods, while for the angular discretization the discrete ordinates method is used; so that presents the development and implementation of a set of numerical quadratures of SQ N type symmetrical with the same weight for each angular direction and these are compared with the quadratures of EQ N type. The two sets of numerical quadratures were implemented in the program AZTRAN to a problem with isotropic medium in XYZ geometry, in steady state using the nodal method RTN-0 (Raviart-Thomas-Nedelec). The analyzed results correspond to the effective multiplication factor k eff and neutron angular flux with approximations from S 4 to S 16 . (Author)
International Nuclear Information System (INIS)
Goncalves, Glenio A.; Orengo, Gilberto; Vilhena, Marco Tullio M.B. de; Graca, Claudio O.
2002-01-01
In this work we present the LTS N solution of the adjoint transport equation for an arbitrary source, testing the aptness of this analytical solution for high order of quadrature in transport problems and comparing some preliminary results with the ANISN computations in a homogeneneous slab geometry. In order to do that we apply the new formulation for the LTS N method based on the invariance projection property, becoming possible to handle problems with arbitrary sources and demanding high order of quadrature or deep penetration. This new approach for the LTS N method is important both for direct and adjoint transport calculations and its development was inspired by the necessity of using generalized adjoint sources for important calculations. Although the mathematical convergence has been proved for an arbitrary source, when the quadrature order or deep penetration is required the LTS N method presents computational overflow even for simple sources (sin, cos, exp, polynomial). With the new formulation we eliminate this drawback and in this work we report the numerical simulations testing the new approach
Differential diagnosis of neurodegenerative dementias with nuclear medicine methods
International Nuclear Information System (INIS)
Kluge, R.
2015-01-01
Full text: Neurodegenerative dementias (NDD) are characterized by insidious onset and gradual progression of cognitive dysfunction, initially relatively focal with respect to cognitive domains and brain regions involved. Nuclear medicine techniques help to clarify differential diagnoses of syndromes such as Alzheimer’s disease (AD), dementia with Lewy bodies (DlB), posterior cortical atrophy (PCA), logopenic primary progressive aphasia (PPA), agrammatic PPA, semantic dementia (SD), behavioral variant frontotemporal dementia (bvFTD) and progressive supranuclear palsy syndrome (PSPS). The process of pathologic changes in the brain may start decades before first clinical symptoms become evident. An early diagnosis already in the pre-clinical phase of the diseases will be of immense importance when expected effective therapeutic options have been introduced. NDDs are histopathologically characterized by accumulation of pathological proteins in the brain like beta amyloid or protein tau. While radiotracers for labeling of protein tau are in preclinical evaluation, different radiotracers labeling amyloid plaques ([11C]PIB, [18F]Florbetapir (Amyvid, Fa. EliLilly), [18F]Florbetaben (Neuraceq, Fa. Piramal), [18F]Flutemetamol (vVzamyl, Fa. Ge) have already been established in clinical use during the last years. In AD these tracers are intensively accumulated in the whole cortical brain. Even an early disease can be excluded in case of a negative amyloid PET. The method is, however, not highly specific since amyloid plaques may also be present in DlB (70 – 80%), FTD (30%) orlogopenicPPA (100%). Neuronal dysfunction goes along with decreased glucose consumption. Different diseases are characterized by different topographical zones of reduced [18F]FDG uptake. In AD the posterior cingular, temporopariatal and (later) frontal cortex are affected, in DlB the pattern is similar, including the occipital cortex, in FTD the frontal cortex is affected, in nonfluent PPA the
Determination of differential pulmonary function by the radioisotopic method
International Nuclear Information System (INIS)
Molinari, J.F.; Chatkin, J.M.; Barreto, S.M.
1991-01-01
A study of twenty-one patients with bronchogenic carcinoma which were submitted to lobectomy or pneumonectomy has been done, with the purpose of evaluation of regional and differential function of the lungs or parts of them. To accomplish this subject the patients underwent simple spirometry with FEV (forced expiratory volume in the first second) and FVC (forced vital capacity) measurements plus quantitative perfusional scintigraphy using 99 Tc-MAA (aggregated albumin). The relationship between these tests allowed the calculation of predictive values of FEV and FVC for the post-operative period through proposed equations. From the third month on after the operation, the patients were again submitted to spirometry with measurement of FEV and FVC to attest the hypothesis that these values were similar to those calculated. The statistical study of these results, utilizing the Student's t test, has demonstrated that the values of FEV and FVC were similar to those found in the postoperative period. These results allowed the conclusion that the radioisotopic method had predictive capacity of FEV and FVC in the lobectomized and pneumonectomized patients and it is a contribution in the evaluation of the differential pulmonary function. (author)
Savoye, Philippe
2009-01-01
In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.
Directory of Open Access Journals (Sweden)
Nicola Ponara
2012-11-01
Full Text Available Regularized Heaviside and Dirac delta function are used in several fields of computational physics and mechanics. Hence the issue of the quadrature of integrals of discontinuous and singular functions arises. In order to avoid ad-hoc quadrature procedures, regularization of the discontinuous and the singular fields is often carried out. In particular, weight functions of the signed distance with respect to the discontinuity interface are exploited. Tornberg and Engquist (Journal of Scientific Computing, 2003, 19: 527–552 proved that the use of compact support weight function is not suitable because it leads to errors that do not vanish for decreasing mesh size. They proposed the adoption of non-compact support weight functions. In the present contribution, the relationship between the Fourier transform of the weight functions and the accuracy of the regularization procedure is exploited. The proposed regularized approach was implemented in the eXtended Finite Element Method. As a three-dimensional example, we study a slender solid characterized by an inclined interface across which the displacement is discontinuous. The accuracy is evaluated for varying position of the discontinuity interfaces with respect to the underlying mesh. A procedure for the choice of the regularization parameters is proposed.
A Detection Algorithm for the BOC Signal Based on Quadrature Channel Correlation
Directory of Open Access Journals (Sweden)
Bo Qian
2018-01-01
Full Text Available In order to solve the problem of detecting a BOC signal, which uses a long-period pseudo random sequence, an algorithm is presented based on quadrature channel correlation. The quadrature channel correlation method eliminates the autocorrelation component of the carrier wave, allowing for the extraction of the absolute autocorrelation peaks of the BOC sequence. If the same lag difference and height difference exist for the adjacent peaks, the BOC signal can be detected effectively using a statistical analysis of the multiple autocorrelation peaks. The simulation results show that the interference of the carrier wave component is eliminated and the autocorrelation peaks of the BOC sequence are obtained effectively without demodulation. The BOC signal can be detected effectively when the SNR is greater than −12 dB. The detection ability can be improved further by increasing the number of sampling points. The higher the ratio of the square wave subcarrier speed to the pseudo random sequence speed is, the greater the detection ability is with a lower SNR. The algorithm presented in this paper is superior to the algorithm based on the spectral correlation.
Büttner, Lars; Czarske, Jürgen
2003-07-01
We report a method for passive optical directional discrimination in laser-Doppler anemometers. For this purpose frequency-shift elements such as acousto-optic modulators, which are bulky and difficult to align during assembly, have traditionally been employed. We propose to use a quadrature homodyne technique to achieve directional discrimination of the fluid flow without any frequency-shift elements. It is based on the employment of two laser wavelengths, which generate two interference fringe systems with a phase shift of a quarter of the common fringe spacing. Measurement signal pairs with a direction-dependent phase shift of +/- pi/2 are generated. As a robust signal-processing technique, the cross-correlation technique is used. The principles of quadrature homodyne laser-Doppler anemometry are investigated. A setup that provides a constant phase shift of pi/2 throughout the entire measurement volume was achieved with both single-mode and multimode radiation. The directional discrimination was successfully verified with wind tunnel measurements. The complete passive technique offers the potential of building miniaturized measurement heads that can be integrated, e.g., into wind tunnel models.
Explicit Gaussian quadrature rules for C^1 cubic splines with symmetrically stretched knot sequence
Ait-Haddou, Rachid
2015-06-19
We provide explicit expressions for quadrature rules on the space of C^1 cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal, that is, it requires minimal number of nodes. Numerical experiments validating the theoretical results and the error estimates of the quadrature rules are also presented.
International Nuclear Information System (INIS)
Minor, B.; Mathews, K.
1995-01-01
The exponential characteristic (EC) spatial quadrature for discrete ordinates neutral particle transport previously introduced in slab geometry is extended here to x-y geometry with rectangular cells. The method is derived and compared with current methods. It is similar to the linear characteristic (LC) quadrature (a linear-linear moments method) but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx + cy), whose parameters are rootsolved to match the known (from the previous iteration) spatial average and first moments of the source over the cell. Similarly, EC assumes exponential distributions of flux along cell edges through which particles enter the cell, with parameters chosen to match the average and first moments of flux, as passed from the adjacent, upstream cells (or as determined by boundary conditions). Like the linear adaptive (LA) method, EC is positive and nonlinear. It is more accurate than LA and does not require subdivision of cells. The nonlinearity has not interfered with convergence. The exponential moment functions, which were introduced with the slab geometry method, are extended to arbitrary dimensions (numbers of arguments) and used to avoid numerical ill conditioning. As in slab geometry, the method approaches O(Δx 4 ) global truncation error on fine-enough meshes, while the error is insensitive to mesh size for coarse meshes. Performance of the method is compared with that of the step characteristic, LC, linear nodal, step adaptive, and LA schemes. The EC method is a strong performer with scattering ratios ranging from 0 to 0.9 (the range tested), particularly so for lower scattering ratios. As in slab geometry, EC is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems
Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors
Barton, Michael; Ait-Haddou, Rachid; Calo, Victor Manuel
2017-01-01
We provide explicit quadrature rules for spaces of C1C1 quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. Each rule is optimal, that is, requires the minimal number of nodes, for a given function space. For each of nn subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/32/3 when compared to the classical Gaussian quadrature for polynomials over each knot span. Numerical experiments show fast convergence, as nn grows, to the “two-third” quadrature rule of Hughes et al. (2010) for infinite domains.
Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors
Bartoň, Michael
2017-03-21
We provide explicit quadrature rules for spaces of C1C1 quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. Each rule is optimal, that is, requires the minimal number of nodes, for a given function space. For each of nn subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/32/3 when compared to the classical Gaussian quadrature for polynomials over each knot span. Numerical experiments show fast convergence, as nn grows, to the “two-third” quadrature rule of Hughes et al. (2010) for infinite domains.
In-phase and quadrature imbalance modeling, estimation, and compensation
Li, Yabo
2013-01-01
This book provides a unified IQ imbalance model and systematically reviews the existing estimation and compensation schemes. It covers the different assumptions and approaches that lead to many models of IQ imbalance. In wireless communication systems, the In-phase and Quadrature (IQ) modulator and demodulator are usually used as transmitter (TX) and receiver (RX), respectively. For Digital-to-Analog Converter (DAC) and Analog-to-Digital Converter (ADC) limited systems, such as multi-giga-hertz bandwidth millimeter-wave systems, using analog modulator and demodulator is still a low power and l
Realization of Quadrature Signal Generator Using Accurate Magnitude Integrator
DEFF Research Database (Denmark)
Xin, Zhen; Yoon, Changwoo; Zhao, Rende
2016-01-01
Second-Order Generalized Integrator based Quadrature Signal Generator (SOGI-QSG) has been widely used in single- or three-phase power converter systems due to its simplicity and flexibility. Howeever, its dynamic response is not onyl decided by its damping gain but also influences by the input...... of the AMI-QSG can thus be as simple as the typical FOS. Besides, the structure of the AMI-QSG is further configurated to be able to extract the dc component and harmonic components. The effectiveness of the proposed structures and the correctness of the theoretical analysis are evaluated by experimental...
Orthogonal functions, discrete variable representation, and generalized gauss quadratures
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2002-01-01
in the original representation. This has been exploited in bound-state, scattering, and time-dependent problems using the so-called, discrete variable representation (DVR). At the core of this approach is the mathematical three-term recursion relationship satisfied by the classical orthogonal functions...... functions, this is not the case. However, they may be computed in a stable numerical fashion, via the recursion. In essence, this is an application of the well-known Lanczos recursion approach. Once the recursion coefficients are known, it is possible to compute the points and weights of quadratures on...
Prostate multimodality image registration based on B-splines and quadrature local energy.
Mitra, Jhimli; Martí, Robert; Oliver, Arnau; Lladó, Xavier; Ghose, Soumya; Vilanova, Joan C; Meriaudeau, Fabrice
2012-05-01
Needle biopsy of the prostate is guided by Transrectal Ultrasound (TRUS) imaging. The TRUS images do not provide proper spatial localization of malignant tissues due to the poor sensitivity of TRUS to visualize early malignancy. Magnetic Resonance Imaging (MRI) has been shown to be sensitive for the detection of early stage malignancy, and therefore, a novel 2D deformable registration method that overlays pre-biopsy MRI onto TRUS images has been proposed. The registration method involves B-spline deformations with Normalized Mutual Information (NMI) as the similarity measure computed from the texture images obtained from the amplitude responses of the directional quadrature filter pairs. Registration accuracy of the proposed method is evaluated by computing the Dice Similarity coefficient (DSC) and 95% Hausdorff Distance (HD) values for 20 patients prostate mid-gland slices and Target Registration Error (TRE) for 18 patients only where homologous structures are visible in both the TRUS and transformed MR images. The proposed method and B-splines using NMI computed from intensities provide average TRE values of 2.64 ± 1.37 and 4.43 ± 2.77 mm respectively. Our method shows statistically significant improvement in TRE when compared with B-spline using NMI computed from intensities with Student's t test p = 0.02. The proposed method shows 1.18 times improvement over thin-plate splines registration with average TRE of 3.11 ± 2.18 mm. The mean DSC and the mean 95% HD values obtained with the proposed method of B-spline with NMI computed from texture are 0.943 ± 0.039 and 4.75 ± 2.40 mm respectively. The texture energy computed from the quadrature filter pairs provides better registration accuracy for multimodal images than raw intensities. Low TRE values of the proposed registration method add to the feasibility of it being used during TRUS-guided biopsy.
Wunschel, David S; Melville, Angela M; Ehrhardt, Christopher J; Colburn, Heather A; Victry, Kristin D; Antolick, Kathryn C; Wahl, Jon H; Wahl, Karen L
2012-05-07
The investigation of crimes involving chemical or biological agents is infrequent, but presents unique analytical challenges. The protein toxin ricin is encountered more frequently than other agents and is found in the seeds of Ricinus communis, commonly known as the castor plant. Typically, the toxin is extracted from castor seeds utilizing a variety of different recipes that result in varying purity of the toxin. Moreover, these various purification steps can also leave or differentially remove a variety of exogenous and endogenous residual components with the toxin that may indicate the type and number of purification steps involved. We have applied three gas chromatography-mass spectrometry (GC-MS) based analytical methods to measure the variation in seed carbohydrates and castor oil ricinoleic acid, as well as the presence of solvents used for purification. These methods were applied to the same samples prepared using four previously identified toxin preparation methods, starting from four varieties of castor seeds. The individual data sets for seed carbohydrate profiles, ricinoleic acid, or acetone amount each provided information capable of differentiating different types of toxin preparations across seed types. However, the integration of the data sets using multivariate factor analysis provided a clear distinction of all samples based on the preparation method, independent of the seed source. In particular, the abundance of mannose, arabinose, fucose, ricinoleic acid, and acetone were shown to be important differentiating factors. These complementary tools provide a more confident determination of the method of toxin preparation than would be possible using a single analytical method.
Hooked differential mobility spectrometry apparatus and method therefore
Shvartsburg, Alexandre A [Richland, WA; Tang, Keqi [Richland, WA; Ibrahim, Yehia M [Richland, WA; Smith, Richard D [Richland, WA
2009-02-17
Disclosed are a device and method for improved interfacing of differential mobility spectrometry (DMS) or field asymmetric waveform ion mobility spectrometry (FAIMS) analyzers of substantially planar geometry to subsequent or preceding instrument stages. Interfacing is achieved using curved DMS elements, where a thick ion beam emitted by planar DMS analyzers or injected into them for ion filtering is compressed to the gap median by DMS ion focusing effect in a spatially inhomogeneous electric field. Resulting thinner beams are more effectively transmitted through necessarily constrained conductance limit apertures to subsequent instrument stages operated at a pressure lower than DMS, and/or more effectively injected into planar DMS analyzers. The technology is synergetic with slit apertures, slit aperture/ion funnels, and high-pressure ion funnel interfaces known in the art which allow for increasing cross-sectional area of MS inlets. The invention may be used in integrated analytical platforms, including, e.g., DMS/MS, LC/DMS/MS, and DMS/IMS/MS that could replace and/or enhance current LC/MS methods, e.g., for proteomics research.
Design and implementation of quadrature bandpass sigma-delta modulator used in low-IF RF receiver
Ge, Binjie; Li, Yan; Yu, Hang; Feng, Xiaoxing
2018-05-01
This paper presents the design and implementation of quadrature bandpass sigma-delta modulator. A pole movement method for transforming real sigma-delta modulator to a quadrature one is proposed by detailed study of the relationship of noise-shaping center frequency and integrator pole position in sigma-delta modulator. The proposed modulator uses sampling capacitor sharing switched capacitor integrator, and achieves a very small feedback coefficient by a series capacitor network, and those two techniques can dramatically reduce capacitor area. Quantizer output-dependent dummy capacitor load for reference voltage buffer can compensate signal-dependent noise that is caused by load variation. This paper designs a quadrature bandpass Sigma-Delta modulator for 2.4 GHz low IF receivers that achieve 69 dB SNDR at 1 MHz BW and -1 MHz IF with 48 MHz clock. The chip is fabricated with SMIC 0.18 μm CMOS technology, it achieves a total power current of 2.1 mA, and the chip area is 0.48 mm2. Project supported by the National Natural Science Foundation of China (Nos. 61471245, U1201256), the Guangdong Province Foundation (No. 2014B090901031), and the Shenzhen Foundation (Nos. JCYJ20160308095019383, JSGG20150529160945187).
CDBA-Based Universal Biquad Filter and Quadrature Oscillator
Directory of Open Access Journals (Sweden)
Worapong Tangsrirat
2008-01-01
Full Text Available The voltage-mode universal biquadratic filter and sinusoidal quadrature oscillator based on the use of current differencing buffered amplifiers (CDBAs as active components have been proposed in this paper. All the proposed configurations employ only two CDBAs and six passive components. The first proposed CDBA-based biquad configuration can realize all the standard types of the biquadratic functions, that is, lowpass, bandpass, highpass, bandstop, and allpass, from the same topology, and can also provide orthogonal tuning of the natural angular frequency (ωo and the bandwidth (BW through separate virtually grounded passive components. By slight modification of the first proposed configuration, the new CDBA-based sinusoidal quadrature oscillator is easily obtained. The oscillation condition and the oscillation frequency are independently adjustable by different virtually grounded resistors. The sensitivity analysis of all proposed circuit configurations is shown to be low. PSPICE simulations and experimental results based upon commercially available AD844-type CFAs are included, which confirm the workability of the proposed circuits.
Benhammouda, Brahim; Vazquez-Leal, Hector
2016-01-01
This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.
Differential methods of localisation of fungal endophytes in the seagrasses
Directory of Open Access Journals (Sweden)
S. Raja
2016-07-01
Full Text Available Sections of three seagrass species (Halophila ovalis, Cymodocea serrulata and Halodule pinifolia were assessed for endophytes based on differential staining using light and fluorescence microscopy method. Acridine orange and aniline blue detected endophytic fungi in 20% and 10% of the segments, respectively, whereas lactophenol cotton blue was more sensitive to detect the fungal hyphae in 70% of the segments. Hyphae were the principal fungal structures generally observed under the cuticle, within the epidermal cells, mesophyll (Parenchyma cells and occasionally within the vascular tissue that varied in type, size and location within the leaf tissue. Present study also recorded the sporulation for the first time from the seagrass endophytes. Successfully amplified products of the ITS region of endophytic fungal DNA, directly from seagrass tissue and also from culture-dependent fungal DNA clearly depicted the presence of endophytic fungi in H. ovalis with two banding patterns (903 and 1381 bp confirming the presence of two dominant fungal genera. The fingerprinting of endophytic fungal community within the seagrass tissue was assessed using denaturing gradient gel electrophoresis (DGGE that derived with multiple bands that clarified the presence of more than one taxon within the seagrass tissue.
Novel IQ imbalance and offset compensation techniques for quadrature mixing radio transceivers
CSIR Research Space (South Africa)
De Witt, JJ
2006-09-01
Full Text Available Despite the advantages that quadrature mixing offers to radio front-ends, its practical use has been limited due to its sensitivity towards gain and phase mismatches between its in-phase and quadrature channels. DC offsets are also a problem when a...
An Improved Second-Order Generalized Integrator Based Quadrature Signal Generator
DEFF Research Database (Denmark)
Xin, Zhen; Wang, Xiongfei; Qin, Zian
2016-01-01
The second-order generalized integrator based quadrature signal generator (SOGI-QSG) is able to produce in-quadrature signals for many applications, such as frequency estimation, grid synchronization, and harmonic extraction. However, the SOGI-QSG is sensitive to input dc and harmonic components...
