Kiris, Cetin; Kwak, Dochan
1995-01-01
The fractional step and the pseudocompressibility methods for the solution of the incompressible Navier-Stokes equations are outlined. The fractional step method is based on finite-volume formulation and uses the pressure and the volume fluxes across the faces of each cell as dependent variables. The momentum equations are solved implicitly and the Poisson equation for the pressure is solved by using the multigrid method. The pseudocompressibility approach uses an implicit-higher-order-upwind differencing scheme for the convective terms together with the Gauss-Seidel line relaxation method. The dependent variables in the pseudocompressibility approach are the pressure and the cartesian velocity components in unstaggered mesh orientation. The 90-degree square duct flow, the wing-tip vortex wake flow and unsteady turbulent flows over an oscillating NACA 0015 airfoil are computed using both the fractional step and the pseudocompressibility methods. The results obtained from two different schemes are compared against experimental measurements.
FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE
Institute of Scientific and Technical Information of China (English)
Yuan Yirang
2005-01-01
Characteristic finite difference fractional step schemes are put forward. The electric Potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The mathematical model of the semiconductor device of heat conduction has been described by a system of four equations. The optimal order estimates in L2 norm are derived for the error in the approximates solution, putting forward a kind of characteristic finite difference fractional step methods.
ALE Fractional Step Finite Element Method for Fluid-Structure Nonlinear Interaction Problem
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.
Development of a three dimensional circulation model based on fractional step method
Abualtayef, Mazen; Kuroiwa, Masamitsu; Seif, Ahmed Khaled; Matsubara, Yuhei; Aly, Ahmed M.; Sayed, Ahmed A.; Sambe, Alioune Nar
2010-03-01
A numerical model was developed for simulating a three-dimensional multilayer hydrodynamic and thermodynamic model in domains with irregular bottom topography. The model was designed for examining the interactions between flow and topography. The model was based on the three-dimensional Navier-Stokes equations and was solved using the fractional step method, which combines the finite difference method in the horizontal plane and the finite element method in the vertical plane. The numerical techniques were described and the model test and application were presented. For the model application to the northern part of Ariake Sea, the hydrodynamic.
Institute of Scientific and Technical Information of China (English)
Yi-rang Yuan
2004-01-01
For compressible two-phase displacement problem,the modified upwind finite difference fractional steps schemes are put forward.Some techniques,such as calculus of variations,commutative law of multiplication of difference operators,decomposition of high order difference operators,the theory of prior estimates and techniques are used.Optimal order estimates in L 2 norm are derived for the error in the approximate solution.This method has already been applied to the numerical simulation of seawater intrusion and migration-accumulation of oil resources.
Modified AOAC three step method (officialmethod 2008.05): consolidation of fractions B and C.
Rastogi, Vipin K; Smith, Lisa S; Wallace, Lalena; Tomasino, Stephen F
2013-01-01
The AOAC Quantitative Three Step Method (TSM; AOAC Official Method SM 2008.05) is validated for testing the efficacy of liquid sporicides against spores of Bacillus subtilis and Bacillus anthracis on selected hard, nonporous, and porous surfaces. The TSM uses 5x5x1 mm inoculated coupons (carriers), which are placed in 400 microL liquid sporicidal agent contained in a microcentrifuge tube. Following exposure of inoculated carriers to the test chemical and subsequent neutralization, viable spores are recovered in three fractions: A (gentle tapping), B (sonication), and C (gentle agitation). The spores in suspension are serially diluted and plated on a recovery medium for enumeration. The plate counts are summed over the three fractions to provide the number of viable spores per carrier, which is log10-transformed to generate a mean log density (LD) value across carriers. As a measure of product efficacy, a log reduction (LR) value is calculated by subtracting the mean LD for treated carriers from the mean LD for control carriers. This paper reports on the comparative evaluation of the current and modified versions of the TSM in order to support a modification to simplify the procedure. The proposed modified TSM (mTSM) consolidates fractions B and C in the same tube. Thus, the sonication (fraction B) and gentle agitation (fraction C) steps are carried out in the same tube, thereby reducing the number of tubes and associated resources and time necessary to complete the test. Glass, steel, pine wood, and ceramic tile carriers were included in the comparative study. Inoculated carriers were evaluated against two preparations of sodium hypochlorite to generate two presumed levels of efficacy (intermediate and high); the control LD and LR values associated with testing each carrier type for the TSM and the mTSM were compared. For control carriers, the mean log densities per carrier (for each carrier material) were not significantly different based on the TSM compared to
Development of a three dimensional circulation model based on fractional step method
Directory of Open Access Journals (Sweden)
Mazen Abualtayef
2010-03-01
Full Text Available A numerical model was developed for simulating a three-dimensional multilayer hydrodynamic and thermodynamic model in domains with irregular bottom topography. The model was designed for examining the interactions between flow and topography. The model was based on the three-dimensional Navier-Stokes equations and was solved using the fractional step method, which combines the finite difference method in the horizontal plane and the finite element method in the vertical plane. The numerical techniques were described and the model test and application were presented. For the model application to the northern part of Ariake Sea, the hydrodynamic and thermodynamic results were predicted. The numerically predicted amplitudes and phase angles were well consistent with the field observations.
Institute of Scientific and Technical Information of China (English)
ZHAO Lan-hao; LI Tong-chun; WANG Ling; HERREROS M. I.; PASTOR M.
2006-01-01
A two-step Taylor-Galerkin fractional-step finite element method, which is of second order accuracy in space and time, was proposed for the three-dimensional free surface problem. With this method, the intermediate velocity was explicitly obtained by neglecting pressure gradient term, and then the velocity was corrected by adding the effects of pressure once the pressure field had been obtained from the pressure Poisson equation. The level set approach was applied to track implicitly the free surface. In order to track the free surface, the transport equation of the level set function was solved at each time step and the level set function is reinitialized through iteration to maintain it as a distance function. The governing equations of the system were discretized by the two- step Taylor-Galerkin method, which is of high-order accuracy and easy to be used. The validity and reliability of this method in this article were proved by two numerical examples.
Institute of Scientific and Technical Information of China (English)
袁益让
1999-01-01
For compressible two-phase displacement problem, a kind of characteristic finite difference fractional steps schemes is put forward and thick and thin grids are used to form a complete set. Some techniques, such as piecewise biquadratic interpolation, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L~2 norm are derived to determine the error in the approximate solution.
Cen, Wei; Hoppe, Ralph; Gu, Ning
2016-09-01
In this paper, we proposed a method to numerically determinate 3-dimensional thermal response due to electromagnetic exposure quickly and accurately. Due to the stability criterion the explicit finite-difference time-domain (FDTD) method works fast only if the spatial step is not set very small. In this paper, the semi-implicit Crank-Nicholson method for time domain discretization with unconditional time stability is proposed, where the idea of fractional steps method was utilized in 3-dimension so that an efficient numerical implementation is obtained. Compared with the explicit FDTD, with similar numerical precision, the proposed method takes less than 1/200 of the execution time.
Institute of Scientific and Technical Information of China (English)
Chang-feng Ma
2004-01-01
This paper provides an convergence analysis of a fractional-step projection method for the controlled-source electromagnetic induction problems in heterogenous electrically conducting media by means of finite element approximations. Error estimates in finite time are given. And it is verified that provided the time step τ is sufficiently small, the proposed algorithm yields for finite time T an error of (O)(hs + τ) in the L2-norm for the magnetic field H, where h is the mesh size and 1/2 ＜ s ≤ 1.
Institute of Scientific and Technical Information of China (English)
YUAN Yirang; LIANG Dong; RUI Hongxing
2006-01-01
Numerical simulation and analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations with initial-boundary problems. For a generic case of a three-dimensional bounded region, the modified method of upwind with finite difference fractional steps procedure is put forward. Optimal order estimates in L2 norm are derived for the error in the approximation solution. The present method has been successfully used in predicting the consequences of seawater intrusion and protection projects.
Institute of Scientific and Technical Information of China (English)
YUAN; Yiran(袁益让)
2002-01-01
For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques,such as implicit-explicit difference scheme, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources.
Institute of Scientific and Technical Information of China (English)
Yirang YUAN
2006-01-01
For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution.This method has already been applied to the numerical simulation of migration-accumulation of oil resources.
Rosas-Castor, J M; Portugal, L; Ferrer, L; Guzmán-Mar, J L; Hernández-Ramírez, A; Cerdà, V; Hinojosa-Reyes, L
2015-05-18
A fully automated modified three-step BCR flow-through sequential extraction method was developed for the fractionation of the arsenic (As) content from agricultural soil based on a multi-syringe flow injection analysis (MSFIA) system coupled to hydride generation-atomic fluorescence spectrometry (HG-AFS). Critical parameters that affect the performance of the automated system were optimized by exploiting a multivariate approach using a Doehlert design. The validation of the flow-based modified-BCR method was carried out by comparison with the conventional BCR method. Thus, the total As content was determined in the following three fractions: fraction 1 (F1), the acid-soluble or interchangeable fraction; fraction 2 (F2), the reducible fraction; and fraction 3 (F3), the oxidizable fraction. The limits of detection (LOD) were 4.0, 3.4, and 23.6 μg L(-1) for F1, F2, and F3, respectively. A wide working concentration range was obtained for the analysis of each fraction, i.e., 0.013-0.800, 0.011-0.900 and 0.079-1.400 mg L(-1) for F1, F2, and F3, respectively. The precision of the automated MSFIA-HG-AFS system, expressed as the relative standard deviation (RSD), was evaluated for a 200 μg L(-1) As standard solution, and RSD values between 5 and 8% were achieved for the three BCR fractions. The new modified three-step BCR flow-based sequential extraction method was satisfactorily applied for arsenic fractionation in real agricultural soil samples from an arsenic-contaminated mining zone to evaluate its extractability. The frequency of analysis of the proposed method was eight times higher than that of the conventional BCR method (6 vs 48 h), and the kinetics of lixiviation were established for each fraction.
Energy Technology Data Exchange (ETDEWEB)
Rosas-Castor, J.M. [Universidad Autónoma de Nuevo León, UANL, Facultad de Ciencias Químicas, Cd. Universitaria, San Nicolás de los Garza, Nuevo León, C.P. 66451 Nuevo León (Mexico); Group of Analytical Chemistry, Automation and Environment, University of Balearic Islands, Cra. Valldemossa km 7.5, 07122 Palma de Mallorca (Spain); Portugal, L.; Ferrer, L. [Group of Analytical Chemistry, Automation and Environment, University of Balearic Islands, Cra. Valldemossa km 7.5, 07122 Palma de Mallorca (Spain); Guzmán-Mar, J.L.; Hernández-Ramírez, A. [Universidad Autónoma de Nuevo León, UANL, Facultad de Ciencias Químicas, Cd. Universitaria, San Nicolás de los Garza, Nuevo León, C.P. 66451 Nuevo León (Mexico); Cerdà, V. [Group of Analytical Chemistry, Automation and Environment, University of Balearic Islands, Cra. Valldemossa km 7.5, 07122 Palma de Mallorca (Spain); Hinojosa-Reyes, L., E-mail: laura.hinojosary@uanl.edu.mx [Universidad Autónoma de Nuevo León, UANL, Facultad de Ciencias Químicas, Cd. Universitaria, San Nicolás de los Garza, Nuevo León, C.P. 66451 Nuevo León (Mexico)
2015-05-18
Highlights: • A fully automated flow-based modified-BCR extraction method was developed to evaluate the extractable As of soil. • The MSFIA–HG-AFS system included an UV photo-oxidation step for organic species degradation. • The accuracy and precision of the proposed method were found satisfactory. • The time analysis can be reduced up to eight times by using the proposed flow-based BCR method. • The labile As (F1 + F2) was <50% of total As in soil samples from As-contaminated-mining zones. - Abstract: A fully automated modified three-step BCR flow-through sequential extraction method was developed for the fractionation of the arsenic (As) content from agricultural soil based on a multi-syringe flow injection analysis (MSFIA) system coupled to hydride generation-atomic fluorescence spectrometry (HG-AFS). Critical parameters that affect the performance of the automated system were optimized by exploiting a multivariate approach using a Doehlert design. The validation of the flow-based modified-BCR method was carried out by comparison with the conventional BCR method. Thus, the total As content was determined in the following three fractions: fraction 1 (F1), the acid-soluble or interchangeable fraction; fraction 2 (F2), the reducible fraction; and fraction 3 (F3), the oxidizable fraction. The limits of detection (LOD) were 4.0, 3.4, and 23.6 μg L{sup −1} for F1, F2, and F3, respectively. A wide working concentration range was obtained for the analysis of each fraction, i.e., 0.013–0.800, 0.011–0.900 and 0.079–1.400 mg L{sup −1} for F1, F2, and F3, respectively. The precision of the automated MSFIA–HG-AFS system, expressed as the relative standard deviation (RSD), was evaluated for a 200 μg L{sup −1} As standard solution, and RSD values between 5 and 8% were achieved for the three BCR fractions. The new modified three-step BCR flow-based sequential extraction method was satisfactorily applied for arsenic fractionation in real agricultural
Fractional-step Tow-Thomas biquad filters
Freeborn, Todd J.; Maundy, Brent; Elwakil, Ahmed
In this paper we propose the use of fractional capacitors in the Tow-Thomas biquad to realize both fractional lowpass and asymmetric bandpass filters of order 0function approximation of the fractional capacitors. MATLAB and PSPICE simulations of first order fractional-step low and bandpass filters of order 1.1, 1.5, and 1.9 are given as examples. Experimental results of fractional low pass filters of order 1.5 implemented with silicon-fabricated fractional capacitors verify the operation of the fractional Tow-Thomas biquad.
Free Modal Algebras Revisited: The Step-by-Step Method
Bezhanishvili, N.; Ghilardi, Silvio; Jibladze, Mamuka
2012-01-01
We review the step-by-step method of constructing finitely generated free modal algebras. First we discuss the global step-by-step method, which works well for rank one modal logics. Next we refine the global step-by-step method to obtain the local step-by-step method, which is applicable beyond ran
Guermond, J.-L.
2011-01-01
In this paper we analyze the convergence properties of a new fractional time-stepping technique for the solution of the variable density incompressible Navier-Stokes equations. The main feature of this method is that, contrary to other existing algorithms, the pressure is determined by just solving one Poisson equation per time step. First-order error estimates are proved, and stability of a formally second-order variant of the method is established. © 2011 Society for Industrial and Applied Mathematics.
Conformable Fractional Nikiforov—Uvarov Method
Karayer, H.; Demirhan, D.; Büyükkılıç, F.
2016-07-01
We introduce conformable fractional Nikiforov—Uvarov (NU) method by means of conformable fractional derivative which is the most natural definition in non-integer calculus. Since, NU method gives exact eigenstate solutions of Schrödinger equation (SE) for certain potentials in quantum mechanics, this method is carried into the domain of fractional calculus to obtain the solutions of fractional SE. In order to demonstrate the applicability of the conformable fractional NU method, we solve fractional SE for harmonic oscillator potential, Woods—Saxon potential, and Hulthen potential.