Design of a quadrature surface coil for hyperpolarized 13C MRS cardiac metabolism studies in pigs
DEFF Research Database (Denmark)
Giovannetti, G.; Frijia, F.; Hartwig, V.
2013-01-01
, the performance of the quadrature coil was compared with the single TX/RX circular and TX/RX butterfly coil, in order to verify the advantage of the proposed configuration over the single coils throughout the volume of interest for cardiac imaging in pig. Finally, the quadrature surface coil was tested...
Digitally generated excitation and near-baseband quadrature detection of rapid scan EPR signals.
Tseitlin, Mark; Yu, Zhelin; Quine, Richard W; Rinard, George A; Eaton, Sandra S; Eaton, Gareth R
2014-12-01
The use of multiple synchronized outputs from an arbitrary waveform generator (AWG) provides the opportunity to perform EPR experiments differently than by conventional EPR. We report a method for reconstructing the quadrature EPR spectrum from periodic signals that are generated with sinusoidal magnetic field modulation such as continuous wave (CW), multiharmonic, or rapid scan experiments. The signal is down-converted to an intermediate frequency (IF) that is less than the field scan or field modulation frequency and then digitized in a single channel. This method permits use of a high-pass analog filter before digitization to remove the strong non-EPR signal at the IF, that might otherwise overwhelm the digitizer. The IF is the difference between two synchronized X-band outputs from a Tektronix AWG 70002A, one of which is for excitation and the other is the reference for down-conversion. To permit signal averaging, timing was selected to give an exact integer number of full cycles for each frequency. In the experiments reported here the IF was 5kHz and the scan frequency was 40kHz. To produce sinusoidal rapid scans with a scan frequency eight times IF, a third synchronized output generated a square wave that was converted to a sine wave. The timing of the data acquisition with a Bruker SpecJet II was synchronized by an external clock signal from the AWG. The baseband quadrature signal in the frequency domain was reconstructed. This approach has the advantages that (i) the non-EPR response at the carrier frequency is eliminated, (ii) both real and imaginary EPR signals are reconstructed from a single physical channel to produce an ideal quadrature signal, and (iii) signal bandwidth does not increase relative to baseband detection. Spectra were obtained by deconvolution of the reconstructed signals for solid BDPA (1,3-bisdiphenylene-2-phenylallyl) in air, 0.2mM trityl OX63 in water, 15 N perdeuterated tempone, and a nitroxide with a 0.5G partially-resolved proton
Barton, Michael; Calo, Victor M.
2016-01-01
We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature rules we recently derived
Application of differential transformation method for solving dengue transmission mathematical model
Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.
2018-03-01
The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.
Directory of Open Access Journals (Sweden)
Shaheed N. Huseen
2013-01-01
Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.
Method for HEPA filter leak scanning with differentiating aerosol detector
Energy Technology Data Exchange (ETDEWEB)
Kovach, B.J.; Banks, E.M.; Wikoff, W.O. [NUCON International, Inc., Columbus, OH (United States)
1997-08-01
While scanning HEPA filters for leaks with {open_quotes}Off the Shelf{close_quote} aerosol detection equipment, the operator`s scanning speed is limited by the time constant and threshold sensitivity of the detector. This is based on detection of the aerosol density, where the maximum signal is achieved when the scanning probe resides over the pinhole longer than several detector time-constants. Since the differential value of the changing signal can be determined by observing only the first small fraction of the rising signal, using a differentiating amplifier will speed up the locating process. The other advantage of differentiation is that slow signal drift or zero offset will not interfere with the process of locating the leak, since they are not detected. A scanning hand-probe attachable to any NUCON{reg_sign} Aerosol Detector displaying the combination of both aerosol density and differentiated signal was designed. 3 refs., 1 fig.
Quadrature entanglement and photon-number correlations accompanied by phase-locking
International Nuclear Information System (INIS)
Adamyan, H. H.; Manvelyan, S. B.; Adamyan, N. H.; Kryuchkyan, G. Yu.
2006-01-01
We investigate quantum properties of phase-locked light beams generated in a nondegenerate optical parametric oscillator (NOPO) with an intracavity waveplate. This investigation continues our previous analysis presented in Phys. Rev. A 69, 053814 (2004), and involves problems of continuous-variable quadrature entanglement in the spectral domain, photon-number correlations as well as the signatures of phase-locking in the Wigner function. We study the role of phase-localizing processes on the quantum correlation effects. The peculiarities of phase-locked NOPO in the self-pulsing instability operational regime are also cleared up. The results are obtained in the P-representation as a quantum-mechanical calculation in the framework of stochastic equations of motion, as well as by numerical simulation based on the method of quantum state diffusion
Quadrature Slotted Surface Coil Pair for Magnetic Resonance Imaging at 4 Tesla: Phantom Study
Directory of Open Access Journals (Sweden)
Solis S.E.
2012-01-01
Full Text Available A coil array was composed of two slotted surface coils forming a structure with two plates at 900, each one having 6 circular slots and is introduced in this paper. Numerical simulations of the magnetic field of this coil array were performed at 170 MHz using the finite element method to study its behaviour. This coil array was developed for brain magnetic resonance imaging to be operated at the resonant frequency of 170 MHz in the transceiver mode and quadrature driven. Numerical simulations demonstrated that electromagnetic interaction between the coil elements is negligible, and that the magnetic field showed a good uniformity. Phantom images were acquired with our coil array and standard pulse sequences on a research-dedicated 4 Tesla scanner. In vitro images showed the feasibility of this coil array for standard pulses and high field magnetic resonance imaging.
Orthogonal functions, discrete variable representation, and generalized gauss quadratures
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2002-01-01
in the original representation. This has been exploited in bound-state, scattering, and time-dependent problems using the so-called, discrete variable representation (DVR). At the core of this approach is the mathematical three-term recursion relationship satisfied by the classical orthogonal functions......, the distinction between spectral and grid approaches becomes blurred. In fact, the two approaches can be related by a similarity transformation. By the exploitation of this idea, calculations can be considerably simplified by removing the need to compute difficult matrix elements of the Hamiltonian...... functions, this is not the case. However, they may be computed in a stable numerical fashion, via the recursion. In essence, this is an application of the well-known Lanczos recursion approach. Once the recursion coefficients are known, it is possible to compute the points and weights of quadratures on...
The application of He's exp-function method to a nonlinear differential-difference equation
International Nuclear Information System (INIS)
Dai Chaoqing; Cen Xu; Wu Shengsheng
2009-01-01
This paper applies He's exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear partial differential equations (NPDEs) or coupled nonlinear partial differential equations (CNPDEs), to a nonlinear differential-difference equation, and some new travelling wave solutions are obtained.
Chen, Ming; Lin, Yong-Qing; Xie, Shuang-Lun; Wu, Hong-Fu; Wang, Jing-Feng
2011-04-01
Hanging drop (HD) culture is used to induce differentiation of embryonic stem cells (ESCs) into other cell types including cardiomyocytes. However, the factors affecting cardiac differentiation of ESCs with this method remain incompletely understood. We have investigated the effects of the starting number of ESCs in embryoid bodies (EBs) and the time of EB adherence to gelatin-coated plates on cardiac differentiation: cardiac differentiation was increased in the EBs by a larger number of ESCs and was decreased by plating EBs at day 4 or earlier. These two factors can thus be optimized to enrich the cardiac differentiation in ESCs using the HD method.
Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).
Murase, Kenya
2016-01-01
In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.
Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method
Directory of Open Access Journals (Sweden)
Hassan A. Zedan
2012-01-01
Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.
Application of Monte Carlo method to solving boundary value problem of differential equations
International Nuclear Information System (INIS)
Zuo Yinghong; Wang Jianguo
2012-01-01
This paper introduces the foundation of the Monte Carlo method and the way how to generate the random numbers. Based on the basic thought of the Monte Carlo method and finite differential method, the stochastic model for solving the boundary value problem of differential equations is built. To investigate the application of the Monte Carlo method to solving the boundary value problem of differential equations, the model is used to solve Laplace's equations with the first boundary condition and the unsteady heat transfer equation with initial values and boundary conditions. The results show that the boundary value problem of differential equations can be effectively solved with the Monte Carlo method, and the differential equations with initial condition can also be calculated by using a stochastic probability model which is based on the time-domain finite differential equations. Both the simulation results and theoretical analyses show that the errors of numerical results are lowered as the number of simulation particles is increased. (authors)
Gaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines
Barton, Michael
2015-10-24
We introduce a new concept for generating optimal quadrature rules for splines. To generate an optimal quadrature rule in a given (target) spline space, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, while preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by changing the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C1C1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C2C2 cubic spline spaces where the rule was only conjectured to date. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.
Gaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines
Barton, Michael; Calo, Victor M.
2015-01-01
We introduce a new concept for generating optimal quadrature rules for splines. To generate an optimal quadrature rule in a given (target) spline space, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, while preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by changing the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C1C1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C2C2 cubic spline spaces where the rule was only conjectured to date. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.
Differential evolution based method for total transfer capability ...
African Journals Online (AJOL)
The application of Differential Evolution (DE) to compute the Total Transfer Capability (TTC) in deregulated market is proposed in this paper. The objective is to maximize a specific point-to-point power transaction without violating system constraints using DE. This algorithm is based on full ac optimal power flow solution to ...
Matrix form of Legendre polynomials for solving linear integro-differential equations of high order
Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.
2017-04-01
This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.
Stochastic fractional differential equations: Modeling, method and analysis
International Nuclear Information System (INIS)
Pedjeu, Jean-C.; Ladde, Gangaram S.
2012-01-01
By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.
Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Ahmet Bekir
2013-01-01
Full Text Available The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.
Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method
International Nuclear Information System (INIS)
Bekir Ahmet; Güner Özkan
2013-01-01
In this paper, we use the fractional complex transform and the (G′/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann—Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations
Partial differential equations with variable exponents variational methods and qualitative analysis
Radulescu, Vicentiu D
2015-01-01
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive meth
Advanced methods for the solution of differential equations
Goldstein, M. E.; Braun, W. H.
1973-01-01
This book is based on a course presented at the Lewis Research Center for engineers and scientists who were interested in increasing their knowledge of differential equations. Those results which can actually be used to solve equations are therefore emphasized; and detailed proofs of theorems are, for the most part, omitted. However, the conclusions of the theorems are stated in a precise manner, and enough references are given so that the interested reader can find the steps of the proofs.
A Novel Method to Identify Differential Pathways in Hippocampus Alzheimer's Disease.
Liu, Chun-Han; Liu, Lian
2017-05-08
BACKGROUND Alzheimer's disease (AD) is the most common type of dementia. The objective of this paper is to propose a novel method to identify differential pathways in hippocampus AD. MATERIAL AND METHODS We proposed a combined method by merging existed methods. Firstly, pathways were identified by four known methods (DAVID, the neaGUI package, the pathway-based co-expressed method, and the pathway network approach), and differential pathways were evaluated through setting weight thresholds. Subsequently, we combined all pathways by a rank-based algorithm and called the method the combined method. Finally, common differential pathways across two or more of five methods were selected. RESULTS Pathways obtained from different methods were also different. The combined method obtained 1639 pathways and 596 differential pathways, which included all pathways gained from the four existing methods; hence, the novel method solved the problem of inconsistent results. Besides, a total of 13 common pathways were identified, such as metabolism, immune system, and cell cycle. CONCLUSIONS We have proposed a novel method by combining four existing methods based on a rank product algorithm, and identified 13 significant differential pathways based on it. These differential pathways might provide insight into treatment and diagnosis of hippocampus AD.
Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Verner Method
Directory of Open Access Journals (Sweden)
T. Jayakumar
2015-01-01
Full Text Available In this paper we study the numerical methods for Fuzzy Differential equations by an application of the Runge-Kutta Verner method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.
International Nuclear Information System (INIS)
Zhang Huiqun
2009-01-01
By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.
International Nuclear Information System (INIS)
Qin Maochang; Fan Guihong
2008-01-01
There are many interesting methods can be utilized to construct special solutions of nonlinear differential equations with constant coefficients. However, most of these methods are not applicable to nonlinear differential equations with variable coefficients. A new method is presented in this Letter, which can be used to find special solutions of nonlinear differential equations with variable coefficients. This method is based on seeking appropriate Bernoulli equation corresponding to the equation studied. Many well-known equations are chosen to illustrate the application of this method
International Nuclear Information System (INIS)
Sanchez G, J.
2015-09-01
The solution of the so-called Canonical problems of neutron transport theory has been given by Case, who developed a method akin to the classical eigenfunction expansion procedure, extended to admit singular eigenfunctions. The solution is given as a set consisting of a Fredholm integral equation coupled with a transcendental equation, which has to be solved for the expansion coefficients by iteration. CASE's method make extensive use of the results of the theory of functions of a complex variable and many successful approaches to solve in an approximate form the above mentioned set have been reported in the literature. We present here an entirely different approach which deals with the canonical problems in a more direct and elementary manner. As far as we know, the original idea for the latter method is due to Carlvik who devised the escape probability approximation to the solution of the neutron transport equation in its integral form. In essence, the procedure consists in assuming a sectionally constant form of the neutron density that in turn yields a set of linear algebraic equations obeyed by the assumed constant values of the density. Very well established techniques of numerical analysis for the solution of integral equations consist in independent approaches that generalize the sectionally constant approach by assuming a sectionally low degree polynomial for the unknown function. This procedure also known as the arbitrary quadratures method is especially suited to deal with cases where the kernel of the integral equation is singular. The author wishes to present the results obtained with the arbitrary quadratures method for the numerical calculation of the monoenergetic neutron density in a critical, homogeneous sphere of finite radius with isotropic scattering. The singular integral equation obeyed by the neutron density in the critical sphere is introduced, an outline of the method's main features is given, and tables and graphs of the density
Energy Technology Data Exchange (ETDEWEB)
Sanchez G, J., E-mail: julian.sanchez@inin.gob.mx [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico)
2015-09-15
The solution of the so-called Canonical problems of neutron transport theory has been given by Case, who developed a method akin to the classical eigenfunction expansion procedure, extended to admit singular eigenfunctions. The solution is given as a set consisting of a Fredholm integral equation coupled with a transcendental equation, which has to be solved for the expansion coefficients by iteration. CASE's method make extensive use of the results of the theory of functions of a complex variable and many successful approaches to solve in an approximate form the above mentioned set have been reported in the literature. We present here an entirely different approach which deals with the canonical problems in a more direct and elementary manner. As far as we know, the original idea for the latter method is due to Carlvik who devised the escape probability approximation to the solution of the neutron transport equation in its integral form. In essence, the procedure consists in assuming a sectionally constant form of the neutron density that in turn yields a set of linear algebraic equations obeyed by the assumed constant values of the density. Very well established techniques of numerical analysis for the solution of integral equations consist in independent approaches that generalize the sectionally constant approach by assuming a sectionally low degree polynomial for the unknown function. This procedure also known as the arbitrary quadratures method is especially suited to deal with cases where the kernel of the integral equation is singular. The author wishes to present the results obtained with the arbitrary quadratures method for the numerical calculation of the monoenergetic neutron density in a critical, homogeneous sphere of finite radius with isotropic scattering. The singular integral equation obeyed by the neutron density in the critical sphere is introduced, an outline of the method's main features is given, and tables and graphs of the density
Pyroelectric effect in tryglicyne sulphate single crystals - Differential measurement method
Trybus, M.
2018-06-01
A simple mathematical model of the pyroelectric phenomenon was used to explain the electric response of the TGS (triglycine sulphate) samples in the linear heating process in ferroelectric and paraelectric phases. Experimental verification of mathematical model was realized. TGS single crystals were grown and four electrode samples were fabricated. Differential measurements of the pyroelectric response of two different regions of the samples were performed and the results were compared with data obtained from the model. Experimental results are in good agreement with model calculations.
DEFF Research Database (Denmark)
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....
Modulator-free quadrature amplitude modulation signal synthesis
Liu, Zhixin; Kakande, Joseph; Kelly, Brian; O'Carroll, John; Phelan, Richard; Richardson, David J.; Slavík, Radan
2014-12-01
The ability to generate high-speed on-off-keyed telecommunication signals by directly modulating a semiconductor laser’s drive current was one of the most exciting prospective applications of the nascent field of laser technology throughout the 1960s. Three decades of progress led to the commercialization of 2.5 Gbit s-1-per-channel submarine fibre optic systems that drove the growth of the internet as a global phenomenon. However, the detrimental frequency chirp associated with direct modulation forced industry to use external electro-optic modulators to deliver the next generation of on-off-keyed 10 Gbit s-1 systems and is absolutely prohibitive for today’s (>)100 Gbit s-1 coherent systems, which use complex modulation formats (for example, quadrature amplitude modulation). Here we use optical injection locking of directly modulated semiconductor lasers to generate complex modulation format signals showing distinct advantages over current and other currently researched solutions.
Non-asymptotic fractional order differentiators via an algebraic parametric method
Liu, Dayan
2012-08-01
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.
Non-asymptotic fractional order differentiators via an algebraic parametric method
Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid
2012-01-01
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.
Numerical methods for the solution of ordinary differential equations
International Nuclear Information System (INIS)
Azeem, M.
1999-01-01
The ode 113 code solves non-stiff differential equations and is a fully variable step, variable order, PECE implementation in terms of modified divided differences of Adams-Bashforth-Moulton family of formulas of order 1-12. The main objectives of this project were to modify PECE mode of ode 113 into PEC mode, study the variable step size and variable order strategy of both the modes and finally, develop the switching strategy between both PECE and PEC modes to minimize the cost of solving the ordinary differential equations. Using some test problems (including stiff, mild stiff and non-stiff), it was found that the PEC mode was more efficient for non-stiff problems at crude and intermediate tolerances and the PECE mode for all problems at the stringent tolerance. An automatic switching strategy was developed using the results observed from the step size and order plots of all the test problems for both the modes and gave the optimum results. (author)
Directory of Open Access Journals (Sweden)
M. A.P. PURCARU
2017-12-01
Full Text Available This paper aims at highlighting some aspects related to assessment as regards its use as a differentiated training strategy for Linear Algebra and Analytic and Differential Geometry courses and seminars. Thus, the following methods of continuous differentiated assessment are analyzed and exemplified: the portfolio, the role play, some interactive methods and practical examinations.
Validation of MIMGO: a method to identify differentially expressed GO terms in a microarray dataset
Yamada, Yoichi; Sawada, Hiroki; Hirotani, Ken-ichi; Oshima, Masanobu; Satou, Kenji
2012-01-01
Abstract Background We previously proposed an algorithm for the identification of GO terms that commonly annotate genes whose expression is upregulated or downregulated in some microarray data compared with in other microarray data. We call these “differentially expressed GO terms” and have named the algorithm “matrix-assisted identification method of differentially expressed GO terms” (MIMGO). MIMGO can also identify microarray data in which genes annotated with a differentially expressed GO...
Directory of Open Access Journals (Sweden)
Mohammad Javad Kharazi Fard
2012-02-01
Full Text Available Background: An enchondroma is a benign and a well-differentiated chondrosarcoma is an invasive chondroid tumor with high recurrence potential. In spite of biologic differences, these two tumors have very similar histopathologic appearance. It has been shown that the biologic nature of the connective tissue around benign and malignant tumors varies in the number of mast cells. The aim of this study was to study the histopathologic distinction of enchondroma and well-differentiated chondrosarcoma using the density of the mast cells in fibrotic capsule. Methods: Twelve enchondroma and 15 well-differentiated chondrosarcoma were collected from Pathology department of Cancer Institute and Central Pathology department of Imam Khomeini Hospital in Tehran. 3 micron paraffin embedded tissue sections were stained by toluidine blue for mast cells counting. Mast cells were counted in fibrous capsule of all cases. Mast cells counts were accomplished in 10 high power fields .The average number of mast cells in 10HPF was determined as an index for each lesion. Mann-Whitney U test was used for statistical analysis. Results: Mean index in enchondroma and well-differentiated chondrosarcoma groups were 0.1±0.12 and 0.31±0.33 respectively, showing a significant difference between number of mast cells in the fibrotic capsule in these two lesions (p=0.028. Comparison of the corresponding points in ROC curve, showed a cut-off point = 0.15, with positive predictive value of 61%, negative predictive value 71%, specificity of 33.3% and sensitivity of 66.7%, (p=0.025. Conclusion: Average density of the mast cells in the surrounding fibrotic capsules of enchondroma and well-differentiated chondrosarcoma along with other criterions, could be a beneficial factor for histologically differentiation between these two lesions.
Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method
International Nuclear Information System (INIS)
Lewandowski, Jerome L.V.
2005-01-01
A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details
Lagrange-Noether method for solving second-order differential equations
Institute of Scientific and Technical Information of China (English)
Wu Hui-Bin; Wu Run-Heng
2009-01-01
The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.
An Algebraic Method for Constructing Exact Solutions to Difference-Differential Equations
International Nuclear Information System (INIS)
Wang Zhen; Zhang Hongqing
2006-01-01
In this paper, we present a method to solve difference differential equation(s). As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions are obtained with the help of Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equation(s).
Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen
2015-01-01
In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential- difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit. PMID:25874457
Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen
2015-01-01
In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit.