Zayernouri, Mohsen; Matzavinos, Anastasios
2016-07-01
We first formulate a fractional class of explicit Adams-Bashforth (A-B) and implicit Adams-Moulton (A-M) methods of first- and second-order accuracy for the time-integration of 0 CD t τ u (x , t) = g (t ; u), τ ∈ (0 , 1 ], where 0 CD t τ denotes the fractional derivative in the Caputo sense. In this fractional setting and in contrast to the standard Adams methods, an extra history load term emerges and the associated weight coefficients are τ-dependent. However when τ = 1, the developed schemes reduce to the well-known A-B and A-M methods with standard coefficients. Hence, in terms of scientific computing, our approach constitutes a minimal modification of the existing Adams libraries. Next, we develop an implicit-explicit (IMEX) splitting scheme for linear and nonlinear fractional PDEs of a general advection-reaction-diffusion type, and we apply our scheme to the time-space fractional Keller-Segel chemotaxis system. In this context, we evaluate the nonlinear advection term explicitly, employing the fractional A-B method in the prediction step, and we treat the corresponding diffusion term implicitly in the correction step using the fractional A-M scheme. Moreover, we perform the corresponding spatial discretization by employing an efficient and spectrally-accurate fractional spectral collocation method. Our numerical experiments exhibit the efficiency of the proposed IMEX scheme in solving nonlinear fractional PDEs.
Institute of Scientific and Technical Information of China (English)
姚磊华
1997-01-01
A generalized upwind scheme with fractional steps for 3-D mathematical models of convection dominating groundwater quality is suggested. The mass transport equation is split into a convection equation and a dispersive equation. The generalized upwind scheme is used to solve the convection equation and the finite element method is used to compute the dispersive equation. These procedures which not only overcome the phenomenon of the negative concentration and numerical dispersion appear frequently with normal FEM or FDM to solve models of convection dominating groundwater transport but also avoid the step for computing each node velocity give a more suitable method to calculate the concentrations of the well points.
Closed-loop step response for tuning PID-fractional-order-filter controllers.
Amoura, Karima; Mansouri, Rachid; Bettayeb, Maâmar; Al-Saggaf, Ubaid M
2016-09-01
Analytical methods are usually applied for tuning fractional controllers. The present paper proposes an empirical method for tuning a new type of fractional controller known as PID-Fractional-Order-Filter (FOF-PID). Indeed, the setpoint overshoot method, initially introduced by Shamsuzzoha and Skogestad, has been adapted for tuning FOF-PID controller. Based on simulations for a range of first order with time delay processes, correlations have been derived to obtain PID-FOF controller parameters similar to those obtained by the Internal Model Control (IMC) tuning rule. The setpoint overshoot method requires only one closed-loop step response experiment using a proportional controller (P-controller). To highlight the potential of this method, simulation results have been compared with those obtained with the IMC method as well as other pertinent techniques. Various case studies have also been considered. The comparison has revealed that the proposed tuning method performs as good as the IMC. Moreover, it might offer a number of advantages over the IMC tuning rule. For instance, the parameters of the fractional controller are directly obtained from the setpoint closed-loop response data without the need of any model of the plant to be controlled.
Podlubny, Igor; Skovranek, Tomas; Vinagre Jara, Blas M; Petras, Ivo; Verbitsky, Viktor; Chen, YangQuan
2013-05-13
In this paper, we further develop Podlubny's matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributed-order derivatives. In this paper, for the first time, we present a variable-step-length approach that we call 'the method of large steps', because it is applied in combination with the matrix approach for each 'large step'. This new method is also illustrated by an easy-to-follow example. The presented approach allows fractional-order and distributed-order differentiation and integration of non-uniformly sampled signals, and opens the way to development of variable- and adaptive-step-length techniques for fractional- and distributed-order differential equations.
Directory of Open Access Journals (Sweden)
Yong-Ju Yang
2013-01-01
Full Text Available The local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators. The obtained results reveal that the method is very effective.
Directory of Open Access Journals (Sweden)
Friedrich Schuler
2015-08-01
Full Text Available The high throughput preparation of emulsions with high internal volume fractions is important for many different applications, e.g., drug delivery. However, most emulsification techniques reach only low internal volume fractions and need stable flow rates that are often difficult to control. Here, we present a centrifugal high throughput step emulsification disk for the fast and easy production of emulsions with high internal volume fractions above 95%. The disk produces droplets at generation rates of up to 3700 droplets/s and, for the first time, enables the generation of emulsions with internal volume fractions of >97%. The coefficient of variation between droplet sizes is very good (4%. We apply our system to show the in situ generation of gel emulsion. In the future, the recently introduced unit operation of centrifugal step emulsification may be used for the high throughput production of droplets as reaction compartments for clinical diagnostics or as starting material for micromaterial synthesis.
Intelligent numerical methods applications to fractional calculus
Anastassiou, George A
2016-01-01
In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.
TWO-STEP CONTROL GRADING METHOD
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The incorrectness of function grading in value engineering has been an essential problem for de- cades. This paper proposes a new method, where the functions under consideration are ranked in queue ac- cording to their importance and then graded quantitatively. By using this method, the reviewers are more aware of the degrees of importance, and therefore will have an easier time grasping the standard and reducing the erroneous grading. In the first step, the sign test is used to discard incorrect data, to count the grading re- sult and to arrange in queue according to the degrees of functional importance. In the second step the queued up functions undergo quantitative grading, where the “average value of fluctuation coefficient” is proposed to determine the control levels and to delete unreasonable data outside the controlled region so as to get more sati- sfactory grading value. The proposed method solves the problem of the incorrectness of function grading in val- ue engineering. It has been proved that the correctness has been raised from the original 70% to over 95% . This new method is not only contributive to the discipline of value engineering but also suitable in the evalu- ation of technical economy.
A short remark on fractional variational iteration method
Energy Technology Data Exchange (ETDEWEB)
He, Ji-Huan, E-mail: hejihuan@suda.edu.cn [National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123 (China)
2011-09-05
This Letter compares the classical variational iteration method with the fractional variational iteration method. The fractional complex transform is introduced to convert a fractional differential equation to its differential partner, so that its variational iteration algorithm can be simply constructed. -- Highlights: → The variational iteration method and its fractional modification are compared. → The demerits arising are overcome by the fractional complex transform. → The Letter provides a powerful tool to solving fractional differential equations.
Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach
Kiris, Cetin; Kwak, Dochan
1999-01-01
A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.
Directory of Open Access Journals (Sweden)
D. Vivek
2016-11-01
Full Text Available In this paper, the improved Euler method is used for solving hybrid fuzzy fractional differential equations (HFFDE of order $q \\in (0, 1 $ under Caputo-type fuzzy fractional derivatives. This method is based on the fractional Euler method and generalized Taylor's formula. The accuracy and efficiency of the proposed method is demonstrated by solving numerical examples.
Directory of Open Access Journals (Sweden)
Wei Li
2014-01-01
Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.
Approximate Solutions of Fractional Riccati Equations Using the Adomian Decomposition Method
Directory of Open Access Journals (Sweden)
Fei Wu
2014-01-01
Full Text Available The fractional derivative equation has extensively appeared in various applied nonlinear problems and methods for finding the model become a popular topic. Very recently, a novel way was proposed by Duan (2010 to calculate the Adomian series which is a crucial step of the Adomian decomposition method. In this paper, it was used to solve some fractional nonlinear differential equations.
Abdel-Salam, Emad A-B; Hassan, Gmal F
2015-01-01
In this paper, the fractional projective Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Burgers equation, the space-time fractional mKdV equation and time fractional biological population model. The solutions are expressed in terms of fractional hyperbolic functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The fractal index for the obtained results is equal to one. Counter examples to compute the fractal index are introduced in appendix.
The Complex-Step-Finite-Difference method
Abreu, Rafael; Stich, Daniel; Morales, Jose
2015-07-01
We introduce the Complex-Step-Finite-Difference method (CSFDM) as a generalization of the well-known Finite-Difference method (FDM) for solving the acoustic and elastic wave equations. We have found a direct relationship between modelling the second-order wave equation by the FDM and the first-order wave equation by the CSFDM in 1-D, 2-D and 3-D acoustic media. We present the numerical methodology in order to apply the introduced CSFDM and show an example for wave propagation in simple homogeneous and heterogeneous models. The CSFDM may be implemented as an extension into pre-existing numerical techniques in order to obtain fourth- or sixth-order accurate results with compact three time-level stencils. We compare advantages of imposing various types of initial motion conditions of the CSFDM and demonstrate its higher-order accuracy under the same computational cost and dispersion-dissipation properties. The introduced method can be naturally extended to solve different partial differential equations arising in other fields of science and engineering.
Feng, Qing-Hua
2014-08-01
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.
PARALLEL MULTI-STAGE & MULTI-STEP METHOD IN ODES
Institute of Scientific and Technical Information of China (English)
Xiao-qiu Song
2000-01-01
In this paper, the theory of parallel multi-stage & multi-step method is dis cussed, which is a form of combining Runge-Kutta method with linear multi-step method that can be used for parallel computation.
Directory of Open Access Journals (Sweden)
Sheng-Ping Yan
2014-01-01
Full Text Available We perform a comparison between the local fractional Adomian decomposition and local fractional function decomposition methods applied to the Laplace equation. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.
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Fanwei Meng
2013-01-01
Full Text Available A new fractional subequation method is proposed for finding exact solutions for fractional partial differential equations (FPDEs. The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. As applications, abundant exact solutions including solitary wave solutions as well as periodic wave solutions for the space-time fractional generalized Hirota-Satsuma coupled KdV equations are obtained by using this method.
Modified Homotopy Analysis Method for Nonlinear Fractional Partial Differential Equations
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D. Ziane
2017-05-01
Full Text Available In this paper, a combined form of natural transform with homotopy analysis method is proposed to solve nonlinear fractional partial differential equations. This method is called the fractional homotopy analysis natural transform method (FHANTM. The FHANTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHANTM is an appropriate method for solving nonlinear fractional partial differentia equation.
Guermond, Jean-Luc
2010-05-01
A new direction-splitting-based fractional time stepping is introduced for solving the incompressible Navier-Stokes equations. The main originality of the method is that the pressure correction is computed by solving a sequence of one-dimensional elliptic problems in each spatial direction. The method is very simple to program in parallel, very fast, and has exactly the same stability and convergence properties as the Poisson-based pressure-correction technique, either in standard or rotational form. © 2010 Académie des sciences.
EXPANSION OF STEP-TRANSITION OPERATOR OF MULTI-STEP METHOD AND ITS APPLICATIONS (I)
Institute of Scientific and Technical Information of China (English)
Yi-fa Tang
2002-01-01
We expand the step-transition operator of any linear multi-step method with order s ≥ 2 up to O(τs+5). And through examples we show how much the perturbation of the step-transition operator caused by the error of initial value is.
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.
Frankowski, Marcin; Zioła-Frankowska, Anetta; Siepak, Jerzy
2013-09-30
The paper presents the fractionation of aluminum in the samples of soil and plants of different species using a selective single-step extraction method. The study was conducted in the area located near a chemical plant, which for many years served as a post-crystallization leachate disposal site storing chemical waste (sector I), and in the area around the site: in Wielkopolski National Park, Rogalin Landscape Park and toward the infiltration ponds at the "Dębina" groundwater well-field for the city of Poznań (Poland) (sector II). The results of aluminum fractionation in samples of soil, leaves and plants showed heavy pollution with aluminum, especially in the water soluble aluminum fraction - Alsw (maximum concentration of aluminum in soil extract was 234.8 ± 4.8 mg kg(-1), in the leaves of Betula pendula it was 107.4 ± 1.8 mg kg(-1) and in the plants of Artemisia vulgaris (root) and Medicago sativa (leaves) it amounted to 464.7 ± 10.7 mg kg(-1)and 146.8 ± 1.2 mg kg(-1) respectively). In addition, the paper presents the problem of organic aluminum fractionation in biological samples and it shows the relationship between aluminum concentration in soil and the analysed woody and herbaceous species.
Lechleitner, Franziska A.; Jamieson, Robert A.; McIntyre, Cameron; Baldini, Lisa M.; Baldini, James U. L.; Eglinton, Timothy I.
2015-04-01
Over the past two decades, speleothems have become one of the most versatile and promising archives for the study of past continental climate. Very precise absolute dating is often possible using the U-Th method, resulting in paleoclimate records of exceptional resolution and accuracy. However, not all speleothems are amenable to this dating method for a variety of reasons (e.g. low U concentrations, high detrital Th etc). This has lead researchers to exclude many otherwise suitable speleothems and cave sites from further investigation. 14C-dating of speleothems has so far not been applicable, due to the 'dead carbon' problem. As drip water percolates through the karst, dissolving CaCO3, a variable amount of 14C-dead carbon is added to the solution. This results in a temporally variable and site-specific reservoir effect, ultimately undermining the development of speleothem 14C -chronologies. However, a number of recent studies have shown a clear link between karst hydrology and associated proxies (e.g., Mg/Ca and δ13C) and this 'dead carbon fraction' (DCF). We take advantage of this relationship to model DCF and its changes using Mg/Ca, δ13C and 14C data from published speleothem records. Using one record for calibration purposes, we build a transfer function for the DCF in relation to δ13C and Mg/Ca, which we then apply to other 14C records. Initial model results are promising; we are able to reconstruct general long-term average DCF within uncertainties of the calculated DCF from the U-Th chronology. Large shifts in DCF related to hydrology are also often detected. In a second step, we apply the model to a speleothem from southern Poland, which so far could not be dated, due to very low U-concentrations. To construct a 14C chronology, the stalagmite was sampled at 5 mm intervals. CaCO3 powders were graphitized and measured by Accelerator Mass Spectrometry (MICADAS) at ETH Zurich. Additional high-resolution (0.1 mm/sample) 14C measurements were performed on
Generalized Kudryashov Method for Time-Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Seyma Tuluce Demiray
2014-01-01
Full Text Available In this study, the generalized Kudryashov method (GKM is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. These time-fractional equations can be turned into another nonlinear ordinary differantial equation by travelling wave transformation. Then, GKM has been implemented to attain exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. Also, some new hyperbolic function solutions have been obtained by using this method. It can be said that this method is a generalized form of the classical Kudryashov method.
Homotopy-based methods for fractional differential equations
Ateş, Inan
2017-01-01
The intention of this thesis is two-fold. The first aim is to describe and apply, series-based, numerical methods to fractional differential equation models. For this, it is needed to distinguish between space-fractional and time-fractional derivatives. The second goal of this thesis is to give a
Directory of Open Access Journals (Sweden)
Emad A.-B. Abdel-Salam
2013-01-01
Full Text Available The fractional Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, space-time fractional Korteweg-de Vries equation, regularized long-wave equation, Boussinesq equation, and Klein-Gordon equation are considered. As a result, abundant types of exact analytical solutions are obtained. These solutions include generalized trigonometric and hyperbolic functions solutions which may be useful for further understanding of the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The periodic and kink solutions are founded as special case.
Directory of Open Access Journals (Sweden)
Fei Xu
2016-01-01
Full Text Available This paper is aimed at constructing fractional power series (FPS solutions of time-space fractional Boussinesq equations using residual power series method (RPSM. Firstly we generalize the idea of RPSM to solve any-order time-space fractional differential equations in high-dimensional space with initial value problems in Rn. Using RPSM, we can obtain FPS solutions of fourth-, sixth-, and 2nth-order time-space fractional Boussinesq equations in R and fourth-order time-space fractional Boussinesq equations in R2 and Rn. Finally, by numerical experiments, it is shown that RPSM is a simple, effective, and powerful method for seeking approximate analytic solutions of fractional differential equations.
Arshad, Muhammad; Lu, Dianchen; Wang, Jun
2017-07-01
In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.