A Simple Method to Find out when an Ordinary Differential Equation Is Separable
Cid, Jose Angel
2009-01-01
We present an alternative method to that of Scott (D. Scott, "When is an ordinary differential equation separable?", "Amer. Math. Monthly" 92 (1985), pp. 422-423) to teach the students how to discover whether a differential equation y[prime] = f(x,y) is separable or not when the nonlinearity f(x, y) is not explicitly factorized. Our approach is…
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…
International Nuclear Information System (INIS)
Borges, Antonio Andrade
1998-01-01
A new method for the calculation of sensitivity coefficients is developed. The new method is a combination of two methodologies used for calculating theses coefficients, which are the differential and the generalized perturbation theory methods. The method utilizes as integral parameter the average flux in an arbitrary region of the system. Thus, the sensitivity coefficient contains only the component corresponding to the neutron flux. To obtain the new sensitivity coefficient, the derivatives of the integral parameter, Φ, with respect to σ are calculated using the perturbation method and the functional derivatives of this generic integral parameter with respect to σ and Φ are calculated using the differential method. (author)
Final Report: Symposium on Adaptive Methods for Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Pernice, Michael; Johnson, Christopher R.; Smith, Philip J.; Fogelson, Aaron
1998-12-08
Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.
Modified Reduced Differential Transform Method for Partial Differential-Algebraic Equations
Directory of Open Access Journals (Sweden)
Brahim Benhammouda
2014-01-01
PDAEs in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful technique to find exact solutions. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend on a perturbation parameter.
International Nuclear Information System (INIS)
Santos, Adimir dos; Borges, A.A.
2000-01-01
A new method for the calculation of sensitivity coefficients is developed. The new method is a combination of two methodologies used for calculating these coefficients, which are the differential and the generalized perturbation theory methods. The proposed method utilizes as integral parameter the average flux in an arbitrary region of the system. Thus, the sensitivity coefficient contains only the component corresponding to the neutron flux. To obtain the new sensitivity coefficient, the derivates of the integral parameter, φ(ξ), with respect to σ are calculated using the perturbation method and the functional derivates of this generic integral parameter with respect to σ and φ are calculated using the differential method. The new method merges the advantages of the differential and generalized perturbation theory methods and eliminates their disadvantages. (author)
Link-based quantitative methods to identify differentially coexpressed genes and gene Pairs
Directory of Open Access Journals (Sweden)
Ye Zhi-Qiang
2011-08-01
Full Text Available Abstract Background Differential coexpression analysis (DCEA is increasingly used for investigating the global transcriptional mechanisms underlying phenotypic changes. Current DCEA methods mostly adopt a gene connectivity-based strategy to estimate differential coexpression, which is characterized by comparing the numbers of gene neighbors in different coexpression networks. Although it simplifies the calculation, this strategy mixes up the identities of different coexpression neighbors of a gene, and fails to differentiate significant differential coexpression changes from those trivial ones. Especially, the correlation-reversal is easily missed although it probably indicates remarkable biological significance. Results We developed two link-based quantitative methods, DCp and DCe, to identify differentially coexpressed genes and gene pairs (links. Bearing the uniqueness of exploiting the quantitative coexpression change of each gene pair in the coexpression networks, both methods proved to be superior to currently popular methods in simulation studies. Re-mining of a publicly available type 2 diabetes (T2D expression dataset from the perspective of differential coexpression analysis led to additional discoveries than those from differential expression analysis. Conclusions This work pointed out the critical weakness of current popular DCEA methods, and proposed two link-based DCEA algorithms that will make contribution to the development of DCEA and help extend it to a broader spectrum.
Fast Numerical Methods for Stochastic Partial Differential Equations
2016-04-15
Particle Swarm Optimization (PSO) method. Inspired by the social behavior of the bird flocking or fish schooling, the particle swarm optimization (PSO...Weerasinghe, Hongmei Chi and Yanzhao Cao, Particle Swarm Optimization Simulation via Optimal Halton Sequences, accepted by Procedia Computer Science (2016...Optimization Simulation via Optimal Halton Sequences, accepted by Procedia Computer Science (2016). 2. Haiyan Tian, Hongmei Chi and Yanzhao Cao
The Embedding Method for Linear Partial Differential Equations
Indian Academy of Sciences (India)
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 ...
Analytic method for solitary solutions of some partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya@firat.edu.tr
2007-10-22
In this Letter by considering an improved tanh function method, we found some exact solutions of the clannish random walker's parabolic equation, the modified Korteweg-de Vries (KdV) equation, and the Sharma-Tasso-Olver (STO) equation with its fission and fusion, the Jaulent-Miodek equation.
Analytic method for solitary solutions of some partial differential equations
International Nuclear Information System (INIS)
Ugurlu, Yavuz; Kaya, Dogan
2007-01-01
In this Letter by considering an improved tanh function method, we found some exact solutions of the clannish random walker's parabolic equation, the modified Korteweg-de Vries (KdV) equation, and the Sharma-Tasso-Olver (STO) equation with its fission and fusion, the Jaulent-Miodek equation
Validation of MIMGO: a method to identify differentially expressed GO terms in a microarray dataset
Directory of Open Access Journals (Sweden)
Yamada Yoichi
2012-12-01
Full Text Available Abstract Background We previously proposed an algorithm for the identification of GO terms that commonly annotate genes whose expression is upregulated or downregulated in some microarray data compared with in other microarray data. We call these “differentially expressed GO terms” and have named the algorithm “matrix-assisted identification method of differentially expressed GO terms” (MIMGO. MIMGO can also identify microarray data in which genes annotated with a differentially expressed GO term are upregulated or downregulated. However, MIMGO has not yet been validated on a real microarray dataset using all available GO terms. Findings We combined Gene Set Enrichment Analysis (GSEA with MIMGO to identify differentially expressed GO terms in a yeast cell cycle microarray dataset. GSEA followed by MIMGO (GSEA + MIMGO correctly identified (p Conclusions MIMGO is a reliable method to identify differentially expressed GO terms comprehensively.
Method for solving the periodic problem for integro-differential equations
Directory of Open Access Journals (Sweden)
Snezhana G. Hristova
1989-05-01
Full Text Available In the paper a monotone-iterative method for approximate finding a couple of minimal and maximal quasisolutions of the periodic problem for a system of integro-differential equations of Volterra type is justified.
Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations
Institute of Scientific and Technical Information of China (English)
2007-01-01
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
The generalized tanh method to obtain exact solutions of nonlinear partial differential equation
Gómez, César
2007-01-01
In this paper, we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations, and we obtain solitons and exact solutions of some important equations of the mathematical physics.
Wavelet Methods for Solving Fractional Order Differential Equations
A. K. Gupta; S. Saha Ray
2014-01-01
Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linea...
Alam Khan, Najeeb; Razzaq, Oyoon Abdul
2016-03-01
In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.
A Novel Method for Analytical Solutions of Fractional Partial Differential Equations
Mehmet Ali Akinlar; Muhammet Kurulay
2013-01-01
A new solution technique for analytical solutions of fractional partial differential equations (FPDEs) is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as...
Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation
Choe, Hui-Chol; Kang, Yong-Suk
2013-01-01
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial conditions and boundary conditions to nonlinear fractional integral equations and consider the relations between them. We present a Spline Collocation Method and prove the existence, uniqueness and convergence of approximate solution as well as error estimatio...
Direct and quadrature inductances measurement of the permanent magnetic linear synchronous machines
Energy Technology Data Exchange (ETDEWEB)
Li Liyi [Electrical Engineering Dept./Harbin Institute of Technology, Harbin 150000 (China); Hong Junjie, E-mail: wizard0663@126.co [School of Engineering/Sun Yat-Sen University, Guangzhou 510006 (China); Wu Hongxing; Kou Baoquan; Liu Rizhong [Electrical Engineering Dept./Harbin Institute of Technology, Harbin 150000 (China)
2011-05-15
Research highlights: {yields} The d- and q-axis inductances are derived theoretically. {yields} The new measurement principle of the d- and q-axis inductances is analyzed. {yields} A corresponding measuring circuit is developed. {yields} Measurement results match those of the FEM well. -- Abstract: Permanent magnetic linear synchronous machines (PMLSMs) are playing a more important role either in transportation systems or magnetic launch systems, for the excellent advantages. It is indispensable to high performance controllers that some machine parameters are known such as the direct axis (d-axis) and quadrature axis (q-axis) inductances. In this paper, self and mutual inductances of the three-phase winding are deduced by basic electric machinery theory, and the measured inductances are analyzed since the mutual inductances and the corresponding terminals among three-phase windings are changing as different phase winding is concerned. The d- and q-axis inductances are measured with the designed circuit, and the experimental measurement method is validated by the comparison between the experimental and finite element method (FEM) results.
Direct and quadrature inductances measurement of the permanent magnetic linear synchronous machines
International Nuclear Information System (INIS)
Li Liyi; Hong Junjie; Wu Hongxing; Kou Baoquan; Liu Rizhong
2011-01-01
Research highlights: → The d- and q-axis inductances are derived theoretically. → The new measurement principle of the d- and q-axis inductances is analyzed. → A corresponding measuring circuit is developed. → Measurement results match those of the FEM well. -- Abstract: Permanent magnetic linear synchronous machines (PMLSMs) are playing a more important role either in transportation systems or magnetic launch systems, for the excellent advantages. It is indispensable to high performance controllers that some machine parameters are known such as the direct axis (d-axis) and quadrature axis (q-axis) inductances. In this paper, self and mutual inductances of the three-phase winding are deduced by basic electric machinery theory, and the measured inductances are analyzed since the mutual inductances and the corresponding terminals among three-phase windings are changing as different phase winding is concerned. The d- and q-axis inductances are measured with the designed circuit, and the experimental measurement method is validated by the comparison between the experimental and finite element method (FEM) results.
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
Abdulle, Assyr
2013-01-01
We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.
International Nuclear Information System (INIS)
Zhi Hongyan
2009-01-01
In this paper, based on the symbolic computing system Maple, the direct method for Lie symmetry groups presented by Sen-Yue Lou [J. Phys. A: Math. Gen. 38 (2005) L129] is extended from the continuous differential equations to the differential-difference equations. With the extended method, we study the well-known differential-difference KP equation, KZ equation and (2+1)-dimensional ANNV system, and both the Lie point symmetry groups and the non-Lie symmetry groups are obtained.
International Nuclear Information System (INIS)
Feng Qinghua
2013-01-01
In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann—Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established. (general)
A Novel Method for Analytical Solutions of Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
Mehmet Ali Akinlar
2013-01-01
Full Text Available A new solution technique for analytical solutions of fractional partial differential equations (FPDEs is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as well as a more general fractional differential equation.
Pulsed Traveling-wave Quadrature Squeezing Using Quasi-phase Matched Lithium Niobate Crystals
Chen, Chao-Hsiang
Interests in generating higher quantum noise squeezing in order to develop methods to enhance optical measurement below the shot-noise limit in various applications has grown in recent years. The noise suppression from squeezing can improve the SNR in coherent optical systems when the returning signal power is weak, such as optical coherence tomography, LADAR, confocal microscopy and low-light coherent imaging. Unlike the generation of squeezing with a continuous wave, which is currently developed mainly for gravitational wave detection in LIGO project, the study of pulsed-traveling waves is focused on industrial, medical and other commercial interests. This dissertation presents the experimental results of pulsed traveling wave squeezing. The intention of the study is to explore the possibility of using quasi-phase matched crystals to generate the highest possible degree of quadrature squeezing. In order to achieve this goal, efforts to test the various effects from spatial Gaussian modes and relative beam waist placement for the second-harmonic pump were carried out in order to further the understanding of limiting factors to pulsed traveling wave squeezing. 20mm and 30mm-long periodically poled lithium noibate (PPLN) crystals were used in the experiment to generate a squeezed vacuum state. A maximum of 4.2+/-0.2dB quadrature squeezing has been observed, and the measured anti-squeezing exceeds 20dB.The phase sensitive amplification (PSA) gain and de-gain performance were also measured to compare the results of measured squeezing. The PPLN crystals can produce high conversion efficiency of second-harmonic generation (SHG) without a cavity. When a long PPLN crystal is used in a squeezer, the beam propagation in the nonlinear medium does not follow the characteristics in thin crystals. Instead, it is operated under the long-crystal criteria, which the crystal length is multiple times longer than the Rayleigh range of the injected beam i n the crystals. Quasi
Directory of Open Access Journals (Sweden)
Rahma Sadat
2018-03-01
Full Text Available In this work, we prove that the integrating factors can be used as a reduction method. Analytical solutions of the Jaulent–Miodek (JM equation are obtained using integrating factors as an extension of a recent work where, through hidden symmetries, the JM was reduced to ordinary differential equations (ODEs. Some of these ODEs had no quadrature. We here derive several new solutions for these non-solvable ODEs.
National Research Council Canada - National Science Library
Stoffell, Kevin M
2006-01-01
.... Performance and device utilization results between the Quadrature Mirror Filter Bank implemented in VHDL, design elements implemented in the C programming language, and calculations made using high...
Safety, dose optimisation and security: the quadrature of the circle
Energy Technology Data Exchange (ETDEWEB)
Hardeman, Frank; Vermeersch, Fernand [Belgian Nuclear Research Centre (SCK.CEN), Boeretang 200, BE-2400 Mol (Belgium)
2010-07-01
The growing concern for potential terrorist acts has lead to a number of new ideas about storing radiological and nuclear materials that are not always compatible with existing practices or infrastructures. This is valid in routine circumstances, but especially poses problems in case of accidents. As such, the management of nuclear safety, radiological protection and security within an evolving world such as a nuclear research centre sometimes looks like implementing the quadrature of the circle. International guidance exists, but is not always easily converted into an adequate policy comprehensible to all levels in a plant, from management to the work floor. Some examples. 1. infrastructure related problems: from a security point of view, fuels are better stored in the heart of a protected zone, while in case of criticality, fire... a more peripheral location is appropriate. 2. Safety related problems: Protection infrastructure may lead to difficulties of evacuation in case of emergencies; access limitations may be a burden in the management of safety interventions, maintenance... 3. Administrative contradictions: inventories of fuel storages and high active sealed sources are a cornerstone of inspections and verifications; yet, this information is a treasure for terrorists aiming at actions to obtain special materials. 4. Dose management: measures taken to secure sources may lead to a dose increase (e.g. labelling of old sources). However, the main difficulty is related to the 'cultural' aspect. There are synergies between safety culture, 'ALARA' culture and security culture. An individual aspect of desirable behaviour (e.g. questioning attitude), complemented with an organisational dimension (e.g. training, raising awareness) are obviously common. The objective is also in line: to avoid reduction of well-being of people, to protect the environment, to prevent damage to facilities. The main difficulties arise however because of the fundamental
Safety, dose optimisation and security: the quadrature of the circle
International Nuclear Information System (INIS)
Hardeman, Frank; Vermeersch, Fernand
2010-01-01
The growing concern for potential terrorist acts has lead to a number of new ideas about storing radiological and nuclear materials that are not always compatible with existing practices or infrastructures. This is valid in routine circumstances, but especially poses problems in case of accidents. As such, the management of nuclear safety, radiological protection and security within an evolving world such as a nuclear research centre sometimes looks like implementing the quadrature of the circle. International guidance exists, but is not always easily converted into an adequate policy comprehensible to all levels in a plant, from management to the work floor. Some examples. 1. infrastructure related problems: from a security point of view, fuels are better stored in the heart of a protected zone, while in case of criticality, fire... a more peripheral location is appropriate. 2. Safety related problems: Protection infrastructure may lead to difficulties of evacuation in case of emergencies; access limitations may be a burden in the management of safety interventions, maintenance... 3. Administrative contradictions: inventories of fuel storages and high active sealed sources are a cornerstone of inspections and verifications; yet, this information is a treasure for terrorists aiming at actions to obtain special materials. 4. Dose management: measures taken to secure sources may lead to a dose increase (e.g. labelling of old sources). However, the main difficulty is related to the 'cultural' aspect. There are synergies between safety culture, 'ALARA' culture and security culture. An individual aspect of desirable behaviour (e.g. questioning attitude), complemented with an organisational dimension (e.g. training, raising awareness) are obviously common. The objective is also in line: to avoid reduction of well-being of people, to protect the environment, to prevent damage to facilities. The main difficulties arise however because of the fundamental differences being
Directory of Open Access Journals (Sweden)
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.
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Ibsen, Lars Bo
2010-01-01
. In current research the authors utilized the Differential Transformation Method (DTM) for solving the nonlinear problem and compared the analytical results with those ones obtained by the 4th order Runge-Kutta Method (RK4) as a numerical method. Further illustration embedded in this paper shows the ability...
DEFF Research Database (Denmark)
Ganji, S.; Barari, Amin; Ibsen, Lars Bo
2012-01-01
. In current research the authors utilized the Differential Transformation Method (DTM) for solving the nonlinear problem and compared the analytical results with those ones obtained by the 4th order Runge-Kutta Method (RK4) as a numerical method. Further illustration embedded in this paper shows the ability...
Khataybeh, S. N.; Hashim, I.
2018-04-01
In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.
A New Method for Research on the Center-Focus Problem of Differential Systems
Zhou, Zhengxin
2014-01-01
We will introduce Mironenko’s method to discuss the Poincaré center-focus problem, and compare the methods of Lyapunov and Mironenko. We apply the Mironenko method to discuss the qualitative behavior of solutions of some planar polynomial differential systems and derive the sufficient conditions for a critical point to be a center.
The MIMIC Method with Scale Purification for Detecting Differential Item Functioning
Wang, Wen-Chung; Shih, Ching-Lin; Yang, Chih-Chien
2009-01-01
This study implements a scale purification procedure onto the standard MIMIC method for differential item functioning (DIF) detection and assesses its performance through a series of simulations. It is found that the MIMIC method with scale purification (denoted as M-SP) outperforms the standard MIMIC method (denoted as M-ST) in controlling…
International Nuclear Information System (INIS)
Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong
2012-01-01
In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.
Study on time of flight property of electron optical systems by differential algebraic method
International Nuclear Information System (INIS)
Cheng Min; Tang Tiantong; Yao Zhenhua
2002-01-01
Differential algebraic method is a powerful and promising technique in computer numerical analysis. When applied to nonlinear dynamics systems, the arbitrary high-order transfer properties of the systems can be computed directly with high precision. In this paper, the principle of differential algebra is applied to study on the time of flight (TOF) property of electron optical systems and their arbitrary order TOF transfer properties can be numerically calculated out. As an example, TOF transfer properties of a uniform magnetic sector field analyzer have been studied by differential algebraic method. Relative errors of the first-order and second-order TOF transfer coefficients of the magnetic sector field analyzer are of the order 10 -11 or smaller compared with the analytic solutions. It is proved that differential algebraic TOF method is of high accuracy and very helpful for high-order TOF transfer property analysis of electron optical systems. (author)
Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).
Murase, Kenya
2016-01-01
Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.
The Telegraph Equation and Its Solution by Reduced Differential Transform Method
Directory of Open Access Journals (Sweden)
Vineet K. Srivastava
2013-01-01
Full Text Available One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM. Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.
Directory of Open Access Journals (Sweden)
HASHEM SABERI NAJAFI
2016-07-01
Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.
Block Hybrid Collocation Method with Application to Fourth Order Differential Equations
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Lee Ken Yap
2015-01-01
Full Text Available The block hybrid collocation method with three off-step points is proposed for the direct solution of fourth order ordinary differential equations. The interpolation and collocation techniques are applied on basic polynomial to generate the main and additional methods. These methods are implemented in block form to obtain the approximation at seven points simultaneously. Numerical experiments are conducted to illustrate the efficiency of the method. The method is also applied to solve the fourth order problem from ship dynamics.
Vinayaka : A Semi-Supervised Projected Clustering Method Using Differential Evolution
Satish Gajawada; Durga Toshniwal
2012-01-01
Differential Evolution (DE) is an algorithm for evolutionary optimization. Clustering problems have beensolved by using DE based clustering methods but these methods may fail to find clusters hidden insubspaces of high dimensional datasets. Subspace and projected clustering methods have been proposed inliterature to find subspace clusters that are present in subspaces of dataset. In this paper we proposeVINAYAKA, a semi-supervised projected clustering method based on DE. In this method DE opt...
International Nuclear Information System (INIS)
Sanchez, J.
2010-10-01
A standard numerical procedure for the solution of singular integral equations is applied to the one-dimensional transport equation for monoenergetic neutrons. As is usual in quadrature methods, the procedure yields an Eigen system whose solution provide, for the critical slab, both the eigenvalue which is proportional to the number of secondary neutrons per collision, and the density as a function of position. The results obtained with two versions of the procedure, differing only in the extent of the basic region to which they are applied, are compared with analytically derived results available for benchmarking. The procedures considered yield consistent results for the calculated neutron densities and eigenvalues. Since the one-dimensional transport kernel and its spatial moments are integrable and their integrals can be put in terms of exponential integral functions, the resulting approximations to the neutron density yield somewhat lengthy but closed, forms. These approximate expressions of the neutron density can be used to render, after they are operated on, closed-form formulas for build-up factors, extrapolation distances or angular densities or employed for other purposes that require an analytical expression of the neutron density. As an example of this latter capability, the results of the calculation of the angular density at the surface of the slab are provided. (Author)
Low-Latitude Solar Wind During the Fall 1998 SOHO-Ulysses Quadrature
Poletto, G.; Suess, S. T.; Biesecker, D. A.; Esser, R.; Gloeckler, G.; Ko, Y.-K.; Zurbuchen, T. H.