Chebyshev Finite Difference Method for Fractional Boundary Value Problems
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Boundary
2015-09-01
Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative
Rajagopal, Karthikeyan; Karthikeyan, Anitha; Duraisamy, Prakash
2016-12-01
In this paper we investigate the control of three-dimensional non-autonomous fractional-order model of a permanent magnet synchronous motor (PMSM) and PI controlled fractional order Induction motor via recursive extended back stepping control technique. A robust generalized weighted controllers are derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results.
Improved step-by-step chromaticity compensation method for chromatic sextupole optimization
Liu, Gang-Wen; Jia, Qi-Ka; Li, Wei-Min; Wang, Lin
2015-01-01
The step-by-step chromaticity compensation method for chromatic sextupole optimization and dynamic aperture increase was proposed by E. Levichev and P. Piminov (E. Levichev and P. Piminov, 2006 [1]). Although this method can be used to enlarge the dynamic aperture of storage ring, it has some drawbacks. In this paper, we combined this method with evolutionary computation algorithms, and proposed an improved version of this method. In the improved method, the drawbacks are avoided, and thus better optimization results can be obtained.
Differential operator multiplication method for fractional differential equations
Tang, Shaoqiang; Ying, Yuping; Lian, Yanping; Lin, Stephen; Yang, Yibo; Wagner, Gregory J.; Liu, Wing Kam
2016-08-01
Fractional derivatives play a very important role in modeling physical phenomena involving long-range correlation effects. However, they raise challenges of computational cost and memory storage requirements when solved using current well developed numerical methods. In this paper, the differential operator multiplication method is proposed to address the issues by considering a reaction-advection-diffusion equation with a fractional derivative in time. The linear fractional differential equation is transformed into an integer order differential equation by the proposed method, which can fundamentally fix the aforementioned issues for select fractional differential equations. In such a transform, special attention should be paid to the initial conditions for the resulting differential equation of higher integer order. Through numerical experiments, we verify the proposed method for both fractional ordinary differential equations and partial differential equations.
An improved 4-step commutation method application for matrix converter
DEFF Research Database (Denmark)
Guo, Yu; Guo, Yougui; Deng, Wenlang
2014-01-01
A novel four-step commutation method is proposed for matrix converter cell, 3 phase inputs to 1 phase output in this paper, which is obtained on the analysis of published commutation methods for matrix converter. The first and fourth step can be shorter than the second or third one. The discussed...... method here is implemented by programming in VHDL language. Finally, the novel method in this paper is verified by experiments....
The step-by-step CFD design method of pressure-compensating emitter
Institute of Scientific and Technical Information of China (English)
Wei Zhengying
2013-01-01
In order to improve the design and research and development (R & D) efficiency of the pressure-compensating drip irrigation emitter,a step-by-step computational fluid dynamics (CFD) design method was proposed based on CFD theory combined with the finite element method.By analyzing its hydraulic performance through the step-by-step CFD method,the prediction pressure-flow curve(p-Q curve) of the pressure-compensat-ing emitter was obtained.Then the test samples were fabricated using rapid prototype and manufacturing (RP & M) technology.The emitters' hydraulic performance experiment was carried out and the experimental p-Q curve was obtained.The step-by-step CFD design method was verified by comparing the experimental p-Q curve with the prediction values,which showed that the prediction values met the experimental results well within the normal range of the emitter's working pressure.On this basis,the effect of the emitter structure on its pressure-compensating performance was studied,which showed that the height of the pressure-compensating region had significant effects on the emitter's pressure-compensating performance.Series products of the pressure-compensating emitter could be designed by changing the region's height.
Solving systems of fractional differential equations using differential transform method
Erturk, Vedat Suat; Momani, Shaher
2008-05-01
This paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. Some examples are solved as illustrations, using symbolic computation. The numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations.
Identification of fractional order systems using modulating functions method
Liu, Dayan
2013-06-01
The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.
Devices, systems, and methods for microscale isoelectric fractionation
Energy Technology Data Exchange (ETDEWEB)
Sommer, Gregory J.; Hatch, Anson V.; Wang, Ying-Chih; Singh, Anup K.
2016-08-09
Embodiments of the present invention provide devices, systems, and methods for microscale isoelectric fractionation. Analytes in a sample may be isolated according to their isoelectric point within a fractionation microchannel. A microfluidic device according to an embodiment of the invention includes a substrate at least partially defining a fractionation microchannel. The fractionation microchannel has at least one cross-sectional dimension equal to or less than 1 mm. A plurality of membranes of different pHs are disposed in the microchannel. Analytes having an isoelectric point between the pH of the membranes may be collected in a region of the fractionation channel between the first and second membranes through isoelectric fractionation.
Directory of Open Access Journals (Sweden)
Emad A-B. Abdel-Salam
2015-06-01
Full Text Available In this paper, the improved fractional Riccati expansion method is proposed to solve fractional differential equations. The method is applied to solve space–time fractional modified Korteweg–de Vries equation, space–time fractional modified regularized long-wave equation, time fractional biological population model, and space–time fractional Klein–Gordon equation. The obtained solutions include generalized trigonometric and hyperbolic functions solutions. Among these solutions, some are found for the first time.
Directory of Open Access Journals (Sweden)
Birol İbiş
2014-01-01
Full Text Available This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE involving Jumarie’s modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM. FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs.
Directory of Open Access Journals (Sweden)
Ammar Ali Neamah
2014-01-01
Full Text Available The paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations.
A STEP-BY-STEP INTEGRAL METHOD FOR ACTIVELY CONTROLLED STRUCTURES
Institute of Scientific and Technical Information of China (English)
蔡国平; 黄金枝
2002-01-01
A new active control method was proposed, in which the analytical control law was deduced by using astep-by-step integral method to differential equation of motion under the condition of static error being zero. Thiscontrol law is terse in mathematical expression and convenient for practical use. The simulation results demon-strate that the proposed method can provide much more remarkable peak-response reduction of seismically excitedstructures than the classical LQR method.
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.
A time stepping method in analysis of nonlinear structural dynamics
Directory of Open Access Journals (Sweden)
Gholampour A. A.
2011-12-01
Full Text Available In this paper a new method is proposed for the direct time integration method for structural dynamics problems. The proposed method assumes second order variations of the acceleration at each time step. Therefore more terms in the Taylor series expansion were used compared to other methods. Because of the increase in order of variations of acceleration, this method has higher accuracy than classical methods. The displacement function is a polynomial with five constants and they are calculated using: two equations for initial conditions (from the end of previous time step, two equations for satisfying the equilibrium at both ends of the time step, and one equation for the weighted residual integration. Proposed method has higher stability and order of accuracy than the other methods.
Monotone method for initial value problem for fractional diffusion equation
Institute of Scientific and Technical Information of China (English)
ZHANG Shuqin
2006-01-01
Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation.
Song, Junqiang; Leng, Hongze; Lu, Fengshun
2014-01-01
We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303
A new method for petroleum fractions and crude oil characterization
Energy Technology Data Exchange (ETDEWEB)
Castells, F. (Univ. of Barcelono (ES)); Miquel, J. (Politechnic Univ. of Catalunya (ES)); Hernandez, J. (Repsol S.A. Co. (ES))
1992-05-01
In this paper a new procedure for petroleum fraction and crude oil characterization is proposed that is based on pseudocomponent breakdown by the integral method. The method requires only the atmospheric true-boiling-point (TBP) distillation curve and whole-fraction density. The pseudocomponents are obtained by sequentially applying an optimization procedure in which the mass balance is accomplished exactly and the molar-balance error is minimized.
An efficient method for solving fractional Hodgkin-Huxley model
Nagy, A. M.; Sweilam, N. H.
2014-06-01
In this paper, we present an accurate numerical method for solving fractional Hodgkin-Huxley model. A non-standard finite difference method (NSFDM) is implemented to study the dynamic behaviors of the proposed model. The Grünwald-Letinkov definition is used to approximate the fractional derivatives. Numerical results are presented graphically reveal that NSFDM is easy to implement, effective and convenient for solving the proposed model.
A new mixed element method for a class of time-fractional partial differential equations.
Liu, Yang; Li, Hong; Gao, Wei; He, Siriguleng; Fang, Zhichao
2014-01-01
A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω) space. Some a priori error estimates in L (2)-norm for the scalar unknown u and in (L (2))(2)-norm for its gradient σ. Moreover, we also discuss a priori error estimates in H (1)-norm for the scalar unknown u.
A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
Yang Liu
2014-01-01
Full Text Available A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple L2Ω2 space replacing the complex H(div;Ω space. Some a priori error estimates in L2-norm for the scalar unknown u and in L22-norm for its gradient σ. Moreover, we also discuss a priori error estimates in H1-norm for the scalar unknown u.
Strong Stability Preserving Two-step Runge–Kutta Methods
Ketcheson, David I.
2011-12-22
We investigate the strong stability preserving (SSP) property of two-step Runge–Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge–Kutta methods have order at most four, we prove that explicit SSP TSRK methods have order at most eight. We present explicit TSRK methods of up to eighth order that were found by numerical search. These methods have larger SSP coefficients than any known methods of the same order of accuracy and may be implemented in a form with relatively modest storage requirements. The usefulness of the TSRK methods is demonstrated through numerical examples, including integration of very high order weighted essentially non-oscillatory discretizations.
Solutions of fractional diffusion equations by variation of parameters method
Directory of Open Access Journals (Sweden)
Mohyud-Din Syed Tauseef
2015-01-01
Full Text Available This article is devoted to establish a novel analytical solution scheme for the fractional diffusion equations. Caputo’s formulation followed by the variation of parameters method has been employed to obtain the analytical solutions. Following the derived analytical scheme, solution of the fractional diffusion equation for several initial functions has been obtained. Graphs are plotted to see the physical behavior of obtained solutions.
Discrete Direct Methods in the Fractional Calculus of Variations
Pooseh, Shakoor; Almeida, Ricardo; Torres, Delfim F. M.
2012-01-01
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann– Liouville fractional derivative. Using the Gr¨unwald–Letnikov definition, we approximate the objective functional in...
Reproducing Kernel Method for Fractional Riccati Differential Equations
Directory of Open Access Journals (Sweden)
X. Y. Li
2014-01-01
Full Text Available This paper is devoted to a new numerical method for fractional Riccati differential equations. The method combines the reproducing kernel method and the quasilinearization technique. Its main advantage is that it can produce good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results are compared with some existing methods to show the accuracy and effectiveness of the present method.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
An efficient method for solving fractional Hodgkin–Huxley model
Energy Technology Data Exchange (ETDEWEB)
Nagy, A.M., E-mail: abdelhameed_nagy@yahoo.com [Department of Mathematics, Faculty of Science, Benha University, 13518 Benha (Egypt); Sweilam, N.H., E-mail: n_sweilam@yahoo.com [Department of Mathematics, Faculty of Science, Cairo University, 12613 Giza (Egypt)
2014-06-13
In this paper, we present an accurate numerical method for solving fractional Hodgkin–Huxley model. A non-standard finite difference method (NSFDM) is implemented to study the dynamic behaviors of the proposed model. The Grünwald–Letinkov definition is used to approximate the fractional derivatives. Numerical results are presented graphically reveal that NSFDM is easy to implement, effective and convenient for solving the proposed model. - Highlights: • An accurate numerical method for solving fractional Hodgkin–Huxley model is given. • Non-standard finite difference method (NSFDM) is implemented to the proposed model. • NSFDM can solve differential equations involving derivatives of non-integer order. • NDFDM is very powerful and efficient technique for solving the proposed model.
An explicit high order method for fractional advection diffusion equations
Sousa, Ercília
2014-12-01
We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1convergence of the numerical method through consistency and stability. The order of convergence varies between two and three and for advection dominated flows is close to three. Although the method is conditionally stable, the restrictions allow wide stability regions. The analysis is confirmed by numerical examples.
On the effect of intrafraction motion in a single fraction step-shoot IMRT.
Zhuang, Tingliang
2015-07-01
The authors studied the respiratory motion effect in a single step-shoot intensity modulated radiotherapy (IMRT) to assess the basic properties of the uncertainty in the delivered dose due to the unknown starting phase of the motion. Using computer simulations, the motion-averaged dose for open beams with various field sizes was calculated for two one-dimensional trajectories with different motion amplitudes at 20 equally spaced starting phases. The properties of the standard deviation (SD) of delivered dose were analyzed. The dependence of SD on the field size, motion amplitude, and delivery time was investigated and experimentally validated. To study effect of number of small monitor unit (MU) segments on the dose uncertainty, the authors generated 1000 pairs of multisegment beams such that each pair consists of two beams with the same total MU and different segment MU. The SD at the central axis point was compared for each pair. The authors proved that the direct time-dependent dose accumulation can be calculated using a convolution formula for a single fraction step-shoot IMRT treatment. Single segment simulation showed that the maximum dose uncertainty occurred symmetrically at the beam penumbra for a sinusoidal motion. For other sinusoidal motions (sin(2n) n > 1), the maximum dose uncertainty occurred at asymmetrical locations and may be beyond the penumbra region. The SD of relative dose periodically varied with delivery time with decreasing envelope for both motion trajectories. The SD of absolute dose was a periodic function of the delivery time for a given field size and motion amplitude and was proved to be true for any periodic motion. The SD reduced to zero when the delivery time was an integer multiple of the motion period. Analytical function σA=3βsin(2)π/Tδt-4/3sin(4)π/Tδt+2/3sin(6)π/Tδt was found to fit the delivery time dependence of the SD for motions studied in this paper and was verified with experimental data and an irregular motion
Application of triple potential step amperometry method for quantitative electroanalysis
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A novel quantitative electroanalysis method, triple potential step amperometry (TPSA), was developed and explained with an example of nitrobenzene analyzing in water. The selectivity of TPSA was improved by controlling the potential step within a narrow interval and using enzyme-modified electrode, the narrow potential step makes the method avoid most interferents, and enzyme-modified electrode can enhance the response of target substance selectively. The peak area was investigated for quantitative calibration, such as nitrobenzene concentration showing a linear relation with the peak area, with the correlation coefficients being 0.9995. The t-test and F-test were applied to evaluating the reliability of TPSA, the results showed that there was no evidence of systematic error for TPSA, and the method was of no significant difference from CV. The merit of fast detecting and few potential changing times make the TPSA suitably applicable to low-cost automatic monitoring equipments.
Plante, Ianik; Devroye, Luc
2017-10-01
Ionizing radiation interacts with the water molecules of the tissues mostly by ionizations and excitations, which result in the formation of the radiation track structure and the creation of radiolytic species such as H.,.OH, H2, H2O2, and e-aq. After their creation, these species diffuse and may chemically react with the neighboring species and with the molecules of the medium. Therefore radiation chemistry is of great importance in radiation biology. As the chemical species are not distributed homogeneously, the use of conventional models of homogeneous reactions cannot completely describe the reaction kinetics of the particles. Actually, many simulations of radiation chemistry are done using the Independent Reaction Time (IRT) method, which is a very fast technique to calculate radiochemical yields but which do not calculate the positions of the radiolytic species as a function of time. Step-by-step (SBS) methods, which are able to provide such information, have been used only sparsely because these are time-consuming in terms of calculation. Recent improvements in computer performance now allow the regular use of the SBS method in radiation chemistry. The SBS and IRT methods are both based on the Green's functions of the diffusion equation (GFDE). In this paper, several sampling algorithms of the GFDE and for the IRT method are presented. We show that the IRT and SBS methods are exactly equivalent for 2-particles systems for diffusion and partially diffusion-controlled reactions between non-interacting particles. We also show that the results obtained with the SBS simulation method with periodic boundary conditions are in agreement with the predictions by classical reaction kinetics theory, which is an important step towards using this method for modelling of biochemical networks and metabolic pathways involved in oxidative stress. Finally, the first simulation results obtained with the code RITRACKS (Relativistic Ion Tracks) are presented.