2002-01-01
Solar and Heliospheric Observatory (SOH0)-Ulysses quadratures occur when the SOHO-Sun-Ulysses-included angle is 90 deg. These offer the opportunity to directly compare properties of plasma parcels, observed by SOHO [Dorningo et al.] in the low corona, with properties of the same parcels measured, in due time, in situ, by Ulysses [ Wenzel et al]. We refer the reader to Suess et al. for an extended discussion of SOHO-Ulysses quadrature geometry. Here it suffices to recall that there are two quadratures per year, as SOHO makes its one-year revolution around the Sun. This, because SOHO is at the L1 Lagrangian point, in essentially the same place as the Earth, while Ulysses is in a near-polar -5-year solar orbit with a perihelion of 1.34 AU and aphelion of 5.4 AU.
Stability of numerical method for semi-linear stochastic pantograph differential equations
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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.
Numerical Hopf bifurcation of Runge-Kutta methods for a class of delay differential equations
International Nuclear Information System (INIS)
Wang Qiubao; Li Dongsong; Liu, M.Z.
2009-01-01
In this paper, we consider the discretization of parameter-dependent delay differential equation of the form y ' (t)=f(y(t),y(t-1),τ),τ≥0,y element of R d . It is shown that if the delay differential equation undergoes a Hopf bifurcation at τ=τ * , then the discrete scheme undergoes a Hopf bifurcation at τ(h)=τ * +O(h p ) for sufficiently small step size h, where p≥1 is the order of the Runge-Kutta method applied. The direction of numerical Hopf bifurcation and stability of bifurcating invariant curve are the same as that of delay differential equation.
Piret, Cécile
2012-05-01
Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in . R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time. © 2012 Elsevier Inc.
A new RBF-Trefftz meshless method for partial differential equations
International Nuclear Information System (INIS)
Cao Leilei; Zhao Ning; Qin Qinghua
2010-01-01
Based on the radial basis functions (RBF) and T-Trefftz solution, this paper presents a new meshless method for numerically solving various partial differential equation systems. First, the analog equation method (AEM) is used to convert the original patial differential equation to an equivalent Poisson's equation. Then, the radial basis functions (RBF) are employed to approxiamate the inhomogeneous term, while the homogeneous solution is obtained by linear combination of a set of T-Trefftz solutions. The present scheme, named RBF-Trefftz has the advantage over the fundamental solution (MFS) method due to the use of nonsingular T-Trefftz solution rather than singular fundamental solutions, so it does not require the artificial boundary. The application and efficiency of the proposed method are validated through several examples which include different type of differential equations, such as Laplace equation, Hellmholtz equation, convectin-diffusion equation and time-dependent equation.
Institute of Scientific and Technical Information of China (English)
CHENG Min; TANG Tiantong; YAO Zhenhua; ZHU Jingping
2001-01-01
Differential algebraic method is apowerful technique in computer numerical analysisbased on nonstandard analysis and formal series the-ory. It can compute arbitrary high order derivativeswith excellent accuracy. The principle of differentialalgebraic method is applied to calculate high orderaberrations of combined electromagnetic focusing sys-tems. As an example, third-order geometric aberra-tion coefficients of an actual combined electromagneticfocusing system were calculated. The arbitrary highorder aberrations are conveniently calculated by dif-ferential algebraic method and the fifth-order aberra-tion diagrams are given.
Directory of Open Access Journals (Sweden)
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.
Quadrature Decomposition by Phase Conjugation and Projection in a Polarizing Beam Splitter
DEFF Research Database (Denmark)
Kjøller, Niels-Kristian; Galili, Michael; Dalgaard, Kjeld
2014-01-01
We propose simultaneous decomposition of the two quadratures of an optical data signal to different outputs of a PBS by degenerate four-wave mixing with orthogonal pumps. The scheme is demonstrated by QPSK to 2×BPSK modulation format conversion with BER<10^{−9}.......We propose simultaneous decomposition of the two quadratures of an optical data signal to different outputs of a PBS by degenerate four-wave mixing with orthogonal pumps. The scheme is demonstrated by QPSK to 2×BPSK modulation format conversion with BER−9....
Cockrell, C. R.
1989-01-01
Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.
Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method
Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.
2013-06-01
In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
2013-01-01
We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer
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
Yousef, Hamood Mohammed; Ismail, Ahmad Izani
2017-11-01
In this paper, Laplace Adomian decomposition method (LADM) was applied to solve Delay differential equations with Boundary Value Problems. The solution is in the form of a convergent series which is easy to compute. This approach is tested on two test problem. The findings obtained exhibit the reliability and efficiency of the proposed method.
Efimova, Olga Yu.
2010-01-01
The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and exact solutions of third-order Kudryashov-Sinelshchikov equation describing nonlinear waves in liquids with gas bubbles.
Functional differential equations—a reciprocity principle
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Lloyd K. Williams
1986-01-01
Full Text Available The functional differential equations proposed for solution here are mainly ordinary differential equations with fairly general argument deviations. Included among them are equations with involutions and some with reflections of the argument. Solutions will be obtained by quadratures in terms of implicitly defined functions. They have a wide range of applicability from the stability theory of differential-difference equations to electrodynamics and biological models.
Meleshko, Sergey V
2005-01-01
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Deterministic factor analysis: methods of integro-differentiation of non-integral order
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Valentina V. Tarasova
2016-12-01
Full Text Available Objective to summarize the methods of deterministic factor economic analysis namely the differential calculus and the integral method. nbsp Methods mathematical methods for integrodifferentiation of nonintegral order the theory of derivatives and integrals of fractional nonintegral order. Results the basic concepts are formulated and the new methods are developed that take into account the memory and nonlocality effects in the quantitative description of the influence of individual factors on the change in the effective economic indicator. Two methods are proposed for integrodifferentiation of nonintegral order for the deterministic factor analysis of economic processes with memory and nonlocality. It is shown that the method of integrodifferentiation of nonintegral order can give more accurate results compared with standard methods method of differentiation using the first order derivatives and the integral method using the integration of the first order for a wide class of functions describing effective economic indicators. Scientific novelty the new methods of deterministic factor analysis are proposed the method of differential calculus of nonintegral order and the integral method of nonintegral order. Practical significance the basic concepts and formulas of the article can be used in scientific and analytical activity for factor analysis of economic processes. The proposed method for integrodifferentiation of nonintegral order extends the capabilities of the determined factorial economic analysis. The new quantitative method of deterministic factor analysis may become the beginning of quantitative studies of economic agents behavior with memory hereditarity and spatial nonlocality. The proposed methods of deterministic factor analysis can be used in the study of economic processes which follow the exponential law in which the indicators endogenous variables are power functions of the factors exogenous variables including the processes
Piret, Cé cile
2012-01-01
Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper
International Nuclear Information System (INIS)
Yang, Xiao-Jun; Srivastava, H.M.; He, Ji-Huan; Baleanu, Dumitru
2013-01-01
In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.
A survey of differentiation methods for national greenhouse gas reduction targets
Energy Technology Data Exchange (ETDEWEB)
Torvanger, Asbjoern; Godal, Odd
1999-11-01
The aim of the report is to contribute to exploring the potential differentiation methods for national greenhouse gas reduction targets. The Kyoto Protocol to the United Nations Framework Convention on Climate Change (UNFCCC) from 1997 established differentiation of targets among countries. A more systematic approach to differentiation would facilitate future negotiations. Three sources of methods or proposals are employed. The first are proposals from the Ad Hoc Group on the Berlin Mandate (AGBM) process from 1995 until the Kyoto Protocol was adopted in December 1997, in all 17 proposals were selected. The second source is the EU`s Triptique approach for differentiation of targets among its member states. The third source is recent academic literature where 8 contributions from the period 1992 to 1998 were included. The proposals are presented in a catalogue style. Based on 4 criteria on the usefulness of proposals or methods for future negotiations we have chosen 5 proposals, a Japanese, French, Norwegian, Brazilian in addition to the EU`s Triptique approach. Some numerical illustrations for the Baltic Sea region are presented. Given the joint Kyoto Protocol reduction target for the region we compare the burden sharing consequences for the proposals. For illustrations we employ the following fairness principles as differentiation methods: 1) The Sovereignty principle. 2) The Egalitarian principle. 3) The Ability to Pay principle. With the aim to evaluate the political feasibility of the various differentiation methods we compare the results across the countries in the Baltic Sea region and divide them into OECD and EIT countries. The outcome of the Kyoto Protocol is interpreted as an example of a politically feasible differentiation scheme. On the basis of the observations we find principles 1) and 2) less interesting. A ranking of the differentiation methods according to political feasibility is made and discussed. Among the countries in the Baltic Sea region
Rosenbaum, J. S.
1976-01-01
If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.
Directory of Open Access Journals (Sweden)
Mishra Vinod
2016-01-01
Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.
Directory of Open Access Journals (Sweden)
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.
47.8 GHz InPHBT quadrature VCO with 22% tuning range
DEFF Research Database (Denmark)
Hadziabdic, Dzenan; Johansen, Tom Keinicke; Krozer, Viktor
2007-01-01
A 38-47.8 GHz quadrature voltage controlled oscillator (QVCO) in InP HBT technology is presented. The measured output power is - 15 dBm. The simulated phase noise ranges from -84 to -86 dBc/Hz at 1 MHz offset. It is believed that this is the first millimetre-wavc QVCO implemented in InP HBT...
A Quantized Analog Delay for an ir-UWB Quadrature Downconversion Autocorrelation Receiver
Bagga, S.; Zhang, L.; Serdijn, W.A.; Long, J.R.; Busking, E.B.
2005-01-01
A quantized analog delay is designed as a requirement for the autocorrelation function in the quadrature downconversion autocorrelation receiver (QDAR). The quantized analog delay is comprised of a quantizer, multiple binary delay lines and an adder circuit. Being the foremost element, the quantizer
Linear and quadrature models for data from treshold measurements of the transient visual system
Brinker, den A.C.
1986-01-01
III this paper two models are considered for the transient visual system at threshold. One is a linear model and the other a model contain ing a quadrature element. Both models are commonly used on evidence from different experimental sources. It is shown that both models act in a similar fashion
International Nuclear Information System (INIS)
Hauser, Eliete Biasotto; Romero, Debora Angrizano
2009-01-01
The main objective of this work is to utilize a new angular quadrature sets based on Legendre and Chebyshev polynomials, and to analyse their effects on the number of LTS N matrix conditioning for the problem of discrete coordinates of neutron transport with two dimension cartesian geometry with isotropic scattering, and an energy group, in non multiplicative homogenous domains
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...
Directory of Open Access Journals (Sweden)
J. Prakash
2016-03-01
Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.
High order aberrations calculation of a hexapole corrector using a differential algebra method
Energy Technology Data Exchange (ETDEWEB)
Kang, Yongfeng, E-mail: yfkang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Zhao, Jingyi, E-mail: jingyi.zhao@foxmail.com [School of Science, Chang’an University, Xi’an 710064 (China); Tang, Tiantong [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China)
2017-02-21
A differential algebraic (DA) method is proved as an unusual and effective tool in numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. In this paper, the differential algebra (DA) method has been employed to compute the high order aberrations up to the fifth order of a practical hexapole corrector including round lenses and hexapole lenses. The program has been developed and tested as well. The electro-magnetic fields of arbitrary point are obtained by local analytic expressions, then field potentials are transformed into new forms which can be operated in the DA calculation. In this paper, the geometric and chromatic aberrations up to fifth order of a practical hexapole corrector system are calculated by the developed program.
Directory of Open Access Journals (Sweden)
V. Z. Stetsyuk
2016-10-01
Full Text Available Informatization in medicine offers a lot of opportunities to enhance quality of medical support, accuracy of diagnosis and provides the use of accumulated experience. Modern program systems are utilized now as additional tools to get appropriate advice. This article offers the way to provide help for neurology department doctor of NCSH «OKHMATDYT» during diagnosis determining. It was decided to design the program system for this purpose based on differential diagnostic model. The key problems in differential diagnosis are symptoms similarity between each other in one disease group and the absence of key symptom. Therefore the differential diagnostic model is needed. It is constructed using the potential function method in characteristics space. This characteristics space is formed by 100-200 points - patients with their symptoms. The main feature of this method here is that the decision function is building during recognition step united with learning that became possible with the help of modern powerful computers.
Ebert, Marcelo R
2018-01-01
This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes...
Directory of Open Access Journals (Sweden)
Z. Pashazadeh Atabakan
2013-01-01
Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.
International Nuclear Information System (INIS)
Feng Qing-Hua
2014-01-01
In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)
Functional analytic methods in complex analysis and applications to partial differential equations
International Nuclear Information System (INIS)
Mshimba, A.S.A.; Tutschke, W.
1990-01-01
The volume contains 24 lectures given at the Workshop on Functional Analytic Methods in Complex Analysis and Applications to Partial Differential Equations held in Trieste, Italy, between 8-19 February 1988, at the ICTP. A separate abstract was prepared for each of these lectures. Refs and figs
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.
DEFF Research Database (Denmark)
Debrabant, Kristian; Samaey, Giovanni; Zieliński, Przemysław
2017-01-01
We present and analyse a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time-scale of individual trajectories and the (slow) time-scale of the macroscopic function of interest. The algorithm combines short...
Directory of Open Access Journals (Sweden)
SURE KÖME
2014-12-01
Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.
WKB: an interactive code for solving differential equations using phase integral methods
International Nuclear Information System (INIS)
White, R.B.
1978-01-01
A small code for the analysis of ordinary differential equations interactively through the use of Phase Integral Methods (WKB) has been written for use on the DEC 10. This note is a descriptive manual for those interested in using the code
Botta, Filippo; Eriksen, Casper; Fontaine, Michael Christophe; Guillot, Gilles
2015-01-01
In a recent paper, Bradburd et al. (2013) proposed a model to quantify the relative effect ofgeographic and environmental distance on genetic differentiation. Here, we enhance this method in several ways. 1. We modify the covariance model so as to fit better with mainstream geostatistical models and
Tang, Kwong-Tin
2007-01-01
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.
Xing, Yanyuan; Yan, Yubin
2018-03-01
Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.
Energy Technology Data Exchange (ETDEWEB)
El-Sayed, A.M.A. [Faculty of Science University of Alexandria (Egypt)]. E-mail: amasyed@hotmail.com; Gaber, M. [Faculty of Education Al-Arish, Suez Canal University (Egypt)]. E-mail: mghf408@hotmail.com
2006-11-20
The Adomian decomposition method has been successively used to find the explicit and numerical solutions of the time fractional partial differential equations. A different examples of special interest with fractional time and space derivatives of order {alpha}, 0<{alpha}=<1 are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of {alpha} are shown graphically for some examples.
New finite volume methods for approximating partial differential equations on arbitrary meshes
International Nuclear Information System (INIS)
Hermeline, F.
2008-12-01
This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)
Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation
Directory of Open Access Journals (Sweden)
S. Balaji
2014-01-01
Full Text Available A Legendre wavelet operational matrix method (LWM is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.
Soliton solution for nonlinear partial differential equations by cosine-function method
International Nuclear Information System (INIS)
Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.
2007-01-01
In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations
High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations
Abdulle, Assyr
2012-01-01
© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.
Fractal-Based Methods and Inverse Problems for Differential Equations: Current State of the Art
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Herb E. Kunze
2014-01-01
Full Text Available We illustrate, in this short survey, the current state of the art of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. We review several methods based on the Collage Theorem and its extensions. We also discuss two innovative applications: the first one is related to a vibrating string model while the second one considers a collage-based approach for solving inverse problems for partial differential equations on a perforated domain.
Evaluating the efficacy of DNA differential extraction methods for sexual assault evidence.
Klein, Sonja B; Buoncristiani, Martin R
2017-07-01
Analysis of sexual assault evidence, often a mixture of spermatozoa and victim epithelial cells, represents a significant portion of a forensic DNA laboratory's case load. Successful genotyping of sperm DNA from these mixed cell samples, particularly with low amounts of sperm, depends on maximizing sperm DNA recovery and minimizing non-sperm DNA carryover. For evaluating the efficacy of the differential extraction, we present a method which uses a Separation Potential Ratio (SPRED) to consider both sperm DNA recovery and non-sperm DNA removal as variables for determining separation efficiency. In addition, we describe how the ratio of male-to-female DNA in the sperm fraction may be estimated by using the SPRED of the differential extraction method in conjunction with the estimated ratio of male-to-female DNA initially present on the mixed swab. This approach may be useful for evaluating or modifying differential extraction methods, as we demonstrate by comparing experimental results obtained from the traditional differential extraction and the Erase Sperm Isolation Kit (PTC © ) procedures. Copyright © 2017 Elsevier B.V. All rights reserved.
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Byoung-Sun Lee
1988-06-01
Full Text Available The differential correction process determining osculating orbital elements as correct as possible at a given instant of time from tracking data of artificial satellite was accomplished. Preliminary orbital elements were used as an initial value of the differential correction procedure and iterated until the residual of real observation(O and computed observation(C was minimized. Tracking satellite was NOAA-9 or TIROS-N series. Two types of tracking data were prediction data precomputed from mean orbital elements of TBUS and real data obtained from tracking 1.707GHz HRPT signal of NOAA-9 using 5 meter auto-track antenna in Radio Research Laboratory. According to tracking data either Gauss method or Herrick-Gibbs method was applied to preliminary orbit determination. In the differential correction stage we used both of the Escobal(1975's analytical method and numerical ones are nearly consistent. And the differentially corrected orbit converged to the same value in spite of the differences between preliminary orbits of each time span.
Khader, M M
2013-10-01
In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.
International Nuclear Information System (INIS)
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.
Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method
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Eman M. A. Hilal
2014-01-01
Full Text Available The aim of this study is to give a good strategy for solving some linear and nonlinear partial differential equations in engineering and physics fields, by combining Laplace transform and the modified variational iteration method. This method is based on the variational iteration method, Laplace transforms, and convolution integral, introducing an alternative Laplace correction functional and expressing the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions.
Comparison of different methods for erythroid differentiation in the K562 cell line.
Shariati, Laleh; Modaress, Mehran; Khanahmad, Hossein; Hejazi, Zahra; Tabatabaiefar, Mohammad Amin; Salehi, Mansoor; Modarressi, Mohammad Hossein
2016-08-01
To compare methods for erythroid differentiation of K562 cells that will be promising in the treatment of beta-thalassemia by inducing γ-globin synthesis. Cells were treated separately with: RPMI 1640 medium without glutamine, RPMI 1640 medium without glutamine supplemented with 1 mM sodium butyrate, RPMI 1640 medium supplemented with 1 mM sodium butyrate, 25 µg cisplatin/ml, 0.1 µg cytosine arabinoside/ml. The highest differentiation (84 %) with minimum toxicity was obtained with cisplatin at 15 µg /ml. Real-time RT-PCR showed that expression of the γ-globin gene was significantly higher in the cells differentiated with cisplatin compared to undifferentiated cells (P < 0.001). Cisplatin is useful in the experimental therapy of ß-globin gene defects and can be considered for examining the basic mechanism of γ-reactivation.
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Shaolin Ji
2013-01-01
Full Text Available This paper is devoted to a stochastic differential game (SDG of decoupled functional forward-backward stochastic differential equation (FBSDE. For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs. Applying the Girsanov transformation method introduced by Buckdahn and Li (2008, the upper and the lower value functions are shown to be deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI equations to the path-dependent ones. By establishing the dynamic programming principal (DPP, we derive that the upper and the lower value functions are the viscosity solutions of the corresponding upper and the lower path-dependent HJBI equations, respectively.
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.
A one-step method for modelling longitudinal data with differential equations.
Hu, Yueqin; Treinen, Raymond
2018-04-06
Differential equation models are frequently used to describe non-linear trajectories of longitudinal data. This study proposes a new approach to estimate the parameters in differential equation models. Instead of estimating derivatives from the observed data first and then fitting a differential equation to the derivatives, our new approach directly fits the analytic solution of a differential equation to the observed data, and therefore simplifies the procedure and avoids bias from derivative estimations. A simulation study indicates that the analytic solutions of differential equations (ASDE) approach obtains unbiased estimates of parameters and their standard errors. Compared with other approaches that estimate derivatives first, ASDE has smaller standard error, larger statistical power and accurate Type I error. Although ASDE obtains biased estimation when the system has sudden phase change, the bias is not serious and a solution is also provided to solve the phase problem. The ASDE method is illustrated and applied to a two-week study on consumers' shopping behaviour after a sale promotion, and to a set of public data tracking participants' grammatical facial expression in sign language. R codes for ASDE, recommendations for sample size and starting values are provided. Limitations and several possible expansions of ASDE are also discussed. © 2018 The British Psychological Society.
The adaptive collision source method for discrete ordinates radiation transport
International Nuclear Information System (INIS)
Walters, William J.; Haghighat, Alireza
2017-01-01
Highlights: • A new adaptive quadrature method to solve the discrete ordinates transport equation. • The adaptive collision source (ACS) method splits the flux into n’th collided components. • Uncollided flux requires high quadrature; this is lowered with number of collisions. • ACS automatically applies appropriate quadrature order each collided component. • The adaptive quadrature is 1.5–4 times more efficient than uniform quadrature. - Abstract: A novel collision source method has been developed to solve the Linear Boltzmann Equation (LBE) more efficiently by adaptation of the angular quadrature order. The angular adaptation method is unique in that the flux from each scattering source iteration is obtained, with potentially a different quadrature order used for each. Traditionally, the flux from every iteration is combined, with the same quadrature applied to the combined flux. Since the scattering process tends to distribute the radiation more evenly over angles (i.e., make it more isotropic), the quadrature requirements generally decrease with each iteration. This method allows for an optimal use of processing power, by using a high order quadrature for the first iterations that need it, before shifting to lower order quadratures for the remaining iterations. This is essentially an extension of the first collision source method, and is referred to as the adaptive collision source (ACS) method. The ACS methodology has been implemented in the 3-D, parallel, multigroup discrete ordinates code TITAN. This code was tested on a several simple and complex fixed-source problems. The ACS implementation in TITAN has shown a reduction in computation time by a factor of 1.5–4 on the fixed-source test problems, for the same desired level of accuracy, as compared to the standard TITAN code.
Enrichment of Female Germline Stem Cells from Mouse Ovaries Using the Differential Adhesion Method
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Meng Wu
2018-04-01
Full Text Available Background/Aims: The isolation and establishment of female germline stem cells (FGSCs is controversial because of questions regarding the reliability and stability of the isolation method using antibody targeting mouse vasa homologue (MVH, and the molecular mechanism of FGSCs self-renewal remains unclear. Thus, there needs to be a simple and reliable method for sorting FGSCs to study them. Methods: We applied the differential adhesion method to enrich FGSCs (DA-FGSCs from mouse ovaries. Through four rounds of purification and 7-9 subsequent passages, DA-FGSC lines were established. In addition, we assessed the role of the phosphoinositide-3 kinase (PI3K-AKT pathway in regulating FGSC self-renewal. Results: The obtained DA-FGSCs spontaneously differentiated into oocyte-like cells in vitro and formed functional eggs in vivo that were fertilized and produced healthy offspring. AKT was rapidly phosphorylated when the proliferation rate of FGSCs increased after 10 passages, and the addition of a chemical PI3K inhibitor prevented FGSCs self-renewal. Furthermore, over-expression of AKT-induced proliferation and differentiation of FGSCs, c-Myc, Oct-4 and Gdf-9 levels were increased. Conclusions: The differential adhesion method provides a more feasible approach and is an easier procedure to establish FGSC lines than traditional methods. The AKT pathway plays an important role in regulation of the proliferation and maintenance of FGSCs. These findings could help promote stem cell studies and provide a better understanding of causes of ovarian infertility, thereby providing potential treatments for infertility.
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Hatice Saadiye Eryılmaz
2017-06-01
Full Text Available Gelatin origin determination has been a crucial issue with respect to religion and health concerns. It is necessary to analyze the origin of gelatin with reliable methods to ensure not only consumer choices but also safety and legal requirements such as labeling. There are many analytical methods developed for detection and/or quantification of gelatin from different sources including bovine, porcine and piscine. These analytical methods can be divided into physicochemical, chromatographic, immunochemical, spectroscopic and molecular methods. Moreover, computational methods have been used in some cases consecutively to ensure sensitivity of the analytical methods. Every method has different advantages and limitations due to their own principles, applied food matrix and process conditions of material. The present review intends to give insight into novel analytical methods and perspectives that have been developed to differentiate porcine, bovine and piscine gelatins and to establish their authenticity. Almost every method can be succeeded in origin determination; however, it is a matter of sensitivity in that some researches fail to ensure sufficient differentiation.
Spectral methods for a nonlinear initial value problem involving pseudo differential operators
International Nuclear Information System (INIS)
Pasciak, J.E.
1982-01-01
Spectral methods (Fourier methods) for approximating the solution of a nonlinear initial value problem involving pseudo differential operators are defined and analyzed. A semidiscrete approximation to the nonlinear equation based on an L 2 projection is described. The semidiscrete L 2 approximation is shown to be a priori stable and convergent under sufficient decay and smoothness assumptions on the initial data. It is shown that the semidiscrete method converges with infinite order, that is, higher order decay and smoothness assumptions imply higher order error bounds. Spectral schemes based on spacial collocation are also discussed
Simple equation method for nonlinear partial differential equations and its applications
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Taher A. Nofal
2016-04-01
Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.
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Fairouz Zouyed
2015-01-01
Full Text Available This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.
Methods of measurement of integral and differential linearity distortions of spectrometry sets
International Nuclear Information System (INIS)
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
Enrichment of Female Germline Stem Cells from Mouse Ovaries Using the Differential Adhesion Method.
Wu, Meng; Xiong, Jiaqiang; Ma, Lingwei; Lu, Zhiyong; Qin, Xian; Luo, Aiyue; Zhang, Jinjin; Xie, Huan; Shen, Wei; Wang, Shixuan
2018-04-28
The isolation and establishment of female germline stem cells (FGSCs) is controversial because of questions regarding the reliability and stability of the isolation method using antibody targeting mouse vasa homologue (MVH), and the molecular mechanism of FGSCs self-renewal remains unclear. Thus, there needs to be a simple and reliable method for sorting FGSCs to study them. We applied the differential adhesion method to enrich FGSCs (DA-FGSCs) from mouse ovaries. Through four rounds of purification and 7-9 subsequent passages, DA-FGSC lines were established. In addition, we assessed the role of the phosphoinositide-3 kinase (PI3K)-AKT pathway in regulating FGSC self-renewal. The obtained DA-FGSCs spontaneously differentiated into oocyte-like cells in vitro and formed functional eggs in vivo that were fertilized and produced healthy offspring. AKT was rapidly phosphorylated when the proliferation rate of FGSCs increased after 10 passages, and the addition of a chemical PI3K inhibitor prevented FGSCs self-renewal. Furthermore, over-expression of AKT-induced proliferation and differentiation of FGSCs, c-Myc, Oct-4 and Gdf-9 levels were increased. The differential adhesion method provides a more feasible approach and is an easier procedure to establish FGSC lines than traditional methods. The AKT pathway plays an important role in regulation of the proliferation and maintenance of FGSCs. These findings could help promote stem cell studies and provide a better understanding of causes of ovarian infertility, thereby providing potential treatments for infertility. © 2018 The Author(s). Published by S. Karger AG, Basel.
Li, Xinji; Hui, Mei; Zhao, Zhu; Liu, Ming; Dong, Liquan; Kong, Lingqin; Zhao, Yuejin
2018-05-01
A differential computation method is presented to improve the precision of calibration for coaxial reverse Hartmann test (RHT). In the calibration, the accuracy of the distance measurement greatly influences the surface shape test, as demonstrated in the mathematical analyses. However, high-precision absolute distance measurement is difficult in the calibration. Thus, a differential computation method that only requires the relative distance was developed. In the proposed method, a liquid crystal display screen successively displayed two regular dot matrix patterns with different dot spacing. In a special case, images on the detector exhibited similar centroid distributions during the reflector translation. Thus, the critical value of the relative displacement distance and the centroid distributions of the dots on the detector were utilized to establish the relationship between the rays at certain angles and the detector coordinates. Experiments revealed the approximately linear behavior of the centroid variation with the relative displacement distance. With the differential computation method, we increased the precision of traditional calibration 10-5 rad root mean square. The precision of the RHT was increased by approximately 100 nm.
Brooks, Larry M; Kuhlman, Benjamin J; McKesson, Doug W; McCloskey, Leo
2013-01-01
The poor interoperability of anthocyanin glycosides measurements by two pH differential methods is documented. Adams-Harbertson, which was proposed for commercial winemaking, was compared to AOAC Official Method 2005.02 for wine. California bottled wines (Pinot Noir, Merlot, and Cabernet Sauvignon) were assayed in a collaborative study (n=105), which found mean precision of Adams-Harbertson winery versus reference measurements to be 77 +/- 20%. Maximum error is expected to be 48% for Pinot Noir, 42% for Merlot, and 34% for Cabernet Sauvignon from reproducibility RSD. Range of measurements was actually 30 to 91% for Pinot Noir. An interoperability study (n=30) found Adams-Harbertson produces measurements that are nominally 150% of the AOAC pH differential method. Large analytical chemistry differences are: AOAC method uses Beer-Lambert equation and measures absorbance at pH 1.0 and 4.5, proposed a priori by Flueki and Francis; whereas Adams-Harbertson uses "universal" standard curve and measures absorbance ad hoc at pH 1.8 and 4.9 to reduce the effects of so-called co-pigmentation. Errors relative to AOAC are produced by Adams-Harbertson standard curve over Beer-Lambert and pH 1.8 over pH 1.0. The study recommends using AOAC Official Method 2005.02 for analysis of wine anthocyanin glycosides.
Mahasuk, Pitchayapa; Chinthaisong, Jittima; Mongkolporn, Orarat
2013-09-01
Chili anthracnose, caused by Colletotrichum spp., is one of the major diseases to chili production in the tropics and subtropics worldwide. Breeding for durable anthracnose resistance requires a good understanding of the resistance mechanisms to different pathotypes and inoculation methods. This study aimed to investigate the inheritances of differential resistances as responding to two different Colletotrichum pathotypes, PCa2 and PCa3 and as by two different inoculation methods, microinjection (MI) and high pressure spray (HP). Detached ripe fruit of Capsicum baccatum 'PBC80' derived F2 and BC1s populations was assessed for anthracnose resistance. Two dominant genes were identified responsible for the differential resistance to anthracnose. One was responsible for the resistance to PCa2 and PCa3 by MI and the other was responsible for the resistance to PCa3 by HP. The two genes were linked with 16.7 cM distance.
Rackauckas, Christopher; Nie, Qing
2017-01-01
Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs.
Harmonic-suppressed quadrature-input frequency divider for OFDM systems
International Nuclear Information System (INIS)
Fu Haipeng; Ren Junyan; Li Wei; Li Ning
2011-01-01
A fully balanced harmonic-suppressed quadrature-input frequency divider is proposed. The frequency divider improves the quadrature phase accuracy at the output by using both input I/Q signals. Compared with conventional dividers, the circuit achieves an output I/Q phase sequence that is independent of the input I/Q phase sequence. Moreover, the third harmonic is effectively suppressed by employing a double degeneration technique. The design is fabricated in TSMC 0.13-μm CMOS and operated at 1.2 V. While locked at 8.5 GHz, the proposed divider measures a maximum third harmonic rejection of 45 dB and a phase noise of −124 dBc/Hz at a 10 MHz offset. The circuit achieves a locking range of 15% while consuming a total current of 4.5 mA. (semiconductor integrated circuits)
Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene.
Oettinger, D; Mendoza, M; Herrmann, H J
2013-07-01
We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as the weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, which satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential the electronic fluid behaves as if it increases its effective viscosity.
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Hasan Bulut
2013-01-01
Full Text Available We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM to some interesting nonhomogeneous fractional ordinary differential equations (FODEs. Finally, we use the solutions to form two-dimensional (2D graphs, by using the symbolic algebra package Mathematica Program 7.
Solving inverse problems for biological models using the collage method for differential equations.
Capasso, V; Kunze, H E; La Torre, D; Vrscay, E R
2013-07-01
In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.
Taguchi method for partial differential equations with application in tumor growth.
Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena
2014-01-01
The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.
What is new in the study of differential equations by group theoretical methods
International Nuclear Information System (INIS)
Winternitz, P.
1986-11-01
Several recent developments have made the application of group theory to the solving of differential equations more powerful than it used to be. The ones discussed here are: 1. The advent of symbol manipulating computer languages that greatly simplify the construction of the symmetry group of an equation 2. Methods of finding all subgroups of a given Lie symmetry group 3. The theory of infinite dimensional Lie algebras 4. The combination of group theory and singularity analysis
On the method of solution of the differential-delay Toda equation
Villarroel, Javier; Ablowitz, Mark J.
1993-09-01
The method of solution of the Toda differential-delay equation, which is a reduction of the Toda equation in 2+1 dimensions, is described. An important feature of the solution process is to obtain and study a novel Riemann-Hilbert problem. The latter problem requires factorization across an infinite number of strips with a suitable branching structure. Explicit soliton solutions are given.
Yousef, Hamood. M.; Ismail, A. I. B. MD.
2017-08-01
Many attempts have been presented to solve the system of Delay Differential Equations (DDE) with Initial Value Problem. As a result, it has shown difficulties when getting the solution or cannot be solved. In this paper, a Variational Iteration Method is employed to find out an approximate solution for the system of DDE with initial value problems. The example illustrates convenient and an efficiency comparison with the exact solution.
Gauss-Arnoldi quadrature for -1φ,φ> and rational Pade-type approximation for Markov-type functions
International Nuclear Information System (INIS)
Knizhnerman, L A
2008-01-01
The efficiency of Gauss-Arnoldi quadrature for the calculation of the quantity -1 φ,φ> is studied, where A is a bounded operator in a Hilbert space and φ is a non-trivial vector in this space. A necessary and a sufficient conditions are found for the efficiency of the quadrature in the case of a normal operator. An example of a non-normal operator for which this quadrature is inefficient is presented. It is shown that Gauss-Arnoldi quadrature is related in certain cases to rational Pade-type approximation (with the poles at Ritz numbers) for functions of Markov type and, in particular, can be used for the localization of the poles of a rational perturbation. Error estimates are found, which can also be used when classical Pade approximation does not work or it may not be efficient. Theoretical results and conjectures are illustrated by numerical experiments. Bibliography: 44 titles
A modification of \\mathsf {WKB} method for fractional differential operators of Schrödinger's type
Sayevand, K.; Pichaghchi, K.
2017-09-01
In this paper, we were concerned with the description of the singularly perturbed differential equations within the scope of fractional calculus. However, we shall note that one of the main methods used to solve these problems is the so-called WKB method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the WKB to the scope of fractional derivative, we proposed a relatively new derivative called the local fractional derivative. By use of properties of local fractional derivative, we extend the WKB method in the scope of the fractional differential equation. By means of this extension, the WKB analysis based on the Borel resummation, for fractional differential operators of WKB type are investigated. The convergence and the Mittag-Leffler stability of the proposed approach is proven. The obtained results are in excellent agreement with the existing ones in open literature and it is shown that the present approach is very effective and accurate. Furthermore, we are mainly interested to construct the solution of fractional Schrödinger equation in the Mittag-Leffler form and how it leads naturally to this semi-classical approximation namely modified WKB.
Workshop on Recent Trends in Complex Methods for Partial Differential Equations
Celebi, A; Tutschke, Wolfgang
1999-01-01
This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech nical Research Council of Turkey and the Middle East Technical University. This workshop is a continuation oftwo workshops from 1988 and 1993 at the In ternational Centre for Theoretical Physics in Trieste, Italy entitled Functional analytic Methods in Complex Analysis and Applications to Partial Differential Equations. Since classical complex analysis of one and several variables has a long tra dition it is of high level. But most of its basic problems are solved nowadays so that within the last few decades it has lost more and more attention. The area of complex and functional analytic methods in partial differential equations, however, is still a growing and flourishing field, in particular as these ...
Noncritical quadrature squeezing in two-transverse-mode optical parametric oscillators
International Nuclear Information System (INIS)
Navarrete-Benlloch, Carlos; Roldan, Eugenio; Valcarcel, German J. de; Romanelli, Alejandro
2010-01-01
In this article we explore the quantum properties of a degenerate optical parametric oscillator when it is tuned to the first family of transverse modes at the down-converted frequency. Recently we found [C. Navarrete-Benlloch et al., Phys. Rev. Lett. 100, 203601 (2008)] that above threshold a TEM 10 mode following a random rotation in the transverse plane emerges in this system (we denote it as the bright mode), breaking thus its rotational invariance. Then, owing to the mode orientation being undetermined, we showed that the phase quadrature of the transverse mode orthogonal to this one (denoted as the dark mode) is perfectly squeezed at any pump level and without an increase in the fluctuations on its amplitude quadrature (which seems to contradict the uncertainty principle). In this article we go further in the study of this system and analyze some important features not considered previously. First we show that the apparent violation of the uncertainty principle is just that -'apparent' - as the conjugate pair of the squeezed quadrature is not another quadrature but the orientation of the bright mode (which is completely undetermined in the long term). We also study a homodyne scheme in which the local oscillator is not perfectly matched to the dark mode, as this could be impossible in real experiments due to the random rotation of the mode, showing that even in this case large levels of noise reduction can be obtained (also including the experimentally unavoidable phase fluctuations). Finally, we show that neither the adiabatic elimination of the pump variables nor the linearization of the quantum equations are responsible for the remarkable properties of the dark mode (which we prove analytically and through numerical simulations, respectively), which were simplifying assumptions used in Navarrete-Benlloch et al. [Phys. Rev. Lett. 100, 203601 (2008)]. These studies show that the production of noncritically squeezed light through spontaneous rotational
An anti-image interference quadrature IF architecture for satellite receivers
Directory of Open Access Journals (Sweden)
He Weidong
2014-08-01
Full Text Available Since Global Navigation Satellite System (GNSS signals span a wide range of frequency, wireless signals coming from other communication systems may be aliased and appear as image interference. In quadrature intermediate frequency (IF receivers, image aliasing due to in-phase and quadrature (I/Q channel mismatches is always a big problem. I/Q mismatches occur because of gain and phase imbalances between quadrature mixers and capacitor mismatches in analog-to-digital converters (ADC. As a result, the dynamic range and performance of a receiver are severely degraded. In this paper, several popular receiver architectures are summarized and the image aliasing problem is investigated in detail. Based on this analysis, a low-IF architecture is proposed for a single-chip solution and a novel and feasible anti-image algorithm is investigated. With this anti-image digital processing, the image reject ratio (IRR can reach approximately above 50 dB, which relaxes image rejection specific in front-end circuit designs and allows cheap and highly flexible analog front-end solutions. Simulation and experimental data show that the anti-image algorithm can work effectively, robustly, and steadily.
Output field-quadrature measurements and squeezing in ultrastrong cavity-QED
Stassi, Roberto; Savasta, Salvatore; Garziano, Luigi; Spagnolo, Bernardo; Nori, Franco
2016-12-01
We study the squeezing of output quadratures of an electro-magnetic field escaping from a resonator coupled to a general quantum system with arbitrary interaction strengths. The generalized theoretical analysis of output squeezing proposed here is valid for all the interaction regimes of cavity-quantum electrodynamics: from the weak to the strong, ultrastrong, and deep coupling regimes. For coupling rates comparable or larger then the cavity resonance frequency, the standard input-output theory for optical cavities fails to calculate the variance of output field-quadratures and predicts a non-negligible amount of output squeezing, even if the system is in its ground state. Here we show that, for arbitrary interaction strength and for general cavity-embedded quantum systems, no squeezing can be found in the output-field quadratures if the system is in its ground state. We also apply the proposed theoretical approach to study the output squeezing produced by: (i) an artificial two-level atom embedded in a coherently-excited cavity; and (ii) a cascade-type three-level system interacting with a cavity field mode. In the latter case the output squeezing arises from the virtual photons of the atom-cavity dressed states. This work extends the possibility of predicting and analyzing the results of continuous-variable optical quantum-state tomography when optical resonators interact very strongly with other quantum systems.
Lin, Tiger W; Das, Anup; Krishnan, Giri P; Bazhenov, Maxim; Sejnowski, Terrence J
2017-10-01
With our ability to record more neurons simultaneously, making sense of these data is a challenge. Functional connectivity is one popular way to study the relationship of multiple neural signals. Correlation-based methods are a set of currently well-used techniques for functional connectivity estimation. However, due to explaining away and unobserved common inputs (Stevenson, Rebesco, Miller, & Körding, 2008 ), they produce spurious connections. The general linear model (GLM), which models spike trains as Poisson processes (Okatan, Wilson, & Brown, 2005 ; Truccolo, Eden, Fellows, Donoghue, & Brown, 2005 ; Pillow et al., 2008 ), avoids these confounds. We develop here a new class of methods by using differential signals based on simulated intracellular voltage recordings. It is equivalent to a regularized AR(2) model. We also expand the method to simulated local field potential recordings and calcium imaging. In all of our simulated data, the differential covariance-based methods achieved performance better than or similar to the GLM method and required fewer data samples. This new class of methods provides alternative ways to analyze neural signals.
International Nuclear Information System (INIS)
Vidal-Codina, F.; Nguyen, N.C.; Giles, M.B.; Peraire, J.
2015-01-01
We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method
Lin, Tiger W.; Das, Anup; Krishnan, Giri P.; Bazhenov, Maxim; Sejnowski, Terrence J.