A Step by Step Method to Improve the Performance of Decision Making Units
Directory of Open Access Journals (Sweden)
M. Izadikhah
2015-03-01
Full Text Available In this paper, we present the concept of context-dependent DEA based on the FDH model by introducing the FDH-attractiveness and FDH-progress for each DMU. By the presented method, not only we can improve the performance of inefficient DMUs, but we can find a target for improvement among the existing efficient DMUs. These targets are observed DMUs and are not some virtual points on the efficiency frontier. Also, the paper presents a step by step method to improve the performance of DMUs by measuring FDH-attractiveness and FDH-progress. One numerical example and a case study consists of 20 Iranian bank branches are given for illustration.
Composite-step product methods for solving nonsymmetric linear systems
Energy Technology Data Exchange (ETDEWEB)
Chan, T.F.; Szeto, T. [Univ. of California, Los Angeles, CA (United States)
1994-12-31
The Biconjugate Gradient (BCG) algorithm is the {open_quotes}natural{close_quotes} generalization of the classical Conjugate Gradient method to nonsymmetric linear systems. It is an attractive method because of its simplicity and its good convergence properties. Unfortunately, BCG suffers from two kinds of breakdowns (divisions by 0): one due to the non-existence of the residual polynomial, and the other due to a breakdown in the recurrence relationship used. There are many look-ahead techniques in existence which are designed to handle these breakdowns. Although the step size needed to overcome an exact breakdown can be computed in principle, these methods can unfortunately be quite complicated for handling near breakdowns since the sizes of the look-ahead steps are variable (indeed, the breakdowns can be incurable). Recently, Bank and Chan introduced the Composite Step Biconjugate Gradient (CSBCG) algorithm, an alternative which cures only the first of the two breakdowns mentioned by skipping over steps for which the BCG iterate is not defined. This is done with a simple modification of BCG which needs only a maximum look-ahead step size of 2 to eliminate the (near) breakdown and to smooth the sometimes erratic convergence of BCG. Thus, instead of a more complicated (but less prone to breakdown) version, CSBCG cures only one kind of breakdown, but does so with a minimal modification to the usual implementation of BCG in the hope that its empirically observed stability will be inherited. The authors note, then, that the Composite Step idea can be incorporated anywhere the BCG polynomial is used; in particular, in product methods such as CGS, Bi-CGSTAB, and TFQMR. Doing this not only cures the breakdown mentioned above, but also takes on the advantages of these product methods, namely, no multiplications by the transpose matrix and a faster convergence rate than BCG.
Luo, Shao-Kai; Dai, Yun; Zhang, Xiao-Tian; He, Jin-Man
2016-10-01
In this paper, we present the fractional Mei symmetrical method of finding conserved quantity and explore its applications to physics. For the fractional generalized Hamiltonian system, we introduce the fractional infinitesimal transformation of Lie groups and, under the transformation, give the fractional Mei symmetrical definition, criterion and determining equation. Then, we present the fractional Mei symmetrical theorem of finding conserved quantity. As the fractional Mei symmetrical method's applications, we respectively find the conserved quantities of a fractional general relativistic Buchduhl model, a fractional three-body model and a fractional Robbins-Lorenz model.
Review of experimental methods for evaluating effective delayed neutron fraction
Energy Technology Data Exchange (ETDEWEB)
Yamane, Yoshihiro [Nagoya Univ. (Japan). School of Engineering
1997-03-01
The International Effective Delayed Neutron Fraction ({beta}{sub eff}) Benchmark Experiments have been carried out at the Fast Critical Assembly of Japan Atomic Energy Research Institute since 1995. Researchers from six countries, namely France, Italy, Russia, U.S.A., Korea, and Japan, participate in this FCA project. Each team makes use of each experimental method, such as Frequency Method, Rossi-{alpha} Method, Nelson Number Method, Cf Neutron Source Method, and Covariance Method. In this report these experimental methods are reviewed. (author)
Method for fractional solid-waste sampling and chemical analysis
DEFF Research Database (Denmark)
Riber, Christian; Rodushkin, I.; Spliid, Henrik
2007-01-01
to repeated particle-size reduction, mixing, and mass reduction until a sufficiently small but representative sample was obtained for digestion prior to chemical analysis. The waste-fraction samples were digested according to their properties for maximum recognition of all the studied substances. By combining...... four subsampling methods and five digestion methods, paying attention to the heterogeneity and the material characteristics of the waste fractions, it was possible to determine 61 substances with low detection limits, reasonable variance, and high accuracy. For most of the substances of environmental...... concern, the waste-sample concentrations were above the detection limit (e.g. Cd gt; 0.001 mg kg-1, Cr gt; 0.01 mg kg-1, Hg gt; 0.002 mg kg-1, Pb gt; 0.005 mg kg-1). The variance was in the range of 5-100%, depending on material fraction and substance as documented by repeated sampling of two highly...
Multigrid methods for space fractional partial differential equations
Jiang, Yingjun; Xu, Xuejun
2015-12-01
We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means the convergence rates of the methods are independent of the mesh size and mesh level. Moreover, our theoretical analysis and convergence results do not require regularity assumptions of the model problems. Numerical results are given to support our theoretical findings.
Modified precise time step integration method of structural dynamic analysis
Institute of Scientific and Technical Information of China (English)
Wang Mengfu; Zhou Xiyuan
2005-01-01
The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method (e.g., an algorithm with an arbitrary order of accuracy) is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.
Comparison of the methods for discrete approximation of the fractional-order operator
Directory of Open Access Journals (Sweden)
Zborovjan Martin
2003-12-01
Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.
A Collocation Method for Solving Fractional Riccati Differential Equation
Directory of Open Access Journals (Sweden)
Yalçın Öztürk
2013-01-01
Full Text Available We have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.
Discrete Direct Methods in the Fractional Calculus of Variations
Pooseh, Shakoor; Torres, Delfim F M
2012-01-01
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends only on the left Riemann-Liouville fractional derivative. Using Grunwald-Letnikov definition, we approximate the objective functional in an equispaced grid as a multi-variable function of the values of the unknown function on mesh points. The problem is then transformed to an ordinary static optimization problem. The solution to the latter problem gives an approximation to the original fractional problem on mesh points.
A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation
Directory of Open Access Journals (Sweden)
Chunye Gong
2014-01-01
Full Text Available The computational complexity of one-dimensional time fractional reaction-diffusion equation is O(N2M compared with O(NM for classical integer reaction-diffusion equation. Parallel computing is used to overcome this challenge. Domain decomposition method (DDM embodies large potential for parallelization of the numerical solution for fractional equations and serves as a basis for distributed, parallel computations. A domain decomposition algorithm for time fractional reaction-diffusion equation with implicit finite difference method is proposed. The domain decomposition algorithm keeps the same parallelism but needs much fewer iterations, compared with Jacobi iteration in each time step. Numerical experiments are used to verify the efficiency of the obtained algorithm.
A retrieval and validation method for shelterbelt vegetation fraction
Institute of Scientific and Technical Information of China (English)
DENG Rong-xin; WANG Wen-juan; LI Ying; ZHAO Dong-bao
2013-01-01
Shelterbelts are important in defending against natural disaster and maintaining ecological balances in farmland.Understanding of the shelterbelt vegetation fraction is fundamental to regional research of shelterbelts using remote sensing.We used SPOT5 imagery with 10×10m spatial resolution in combination with knowledge of the characteristics of shelterbelts to develop a method for retrieval of the vegetation fraction of shelterbelts by the pixel un-mixing model.We then used the method to retrieve values for shelterbelts in study area.By combining the parameters of photographic images with characteristics of shelterbelts,we developed a method for measuring the vegetation fraction of shelterbelts based on an advanced photographic method.We then measured the actual values to validate the retrieval result.The multiple correlation coefficients between the retrieved and measured values were 0.715.Our retrieval and measuring methods presented in this paper accurately reflect field conditions.We suggest that this method is useful to describe shelterbelt structure using remote sensing.
Design of a Fractional Order Phase Shaper for Iso-damped Control of a PHWR under Step-back Condition
Saha, Suman; Ghosh, Ratna; Goswami, Bhaswati; Balasubramanian, R; Chandra, A K; Das, Shantanu; Gupta, Amitava; 10.1109/TNS.2010.2047405
2012-01-01
Phase shaping using fractional order (FO) phase shapers has been proposed by many contemporary researchers as a means of producing systems with iso-damped closed loop response due to a stepped variation in input. Such systems, with the closed loop damping remaining invariant to gain changes can be used to produce dead-beat step response with only rise time varying with gain. This technique is used to achieve an active step-back in a Pressurized Heavy Water Reactor (PHWR) where it is desired to change the reactor power to a pre-determined value within a short interval keeping the power undershoot as low as possible. This paper puts forward an approach as an alternative for the present day practice of a passive step-back mechanism where the control rods are allowed to drop during a step-back action by gravity, with release of electromagnetic clutches. The reactor under a step-back condition is identified as a system using practical test data and a suitable Proportional plus Integral plus Derivative (PID) contro...
A Class of Multiderivative Hybrid One-step Methods
Institute of Scientific and Technical Information of China (English)
Feng-jian Yang; Xin-ming Chen; Ai-guo Zhang
2002-01-01
This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximations to function exp (q). The algorithms fall into the catalogue of implicit formula, which involves sth order derivative and s+1 free parameters. The order of the algorithms satisfies s+1≤p≤2s+2. The stability of the methods is also studied, necessary and sufficient conditions for A-stability and L-stability are given. In addition, some examples are also given to demonstrate the method presented.
Method for Attaining Caraway Seed Oil Fractions with Different Composition.
Shiwakoti, Santosh; Poudyal, Shital; Saleh, Osama; Astatkie, Tess; Zheljazkov, Valtcho D
2016-06-01
Caraway (Carum carvi L.) is a medicinal and aromatic plant; its seeds (fruits) are used as spice and they contain essential oils. We hypothesized that by collecting caraway oil at different time points during the extraction process, we could obtain oil fractions with distinct chemical composition. A hydrodistillation time (HDT) study was conducted to test the hypothesis. The caraway seed oil fractions were collected at eight different HDT (at 0 - 2, 2 - 7, 7 - 15, 15 - 30, 30 - 45, 45 - 75, 75 - 105, and 105 - 135 min). Additionally, a non-stop HD for 135 min was conducted as a control. Most of the oil was eluted early in the HD process. The non-stop HDT treatment yielded 2.76% oil by weight. Of the 24 essential oil constituents, limonene (77 - 19% of the total oil) and carvone (20 - 79%) were the major ones. Other constituents included myrcene (0.72 - 0.16%), trans-carveol (0.07 - 0.39%), and β-caryophyllene (0.07 - 0.24%). Caraway seed oil with higher concentration of limonene can be obtained by sampling oil fractions early in HD process; conversely, oil with high concentration of carvone can be obtained by excluding the fractions eluted early in the HD process. We demonstrated a method of obtaining caraway seed oil fractions with various and unique composition. These novel oil fractions with unique composition are not commercially available and could have much wider potential uses, and also target different markets compared to the typical caraway essential oil.
Lattice Boltzmann method for the fractional advection-diffusion equation.
Zhou, J G; Haygarth, P M; Withers, P J A; Macleod, C J A; Falloon, P D; Beven, K J; Ockenden, M C; Forber, K J; Hollaway, M J; Evans, R; Collins, A L; Hiscock, K M; Wearing, C; Kahana, R; Villamizar Velez, M L
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β, the fractional order α, and the single relaxation time τ, the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.
Lattice Boltzmann method for the fractional advection-diffusion equation
Zhou, J. G.; Haygarth, P. M.; Withers, P. J. A.; Macleod, C. J. A.; Falloon, P. D.; Beven, K. J.; Ockenden, M. C.; Forber, K. J.; Hollaway, M. J.; Evans, R.; Collins, A. L.; Hiscock, K. M.; Wearing, C.; Kahana, R.; Villamizar Velez, M. L.
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.
A General Method for Designing Fractional Order PID Controller
Directory of Open Access Journals (Sweden)
Marzieh Safaei
2013-01-01
Full Text Available The idea of using fractional order calculus in control became apparent when this kind of calculus was accepted as a powerful tool in many applications. This resulted in a new generation of PID controller called fractional order PID Controller, named as Controller. controller is more flexible and provides a better response with larger stability region as compared with standard PID controller. This paper presents a simple and reliable method for finding the family of controllers. The required calculations are done in frequency domain based on frequency response of the system and the stability region is specified in the parameters space. This method can be used for time-delay systems and, more generally, for any system with no transfer function.
Array processors based on Gaussian fraction-free method
Energy Technology Data Exchange (ETDEWEB)
Peng, S.; Sedukhin, S. [Aizu Univ., Aizuwakamatsu, Fukushima (Japan); Sedukhin, I.
1998-03-01
The design of algorithmic array processors for solving linear systems of equations using fraction-free Gaussian elimination method is presented. The design is based on a formal approach which constructs a family of planar array processors systematically. These array processors are synthesized and analyzed. It is shown that some array processors are optimal in the framework of linear allocation of computations and in terms of number of processing elements and computing time. (author)
Multiple-time-stepping generalized hybrid Monte Carlo methods
Energy Technology Data Exchange (ETDEWEB)
Escribano, Bruno, E-mail: bescribano@bcamath.org [BCAM—Basque Center for Applied Mathematics, E-48009 Bilbao (Spain); Akhmatskaya, Elena [BCAM—Basque Center for Applied Mathematics, E-48009 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao (Spain); Reich, Sebastian [Universität Potsdam, Institut für Mathematik, D-14469 Potsdam (Germany); Azpiroz, Jon M. [Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC), P.K. 1072, Donostia (Spain)
2015-01-01
Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2–4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC). The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems.
Fractionation study in bioleached metallurgy wastes using six-step sequential extraction.
Krasnodebska-Ostrega, Beata; Pałdyna, Joanna; Kowalska, Joanna; Jedynak, Łukasz; Golimowski, Jerzy
2009-08-15
The stored metallurgy wastes contain residues from ore processing operations that are characterized by relatively high concentrations of heavy metals. The bioleaching process makes use of bacteria to recover elements from industrial wastes and to decrease potential risk of environmental contamination. Wastes were treated by solutions containing bacteria. In this work, the optimized six-stage sequential extraction procedure was applied for the fractionation of Ni, Cr, Fe, Mn, Cu and Zn in iron-nickel metallurgy wastes deposited in Southern Poland (Szklary). Fractionation and total concentrations of elements in wastes before and after various bioleaching treatments were studied. Analyses of the extracts were performed by ICP-MS and FAAS. To achieve the most effective bioleaching of Zn, Cr, Ni, Cu, Mn, Fe the usage of both autotrophic and heterotrophic bacteria in sequence, combined with flushing of the residue after bioleaching is required. 80-100% of total metal concentrations were mobilized after the proposed treatment. Wastes treated according to this procedure could be deposited without any risk of environmental contamination and additionally the metals could be recovered for industrial purposes.
Saha Ray, S.