2017-01-01
With our ability to record more neurons simultaneously, making sense of these data is a challenge. Functional connectivity is one popular way to study the relationship of multiple neural signals. Correlation-based methods are a set of currently well-used techniques for functional connectivity estimation. However, due to explaining away and unobserved common inputs (Stevenson, Rebesco, Miller, & Körding, 2008), they produce spurious connections. The general linear model (GLM), which models spike trains as Poisson processes (Okatan, Wilson, & Brown, 2005; Truccolo, Eden, Fellows, Donoghue, & Brown, 2005; Pillow et al., 2008), avoids these confounds. We develop here a new class of methods by using differential signals based on simulated intracellular voltage recordings. It is equivalent to a regularized AR(2) model. We also expand the method to simulated local field potential recordings and calcium imaging. In all of our simulated data, the differential covariance-based methods achieved performance better than or similar to the GLM method and required fewer data samples. This new class of methods provides alternative ways to analyze neural signals. PMID:28777719
Stability of generalized Runge-Kutta methods for stiff kinetics coupled differential equations
International Nuclear Information System (INIS)
Aboanber, A E
2006-01-01
A stability and efficiency improved class of generalized Runge-Kutta methods of order 4 are developed for the numerical solution of stiff system kinetics equations for linear and/or nonlinear coupled differential equations. The determination of the coefficients required by the method is precisely obtained from the so-called equations of condition which in turn are derived by an approach based on Butcher series. Since the equations of condition are fewer in number, free parameters can be chosen for optimizing any desired feature of the process. A further related coefficient set with different values of these parameters and the region of absolute stability of the method have been introduced. In addition, the A(α) stability properties of the method are investigated. Implementing the method in a personal computer estimated the accuracy and speed of calculations and verified the good performances of the proposed new schemes for several sample problems of the stiff system point kinetics equations with reactivity feedback
Chang, Gregory; Wiggins, Graham C.; Xia, Ding; Lattanzi, Riccardo; Madelin, Guillaume; Raya, Jose G.; Finnerty, Matthew; Fujita, Hiroyuki; Recht, Michael P.; Regatte, Ravinder R.
2011-01-01
Purpose To compare a new birdcage-transmit, 28 channel-receive array (28 Ch) coil and a quadrature volume coil for 7 Tesla morphologic MRI and T2 mapping of knee cartilage. Methods The right knees of ten healthy subjects were imaged on a 7 Tesla whole body MR scanner using both coils. 3-dimensional fast low-angle shot (3D-FLASH) and multi-echo spin-echo (MESE) sequences were implemented. Cartilage signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), thickness, and T2 values were assessed. Results SNR/CNR was 17–400% greater for the 28 Ch compared to the quadrature coil (p≤0.005). Bland-Altman plots show mean differences between measurements of tibial/femoral cartilage thickness and T2 values obtained with each coil to be small (−0.002±0.009 cm/0.003±0.011 cm) and large (−6.8±6.7 ms/−8.2±9.7 ms), respectively. For the 28 Ch coil, when parallel imaging with acceleration factors (AF) 2, 3, and 4 was performed, SNR retained was: 62–69%, 51–55%, and 39–45%. Conclusion A 28 Ch knee coil provides increased SNR/CNR for 7T cartilage morphologic imaging and T2 mapping. Coils should be switched with caution during clinical studies because T2 values may differ. The greater SNR of the 28 Ch coil could be used to perform parallel imaging with AF2 and obtain similar SNR as the quadrature coil. PMID:22095723
A method for exponential propagation of large systems of stiff nonlinear differential equations
Friesner, Richard A.; Tuckerman, Laurette S.; Dornblaser, Bright C.; Russo, Thomas V.
1989-01-01
A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.
Reproducing kernel method with Taylor expansion for linear Volterra integro-differential equations
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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.
[Exercise laryngoscopy: a new method for the differential diagnosis of dyspnea on exertion].
Tervonen, Hanna; Iljukov, Sergei; Niskanen, Minna-Liisa; Vilkman, Erkki; Sovijärvi, Anssi; Aaltonen, Leena-Maija
2011-01-01
Exertional dyspnea originating from the laryngeal level can be established with certainty only if the paradoxical vocal cord adduction is observed during dyspnea. We have developed a novel diagnostic method, exercise laryngoscopy, which involves observation of the larynx with a flexible endoscope applied via the nose during a bicycle ergometry test. It has been our aim to improve the differential diagnosis of dyspnea on exertion and thus also reduce unnecessary antiasthmatic medication. Exercise laryngoscopy allows examination in the out-patient clinics because the method is well tolerated.
Stochastic Perron's method and elementary strategies for zero-sum differential games
Sîrbu, Mihai
2013-01-01
We develop here the Stochastic Perron Method in the framework of two-player zero-sum differential games. We consider the formulation of the game where both players play, symmetrically, feed-back strategies (as in [CR09] or [PZ12]) as opposed to the Elliott-Kalton formulation prevalent in the literature. The class of feed-back strategies we use is carefully chosen so that the state equation admits strong solutions and the technicalities involved in the Stochastic Perron Method carry through in...
The Spectral/hp-Finite Element Method for Partial Differential Equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2009-01-01
dimensions. In the course the chosen programming environment is Matlab, however, this is by no means a necessary requirement. The mathematical level needed to grasp the details of this set of notes requires an elementary background in mathematical analysis and linear algebra. Each chapter is supplemented......This set of lecture notes provides an elementary introduction to both the classical Finite Element Method (FEM) and the extended Spectral/$hp$-Finite Element Method for solving Partial Differential Equations (PDEs). Many problems in science and engineering can be formulated mathematically...
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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.
Asiri, Sharefa M.; Laleg-Kirati, Taous-Meriem
2016-01-01
In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear
Germain, Pierre-Luc
2016-06-20
RNA sequencing (RNAseq) has become the method of choice for transcriptome analysis, yet no consensus exists as to the most appropriate pipeline for its analysis, with current benchmarks suffering important limitations. Here, we address these challenges through a rich benchmarking resource harnessing (i) two RNAseq datasets including ERCC ExFold spike-ins; (ii) Nanostring measurements of a panel of 150 genes on the same samples; (iii) a set of internal, genetically-determined controls; (iv) a reanalysis of the SEQC dataset; and (v) a focus on relative quantification (i.e. across-samples). We use this resource to compare different approaches to each step of RNAseq analysis, from alignment to differential expression testing. We show that methods providing the best absolute quantification do not necessarily provide good relative quantification across samples, that count-based methods are superior for gene-level relative quantification, and that the new generation of pseudo-alignment-based software performs as well as established methods, at a fraction of the computing time. We also assess the impact of library type and size on quantification and differential expression analysis. Finally, we have created a R package and a web platform to enable the simple and streamlined application of this resource to the benchmarking of future methods.
Germain, Pierre-Luc; Vitriolo, Alessandro; Adamo, Antonio; Laise, Pasquale; Das, Vivek; Testa, Giuseppe
2016-01-01
RNA sequencing (RNAseq) has become the method of choice for transcriptome analysis, yet no consensus exists as to the most appropriate pipeline for its analysis, with current benchmarks suffering important limitations. Here, we address these challenges through a rich benchmarking resource harnessing (i) two RNAseq datasets including ERCC ExFold spike-ins; (ii) Nanostring measurements of a panel of 150 genes on the same samples; (iii) a set of internal, genetically-determined controls; (iv) a reanalysis of the SEQC dataset; and (v) a focus on relative quantification (i.e. across-samples). We use this resource to compare different approaches to each step of RNAseq analysis, from alignment to differential expression testing. We show that methods providing the best absolute quantification do not necessarily provide good relative quantification across samples, that count-based methods are superior for gene-level relative quantification, and that the new generation of pseudo-alignment-based software performs as well as established methods, at a fraction of the computing time. We also assess the impact of library type and size on quantification and differential expression analysis. Finally, we have created a R package and a web platform to enable the simple and streamlined application of this resource to the benchmarking of future methods.
Processing methods for differential analysis of LC/MS profile data
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Orešič Matej
2005-07-01
Full Text Available Abstract Background Liquid chromatography coupled to mass spectrometry (LC/MS has been widely used in proteomics and metabolomics research. In this context, the technology has been increasingly used for differential profiling, i.e. broad screening of biomolecular components across multiple samples in order to elucidate the observed phenotypes and discover biomarkers. One of the major challenges in this domain remains development of better solutions for processing of LC/MS data. Results We present a software package MZmine that enables differential LC/MS analysis of metabolomics data. This software is a toolbox containing methods for all data processing stages preceding differential analysis: spectral filtering, peak detection, alignment and normalization. Specifically, we developed and implemented a new recursive peak search algorithm and a secondary peak picking method for improving already aligned results, as well as a normalization tool that uses multiple internal standards. Visualization tools enable comparative viewing of data across multiple samples. Peak lists can be exported into other data analysis programs. The toolbox has already been utilized in a wide range of applications. We demonstrate its utility on an example of metabolic profiling of Catharanthus roseus cell cultures. Conclusion The software is freely available under the GNU General Public License and it can be obtained from the project web page at: http://mzmine.sourceforge.net/.
Wei, Shi-Tong; Sun, Yong-Hua; Zong, Shi-Hua
2017-09-01
The aim of the current study was to identify hub pathways of rheumatoid arthritis (RA) using a novel method based on differential pathway network (DPN) analysis. The present study proposed a DPN where protein‑protein interaction (PPI) network was integrated with pathway‑pathway interactions. Pathway data was obtained from background PPI network and the Reactome pathway database. Subsequently, pathway interactions were extracted from the pathway data by building randomized gene‑gene interactions and a weight value was assigned to each pathway interaction using Spearman correlation coefficient (SCC) to identify differential pathway interactions. Differential pathway interactions were visualized using Cytoscape to construct a DPN. Topological analysis was conducted to identify hub pathways that possessed the top 5% degree distribution of DPN. Modules of DPN were mined according to ClusterONE. A total of 855 pathways were selected to build pathway interactions. By filtrating pathway interactions of weight values >0.7, a DPN with 312 nodes and 791 edges was obtained. Topological degree analysis revealed 15 hub pathways, such as heparan sulfate/heparin‑glycosaminoglycan (HS‑GAG) degradation, HS‑GAG metabolism and keratan sulfate degradation for RA based on DPN. Furthermore, hub pathways were also important in modules, which validated the significance of hub pathways. In conclusion, the proposed method is a computationally efficient way to identify hub pathways of RA, which identified 15 hub pathways that may be potential biomarkers and provide insight to future investigation and treatment of RA.
A reconstruction method for cone-beam differential x-ray phase-contrast computed tomography.
Fu, Jian; Velroyen, Astrid; Tan, Renbo; Zhang, Junwei; Chen, Liyuan; Tapfer, Arne; Bech, Martin; Pfeiffer, Franz
2012-09-10
Most existing differential phase-contrast computed tomography (DPC-CT) approaches are based on three kinds of scanning geometries, described by parallel-beam, fan-beam and cone-beam. Due to the potential of compact imaging systems with magnified spatial resolution, cone-beam DPC-CT has attracted significant interest. In this paper, we report a reconstruction method based on a back-projection filtration (BPF) algorithm for cone-beam DPC-CT. Due to the differential nature of phase contrast projections, the algorithm restrains from differentiation of the projection data prior to back-projection, unlike BPF algorithms commonly used for absorption-based CT data. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a micro-focus x-ray tube source. Moreover, the numerical simulation and experimental results demonstrate that the proposed method can deal with several classes of truncated cone-beam datasets. We believe that this feature is of particular interest for future medical cone-beam phase-contrast CT imaging applications.
Methods for differentiating identity and sources of mixed petroleum pollutants in the environment
International Nuclear Information System (INIS)
Kaplan, I.R.; Alimi, H.; Lee, R.P.
1993-01-01
When crude or refined oil products enter the environment they begin to degrade by numerous microbiological or physical processes. The result of such changes is to alter the molecular composition of the product so that its source is unrecognizable by application of conventional EPA-type methodology. Numerous methods have been devised in the petroleum exploration industry to characterize source rock bitumens and reservoir hydrocarbons. A modification of these methods has been successfully applied at the authors company to identify the source of the fugitive hydrocarbons. For mildly altered products a statistical comparison is made using pattern recognition of the n-alkane distribution between C 10 -C 35 for heavy products and C 3 -C 10 for the gasoline range products. For highly altered products, a search is made for complex organic molecules that have undergone the least alteration, which include long chain polynuclear aromatic hydrocarbons and the polycyclic paraffinic hydrocarbons. These biomarker compounds have many isomeric forms which help characterize their sources. Elemental composition; especially sulfur, vanadium and nickel, and other transition and base metals help differentiate crude oil from refined products. Lead alkyls and MTBE are especially useful in determining residence time of gasoline products in soil and ground water. Petroporphyrin characterization can help differentiate crude oil from heavy refined oils or fluids. Stable isotope ratios are particularly useful for differentiating sources of highly altered petroleum products
International Nuclear Information System (INIS)
Bouferguene, Ahmed; Safouhi, Hassan
2006-01-01
In a previous work (Bouferguene 2005 J. Phys. A: Math. Gen. 38 3923), we have shown that in the framework of the Gaussian integral transform, multi-centre integrals over Slater type functions can be evaluated to an acceptable accuracy using a tailored Gauss quadrature in which the weight function has the form W(σ, τ; z) = z ν exp(-σz - τ/z). To be considered a solution worth implementing within a software for routine use in ab initio molecular simulations, the method must also prove to be at least as efficient as those methods previously published in the literature. Two major results are provided in this paper. Firstly, an improvement of the procedure used to generate the roots and weights of the Gauss-Bessel quadrature is proposed. Secondly, a computational cost analysis of the present method and the SD-bar (Safouhi 2001 J. Phys. A: Math. Gen. 34 2801) based approach are compared, hence proving the equivalence of the two from a complexity point of view
Method of Monitoring Urban Area Deformation Based on Differential TomoSAR
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WANG Aichun
2016-12-01
Full Text Available While the use of differential TomoSAR based on compressive sensing (CS makes it possible to solve the layover problem and reconstruct the deformation information of an observed urban area scene acquired by moderate-high resolution SAR satellite, the performance of the reconstruction decreases for a sparse and structural observed scene due to ignoring the structural characteristics of the observed scene. To deal with this issue, the method for differential SAR tomography based on Khatri-Rao subspace and block compressive sensing (KRS-BCS is proposed. The proposed method changes the reconstruction of the sparse and structural observed scene into a BCS problem under Khatri-Rao subspace, using the structure information of the observed scene and Khatri-Rao product property of the reconstructed observation matrix for differential TomoSAR, such that the KRS-BCS problem is efficiently solved with a block sparse l1/l2 norm optimization signal model, and the performance of resolution capability and reconstruction estimation is compared and analyzed qualitatively and quantitatively by the theoretical analysis and the simulation experiments, all of the results show the propose KRS-BCS method practicably overcomes the problems of CS method, as well as, quite maintains the high resolution characteristics, effectively reduces the probability of false scattering target and greatly improves the reconstruction accurate of scattering point. Finally, the application is taking the urban area of the Mobara(in Chiba, Japan as the test area and using 34 ENVISAT-ASAR images, the accuracy is verifying with the reference deformations derived from first level point data and GPS tracking data, the results show the trend is consistent and the overall deviation is small between reconstruction deformations of the propose KRS-BCS method and the reference deformations, and the accuracy is high in the estimation of the urban area deformation.
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A. H. Bhrawy
2014-01-01
Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.
Chaskalovic, Joël
2014-01-01
This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material, as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic
Evaluation of biochemical and molecular methods for Lactobacillus reuteri strains differentiation.
Andrea, Bilková; Hana, Kiňová Sepová; Martina, Dubničková; Hyacinta, Májeková; František, Bilka
2015-03-01
Several biochemical and molecular methods were used for discrimination of four Lactobacillus reuteri strains isolated from goatling and lamb stomach mucosa. Internal transcribed spacer (ITS)-PCR method and protein analysis by SDS-PAGE and MALDI-TOF showed to be suitable for strain discrimination whereas ITS-PCR/RFLP and enterobacterial repetitive intergenic consensus (ERIC)-PCR were not strain specific. The used methods differentiated tested strains into distinct groups; however, the location of strains in groups varied. Consistency in results was observed in the case of L. reuteri E and L. reuteri KO4m that were clustered into the same groups using all techniques, except of MALDI-TOF MS. The last one grouped goatling strains and lamb isolate into separate clusters. All investigated methods, except of ITS-PCR/RFLP and ERIC-PCR, were assessed as appropriate for distinguishing of L. reuteri strains.
An inverse method for non linear ablative thermics with experimentation of automatic differentiation
Energy Technology Data Exchange (ETDEWEB)
Alestra, S [Simulation Information Technology and Systems Engineering, EADS IW Toulouse (France); Collinet, J [Re-entry Systems and Technologies, EADS ASTRIUM ST, Les Mureaux (France); Dubois, F [Professor of Applied Mathematics, Conservatoire National des Arts et Metiers Paris (France)], E-mail: stephane.alestra@eads.net, E-mail: jean.collinet@astrium.eads.net, E-mail: fdubois@cnam.fr
2008-11-01
Thermal Protection System is a key element for atmospheric re-entry missions of aerospace vehicles. The high level of heat fluxes encountered in such missions has a direct effect on mass balance of the heat shield. Consequently, the identification of heat fluxes is of great industrial interest but is in flight only available by indirect methods based on temperature measurements. This paper is concerned with inverse analyses of highly evolutive heat fluxes. An inverse problem is used to estimate transient surface heat fluxes (convection coefficient), for degradable thermal material (ablation and pyrolysis), by using time domain temperature measurements on thermal protection. The inverse problem is formulated as a minimization problem involving an objective functional, through an optimization loop. An optimal control formulation (Lagrangian, adjoint and gradient steepest descent method combined with quasi-Newton method computations) is then developed and applied, using Monopyro, a transient one-dimensional thermal model with one moving boundary (ablative surface) that has been developed since many years by ASTRIUM-ST. To compute numerically the adjoint and gradient quantities, for the inverse problem in heat convection coefficient, we have used both an analytical manual differentiation and an Automatic Differentiation (AD) engine tool, Tapenade, developed at INRIA Sophia-Antipolis by the TROPICS team. Several validation test cases, using synthetic temperature measurements are carried out, by applying the results of the inverse method with minimization algorithm. Accurate results of identification on high fluxes test cases, and good agreement for temperatures restitutions, are obtained, without and with ablation and pyrolysis, using bad fluxes initial guesses. First encouraging results with an automatic differentiation procedure are also presented in this paper.
Directory of Open Access Journals (Sweden)
A. A. Hemeda
2013-01-01
Full Text Available An extension of the so-called new iterative method (NIM has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM and the variational iteration method (VIM reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.
Kieseler, Jan
2017-11-01
A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of systematic uncertainties. As a result of beneficial constraints from the data all such fitted parameters are correlated among each other. The best approach for a combination of these measurements would be the maximization of a combined likelihood, for which the full fit model of each measurement and the original data are required. However, only in rare cases this information is publicly available. In absence of this information most commonly used combination methods are not able to account for these correlations between uncertainties, which can lead to severe biases as shown in this article. The method discussed here provides a solution for this problem. It relies on the public result and its covariance or Hessian, only, and is validated against the combined-likelihood approach. A dedicated software package implementing this method is also presented. It provides a text-based user interface alongside a C++ interface. The latter also interfaces to ROOT classes for simple combination of binned measurements such as differential cross sections.
Energy Technology Data Exchange (ETDEWEB)
Kieseler, Jan [CERN, Geneva (Switzerland)
2017-11-15
A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of systematic uncertainties. As a result of beneficial constraints from the data all such fitted parameters are correlated among each other. The best approach for a combination of these measurements would be the maximization of a combined likelihood, for which the full fit model of each measurement and the original data are required. However, only in rare cases this information is publicly available. In absence of this information most commonly used combination methods are not able to account for these correlations between uncertainties, which can lead to severe biases as shown in this article. The method discussed here provides a solution for this problem. It relies on the public result and its covariance or Hessian, only, and is validated against the combined-likelihood approach. A dedicated software package implementing this method is also presented. It provides a text-based user interface alongside a C++ interface. The latter also interfaces to ROOT classes for simple combination of binned measurements such as differential cross sections. (orig.)
Shiraishi, Emi; Maeda, Kazuhiro; Kurata, Hiroyuki
2009-02-01
Numerical simulation of differential equation systems plays a major role in the understanding of how metabolic network models generate particular cellular functions. On the other hand, the classical and technical problems for stiff differential equations still remain to be solved, while many elegant algorithms have been presented. To relax the stiffness problem, we propose new practical methods: the gradual update of differential-algebraic equations based on gradual application of the steady-state approximation to stiff differential equations, and the gradual update of the initial values in differential-algebraic equations. These empirical methods show a high efficiency for simulating the steady-state solutions for the stiff differential equations that existing solvers alone cannot solve. They are effective in extending the applicability of dynamic simulation to biochemical network models.
International Nuclear Information System (INIS)
Katsaounis, T D
2005-01-01
The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall
International Nuclear Information System (INIS)
Rossi, Lubianka Ferrari Russo
2014-01-01
The main target of this study is to introduce a new method for calculating the coefficients of sensibility through the union of differential method and generalized perturbation theory, which are the two methods generally used in reactor physics to obtain such variables. These two methods, separated, have some issues turning the sensibility coefficients calculation slower or computationally exhaustive. However, putting them together, it is possible to repair these issues and build a new equation for the coefficient of sensibility. The method introduced in this study was applied in a PWR reactor, where it was performed the sensibility analysis for the production and 239 Pu conversion rate during 120 days (1 cycle) of burnup. The computational code used for both burnup and sensibility analysis, the CINEW, was developed in this study and all the results were compared with codes widely used in reactor physics, such as CINDER and SERPENT. The new mathematical method for calculating the sensibility coefficients and the code CINEW provide good numerical agility and also good efficiency and security, once the new method, when compared with traditional ones, provide satisfactory results, even when the other methods use different mathematical approaches. The burnup analysis, performed using the code CINEW, was compared with the code CINDER, showing an acceptable variation, though CINDER presents some computational issues due to the period it was built. The originality of this study is the application of such method in problems involving temporal dependence and, not least, the elaboration of the first national code for burnup and sensitivity analysis. (author)
International Nuclear Information System (INIS)
Kestens, V.; Zeleny, R.; Auclair, G.; Held, A.; Roebben, G.; Linsinger, T.P.J.
2011-01-01
Highlights: → Purity assessment of polycyclic aromatic hydrocarbons and chloramphenicol by DSC. → DSC results compared with traditional purity methods. → Different methods give different results, multiple method approach recommended. → DSC sensitive to impurities that have similar structures as main component. - Abstract: In this study the validity and suitability of differential scanning calorimetry (DSC) to determine the purity of selected polycyclic aromatic hydrocarbons and chloramphenicol has been investigated. The study materials were two candidate certified reference materials (CRMs), 6-methylchrysene and benzo[a]pyrene, and two different batches of commercially available highly pure chloramphenicol. The DSC results were compared with those obtained by other methods, namely gas and liquid chromatography with mass spectrometric detection, liquid chromatography with diode array detection, and quantitative nuclear magnetic resonance. The purity results obtained by these different analytical methods confirm the well-known challenges of comparing results of different method-defined measurands. In comparison with other methods, DSC has a much narrower working range. This limits the applicability of DSC as purity determination method, for instance during the assignment of the purity value of a CRM. Nevertheless, this study showed that DSC can be a powerful technique to detect impurities that are structurally very similar to the main purity component. From this point of view, and because of its good repeatability, DSC can be considered as a valuable technique to investigate the homogeneity and stability of candidate purity CRMs.
Gan, Lei; Zhang, Chunxia; Shangguan, Fangqin; Li, Xiuping
2012-06-01
The continuous cooling crystallization of a blast furnace slag was studied by the application of the differential scanning calorimetry (DSC) method. A kinetic model describing the correlation between the evolution of the degree of crystallization with time was obtained. Bulk cooling experiments of the molten slag coupled with numerical simulation of heat transfer were conducted to validate the results of the DSC methods. The degrees of crystallization of the samples from the bulk cooling experiments were estimated by means of the X-ray diffraction (XRD) and the DSC method. It was found that the results from the DSC cooling and bulk cooling experiments are in good agreement. The continuous cooling transformation (CCT) diagram of the blast furnace slag was constructed according to crystallization kinetic model and experimental data. The obtained CCT diagram characterizes with two crystallization noses at different temperature ranges.
The large discretization step method for time-dependent partial differential equations
Haras, Zigo; Taasan, Shlomo
1995-01-01
A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.
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.
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Srivastava, A.C.; Hazarika, G.C.
1990-01-01
An algorithm based on the shooting method has been developed for the solution of a two-point boundary value problem consisting of a system of third order simultaneous ordinary differential equations. The Falkner-Skan equations for electrically conducting viscous fluid with applied magnetic field has been solved by using this algorithm for various values of the wedge angle and magnetic parameters. The shooting method seems to be well convergent for a system as the results are in good agreement with those obtained by other methods. It is observed that both viscous boundary layer and magnetic boundary layer decrease while velocity as well as magnetic field increase with the increase of the wedge angle. (author). 6 tabs., 7 refs
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
Spectrum interrogation of fiber acoustic sensor based on self-fitting and differential method.
Fu, Xin; Lu, Ping; Ni, Wenjun; Liao, Hao; Wang, Shun; Liu, Deming; Zhang, Jiangshan
2017-02-20
In this article, we propose an interrogation method of fiber acoustic sensor to recover the time-domain signal from the sensor spectrum. The optical spectrum of the sensor will show a ripple waveform when responding to acoustic signal due to the scanning process in a certain wavelength range. The reason behind this phenomenon is the dynamic variation of the sensor spectrum while the intensity of different wavelength is acquired at different time in a scanning period. The frequency components can be extracted from the ripple spectrum assisted by the wavelength scanning speed. The signal is able to be recovered by differential between the ripple spectrum and its self-fitted curve. The differential process can eliminate the interference caused by environmental perturbations such as temperature or refractive index (RI), etc. The proposed method is appropriate for fiber acoustic sensors based on gratings or interferometers. A long period grating (LPG) is adopted as an acoustic sensor head to prove the feasibility of the interrogation method in experiment. The ability to compensate the environmental fluctuations is also demonstrated.
Directory of Open Access Journals (Sweden)
Minggang Dong
2014-01-01
Full Text Available Motivated by recent advancements in differential evolution and constraints handling methods, this paper presents a novel modified oracle penalty function-based composite differential evolution (MOCoDE for constrained optimization problems (COPs. More specifically, the original oracle penalty function approach is modified so as to satisfy the optimization criterion of COPs; then the modified oracle penalty function is incorporated in composite DE. Furthermore, in order to solve more complex COPs with discrete, integer, or binary variables, a discrete variable handling technique is introduced into MOCoDE to solve complex COPs with mix variables. This method is assessed on eleven constrained optimization benchmark functions and seven well-studied engineering problems in real life. Experimental results demonstrate that MOCoDE achieves competitive performance with respect to some other state-of-the-art approaches in constrained optimization evolutionary algorithms. Moreover, the strengths of the proposed method include few parameters and its ease of implementation, rendering it applicable to real life. Therefore, MOCoDE can be an efficient alternative to solving constrained optimization problems.
Survey of the status of finite element methods for partial differential equations
Temam, Roger
1986-01-01
The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.
Operational method of solution of linear non-integer ordinary and partial differential equations.
Zhukovsky, K V
2016-01-01
We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.
Directory of Open Access Journals (Sweden)
Henrik Haspel
2010-06-01
Full Text Available In dielectric relaxation spectroscopy the conduction contribution often hampers the evaluation of dielectric spectra, especially in the low-frequency regime. In order to overcome this the logarithmic derivative technique could be used, where the calculation of the logarithmic derivative of the real part of the complex permittivity function is needed. Since broadband dielectric measurement provides discrete permittivity function, numerical differentiation has to be used. Applicability of the Savitzky-Golay convolution method in the derivative analysis is examined, and a detailed investigation of the influential parameters (frequency, spectrum resolution, peak shape is presented on synthetic dielectric data.
DEFF Research Database (Denmark)
Botta, Filippo; Eriksen, Casper; Fontaine, Michaël C.
2015-01-01
1. In a recent paper, Bradburd et al. (Evolution, 67, 2013, 3258) proposed a model to quantify the relative effect of geographic and environmental distance on genetic differentiation. Here, we enhance this method in several ways. 2. We modify the covariance model so as to fit better with mainstre...... available as an R package called sunder. It takes as input georeferenced allele counts at the individual or population level for co-dominant markers. Program homepage: http://www2.imm.dtu.dk/~gigu/Sunder/....
International Nuclear Information System (INIS)
Ka-Lin, Su; Yuan-Xi, Xie
2010-01-01
By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. (general)
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…
A broken promise: microbiome differential abundance methods do not control the false discovery rate.
Hawinkel, Stijn; Mattiello, Federico; Bijnens, Luc; Thas, Olivier
2017-08-22
High-throughput sequencing technologies allow easy characterization of the human microbiome, but the statistical methods to analyze microbiome data are still in their infancy. Differential abundance methods aim at detecting associations between the abundances of bacterial species and subject grouping factors. The results of such methods are important to identify the microbiome as a prognostic or diagnostic biomarker or to demonstrate efficacy of prodrug or antibiotic drugs. Because of a lack of benchmarking studies in the microbiome field, no consensus exists on the performance of the statistical methods. We have compared a large number of popular methods through extensive parametric and nonparametric simulation as well as real data shuffling algorithms. The results are consistent over the different approaches and all point to an alarming excess of false discoveries. This raises great doubts about the reliability of discoveries in past studies and imperils reproducibility of microbiome experiments. To further improve method benchmarking, we introduce a new simulation tool that allows to generate correlated count data following any univariate count distribution; the correlation structure may be inferred from real data. Most simulation studies discard the correlation between species, but our results indicate that this correlation can negatively affect the performance of statistical methods. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Leak Rate Quantification Method for Gas Pressure Seals with Controlled Pressure Differential
Daniels, Christopher C.; Braun, Minel J.; Oravec, Heather A.; Mather, Janice L.; Taylor, Shawn C.
2015-01-01
An enhancement to the pressure decay leak rate method with mass point analysis solved deficiencies in the standard method. By adding a control system, a constant gas pressure differential across the test article was maintained. As a result, the desired pressure condition was met at the onset of the test, and the mass leak rate and measurement uncertainty were computed in real-time. The data acquisition and control system were programmed to automatically stop when specified criteria were met. Typically, the test was stopped when a specified level of measurement uncertainty was attained. Using silicone O-ring test articles, the new method was compared with the standard method that permitted the downstream pressure to be non-constant atmospheric pressure. The two methods recorded comparable leak rates, but the new method recorded leak rates with significantly lower measurement uncertainty, statistical variance, and test duration. Utilizing this new method in leak rate quantification, projects will reduce cost and schedule, improve test results, and ease interpretation between data sets.
Fuegemann, Christopher J; Samraj, Ajoy K; Walsh, Stuart; Fleischmann, Bernd K; Jovinge, Stefan; Breitbach, Martin
2010-12-01
Herein, we describe two protocols for the in vitro differentiation of mouse embryonic stem cells (mESCs) into cardiomyocytes. mESCs are pluripotent and can be differentiated into cells of all three germ layers, including cardiomyocytes. The methods described here facilitate the differentiation of mESCs into the different cardiac subtypes (atrial-, ventricular-, nodal-like cells). The duration of cell culture determines whether preferentially early- or late-developmental stage cardiomyocytes can be obtained preferentially. This approach allows the investigation of cardiomyocyte development and differentiation in vitro, and also allows for the enrichment and isolation of physiologically intact cardiomyocytes for transplantation purposes. © 2010 by John Wiley & Sons, Inc.
Directory of Open Access Journals (Sweden)
Mehmet Tarik Atay
2013-01-01
Full Text Available The Variational Iteration Method (VIM and Modified Variational Iteration Method (MVIM are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM and the Modified Variational Iteration Method (MVIM are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.
DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.
2008-06-01
For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).
International Nuclear Information System (INIS)
Song Lina; Wang Weiguo
2010-01-01
In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.
Edge detection of optical subaperture image based on improved differential box-counting method
Li, Yi; Hui, Mei; Liu, Ming; Dong, Liquan; Kong, Lingqin; Zhao, Yuejin
2018-01-01
Optical synthetic aperture imaging technology is an effective approach to improve imaging resolution. Compared with monolithic mirror system, the image of optical synthetic aperture system is often more complex at the edge, and as a result of the existence of gap between segments, which makes stitching becomes a difficult problem. So it is necessary to extract the edge of subaperture image for achieving effective stitching. Fractal dimension as a measure feature can describe image surface texture characteristics, which provides a new approach for edge detection. In our research, an improved differential box-counting method is used to calculate fractal dimension of image, then the obtained fractal dimension is mapped to grayscale image to detect edges. Compared with original differential box-counting method, this method has two improvements as follows: by modifying the box-counting mechanism, a box with a fixed height is replaced by a box with adaptive height, which solves the problem of over-counting the number of boxes covering image intensity surface; an image reconstruction method based on super-resolution convolutional neural network is used to enlarge small size image, which can solve the problem that fractal dimension can't be calculated accurately under the small size image, and this method may well maintain scale invariability of fractal dimension. The experimental results show that the proposed algorithm can effectively eliminate noise and has a lower false detection rate compared with the traditional edge detection algorithms. In addition, this algorithm can maintain the integrity and continuity of image edge in the case of retaining important edge information.
Differential equation methods for simulation of GFP kinetics in non-steady state experiments.
Phair, Robert D
2018-03-15
Genetically encoded fluorescent proteins, combined with fluorescence microscopy, are widely used in cell biology to collect kinetic data on intracellular trafficking. Methods for extraction of quantitative information from these data are based on the mathematics of diffusion and tracer kinetics. Current methods, although useful and powerful, depend on the assumption that the cellular system being studied is in a steady state, that is, the assumption that all the molecular concentrations and fluxes are constant for the duration of the experiment. Here, we derive new tracer kinetic analytical methods for non-steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes and linking them to a separate set of differential equations governing the kinetics of the fluorescent tracer. Linking the two sets of equations is based on a new application of the fundamental tracer principle of indistinguishability and, unlike current methods, supports correct dependence of tracer kinetics on cellular dynamics. This approach thus provides a general mathematical framework for applications of GFP fluorescence microscopy (including photobleaching [FRAP, FLIP] and photoactivation to frequently encountered experimental protocols involving physiological or pharmacological perturbations (e.g., growth factors, neurotransmitters, acute knockouts, inhibitors, hormones, cytokines, and metabolites) that initiate mechanistically informative intracellular transients. When a new steady state is achieved, these methods automatically reduce to classical steady state tracer kinetic analysis. © 2018 Phair. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).
Energy Technology Data Exchange (ETDEWEB)
Carella, Alfredo Raul
2012-09-15
Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)
International Nuclear Information System (INIS)
Siddiqi, S.H.; Hwangbo, C.C.; Silcox, V.; Good, R.C.; Snider, D.E. Jr.; Middlebrook, G.
1984-01-01
Rapid methods for the differentiation of Mycobacterium tuberculosis/M. bovis (TB complex) from other mycobacteria (MOTT bacilli) were developed and evaluated in a three-phase study. In the first phase, techniques for identification of Mycobacterium species were developed by using radiometric technology and BACTEC Middlebrook 7H12 liquid medium. Based on 14 CO 2 evolution, characteristic growth patterns were established for 13 commonly encountered mycobacterial species. Mycobacteria belonging to the TB complex were differentiated from other mycobacteria by cellular morphology and rate of 14 CO 2 evolution. For further differentiation, radiometric tests for niacin production and inhibition by Q-nitro-alpha-acetyl amino-beta-hydroxy-propiophenone (NAP) were developed. In the second phase, 100 coded specimens on Lowenstein-Jensen medium were identified as members of the TB complex, MOTT bacilli, bacteria other than mycobacteria, or ''no viable organisms'' within 3 to 12 (average 6.4) days of receipt from the Centers for Disease Control. Isolation and identification of mycobacteria from 20 simulated sputum specimens were carried out in phase III. Out of 20 sputum specimens, 16 contained culturable mycobacteria, and all of the positives were detected by the BACTEC method in an average of 7.3 days. The positive mycobacterial cultures were isolated and identified as TB complex or MOTT bacilli in an average of 12.8 days. The radiometric NAP test was found to be highly sensitive and specific for a rapid identification of TB complex, whereas the radiometric niacin test was found to have some inherent problems. Radiometric BACTEC and conventional methodologies were in complete agreement in Phase II as well as in Phase III
International Nuclear Information System (INIS)
Yu, Y H; Cheng, B
2012-01-01
The measurement of flow of tubular pump, in which the differential pressure of two measuring points within inlet passage is replaced by the mean differential pressure of two specified section of inlet passage to calibrate the relationship between flow and differential pressure, is developed. The numerical simulation on differential pressure of two measuring points within inlet passage, which is started before the pump set test, is carried out with the standard k-ε turbulence model and SIMPLEC algorithm. The comparison of the relationships between flow and differential pressure fitted respectively with the data from numerical simulation and pump set test shows that the calibration accuracy about two different sources of data is nearly same. The conclusion can be drawn that the calibration of the relationship between flow and differential pressure with CFD is feasible. The CFD-based flow measurement method, as a more simple and convenient way, can be applied in tubular pumps.
Directory of Open Access Journals (Sweden)
Priya Datta
2012-01-01
Full Text Available Aims: Carbapenems are usually the choice of antimicrobials in infections caused by Enterobacteriaceae bacteria-producing ESBL (extended spectrum β-lactamases and Amp C. Resistance to carbapenems is mostly due to production of enzymes - Carbapenemases, which are divided into Ambler Classes A, B and D. Phenotypic detection and differentiation of types of Carbapenemases in carbapenem-resistant Enterobacteriaceae (CRE is important for proper infection control and appropriate patient management. Materials and Methods: The present study done in a tertiary care hospital from North India differentiates Class A (KPC type and B (MBL type carbapenemases among Enterobacteriaceae isolates by simple phenotypic method that uses both the inhibitors EDTA and phenylboronic acid. Results: Total of 330 strains of Enterobacteriaceae were included in the study. Out of these 330 strains, 26 strains were resistant to carbapenems. The prevalence of CRE in our Institute is 7.87% (26/330. Conclusions: The prevalence of Enterobacteriaceae strains producing MBL type carbapenemase in our health care setup is 5.75% (19/330. None of the strains among the carbapenem-resistant bacterial isolates showed production of KPC enzyme. The need of the hour is simple, rapid and cost effective tests which will be able to identify and distinguish resistant pathogens for improved patient outcome, facilitating efficient infection control and reducing the escalation of resistance.
International Nuclear Information System (INIS)
Pokrovskij, A.V.; Kvasnitsa, M.S.
1979-01-01
Given are the estimates of information capabilities of the differential method for measuring radiation flux in radiation defectoscopy as well as efficiency of application of automatic radiation facilities to control taking into account the statistical regularities of product thickness fluctuations. Dependences of signal to noise ratio on the regularities of product thickness fluctuations have been found and optimization, on this basis, of the design and parameters of processing instrumentation was carried out. It is shown, that with 60-80 mm interval of product thickness fluctuations correlation (welded joints) it is expedient to use two radiation beams with their crossing on a mean product plane. When the interval of correlation of thickness fluctuations is great it is effective to use the geometry of radioscopy with parallel radiation beams. This permits to use only one radiation source without significant reducing the compensation efficiency, that in most cases simplifies the development and application of radiometric systems. Thus the efficiency of applying the differential method for radiation beam detection to compensate product thickness fluctuations is primarily determined by statistical regularities of the given fluctuations. The account of the regularities in the development of the processing instrumentation results in the most complete extraction of useful information, containing in the radiation beams being detected
Solving delay differential equations in S-ADAPT by method of steps.
Bauer, Robert J; Mo, Gary; Krzyzanski, Wojciech
2013-09-01
S-ADAPT is a version of the ADAPT program that contains additional simulation and optimization abilities such as parametric population analysis. S-ADAPT utilizes LSODA to solve ordinary differential equations (ODEs), an algorithm designed for large dimension non-stiff and stiff problems. However, S-ADAPT does not have a solver for delay differential equations (DDEs). Our objective was to implement in S-ADAPT a DDE solver using the methods of steps. The method of steps allows one to solve virtually any DDE system by transforming it to an ODE system. The solver was validated for scalar linear DDEs with one delay and bolus and infusion inputs for which explicit analytic solutions were derived. Solutions of nonlinear DDE problems coded in S-ADAPT were validated by comparing them with ones obtained by the MATLAB DDE solver dde23. The estimation of parameters was tested on the MATLB simulated population pharmacodynamics data. The comparison of S-ADAPT generated solutions for DDE problems with the explicit solutions as well as MATLAB produced solutions which agreed to at least 7 significant digits. The population parameter estimates from using importance sampling expectation-maximization in S-ADAPT agreed with ones used to generate the data. Published by Elsevier Ireland Ltd.
Recent symbolic summation methods to solve coupled systems of differential and difference equations
International Nuclear Information System (INIS)
Schneider, Carsten; Bluemlein, Johannes; Freitas, Abilio de
2014-07-01
We outline a new algorithm to solve coupled systems of differential equations in one continuous variable x (resp. coupled difference equations in one discrete variable N) depending on a small parameter ε: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in ε if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the ε-expansion of a ladder graph with 6 massive fermion lines.
Directory of Open Access Journals (Sweden)
Alice Jernigan
2015-01-01
Full Text Available Capillary electrophoresis single-strand conformational polymorphism (CE-SSCP was explored as a fast and inexpensive method to differentiate both prokaryotic (blue-green and eukaryotic (green and brown algae. A selection of two blue-green algae (Nostoc muscorum and Anabaena inaequalis, five green algae (Chlorella vulgaris, Oedogonium foveolatum, Mougeotia sp., Scenedesmus quadricauda, and Ulothrix fimbriata, and one brown algae (Ectocarpus sp. were examined and CE-SSCP electropherogram “fingerprints” were compared to each other for two variable regions of either the 16S or 18S rDNA gene. The electropherogram patterns were remarkably stable and consistent for each particular species. The patterns were unique to each species, although some common features were observed between the different types of algae. CE-SSCP could be a useful method for monitoring changes in an algae species over time as potential shifts in species occurred.