2013-12-01
In this paper, the modified fractional reduced differential transform method (MFRDTM) has been proposed and it is implemented for solving fractional KdV (Korteweg-de Vries) equations. The fractional derivatives are described in the Caputo sense. In this paper, the reduced differential transform method is modified to be easily employed to solve wide kinds of nonlinear fractional differential equations. In this new approach, the nonlinear term is replaced by its Adomian polynomials. Thus the nonlinear initial-value problem can be easily solved with less computational effort. In order to show the power and effectiveness of the present modified method and to illustrate the pertinent features of the solutions, several fractional KdV equations with different types of nonlinearities are considered. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of fractional KdV equations.
Directory of Open Access Journals (Sweden)
R. Yulita Molliq
2012-01-01
Full Text Available In this study, fractional Rosenau-Hynam equations is considered. We implement relatively new analytical techniques, the variational iteration method and the homotopy perturbation method, for solving this equation. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for fractional Rosenau-Hynam equations. In these schemes, the solution takes the form of a convergent series with easily computable components. The present methods perform extremely well in terms of efficiency and simplicity.
Experimental facility and void fraction calibration methods for impedance probes
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Fernando L. de; Rocha, Marcelo S., E-mail: floliveira@ipen.br, E-mail: msrocha@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)
2013-07-01
An experimental facility was designed and constructed with aims of to calibrate a capacitance probe for gas-liquid flow void fraction measurements. The facility is composed of a metallic hack with a vertical 2,300 mm high glass tube with 38 mm ID with stagnant water and compressed air bubbling system simulating the gas phase (vapor). At the lower part, a mixing section with a porous media element releases the air bubbles into the water, and the compressed air flow is measured by two calibrated rotameters. At the upper part a stagnant water tank separates the liquid and gas. Two pressure taps are located near the lower and upper sides of the glass tube for pressure difference measurement. The pressure difference is used for low void fraction values (0-15%) calibration methods, as described in the work. Two electrically controlled quick closing valves are installed between the porous media element and the upward separation tank for high void fraction values measurement (15-50%) used to calibrate the capacitance probe. The experimental facility design, construction, capacitance probe calibration methods and results, as well as flow pattern visualization, are presented. Finally, the capacitance probe will be installed on a natural circulation circuit mounted at the Nuclear Engineering Center (CEN/IPEN/CNEN-SP) for measurement of the instantaneous bulk void. Instantaneous signals generated by the capacitance probe will allow the determination of natural circulation loop global energy balance. (author)
Intelligent numerical methods II applications to multivariate fractional calculus
Anastassiou, George A
2016-01-01
In this short monograph Newton-like and other similar numerical methods with applications to solving multivariate equations are developed, which involve Caputo type fractional mixed partial derivatives and multivariate fractional Riemann-Liouville integral operators. These are studied for the first time in the literature. The chapters are self-contained and can be read independently. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this short monograph is suitable for researchers, graduate students, to be used in graduate classes and seminars of the above subjects, also to be in all science and engineering libraries.
Directory of Open Access Journals (Sweden)
Abdollah BORHANIFAR
2013-01-01
Full Text Available In this study fractional Poisson equation is scrutinized through finite difference using shifted Grünwald estimate. A novel method is proposed numerically. The existence and uniqueness of solution for the fractional Poisson equation are proved. Exact and numerical solution are constructed and compared. Then numerical result shows the efficiency of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Morais, A. P. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Salgado de Oliveira University, Marechal Deodoro Street, 217 – Centro, Niterói, Rio de Janeiro (Brazil); Pino, A. V. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Souza, M. N. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Electronics Department at Polytechnic School, Federal University of Rio de Janeiro, Centro de Tecnologia Bloco H sala 217, Ilha do Fundão, Rio de Janeiro (Brazil)
2016-08-15
This in vitro study evaluated the diagnostic performance of an alternative electric bioimpedance spectroscopy technique (BIS-STEP) detect questionable occlusal carious lesions. Six specialists carried out the visual (V), radiography (R), and combined (VR) exams of 57 sound or non-cavitated occlusal carious lesion teeth classifying the occlusal surfaces in sound surface (H), enamel caries (EC), and dentinal caries (DC). Measurements were based on the current response to a step voltage excitation (BIS-STEP). A fractional electrical model was used to predict the current response in the time domain and to estimate the model parameters: Rs and Rp (resistive parameters), and C and α (fractional parameters). Histological analysis showed caries prevalence of 33.3% being 15.8% hidden caries. Combined examination obtained the best traditional diagnostic results with specificity = 59.0%, sensitivity = 70.9%, and accuracy = 60.8%. There were statistically significant differences in bioimpedance parameters between the H and EC groups (p = 0.016) and between the H and DC groups (Rs, p = 0.006; Rp, p = 0.022, and α, p = 0.041). Using a suitable threshold for the Rs, we obtained specificity = 60.7%, sensitivity = 77.9%, accuracy = 73.2%, and 100% of detection for deep lesions. It can be concluded that BIS-STEP method could be an important tool to improve the detection and management of occlusal non-cavitated primary caries and pigmented sites.
Morais, A. P.; Pino, A. V.; Souza, M. N.
2016-08-01
This in vitro study evaluated the diagnostic performance of an alternative electric bioimpedance spectroscopy technique (BIS-STEP) detect questionable occlusal carious lesions. Six specialists carried out the visual (V), radiography (R), and combined (VR) exams of 57 sound or non-cavitated occlusal carious lesion teeth classifying the occlusal surfaces in sound surface (H), enamel caries (EC), and dentinal caries (DC). Measurements were based on the current response to a step voltage excitation (BIS-STEP). A fractional electrical model was used to predict the current response in the time domain and to estimate the model parameters: Rs and Rp (resistive parameters), and C and α (fractional parameters). Histological analysis showed caries prevalence of 33.3% being 15.8% hidden caries. Combined examination obtained the best traditional diagnostic results with specificity = 59.0%, sensitivity = 70.9%, and accuracy = 60.8%. There were statistically significant differences in bioimpedance parameters between the H and EC groups (p = 0.016) and between the H and DC groups (Rs, p = 0.006; Rp, p = 0.022, and α, p = 0.041). Using a suitable threshold for the Rs, we obtained specificity = 60.7%, sensitivity = 77.9%, accuracy = 73.2%, and 100% of detection for deep lesions. It can be concluded that BIS-STEP method could be an important tool to improve the detection and management of occlusal non-cavitated primary caries and pigmented sites.
Gésan-Guiziou, G; Daufin, G; Timmer, M; Allersma, D; van der Horst, C
1999-05-01
Fractions enriched with alpha-lactalbumin (alpha-la) and beta-lactoglobulin (beta-lg) were produced by a process comprising the following successive steps: clarification-defatting of whey protein concentrate, precipitation of alpha-lactalbumin, separation of soluble beta-lactoglobulin, washing the precipitate, solubilization of the precipitate, concentration and purification of alpha-la. The present study evaluated the performance of the process, firstly on a laboratory scale with acid whey and then on a pilot scale with Gouda cheese whey. In both cases soluble beta-lg was separated from the precipitate using diafiltration or microfiltration and the purities of alpha-la and beta-lg were in the range 52-83 and 85-94% respectively. The purity of the beta-lg fraction was higher using acid whey, which does not contain caseinomacropeptide, than using sweet whey. With the pilot scale plant, the recoveries (6% for alpha-la; 51% for beta-lg) were disappointing, but ways of improving each step in the process are discussed.
A three-step metal fractionation scheme for fly ashes collected in an Argentine thermal power plant
Energy Technology Data Exchange (ETDEWEB)
Patricia Smichowski; Griselda Polla; Dario Gomez; Antonio Jose Fernandez Espinosa; Ana Calleja Lopez [Comision Nacional de Energia Atomica, Buenos Aires (Argentina)
2008-06-15
A new three-step fractionation scheme was applied to study the distribution of Al, As, Cd, Cr, Cu, Fe, Mn, Mo, Ni, Pb, S, Sb, Ti, V and Zn in fly ashes collected in the electrostatic precipitator of a thermal power plant in the city of San Nicolas (Argentina). Seven samples were collected during one week of operation in 2005. For the fractionation, the scheme applied consisted of extracting the elements in three fractions: (i) soluble and exchangeable elements, (ii) carbonates, oxides and reducible elements and (iii) residual elements. Metals and metalloids at {mu}g g{sup -1} level were determined in each fraction by plasma based techniques namely, inductively coupled plasma optical emission spectrometry (ICP OES) and inductively coupled plasma mass spectrometry (ICP-MS). For validation, a certified reference materials NIST SRM 2711 (Montana soil) was subject to the same chemical sequential extraction procedure. X-ray diffraction powder (XRD) analysis and scanning electron microscopy (SEM) were used to characterize the major minerals present in the matrix. The predominant phases found in the total samples were mullite, quartz, iron oxides and lime. Total analyte concentration varied (in {mu}g g{sup -1}) from 1.54 for Cd to 30 600 for Al. The leachability of the 15 elements under study proved to be different. All the elements (except Cd and Pb) were detected in the soluble fraction in the order: Cu (0.10%) {approximately} Mn (0.13%) {lt} Ni (0.17%) {approximately} Ti (0.19%) {approximately} Fe (0.20%) {approximately} As (0.21%) {lt} Zn (0.86%) {lt} Al (1.3%) {lt} Cr (2.9%) {lt} V (3.9%) {lt} Sb (6.9%) {lt} Mo (45.1%) {lt} S (58.0%). Percentages higher than 20% of S (24.1%) {lt} V (27.5%) {lt} Mn (29.0%) were detected in the second fraction. Al, As, Cr, Cd, Cu, Fe, Ni, Pb, Sb and Zn were mostly associated to the residual fraction. Recoveries of the overall procedure varied between 106% (Mo) and 72% (Cr). 21 refs., 5 figs., 7 tabs.
Directory of Open Access Journals (Sweden)
Baojian Hong
2014-01-01
Full Text Available Based on He’s variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS. The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations.
An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems
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Mohammad Maleki
2012-01-01
Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.
One-step method for the production of nanofluids
Energy Technology Data Exchange (ETDEWEB)
Kostic, Milivoje (Sycamore, IL); Golubovic, Mihajlo (Chicago, IL); Hull, John (Downers Grove, IL); Choi, Stephen U. S. (Naperville, IL)
2011-08-16
A one step method and system for producing nanofluids by a nanoparticle-source evaporation and deposition of the evaporant into a base fluid. The base fluid such oil or ethylene glycol is placed in a rotating cylindrical drum having an adjustable heater-boat-evaporator and heat exchanger-cooler apparatus. As the drum rotates, a thin liquid layer is formed on the inside surface of the drum. An insulated heater-boat-evaporator having an evaporant material (nanoparticle-source) placed within its boat evaporator is adjustably positioned near a portion of the rotating thin liquid layer, the evaporant material being heated thereby evaporating a portion of the evaporant material and forming nanoparticles, the nanoparticles absorbed by the liquid film to form nanofluid.
One-step method for the production of nanofluids
Energy Technology Data Exchange (ETDEWEB)
Kostic, Milivoje (Chicago, IL); Golubovic, Mihajlo (Chicago, IL); Hull, John R. (Downers Grove, IL); Choi, Stephen U. S. (Napersville, IL)
2010-05-18
A one step method and system for producing nanofluids by a particle-source evaporation and deposition of the evaporant into a base fluid. The base fluid such (i.e. ethylene glycol) is placed in a rotating cylindrical drum having an adjustable heater-boat-evaporator and heat exchanger-cooler apparatus. As the drum rotates, a thin liquid layer is formed on the inside surface of the drum. A heater-boat-evaporator having an evaporant material (particle-source) placed within its boat evaporator is adjustably positioned near a portion of the rotating thin liquid layer, the evaporant material being heated thereby evaporating a portion of the evaporant material, the evaporated material absorbed by the liquid film to form nanofluid.
Jing,Lei; Cheng, Zixue; Wang, Junbo; Zhou, Yinghui
2011-01-01
Embedded system technologies are undergoing dramatic change. Competent embedded system engineers are becoming a scarce resource in the industry. Given this, universities should revise their specialist education to meet industry demands. In this paper, a spirally tight-coupled step-by-step educational method, based on an analysis of industry…
Jing,Lei; Cheng, Zixue; Wang, Junbo; Zhou, Yinghui
2011-01-01
Embedded system technologies are undergoing dramatic change. Competent embedded system engineers are becoming a scarce resource in the industry. Given this, universities should revise their specialist education to meet industry demands. In this paper, a spirally tight-coupled step-by-step educational method, based on an analysis of industry…
On Sumudu Transform Method in Discrete Fractional Calculus
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Fahd Jarad
2012-01-01
Full Text Available In this paper, starting from the definition of the Sumudu transform on a general time scale, we define the generalized discrete Sumudu transform and present some of its basic properties. We obtain the discrete Sumudu transform of Taylor monomials, fractional sums, and fractional differences. We apply this transform to solve some fractional difference initial value problems.
Directory of Open Access Journals (Sweden)
Alfredo Cassano
2015-04-01
Full Text Available Commercial nanofiltration (NF membranes in spiral-wound configuration (NP030 from Microdyn Nadir and Desal DK from GE Water & Process Technologies were used in a sequential design in order to produce a separated fraction of phenolic and sugar compounds from an aqueous artichoke extract. For both membranes, the effect of transmembrane pressure (TMP on the permeation flux was evaluated. In optimized conditions of TMP, the NP030 membrane exhibited high rejections of apigenin, cynarin and chlorogenic acid (higher than 85%; on the other hand, very low rejections of fructose, glucose and sucrose (lower than 4% were measured. Starting from an extract with a total antioxidant activity (TAA of 5.28 mM trolox a retentate fraction with a TAA of 47.75 mM trolox was obtained. The NF permeate from the NP030 membrane was processed with the Desal DK membrane in optimized conditions of TMP producing a permeate stream free of phenolic and sugar compounds. Accordingly, as most part of phenolic compounds was removed in the first NF step, the concentration of sugar compounds in the NF retentate had much higher results than that of phenolic compounds.
A method for purifying butyric crude oil fractions
Energy Technology Data Exchange (ETDEWEB)
Saskovets, V.V.; Gayle, A.A.; Proskuryakov, V.A.; Semenov, L.V.; Zakharov, A.P.
1983-01-01
In a method for purification of butyric fractions of oil through extraction by a selective solvent, in order to increase the output and to improve the quality of the purified oil, 2,5-dimethyl-1,3,4-oxadiazole of the cited formula, or its mixture with 80 to 90 percent furfural is used as the selective solvent. The solvent is produced through a reaction between hydrazine and an acetic anhydride. The solvent is a colorless liquid with a weak characteristic smell, and is easily dissolved in water with a boiling point of 178 degrees and density at 4-20/sup 0/ of 1.0963. The solvent is thermally stable: after boiling at 220 degrees, its viscosity is essentially the same.
Simplified triangle method for estimating evaporative fraction over soybean crops
Silva-Fuzzo, Daniela Fernanda; Rocha, Jansle Vieira
2016-10-01
Accurate estimates are emerging with technological advances in remote sensing, and the triangle method has demonstrated to be a useful tool for the estimation of evaporative fraction (EF). The purpose of this study was to estimate the EF using the triangle method at the regional level. We used data from the Moderate Resolution Imaging Spectroradiometer orbital sensor, referring to indices of surface temperature and vegetation index for a 10-year period (2002/2003 to 2011/2012) of cropping seasons in the state of Paraná, Brazil. The triangle method has shown considerable results for the EF, and the validation of the estimates, as compared to observed data of climatological water balance, showed values >0.8 for modified "d" of Wilmott and R2 values between 0.6 and 0.7 for some counties. The errors were low for all years analyzed, and the test showed that the estimated data are very close to the observed data. Based on statistical validation, we can say that the triangle method is a consistent tool, is useful as it uses only images of remote sensing as variables, and can provide support for monitoring large-scale agroclimatic, specially for countries of great territorial dimensions, such as Brazil, which lacks a more dense network of meteorological ground stations, i.e., the country does not appear to cover a large field for data.
On fractional control method for four-wheel-steering vehicle
Institute of Scientific and Technical Information of China (English)
CHEN Ning; CHEN Nan; CHEN YanDong
2009-01-01
Four-wheel-steering (4WS) system can enhance vehicle cornering ability by steering the rear wheels in accordance with the front wheels steering and vehicle status. With such steering control system, it becomes possible to improve the lateral stability and handling performance, in this paper, a new control method for 4WS vehicle is proposed, its rear wheels steering angle is in accordance with the angle of front wheels steering and vehicle yaw rate, and the effects of front wheels steering angle velocity are considered by adopting the fractional derivative theory. Some design specifications for control law are also given. The effects of the control method are verified by a kind of numerical scheme presented in this paper. The dynamic characteristics such as the side-slip angle and the yaw angle velocity of the vehicle gravity center are compared among three kinds of vehicles with different control methods. And the kinematics characteristics such as turning radius between 4WS and 2WS are also discussed. Nu-merical simulation shows that the control method presented can improve the transient response and reduce the turning radius of 4WS vehicle.
On fractional control method for four-wheel-steering vehicle
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Four-wheel-steering (4WS) system can enhance vehicle cornering ability by steering the rear wheels in accordance with the front wheels steering and vehicle status. With such steering control system, it becomes possible to improve the lateral stability and handling performance. In this paper, a new control method for 4WS vehicle is proposed, its rear wheels steering angle is in accordance with the angle of front wheels steering and vehicle yaw rate, and the effects of front wheels steering angle velocity are considered by adopting the fractional derivative theory. Some design specifications for control law are also given. The effects of the control method are verified by a kind of numerical scheme presented in this paper. The dynamic characteristics such as the side-slip angle and the yaw angle velocity of the vehicle gravity center are compared among three kinds of vehicles with different control methods. And the kinematics characteristics such as turning radius between 4WS and 2WS are also discussed. Nu- merical simulation shows that the control method presented can improve the transient response and reduce the turning radius of 4WS vehicle.
Directory of Open Access Journals (Sweden)
U. Dusek
2014-01-01
Full Text Available We thoroughly characterized a system for thermal separation of organic carbon (OC and elemental carbon (EC for subsequent radiocarbon analysis. Different organic compounds as well as ambient aerosol filter samples were introduced into an oven system and combusted to CO2 in pure O2. The main objective was to test which combustion times and temperatures are best suited to separate OC and EC. The final separation step for OC was combustion at 360 °C for 15 min. Combustion at this temperature proved enough to remove several organic test substances from the filter (including high molecular weight humic acid but did not remove substantial amounts of EC. For isolation of EC, OC first needs to be completely removed from the filter. This was achieved by water extraction of the filter, followed by combustion of the water insoluble OC at 360 °C and combustion at an intermediate temperature step of 2 min at 450 °C. This last step removed the most refractory OC together with some EC. Finally, the remaining EC was combusted to CO2 at 650 °C. The recovery of black carbon after the intermediate 450 °C step was approximately 80%. Several tests provided strong evidence that OC was removed efficiently during the intermediate temperature step: (i brown carbon, indicative of refractory OC, was removed; (ii the fraction modern of EC did not decrease significantly if the temperature of the intermediate step was further increased. Based on tests with various organic compounds, we estimated that charred organic carbon could contribute 4–8% to an elemental carbon sample that was isolated according to our method.
EXPANSION OF STEP-TRANSITION OPERATOR OF MULTI-STEP METHOD AND ITS APPLICATIONS (II)
Institute of Scientific and Technical Information of China (English)
Yi-fa Tang
2002-01-01
We give some formulae for calculation of the expansions for (1) composition of step-transition operators (STO) of any two difference schemes (DS) for ODE's, (2) inverse operator of STO of any DS, and (3) conjugate operator of STO of any DS.
The (G'/G)-expansion method for the nonlinear time fractional differential equations
Unsal, Omer; Guner, Ozkan; Bekir, Ahmet; Cevikel, Adem C.
2017-01-01
In this paper, we obtain exact solutions of two time fractional differential equations using Jumarie's modified Riemann-Liouville derivative which is encountered in mathematical physics and applied mathematics; namely (3 + 1)-dimensional time fractional KdV-ZK equation and time fractional ADR equation by using fractional complex transform and (G/'G )-expansion method. It is shown that the considered transform and method are very useful in solving nonlinear fractional differential equations.
Simplistic design methods for moderate-sloped stepped chutes
Numerous contributions have been made on the hydraulic properties of the air entrainment inception point and aerated flow region especially for steep, stepped chutes. Stepped chutes applied to aging embankment dams to address inadequate spillway capacity and to provide overtopping protection is a g...
Directory of Open Access Journals (Sweden)
Taohua Liu
2017-01-01
Full Text Available Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K and computational cost of O(KlogK. Traditionally, the Gaussian elimination method requires storage of O(K2 and computational cost of O(K3. Finally, the accuracy and efficiency of the method are checked with a numerical example.
Tau-Path Following Method for Solving the Riccati Equation with Fractional Order
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Muhammed I. Syam
2014-01-01
Full Text Available A formulation for the fractional Legendre functions is constructed to find the solution of the fractional Riccati equation. The fractional derivative is described in the Caputo sense. The method is based on the Tau Legendre and path following methods. Theoretical and numerical results are presented. Analysis for the presented method is given.
Solving Fractional Partial Differential Equations with Corrected Fourier Series Method
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Nor Hafizah Zainal
2014-01-01
Full Text Available The corrected Fourier series (CFS is proposed for solving partial differential equations (PDEs with fractional time derivative on a finite domain. In the previous work, we have been solving partial differential equations by using corrected Fourier series. The fractional derivatives are described in Riemann sense. Some numerical examples are presented to show the solutions.
Advanced methods in the fractional calculus of variations
Malinowska, Agnieszka B; Torres, Delfim F M
2015-01-01
This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler–Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Stur...
Two-Step Camera Calibration Method Developed for Micro UAV'S
Gašparović, M.; Gajski, D.
2016-06-01
The development of unmanned aerial vehicles (UAVs) and continuous price reduction of unmanned systems attracted us to this research. Professional measuring systems are dozens of times more expensive and often heavier than "amateur", non-metric UAVs. For this reason, we tested the DJI Phantom 2 Vision Plus UAV. Phantom's smaller mass and velocity can develop less kinetic energy in relation to the professional measurement platforms, which makes it potentially less dangerous for use in populated areas. In this research, we wanted to investigate the ability of such non-metric UAV and find the procedures under which this kind of UAV may be used for the photogrammetric survey. It is important to emphasize that UAV is equipped with an ultra wide-angle camera with 14MP sensor. Calibration of such cameras is a complex process. In the research, a new two-step process is presented and developed, and the results are compared with standard one-step camera calibration procedure. Two-step process involves initially removed distortion on all images, and then uses these images in the phototriangulation with self-calibration. The paper presents statistical indicators which proved that the proposed two-step process is better and more accurate procedure for calibrating those types of cameras than standard one-step calibration. Also, we suggest two-step calibration process as the standard for ultra-wideangle cameras for unmanned aircraft.
Directory of Open Access Journals (Sweden)
Xiang-Chao Shi
2016-02-01
Full Text Available The fractional reaction diffusion equation is one of the popularly used fractional partial differential equations in recent years. The fast Adomian decomposition method is used to obtain the solution of the Cauchy problem. Also, the analytical scheme is extended to the fractional one where the Taylor series is employed. In comparison with the classical Adomian decomposition method, the ratio of the convergence is increased. The method is more reliable for the fractional partial differential equations.
Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order
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Johnston S. J.
2016-01-01
Full Text Available The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.
Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order
Johnston, S. J.; Jafari, H.; Moshokoa, S. P.; Ariyan, V. M.; Baleanu, D.
2016-07-01
The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.
DEFF Research Database (Denmark)
Rasmussen, Christian Jørgen
2001-01-01
Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method.......Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method....
Algorithms for the Fractional Calculus: A Selection of Numerical Methods
Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.
2003-01-01
Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.
A New Type of Fractional Lie Symmetrical Method and its Applications
Zhang, Xiao-Tian; He, Jin-Man; Luo, Shao-Kai
2017-03-01
In this paper, we present a new type of fractional Lie symmetrical method for finding conserved quantities and explore its applications. For the fractional generalized Hamiltonian system, we introduce a new kind of single-parameter fractional infinitesimal transformation of Lie group in α-1 order space and, under this transformation, give the invariance of the fractional dynamical system and the fractional Lie symmetrical determining equation. Further, a number of important relationships of the fractional Lie symmetrical method are investigated, which reveal the interior properties of the system. By using these relationships, a fractional Lie symmetrical basic integral variable relation and a new fractional Lie symmetrical conservation law are presented. The new conserved quantity is constructed base on fractional Lie symmetrical infinitesimal generators and the interior properties of the system itself, without solving the complicated structural equation. Furthermore, the fractional Lie symmetrical method is applied to the fractional generalized Hamiltonian system of even dimensions. Also, as the new fractional Lie symmetrical method's applications, we respectively find the conserved quantities of a fractional Duffing oscillator model and a fractional Lotka biochemical oscillator model.
Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size
Hadjimichael, Yiannis
2016-09-08
Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and three) with variable step size, and prove their optimality, stability, and convergence. The choice of step size for multistep SSP methods is an interesting problem because the allowable step size depends on the SSP coefficient, which in turn depends on the chosen step sizes. The description of the methods includes an optimal step-size strategy. We prove sharp upper bounds on the allowable step size for explicit SSP linear multistep methods and show the existence of methods with arbitrarily high order of accuracy. The effectiveness of the methods is demonstrated through numerical examples.
Variational iteration method for solving the time-fractional diffusion equations in porous medium
Institute of Scientific and Technical Information of China (English)
Wu Guo-Cheng
2012-01-01
The variational iteration method is successfully extended to the case of solving fractional differential equations,and the Lagrange multiplier of the method is identified in a more accurate way.Some diffusion models with fractional derivatives are investigated analytically,and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.
Indian Academy of Sciences (India)
Wenjun Liu; Kewang Chen
2013-09-01
In this paper, we implemented the functional variable method and the modified Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled KdV system. This method is extremely simple but effective for handling nonlinear time-fractional differential equations.
Exponential rational function method for space-time fractional differential equations
Aksoy, Esin; Kaplan, Melike; Bekir, Ahmet
2016-04-01
In this paper, exponential rational function method is applied to obtain analytical solutions of the space-time fractional Fokas equation, the space-time fractional Zakharov Kuznetsov Benjamin Bona Mahony, and the space-time fractional coupled Burgers' equations. As a result, some exact solutions for them are successfully established. These 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. The exact solutions obtained by the proposed method indicate that the approach is easy to implement and effective.
Solution to the Linear Fractional Differential Equation Using Adomian Decomposition Method
Directory of Open Access Journals (Sweden)
Jin-Fa Cheng
2011-01-01
Full Text Available We obtain the analytical general solution of the linear fractional differential equations with constant coefficients by Adomian decomposition method under nonhomogeneous initial value condition, which is in the sense of the Caputo fractional derivative.
Multi-time-step domain coupling method with energy control
DEFF Research Database (Denmark)
Mahjoubi, N.; Krenk, Steen
2010-01-01
the individual time step. It is demonstrated that displacement continuity between the subdomains leads to cancelation of the interface contributions to the energy balance equation, and thus stability and algorithmic damping properties of the original algorithms are retained. The various subdomains can...
Rautenberg, Tamlyn; Hulme, Claire; Edlin, Richard
2016-01-01
Background Although guidance on good research practice in health economic modeling is widely available, there is still a need for a simpler instructive resource which could guide a beginner modeler alongside modeling for the first time. Aim To develop a beginner’s guide to be used as a handheld guide contemporaneous to the model development process. Methods A systematic review of best practice guidelines was used to construct a framework of steps undertaken during the model development process. Focused methods review supplemented this framework. Consensus was obtained among a group of model developers to review and finalize the content of the preliminary beginner’s guide. The final beginner’s guide was used to develop cost-effectiveness models. Results Thirty-two best practice guidelines were data extracted, synthesized, and critically evaluated to identify steps for model development, which formed a framework for the beginner’s guide. Within five phases of model development, eight broad submethods were identified and 19 methodological reviews were conducted to develop the content of the draft beginner’s guide. Two rounds of consensus agreement were undertaken to reach agreement on the final beginner’s guide. To assess fitness for purpose (ease of use and completeness), models were developed independently and by the researcher using the beginner’s guide. Conclusion A combination of systematic review, methods reviews, consensus agreement, and validation was used to construct a step-by-step beginner’s guide for developing decision analytical cost-effectiveness models. The final beginner’s guide is a step-by-step resource to accompany the model development process from understanding the problem to be modeled, model conceptualization, model implementation, and model checking through to reporting of the model results. PMID:27785080
On an Estimation Method for an Alternative Fractionally Cointegrated Model
DEFF Research Database (Denmark)
Carlini, Federico; Łasak, Katarzyna
In this paper we consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than models proposed in Granger (1986) and Johansen (2008, 2009). We discuss the identification issues of the model of Avarucci (2007), following...
Lie group analysis method for two classes of fractional partial differential equations
Chen, Cheng; Jiang, Yao-Lin
2015-09-01
In this paper we deal with two classes of fractional partial differential equation: n order linear fractional partial differential equation and nonlinear fractional reaction diffusion convection equation, by using the Lie group analysis method. The infinitesimal generators general formula of n order linear fractional partial differential equation is obtained. For nonlinear fractional reaction diffusion convection equation, the properties of their infinitesimal generators are considered. The four special cases are exhaustively investigated respectively. At the same time some examples of the corresponding case are also given. So it is very convenient to solve the infinitesimal generator of some fractional partial differential equation.
Directory of Open Access Journals (Sweden)
Yan Li-Mei
2013-01-01
Full Text Available The purpose of this paper is to extend the homotopy perturbation method to fractional heat transfer and porous media equations with the help of the Laplace transform. The fractional derivatives described in this paper are in the Caputo sense. The algorithm is demonstrated to be direct and straightforward, and can be used for many other non-linear fractional differential equations.
Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation
Energy Technology Data Exchange (ETDEWEB)
Song, Lina [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)]. E-mail: songlina1981@yahoo.com.cn; Zhang, Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2007-07-16
In the Letter, homotopy analysis method that developed for integer-order differential equation is directly extended to derive explicit and numerical solutions of nonlinear fractional differential equation for the first time. The fractional derivatives are described in the Caputo sense. To our knowledge, the Letter represents the first available numerical solutions of the fractional KdV-Burgers-Kuramoto equation.