International Nuclear Information System (INIS)
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)
Abulkibash, Abdalla M; Sultan, Salah M; Al-Olyan, Abeer M; Al-Ghannam, Sheikha M
2003-10-17
A simple and rapid differential electrolytic potentiometric titration method for the determination of ciprofloxacin was developed. The work is based on the fast complexation reaction between iron(III) and ciprofloxacin in a ratio of 1:3, respectively, in sulfuric acid media of 0.09 mol dm(-3). Among the electrodes tested silver amalgam electrodes were found to be a suitable indicating system. By applying a current density of 0.5 muA cm(-2) to these electrodes and using iron(III) solution of 0.097 mol dm(-3) as a titrant, normal titration curves were obtained. The method was successfully applied for the determination of ciprofloxacin in drug formulations as low as 4.0 ppm.
Stable multi-domain spectral penalty methods for fractional partial differential equations
Xu, Qinwu; Hesthaven, Jan S.
2014-01-01
We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.
Recent symbolic summation methods to solve coupled systems of differential and difference equations
Energy Technology Data Exchange (ETDEWEB)
Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Freitas, Abilio de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2014-07-15
We outline a new algorithm to solve coupled systems of differential equations in one continuous variable x (resp. coupled difference equations in one discrete variable N) depending on a small parameter ε: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in ε if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the ε-expansion of a ladder graph with 6 massive fermion lines.
Kim, Jaehee; Ogden, Robert Todd; Kim, Haseong
2013-10-18
Time course gene expression experiments are an increasingly popular method for exploring biological processes. Temporal gene expression profiles provide an important characterization of gene function, as biological systems are both developmental and dynamic. With such data it is possible to study gene expression changes over time and thereby to detect differential genes. Much of the early work on analyzing time series expression data relied on methods developed originally for static data and thus there is a need for improved methodology. Since time series expression is a temporal process, its unique features such as autocorrelation between successive points should be incorporated into the analysis. This work aims to identify genes that show different gene expression profiles across time. We propose a statistical procedure to discover gene groups with similar profiles using a nonparametric representation that accounts for the autocorrelation in the data. In particular, we first represent each profile in terms of a Fourier basis, and then we screen out genes that are not differentially expressed based on the Fourier coefficients. Finally, we cluster the remaining gene profiles using a model-based approach in the Fourier domain. We evaluate the screening results in terms of sensitivity, specificity, FDR and FNR, compare with the Gaussian process regression screening in a simulation study and illustrate the results by application to yeast cell-cycle microarray expression data with alpha-factor synchronization.The key elements of the proposed methodology: (i) representation of gene profiles in the Fourier domain; (ii) automatic screening of genes based on the Fourier coefficients and taking into account autocorrelation in the data, while controlling the false discovery rate (FDR); (iii) model-based clustering of the remaining gene profiles. Using this method, we identified a set of cell-cycle-regulated time-course yeast genes. The proposed method is general and can be
Directory of Open Access Journals (Sweden)
Chao Wang
2018-02-01
Full Text Available The design and calibration of the cross-correlator are crucial issues for interferometric imaging systems. In this paper, an analog complex cross-correlator with output DC offsets and amplitudes calibration capability is proposed for interferometric passive millimeter-wave security sensing applications. By employing digital potentiometers in the low frequency amplification circuits of the correlator, the outputs characteristics of the correlator could be digitally controlled. A measurement system and a corresponding calibration scheme were developed in order to eliminate the output DC offsets and the quadrature amplitude error between the in-phase and the quadrature correlating subunits of the complex correlator. By using vector modulators to provide phase controllable correlated noise signals, the measurement system was capable of obtaining the output correlation circle of the correlator. When injected with −18 dBm correlated noise signals, the calibrated quadrature amplitude error was 0.041 dB and the calibrated DC offsets were under 26 mV, which was only 7.1% of the uncalibrated value. Furthermore, we also described a quadrature errors calibration algorithm in order to estimate the quadrature phase error and in order to improve the output phase accuracy of the correlator. After applying this calibration, we were able to reduce the output phase error of the correlator to 0.3°.
Statistical methods for detecting differentially abundant features in clinical metagenomic samples.
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James Robert White
2009-04-01
Full Text Available Numerous studies are currently underway to characterize the microbial communities inhabiting our world. These studies aim to dramatically expand our understanding of the microbial biosphere and, more importantly, hope to reveal the secrets of the complex symbiotic relationship between us and our commensal bacterial microflora. An important prerequisite for such discoveries are computational tools that are able to rapidly and accurately compare large datasets generated from complex bacterial communities to identify features that distinguish them.We present a statistical method for comparing clinical metagenomic samples from two treatment populations on the basis of count data (e.g. as obtained through sequencing to detect differentially abundant features. Our method, Metastats, employs the false discovery rate to improve specificity in high-complexity environments, and separately handles sparsely-sampled features using Fisher's exact test. Under a variety of simulations, we show that Metastats performs well compared to previously used methods, and significantly outperforms other methods for features with sparse counts. We demonstrate the utility of our method on several datasets including a 16S rRNA survey of obese and lean human gut microbiomes, COG functional profiles of infant and mature gut microbiomes, and bacterial and viral metabolic subsystem data inferred from random sequencing of 85 metagenomes. The application of our method to the obesity dataset reveals differences between obese and lean subjects not reported in the original study. For the COG and subsystem datasets, we provide the first statistically rigorous assessment of the differences between these populations. The methods described in this paper are the first to address clinical metagenomic datasets comprising samples from multiple subjects. Our methods are robust across datasets of varied complexity and sampling level. While designed for metagenomic applications, our software
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.
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Ching-Lin Hsiao
Full Text Available Advances in biotechnology have resulted in large-scale studies of DNA methylation. A differentially methylated region (DMR is a genomic region with multiple adjacent CpG sites that exhibit different methylation statuses among multiple samples. Many so-called "supervised" methods have been established to identify DMRs between two or more comparison groups. Methods for the identification of DMRs without reference to phenotypic information are, however, less well studied. An alternative "unsupervised" approach was proposed, in which DMRs in studied samples were identified with consideration of nature dependence structure of methylation measurements between neighboring probes from tiling arrays. Through simulation study, we investigated effects of dependencies between neighboring probes on determining DMRs where a lot of spurious signals would be produced if the methylation data were analyzed independently of the probe. In contrast, our newly proposed method could successfully correct for this effect with a well-controlled false positive rate and a comparable sensitivity. By applying to two real datasets, we demonstrated that our method could provide a global picture of methylation variation in studied samples. R source codes to implement the proposed method were freely available at http://www.csjfann.ibms.sinica.edu.tw/eag/programlist/ICDMR/ICDMR.html.
Discrete elements method of neutral particle transport
International Nuclear Information System (INIS)
Mathews, K.A.
1983-01-01
A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method
International Nuclear Information System (INIS)
Flip, A.; Pang, H.F.; D'Angelo, A.
1995-01-01
Due to the persistent uncertainties: ∼ 5 % (the uncertainty, here and there after, is at 1σ) in the prediction of the 'reactivity scale' (β eff ) for a fast power reactor, an international project was recently initiated in the framework of the OECD/NEA activities for reevaluation, new measurements and integral benchmarking of delayed neutron (DN) data and related kinetic parameters (principally β eff ). Considering that the major part of this uncertainty is due to uncertainties in the DN yields (v d ) and the difficulty for further improvement of the precision in differential (e.g. Keepin's method) measurements, an international cooperative strategy was adopted aiming at extracting and consistently interpreting information from both differential (nuclear) and integral (in reactor) measurements. The main problem arises from the integral side; thus the idea was to realize β eff like measurements (both deterministic and noise) in 'clean' assemblies. The 'clean' calculational context permitted the authors to develop a theory allowing to link explicitly this integral experimental level with the differential one, via a unified 'Master Model' which relates v d and measurables quantities (on both levels) linearly. The combined error analysis is consequently largely simplified and the final uncertainty drastically reduced (theoretically, by a factor √3). On the other hand the same theoretical development leading to the 'Master Model', also resulted in a structured scheme of approximations of the general (stochastic) Boltzmann equation allowing a consistent analysis of the large range of measurements concerned (stochastic, dynamic, static ... ). This paper is focused on the main results of this theoretical development and its application to the analysis of the Preliminary results of the BERENICE program (β eff measurements in MASURCA, the first assembly in CADARACHE-FRANCE)
ICM: an Integrated Compartment Method for numerically solving partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Yeh, G.T.
1981-05-01
An integrated compartment method (ICM) is proposed to construct a set of algebraic equations from a system of partial differential equations. The ICM combines the utility of integral formulation of finite element approach, the simplicity of interpolation of finite difference approximation, and the flexibility of compartment analyses. The integral formulation eases the treatment of boundary conditions, in particular, the Neumann-type boundary conditions. The simplicity of interpolation provides great economy in computation. The flexibility of discretization with irregular compartments of various shapes and sizes offers advantages in resolving complex boundaries enclosing compound regions of interest. The basic procedures of ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. The Navier-Stokes equations are used as an example of how to derive the corresponding ICM alogrithm for a given set of partial differential equations. Because of the structure of the algorithm, the basic computer program remains the same for cases in one-, two-, or three-dimensional problems.
SIVA/DIVA- INITIAL VALUE ORDINARY DIFFERENTIAL EQUATION SOLUTION VIA A VARIABLE ORDER ADAMS METHOD
Krogh, F. T.
1994-01-01
The SIVA/DIVA package is a collection of subroutines for the solution of ordinary differential equations. There are versions for single precision and double precision arithmetic. These solutions are applicable to stiff or nonstiff differential equations of first or second order. SIVA/DIVA requires fewer evaluations of derivatives than other variable order Adams predictor-corrector methods. There is an option for the direct integration of second order equations which can make integration of trajectory problems significantly more efficient. Other capabilities of SIVA/DIVA include: monitoring a user supplied function which can be separate from the derivative; dynamically controlling the step size; displaying or not displaying output at initial, final, and step size change points; saving the estimated local error; and reverse communication where subroutines return to the user for output or computation of derivatives instead of automatically performing calculations. The user must supply SIVA/DIVA with: 1) the number of equations; 2) initial values for the dependent and independent variables, integration stepsize, error tolerance, etc.; and 3) the driver program and operational parameters necessary for subroutine execution. SIVA/DIVA contains an extensive diagnostic message library should errors occur during execution. SIVA/DIVA is written in FORTRAN 77 for batch execution and is machine independent. It has a central memory requirement of approximately 120K of 8 bit bytes. This program was developed in 1983 and last updated in 1987.
Directory of Open Access Journals (Sweden)
Ganglong Yang
Full Text Available The best way to increase patient survival rate is to identify patients who are likely to progress to muscle-invasive or metastatic disease upfront and treat them more aggressively. The human cell lines HCV29 (normal bladder epithelia, KK47 (low grade nonmuscle invasive bladder cancer, NMIBC, and YTS1 (metastatic bladder cancer have been widely used in studies of molecular mechanisms and cell signaling during bladder cancer (BC progression. However, little attention has been paid to global quantitative proteome analysis of these three cell lines. We labeled HCV29, KK47, and YTS1 cells by the SILAC method using three stable isotopes each of arginine and lysine. Labeled proteins were analyzed by 2D ultrahigh-resolution liquid chromatography LTQ Orbitrap mass spectrometry. Among 3721 unique identified and annotated proteins in KK47 and YTS1 cells, 36 were significantly upregulated and 74 were significantly downregulated with >95% confidence. Differential expression of these proteins was confirmed by western blotting, quantitative RT-PCR, and cell staining with specific antibodies. Gene ontology (GO term and pathway analysis indicated that the differentially regulated proteins were involved in DNA replication and molecular transport, cell growth and proliferation, cellular movement, immune cell trafficking, and cell death and survival. These proteins and the advanced proteome techniques described here will be useful for further elucidation of molecular mechanisms in BC and other types of cancer.
A Differential Approach to Choosing Extracorporeal Detoxification Methods for Abdominal Sepsis
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L. Ye Shukevich
2005-01-01
Full Text Available A differential approach to choosing the methods of extracorporeal detoxification in the complex treatment of abdominal sepsis in the context of endogenous intoxication in order to enhance the efficiency of medical measures was pathogeneti-cally substantiated. In 51 patients diagnosed as having abdominal sepsis, the latter was characterized as the endogenous intoxication syndrome in relation to the accumulation of low and medium molecular-weight substances (plasma and red blood cells in the body and their physiological elimination with urine. An original formula was used to calculate the integral marker – the endogenous intoxication index correlating with the routine severity rating scales APACHE II and SOFA and reflecting the severity of endotoxicosis. According to the values of the endogenous intoxication index and to the sum of scores by the APACHE II and SOFA scales, the patients were divided into 3 groups of the clinicopathogenetic types of endogenous intoxication. According to the type of endogenous intoxication, the authors proposed a differential approach to choosing the modes of efferent therapy for abdominal sepsis: high-volume plasmapheresis in the subcompensated type and prolonged venovenous hemofiltration, which improved the results of treatment and reduced mortality rates.
Goswami, Deepjyoti; Pani, Amiya K.; Yadav, Sangita
2013-01-01
In the first part of this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to the standard mixed method for PIDE, the present method does not bank on a
Pawluski, Jodi L.; van Donkelaar, Eva; Abrams, Zipporah; Steinbusch, Harry W. M.; Charlier, Thierry D.
2014-01-01
Selective serotonin reuptake inhibitor medications are one of the most common treatments for mood disorders. In humans, these medications are taken orally, usually once per day. Unfortunately, administration of antidepressant medications in rodent models is often through injection, oral gavage, or minipump implant, all relatively stressful procedures. The aim of the present study was to investigate how administration of the commonly used SSRI, fluoxetine, via a wafer cookie, compares to fluoxetine administration using an osmotic minipump, with regards to serum drug levels and hippocampal plasticity. For this experiment, adult female Sprague-Dawley rats were divided over the two administration methods: (1) cookie and (2) osmotic minipump and three fluoxetine treatment doses: 0, 5, or 10 mg/kg/day. Results show that a fluoxetine dose of 5 mg/kg/day, but not 10 mg/kg/day, results in comparable serum levels of fluoxetine and its active metabolite norfluoxetine between the two administration methods. Furthermore, minipump administration of fluoxetine resulted in higher levels of cell proliferation in the granule cell layer (GCL) at a 5 mg dose compared to a 10 mg dose. Synaptophysin expression in the GCL, but not CA3, was significantly lower after fluoxetine treatment, regardless of administration method. These data suggest that the administration method and dose of fluoxetine can differentially affect hippocampal plasticity in the adult female rat. PMID:24757568
An odor interaction model of binary odorant mixtures by a partial differential equation method.
Yan, Luchun; Liu, Jiemin; Wang, Guihua; Wu, Chuandong
2014-07-09
A novel odor interaction model was proposed for binary mixtures of benzene and substituted benzenes by a partial differential equation (PDE) method. Based on the measurement method (tangent-intercept method) of partial molar volume, original parameters of corresponding formulas were reasonably displaced by perceptual measures. By these substitutions, it was possible to relate a mixture's odor intensity to the individual odorant's relative odor activity value (OAV). Several binary mixtures of benzene and substituted benzenes were respectively tested to establish the PDE models. The obtained results showed that the PDE model provided an easily interpretable method relating individual components to their joint odor intensity. Besides, both predictive performance and feasibility of the PDE model were proved well through a series of odor intensity matching tests. If combining the PDE model with portable gas detectors or on-line monitoring systems, olfactory evaluation of odor intensity will be achieved by instruments instead of odor assessors. Many disadvantages (e.g., expense on a fixed number of odor assessors) also will be successfully avoided. Thus, the PDE model is predicted to be helpful to the monitoring and management of odor pollutions.
An Odor Interaction Model of Binary Odorant Mixtures by a Partial Differential Equation Method
Directory of Open Access Journals (Sweden)
Luchun Yan
2014-07-01
Full Text Available A novel odor interaction model was proposed for binary mixtures of benzene and substituted benzenes by a partial differential equation (PDE method. Based on the measurement method (tangent-intercept method of partial molar volume, original parameters of corresponding formulas were reasonably displaced by perceptual measures. By these substitutions, it was possible to relate a mixture’s odor intensity to the individual odorant’s relative odor activity value (OAV. Several binary mixtures of benzene and substituted benzenes were respectively tested to establish the PDE models. The obtained results showed that the PDE model provided an easily interpretable method relating individual components to their joint odor intensity. Besides, both predictive performance and feasibility of the PDE model were proved well through a series of odor intensity matching tests. If combining the PDE model with portable gas detectors or on-line monitoring systems, olfactory evaluation of odor intensity will be achieved by instruments instead of odor assessors. Many disadvantages (e.g., expense on a fixed number of odor assessors also will be successfully avoided. Thus, the PDE model is predicted to be helpful to the monitoring and management of odor pollutions.
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
Babuška, Ivo; Nobile, Fabio; Tempone, Raul
2010-01-01
This work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms. These input data are assumed to depend on a finite number of random variables. The method consists of a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space, and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. It treats easily a wide range of situations, such as input data that depend nonlinearly on the random variables, diffusivity coefficients with unbounded second moments, and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate exponential convergence of the “probability error” with respect to the number of Gauss points in each direction of the probability space, under some regularity assumptions on the random input data. Numerical examples show the effectiveness of the method. Finally, we include a section with developments posterior to the original publication of this work. There we review sparse grid stochastic collocation methods, which are effective collocation strategies for problems that depend on a moderately large number of random variables.
Directory of Open Access Journals (Sweden)
Jodi L. Pawluski
2014-01-01
Full Text Available Selective serotonin reuptake inhibitor medications are one of the most common treatments for mood disorders. In humans, these medications are taken orally, usually once per day. Unfortunately, administration of antidepressant medications in rodent models is often through injection, oral gavage, or minipump implant, all relatively stressful procedures. The aim of the present study was to investigate how administration of the commonly used SSRI, fluoxetine, via a wafer cookie, compares to fluoxetine administration using an osmotic minipump, with regards to serum drug levels and hippocampal plasticity. For this experiment, adult female Sprague-Dawley rats were divided over the two administration methods: (1 cookie and (2 osmotic minipump and three fluoxetine treatment doses: 0, 5, or 10 mg/kg/day. Results show that a fluoxetine dose of 5 mg/kg/day, but not 10 mg/kg/day, results in comparable serum levels of fluoxetine and its active metabolite norfluoxetine between the two administration methods. Furthermore, minipump administration of fluoxetine resulted in higher levels of cell proliferation in the granule cell layer (GCL at a 5 mg dose compared to a 10 mg dose. Synaptophysin expression in the GCL, but not CA3, was significantly lower after fluoxetine treatment, regardless of administration method. These data suggest that the administration method and dose of fluoxetine can differentially affect hippocampal plasticity in the adult female rat.
International Nuclear Information System (INIS)
Kupka, F.
1997-11-01
This thesis deals with the extension of sparse grid techniques to spectral methods for the solution of partial differential equations with periodic boundary conditions. A review on boundary and initial-boundary value problems and a discussion on numerical resolution is used to motivate this research. Spectral methods are introduced by projection techniques, and by three model problems: the stationary and the transient Helmholtz equations, and the linear advection equation. The approximation theory on the hyperbolic cross is reviewed and its close relation to sparse grids is demonstrated. This approach extends to non-periodic problems. Various Sobolev spaces with dominant mixed derivative are introduced to provide error estimates for Fourier approximation and interpolation on the hyperbolic cross and on sparse grids by means of Sobolev norms. The theorems are immediately applicable to the stability and convergence analysis of sparse grid spectral methods. This is explicitly demonstrated for the three model problems. A variant of the von Neumann condition is introduced to simplify the stability analysis of the time-dependent model problems. The discrete Fourier transformation on sparse grids is discussed together with its software implementation. Results on numerical experiments are used to illustrate the performance of the new method with respect to the smoothness properties of each example. The potential of the method in mathematical modelling is estimated and generalizations to other sparse grid methods are suggested. The appendix includes a complete Fortran90 program to solve the linear advection equation by the sparse grid Fourier collocation method and a third-order Runge-Kutta routine for integration in time. (author)
Energy Technology Data Exchange (ETDEWEB)
Yan, Yan [Department of Physics, Huazhong Normal University, Wuhan (China); School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou (China); Zhu, Jia-pei [Department of Physics, Honghe University, Mengzi (China); Zhao, Shao-ming; Li, Gao-xiang [Department of Physics, Huazhong Normal University, Wuhan (China)
2015-01-01
The quadrature squeezing of a mechanical resonator (MR) coupled with two quantum dots (QDs) through the electromechanical coupling, where the QDs are driven by a strong and two weak laser fields is investigated. By tuning the gate voltage, the electron can be trapped in a quantum pure state. Under certain conditions, the discrepancies between the transition frequency and that of two weak fields are compensated by the phonons induced by the electromechanical coupling of the MR with QDs. In this case, some dissipative processes occur resonantly. The phonons created and (or) annihilated in these dissipative processes are correlated thus leading to the quadrature squeezing of the MR. A squeezed vacuum reservoir for the MR is built up. By tuning the gate voltage to control the energy structure of the QDs, the present squeezing scheme has strong resistance against the dephasing processes of the QDs in low temperature limit. The role of the temperature of the phonon reservoir is to damage squeezing of the MR. (copyright 2014 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)