Directory of Open Access Journals (Sweden)
Rautenberg T
2016-10-01
Full Text Available Tamlyn Rautenberg,1 Claire Hulme,2 Richard Edlin,3 1Health Economics and HIV/AIDS Research Division (HEARD, University of Kwazulu Natal, KwaZulu Natal, South Africa; 2Leeds Institute of Health Sciences (LIHS, Academic Unit of Health Economics (AUHE, University of Leeds, West Yorkshire, United Kingdom; 3Faculty of Medical and Health Sciences, University of Auckland, Auckland, New Zealand Background: Although guidance on good research practice in health economic modeling is widely available, there is still a need for a simpler instructive resource which could guide a beginner modeler alongside modeling for the first time. Aim: To develop a beginner’s guide to be used as a handheld guide contemporaneous to the model development process. Methods: A systematic review of best practice guidelines was used to construct a framework of steps undertaken during the model development process. Focused methods review supplemented this framework. Consensus was obtained among a group of model developers to review and finalize the content of the preliminary beginner’s guide. The final beginner’s guide was used to develop cost-effectiveness models. Results: Thirty-two best practice guidelines were data extracted, synthesized, and critically evaluated to identify steps for model development, which formed a framework for the beginner’s guide. Within five phases of model development, eight broad submethods were identified and 19 methodological reviews were conducted to develop the content of the draft beginner’s guide. Two rounds of consensus agreement were undertaken to reach agreement on the final beginner’s guide. To assess fitness for purpose (ease of use and completeness, models were developed independently and by the researcher using the beginner’s guide. Conclusion: A combination of systematic review, methods reviews, consensus agreement, and validation was used to construct a step-by-step beginner’s guide for developing decision analytical
Combined Effects of Numerical Method Type and Time Step on Water Stressed Actual Crop ET
Directory of Open Access Journals (Sweden)
B. Ghahraman
2016-02-01
Full Text Available Introduction: Actual crop evapotranspiration (Eta is important in hydrologic modeling and irrigation water management issues. Actual ET depends on an estimation of a water stress index and average soil water at crop root zone, and so depends on a chosen numerical method and adapted time step. During periods with no rainfall and/or irrigation, actual ET can be computed analytically or by using different numerical methods. Overal, there are many factors that influence actual evapotranspiration. These factors are crop potential evapotranspiration, available root zone water content, time step, crop sensitivity, and soil. In this paper different numerical methods are compared for different soil textures and different crops sensitivities. Materials and Methods: During a specific time step with no rainfall or irrigation, change in soil water content would be equal to evapotranspiration, ET. In this approach, however, deep percolation is generally ignored due to deep water table and negligible unsaturated hydraulic conductivity below rooting depth. This differential equation may be solved analytically or numerically considering different algorithms. We adapted four different numerical methods, as explicit, implicit, and modified Euler, midpoint method, and 3-rd order Heun method to approximate the differential equation. Three general soil types of sand, silt, and clay, and three different crop types of sensitive, moderate, and resistant under Nishaboor plain were used. Standard soil fraction depletion (corresponding to ETc=5 mm.d-1, pstd, below which crop faces water stress is adopted for crop sensitivity. Three values for pstd were considered in this study to cover the common crops in the area, including winter wheat and barley, cotton, alfalfa, sugar beet, saffron, among the others. Based on this parameter, three classes for crop sensitivity was considered, sensitive crops with pstd=0.2, moderate crops with pstd=0.5, and resistive crops with pstd=0
Institute of Scientific and Technical Information of China (English)
FENG Qing-Hua
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.
Feng, Qing-Hua
2013-05-01
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.
Nakazato, Tetsuya; Akasaka, Mikio; Tao, Hiroaki
2006-11-01
A microwave-assisted continuous-flow sequential extraction system was developed for rapid fractionation analysis of heavy metals in soil. Insertion of pressure-adjusted air between the extractants provided stable flows of the extractants without mutual mixing and back-pressure influence of a column packed with soil, thereby facilitating reliable continuous-flow extractions. In addition, use of pure water as a pumping solvent removed metal contamination because of direct contact between corrosive extractants and the pump containing metallic materials. Focused microwave irradiation to the soil accelerated the selective extractions of the acid-soluble and reducible fractions of heavy metals in soil in the first and second steps of the sequential extraction conditions, as defined by the Commission of the European Bureau of Reference (BCR). The microwave-assisted continuous-flow extraction provided high correlations in amounts of six heavy metals except Zn in the first step and Cu in the second step extracted from a reference sludge soil, BCR CRM 483, with a conventional batchwise extraction proposed by BCR; continuous-flow extraction assisted by conductive heating provided lower correlations for all the six metals. The proposed method drastically reduced the time required for the sequence extraction to ca. 65 min without losing accuracy and precision of the fractionation analysis of heavy metals in soil, whereas the BCR batchwise method requires ca. 33 h.
Solving linear fractional-order differential equations via the enhanced homotopy perturbation method
Energy Technology Data Exchange (ETDEWEB)
Naseri, E; Ghaderi, R; Sadati, J; Mahmoudian, M; Hosseinnia, S H [Intelligent System Research Group, Babol, Noushirvani University of Technology, Faculty of Electrical and Computer Engineering, PO Box 47135-484, Babol (Iran, Islamic Republic of); Ranjbar N, A [Golestan University, Gorgan (Iran, Islamic Republic of); Momani, S [Mutah University, PO Box 7, Al-Karak (Jordan)], E-mail: h.hoseinnia@stu.nit.ac.ir, E-mail: a.ranjbar@nit.ac.ir, E-mail: shahermm@yahoo.com
2009-10-15
The linear fractional differential equation is solved using the enhanced homotopy perturbation method (EHPM). In this method, the convergence has been provided by selecting a stabilizing linear part. The most significant features of this method are its simplicity and its excellent accuracy and convergence for the whole range of fractional-order differential equations.
Solving linear fractional-order differential equations via the enhanced homotopy perturbation method
Naseri, E.; Ghaderi, R.; Ranjbar N, A.; Sadati, J.; Mahmoudian, M.; Hosseinnia, S. H.; Momani, S.
2009-10-01
The linear fractional differential equation is solved using the enhanced homotopy perturbation method (EHPM). In this method, the convergence has been provided by selecting a stabilizing linear part. The most significant features of this method are its simplicity and its excellent accuracy and convergence for the whole range of fractional-order differential equations.
Directory of Open Access Journals (Sweden)
Yan Sheng-Ping
2015-01-01
Full Text Available In this article, we first propose the local fractional Laplace series expansion method, which is a coupling method of series expansion method and Laplace transform via local fractional differential operator. An illustrative example for handling the diffusion equation arising in fractal heat transfer is given.
Various methods for solving time fractional KdV-Zakharov-Kuznetsov equation
Guner, Ozkan; Aksoy, Esin; Bekir, Ahmet; Cevikel, Adem C.
2016-06-01
This paper presents the exact analytical solution of the (3+1)-dimensional time fractional KdV-Zakharov-Kuznetsov (KdV-ZK) equation with the help of the Kudryashov method, the exp-function method and the functional variable method. The fractional derivatives are described in Jumarie's sense.
A method for isolating piperylenes from the C5 fraction of pyrolysis gasolines
Energy Technology Data Exchange (ETDEWEB)
Messinger, T.; Pop, G.; Purvutolu, T.
1980-11-30
A method is patented for separating piperylenes from the C5 fraction of pyrolysis benzine. The starting raw material is fractionated to remove the volatile C5 components (with a boiling point of less than 38 degrees), while the remainder is fractionated, removing the upper fraction which contains piperylenes (a boiling point of 38 to 45 degrees); this fraction is subjected to extractive distillation, distilling away the residues of the C5 components; the residual product is fractionated, producing in the distillate a mixture of piperylene, acetylenes and cyclopentadienes which is shifted to the zone of extractive distillation, producing in the distillate a piperylene concentrated which is then purified by known chemical means, producing a piperylene concentrate enriched with a transisomer. The residue from the fractionation is fractionated in another tower, from the top of which the piperylene concentrated, enriched with a cis isomer is distilled off.
Blumrich, Matthias A.; Salapura, Valentina
2010-11-02
An apparatus and method are disclosed for single-stepping coherence events in a multiprocessor system under software control in order to monitor the behavior of a memory coherence mechanism. Single-stepping coherence events in a multiprocessor system is made possible by adding one or more step registers. By accessing these step registers, one or more coherence requests are processed by the multiprocessor system. The step registers determine if the snoop unit will operate by proceeding in a normal execution mode, or operate in a single-step mode.
CSIR Research Space (South Africa)
Wilke, DN
2012-07-01
Full Text Available , and is based on a Taylor series expansion using a pure imaginary step. The complex-step method is not subject to subtraction errors as with finite difference approaches when computing first order sensitivities and therefore allows for much smaller step sizes...
Directory of Open Access Journals (Sweden)
Shehu Maitama
2016-01-01
Full Text Available A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM and a well-known method, Homotopy Perturbation Method (HPM. In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear term is calculated using He’s polynomial. The proposed analytical method reduces the computational size and avoids round-off errors. Exact solution of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method.
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C. Aghnatios
2014-02-01
provides information on the necessary strength for the solubilisation of a given element and its lability. The behaviour of the elemental fractional solubility is sorted into two groups: (i Ca, Sr, Ba, Mn, P constitute group 1, with a solubility between 23% and 70% and with a maximum solubility at pH 3; (ii whereas in group 2 (Al, Fe, the solubility is less than 2% with the highest release at pH 1. Similar solubility patterns in group 1 for Ca, P and Mn suggest a~possible association of the elements in the same minerals, most probably carbonates, which gives phosphorus an unexpected high lability.
Hesameddini, Esmail; Rahimi, Azam
2015-05-01
In this article, we propose a new approach for solving fractional partial differential equations with variable coefficients, which is very effective and can also be applied to other types of differential equations. The main advantage of the method lies in its flexibility for obtaining the approximate solutions of time fractional and space fractional equations. The fractional derivatives are described based on the Caputo sense. Our method contains an iterative formula that can provide rapidly convergent successive approximations of the exact solution if such a closed form solution exists. Several examples are given, and the numerical results are shown to demonstrate the efficiency of the newly proposed method.
Huang, Qing; Wang, Li-Zhen; Zuo, Su-Li
2016-02-01
In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann-Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada-Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed. Supported by the National Natural Science Foundation of China under Grant Nos. 11101332, 11201371, 11371293 and the Natural Science Foundation of Shaanxi Province under Grant No. 2015JM1037
First attempt to overcome the disaster of Dirac sea in imaginary time step method
Institute of Scientific and Technical Information of China (English)
ZHANG Ying; LIANG Hao-Zhao; MENG Jie
2009-01-01
Efforts have been made to solve the Dirac equation with axially deformed scalar and vector Woods-Saxon potentials in the coordinate space with the imaginary time step method. The results of the single-particle energies thus obtained are consistent with those calculated with the basis expansion method, which demonstrates the feasibility of the imaginary time step method for the relativistic static problems.
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Treena Basu
2015-10-01
Full Text Available This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2 for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3 per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N and a computational cost of O(N logN per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.
Exact solutions of the time-fractional Fisher equation by using modified trial equation method
Tandogan, Yusuf Ali; Bildik, Necdet
2016-06-01
In this study, modified trial equation method has been proposed to obtain precise solutions of nonlinear fractional differential equation. Using the modified test equation method, we obtained some new exact solutions of the time fractional nonlinear Fisher equation. The obtained results are classified as a soliton solution, singular solutions, rational function solutions and periodic solutions.
Das, S.; Yadav, V. K.
2016-10-01
We study the chaos control and the function projective synchronization of a fractional-order T-system and Lorenz chaotic system using the backstepping method. Based on stability theory, we consider the condition for the local stability of nonlinear three-dimensional commensurate fractional-order system. Using the feedback control method, we control the chaos in the considered fractional-order T-system. We simulate the function projective synchronization between the fractional-order T-system and Lorenz system numerically using MATLAB and depict the results with plots.
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Özkan Güner
2014-01-01
Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.
Institute of Scientific and Technical Information of China (English)
SUN Peiyan; GAO Zhenhui; CAO Lixin; WANG Xinping; ZHOU Qing; ZHAO Yuhui; LI Guangmei
2011-01-01
In recent years, oil spill accidents occur frequently in the marine area of China. Finding out the spilled oil source is a key step in the relevant investigation. In this paper, a step-by-step fingerprinting identification method was used in a spilled oil accident in the Bohai Sea in 2002. Advanced chemical fingerprinting and data interpretation techniques were used to characterize the chemical composition and determine the possible sources of two spilled oil samples. The original gas chromatography -flame ionization detection (GC-FID) chromatogram of saturated hydrocarbons was compared. The gas chromatography-mass spectrometry (GC/MS)chromatograms of aromatic hydrocarbons terpane and sterane, n-alkane and poly-aromatic hydrocarbons (PAHs) were analyzed. The correlation analysis on diagnostic ratios was performed with Student's t-test. It is found that the oil fingerprinting of the spilled oil (designated as szl) from the polluted sand beach was identical with the suspected oil (designated as kyl) from a nearby crude oil refinery factory. They both showed the fingerprinting character of mixed oil. The oil fingerprinting of the spilled oil (designated as msl) collected from the port was significantly different from oil kyl and oil szl and was with a lubricating oil fingerprint character. The identification result not only gave support for the spilled oil investigation, but also served as an example for studying spilled oil accidents.
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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.
Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials”
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Ji-Huan He
2012-01-01
boundary value problems. This note concludes that the method is a modified variational iteration method using He’s polynomials. A standard variational iteration algorithm for fractional differential equations is suggested.
Soucemarianadin, Laure; Cécillon, Lauric; Chenu, Claire; Baudin, François; Nicolas, Manuel; Savignac, Florence; Barré, Pierre
2017-04-01
Soil organic matter (SOM) is the biggest terrestrial carbon reservoir, storing 3 to 4 times more carbon than the atmosphere. However, despite its major importance for climate regulation SOM dynamics remains insufficiently understood. For instance, there is still no widely accepted method to assess SOM lability. Soil respiration tests and particulate organic matter (POM) obtained by different fractionation schemes have been used for decades and are now considered as classical estimates of very labile and labile soil organic carbon (SOC), respectively. But the pertinence of these methods to characterize SOM turnover can be questioned. Moreover, they are very time-consuming and their reproducibility might be an issue. Alternate ways of determining the labile SOC component are thus well-needed. Thermal analyses have been used to characterize SOM among which Rock-Eval 6 (RE6) analysis of soil has shown promising results in the determination of SOM biogeochemical stability (Gregorich et al., 2015; Barré et al., 2016). Using a large set of samples of French forest soils representing contrasted pedoclimatic conditions, including deep samples (up to 1 m depth), we compared different techniques used for SOM lability assessment. We explored whether results from soil respiration test (10-week laboratory incubations), SOM size-density fractionation and RE6 thermal analysis were comparable and how they were correlated. A set of 222 (respiration test and RE6), 103 (SOM fractionation and RE6) and 93 (respiration test, SOM fractionation and RE6) forest soils samples were respectively analyzed and compared. The comparison of the three methods (n = 93) using a principal component analysis separated samples from the surface (0-10 cm) and deep (40-80 cm) layers, highlighting a clear effect of depth on the short-term persistence of SOC. A correlation analysis demonstrated that, for these samples, the two classical methods of labile SOC determination (respiration and SOM fractionation
A TWO-STEP EXPLICIT METHOD FOR A CLASS OF LINEAR PERIODIC INITIAL VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
李庆宏; 罗亮生; 吴新元
2003-01-01
This paper presents a two-step explicit method of order four for solving aclass of linear periodic initial value problems. At each computational step, only tworight function evaluations and one derivative evaluation are employed. Basing on aspecial vector operation, the method can be extended to the vector-applicable in multi-dimensional space.
Improved Full-Newton-Step Infeasible Interior-Point Method for Linear Complementarity Problems
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Goran Lešaja
2016-04-01
Full Text Available We present an Infeasible Interior-Point Method for monotone Linear Complementarity Problem (LCP which is an improved version of the algorithm given in [13]. In the earlier version, each iteration consisted of one feasibility step and few centering steps. The improved version guarantees that after one feasibility step, the new iterate is feasible and close enough to the central path thanks to the much tighter proximity estimate which is based on the new lemma introduced in [18]. Thus, the centering steps are eliminated. Another advantage of this method is the use of full-Newton-steps, that is, no calculation of the step size is required. The preliminary implementation and numerical results demonstrate the advantage of the improved version of the method in comparison with the old one.
Stability analysis for impulsive fractional hybrid systems via variational Lyapunov method
Yang, Ying; He, Yong; Wang, Yong; Wu, Min
2017-04-01
This paper investigates the stability properties for a class of impulsive Caputo fractional-order hybrid systems with impulse effects at fixed moments. By utilizing the variational Lyapunov method, a fractional variational comparison principle is established. Some stability and instability criteria in terms of two measures are obtained. These results generalize the known ones, extending the corresponding theory of impulsive fractional differential systems. An example is given to demonstrate their effectiveness.
Wei, Meng; Chen, Jiajun
2016-11-01
A multi-step soil washing test using a typical chelating agent (Na2EDTA), organic acid (oxalic acid), and inorganic weak acid (phosphoric acid) was conducted to remediate soil contaminated with heavy metals near an arsenic mining area. The aim of the test was to improve the heavy metal removal efficiency and investigate its influence on metal fractionation and the spectroscopy characteristics of contaminated soil. The results indicated that the orders of the multi-step washing were critical for the removal efficiencies of the metal fractions, bioavailability, and potential mobility due to the different dissolution levels of mineral fractions and the inter-transformation of metal fractions by XRD and FT-IR spectral analyses. The optimal soil washing options were identified as the Na2EDTA-phosphoric-oxalic acid (EPO) and phosphoric-oxalic acid-Na2EDTA (POE) sequences because of their high removal efficiencies (approximately 45 % for arsenic and 88 % for cadmium) and the minimal harmful effects that were determined by the mobility and bioavailability of the remaining heavy metals based on the metal stability (I R ) and modified redistribution index ([Formula: see text]).
The method validation step of biological dosimetry accreditation process
Energy Technology Data Exchange (ETDEWEB)
Roy, L.; Voisin, P.A.; Guillou, A.C.; Busset, A.; Gregoire, E.; Buard, V.; Delbos, M.; Voisin, Ph. [Institut de Radioprotection et de Surete Nucleaire, LDB, 92 - Fontenay aux Roses (France)
2006-07-01
One of the missions of the Laboratory of Biological Dosimetry (L.D.B.) of the Institute for Radiation and Nuclear Safety (I.R.S.N.) is to assess the radiological dose after an accidental overexposure suspicion to ionising radiation, by using radio-induced changes of some biological parameters. The 'gold standard' is the yield of dicentrics observed in patients lymphocytes, and this yield is converted in dose using dose effect relationships. This method is complementary to clinical and physical dosimetry, for medical team in charge of the patients. To obtain a formal recognition of its operational activity, the laboratory decided three years ago, to require an accreditation, by following the recommendations of both 17025 General Requirements for the Competence of Testing and Calibration Laboratories and 19238 Performance criteria for service laboratories performing biological dosimetry by cyto-genetics. Diagnostics, risks analysis were realized to control the whole analysis process leading to documents writing. Purchases, personnel department, vocational training were also included in the quality system. Audits were very helpful to improve the quality system. One specificity of this technique is that it is not normalized therefore apart from quality management aspects, several technical points needed some validations. An inventory of potentially influent factors was carried out. To estimate their real effect on the yield of dicentrics, a Placket-Burman experimental design was conducted. The effect of seven parameters was tested: the BUdr (bromodeoxyuridine), PHA (phytohemagglutinin) and colcemid concentration, the culture duration, the incubator temperature, the blood volume and the medium volume. The chosen values were calculated according to the uncertainties on the way they were measured i.e. pipettes, thermometers, test tubes. None of the factors has a significant impact on the yield of dicentrics. Therefore the uncertainty linked to their use was
Residual power series method for fractional Burger types equations
Kumar, Amit; Kumar, Sunil
2016-12-01
We present an analytic algorithm to solve the generalized Berger-Fisher (B-F) equation, B-F equation, generalized Fisher equation and Fisher equation by using residual power series method (RPSM), which is based on the generalized Taylor's series formula together with the residual error function. In all the cases obtained results are verified through the different graphical representation. Comparison of the results obtained by the present method with exact solution reveals that the accuracy and fast convergence of the proposed method.
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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.
Energy Technology Data Exchange (ETDEWEB)
Odibat, Zaid [Prince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa' Applied University, Salt 19117 (Jordan)], E-mail: odibat@bau.edu.jo; Momani, Shaher [Department of Mathematics, Mutah University, P.O. Box 7, Al-Karak (Jordan)], E-mail: shahermm@yahoo.com
2008-04-15
In this paper, a modification of He's homotopy perturbation method is presented. The new modification extends the application of the method to solve nonlinear differential equations of fractional order. In this method, which does not require a small parameter in an equation, a homotopy with an imbedding parameter p element of [0, 1] is constructed. The proposed algorithm is applied to the quadratic Riccati differential equation of fractional order. The results reveal that the method is very effective and convenient for solving nonlinear differential equations of fractional order.
Directory of Open Access Journals (Sweden)
C. Ünlü
2013-01-01
Full Text Available A modification of the variational iteration method (VIM for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.
ETAAS method for the determination of Cd, Cr, Cu, Mn and Se in blood fractions and whole blood
Energy Technology Data Exchange (ETDEWEB)
Prohaska, C.; Pomazal, K.; Steffan, I. [Technische Univ., Vienna (Austria). Inst. fuer Analytische Chemie
2000-11-01
An electrothermal atomic absorption method (ETAAS) for the direct determination of trace elements (Cd, Cr, Cu, Mn, Se) both in blood fractions (erythrocytes, plasma and lymphocytes) and whole blood was developed. Zeeman background correction and graphite tubes with L'vov platforms were used. Samples were diluted with HNO{sub 3}/Triton X-100 and pipetted directly into the graphite tube. Ashing, pretreatment and atomization steps were optimized carefully for the different fractions and elements applying different matrix modifiers for each element. For the lymphocyte fraction a multi-fold injection technique was applied. Low detection limits of the ETAAS method (Cd 0.13 {mu}g/L, Cr 0.11 {mu}g/L, Cu 0.52 {mu}g/L, Mn 0.13 {mu}g/L, Se 0.7 {mu}g/L of whole blood) combined with small quantities of sample necessary for analysis allow determination of trace elements in this matrix. Verification of possible differences in the trace element status of humans was performed with statistical significance (P < 0.05). In addition, a contribution to the determination of normal values of essential elements was achieved. The method was applied for determination of trace elements in human blood and blood fractions of two groups (n = 50) different in health status. (orig.)
Drobyshev, Alexei L; Machka, Christine; Horsch, Marion; Seltmann, Matthias; Liebscher, Volkmar; Hrabé de Angelis, Martin; Beckers, Johannes
2003-01-15
The cDNA-chip technology is a highly versatile tool for the comprehensive analysis of gene expression at the transcript level. Although it has been applied successfully in expression profiling projects, there is an ongoing dispute concerning the quality of such expression data. The latter critically depends on the specificity of hybridisation. SAFE (specificity assessment from fractionation experiments) is a novel method to discriminate between non- specific cross-hybridisation and specific signals. We applied in situ fractionation of hybridised target on DNA-chips by means of repeated washes with increasing stringencies. Different fractions of hybridised target are washed off at defined stringencies and the collected fluorescence intensity data at each step comprise the fractionation curve. Based on characteristic features of the fractionation curve, unreliable data can be filtered and eliminated from subsequent analyses. The approach described here provides a novel experimental tool to identify probes that produce specific hybridisation signals in DNA-chip expression profiling approaches. The iterative use of the SAFE procedure will result in increasingly reliable sets of probes for microarray experiments and significantly improve the overall efficiency and reliability of RNA expression profiling data from DNA-chip experiments.
Avila Ruiz, Geraldine; Arts, Anke; Minor, Marcel; Schutyser, Maarten
2016-01-01
Combination of dry and aqueous fractionation is investigated to obtain protein-rich fractions from quinoa in a milder and more sustainable way compared to conventional wet fractionation. Dry fractionation of quinoa involved milling and subsequent air classification, generating a protein-enriched
Fermentation, fractionation and purification of streptokinase by chemical reduction method
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M Niakan
2011-05-01
Full Text Available Background and Objectives: Streptokinase is used clinically as an intravenous thrombolytic agent for the treatment of acute myocardial infarction and is commonly prepared from cultures of Streptococcus equisimilis strain H46A. The objective of the present study was the production of streptokinase from strain H46A and purification by chemical reduction method."nMaterials and Methods: The rate of streptokinase production evaluated under the effect of changes on some fermentation factors. Moreover, due to the specific structure of streptokinase, a chemical reduction method employed for the purification of streptokinase from the fermentation broth. The H46A strain of group C streptococcus, was grown in a fermentor. The proper pH adjusted with NaOH under glucose feeding in an optimum temperature. The supernatant of the fermentation product was sterilized by filtration and concentrated by ultrafiltration. The pH of the concentrate was adjusted, cooled, and precipitated by methanol. Protein solution was reduced with dithiothreitol (DTT. Impurities settled down by aldrithiol-2 and the biological activity of supernatant containing streptokinase was determined."nResults: In the fed -batch culture, the rate of streptokinase production increased over two times as compared with the batch culture and the impurities were effectively separated from streptokinase by reduction method."nConclusion: Improvements in SK production are due to a decrease in lag phase period and increase in the growth rate of logarithmic phase. The methods of purification often result in unacceptable losses of streptokinase, but the chemical reduction method give high yield of streptokinase and is easy to perform it.
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.
Frontier in nanoscale flows fractional calculus and analytical methods
Lewis, Roland; Liu, Hong-yan
2014-01-01
This ebook covers the basic properties of nanoscale flows, and various analytical and numerical methods for nanoscale flows and environmental flows. This ebook is a good reference not only for audience of the journal, but also for various communities in mathematics, nanotechnology and environmental science.
Method and apparatus for separating a non-ferrous metal-comprising fraction from ferrous scrap
Rem, P.C.; Berkhout, S.P.M.
2010-01-01
Method for separating a non-ferrous metal-comprising fraction from ferrous scrap, wherein the ferrous scrap is conveyed to a processing device for separating the non-ferrous metal-comprising fraction from the remainder of the ferrous scrap. The processing device supplies a beam of water, and the fer
New iterative method for fractional gas dynamics and coupled Burger's equations.
Al-Luhaibi, Mohamed S
2015-01-01
This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger's equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.
Exact solutions of some fractional differential equations by various expansion methods
Topsakal, Muammer; Guner, Ozkan; Bekir, Ahmet; Unsal, Omer
2016-10-01
In this paper, we construct the exact solutions of some nonlinear spacetime fractional differential equations involving modified Riemann-Liouville derivative in mathematical physics and applied mathematics; namely the fractional modified Benjamin-Bona- Mahony (mBBM) and Kawahara equations by using G'/G and (G'/G, 1/G)-expansion methods.
The Jacobi Elliptic Equation Method for Solving Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
Bin Zheng
2014-01-01
demonstrating the validity of this method, we apply it to solve the space fractional coupled Konopelchenko-Dubrovsky (KD equations and the space-time fractional Fokas equation. As a result, some exact solutions for them including the hyperbolic function solutions, trigonometric function solutions, rational function solutions, and Jacobi elliptic function solutions are successfully found.
Local fractional Euler’s method for the steady heat-conduction problem
Directory of Open Access Journals (Sweden)
Gao Feng
2016-01-01
Full Text Available In this paper, the local fractional Euler’s method is proposed to consider the steady heat-conduction problem for the first time. The numerical solution for the local fractional heat-relaxation equation is presented. The comparison between numerical and exact solutions is discussed.
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.
Directory of Open Access Journals (Sweden)
Mridula Garg
2011-12-01
Full Text Available In the present paper, we use generalized differential transform method (GDTM to derive solutions of some linear and nonlinear space-time fractional Fokker–Planck equations (FPE in closed form. The space and time fractional derivatives are considered in Caputo sense and the solutions are obtained in terms of Mittag-Leffler functions.
Fractionation of elements in soils, sludges and sediments: batch and dynamic methods
Fedotov, P. S.; Spivakov, B. Ya
2008-07-01
Methods and approaches employed in the fractionation of elements according to their physicochemical mobility and bioavailability in soils, sludges and sediments are generalised. Comparative analysis of sequential extraction schemes for heavy metals, arsenic, selenium and phosphorus is performed. Special consideration is given to the flow-through fractionation and kinetic aspects of selective leaching.
Method and apparatus for separating a non-ferrous metal-comprising fraction from ferrous scrap
Rem, P.C.; Berkhout, S.P.M.
2010-01-01
Method for separating a non-ferrous metal-comprising fraction from ferrous scrap, wherein the ferrous scrap is conveyed to a processing device for separating the non-ferrous metal-comprising fraction from the remainder of the ferrous scrap. The processing device supplies a beam of water, and the
The influence of preparation method on measured carbon fractions in tree tissues.
Jones, Dryw A; O'Hara, Kevin L
2016-09-01
Carbon fractions of tree tissues are a key component of forest carbon mass estimation. Several methods have been used to measure carbon fractions, yet no comprehensive comparison between methods has been performed. We found significant differences between carbon fractions derived from four sample preparation methods: oven-drying, vacuum desiccation, freeze-drying, and a new method that consisted of (i) not drying samples, (ii) cutting samples instead of grinding them, (iii) measuring carbon content of samples, (iv) oven-drying remaining sample material and (v) using mass measurements of remaining sample material before and after oven-drying to adjust measured carbon fraction values to an oven-dry basis (minimize the loss of carbon (MLC) method). Oven-drying, freeze-drying and vacuum desiccation resulted in lower average carbon fraction estimates than the MLC method, suggesting that they do not capture as much of the carbon present in tree tissues. Further analysis showed significant, though small, differences in carbon fractions between powdered samples and samples excised from tree core segments with a razor blade. Powdered samples were found to have lower carbon fractions than the excised samples, indicating that some carbon is lost when samples are powdered instead of cut. Utilization of the MLC method captured an average of 1.4% more carbon on an oven-drying basis than freeze-drying, the next best method. Additionally, when applied to different tree tissue types, these methods measured different volatile carbon fractions, indicating that studies attempting to quantify volatile carbon and total carbon fraction in trees should measure all tissue types present.
Acupuncture Treatment of Acute Cerebral Infarction by the‘Three-Step Needling’Method
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Objective: To observe the therapeutic effects of acupuncture treatment by the‘Three-Step Needling’Method for acute cerebral infarction. Method: While receiving the routine medical treatment, 68 cases were treated by the acupuncture method of‘Three-Step Needling’. Results: 27 of the 68 cases were basically cured, 23markedly improved, 15 improved, and 3 failed, the total effective rate being 95.59%. Conclusion: The acupuncture method of‘Three-Step Needling’can give quite good therapeutic effects for acute cerebral infarction.
Directory of Open Access Journals (Sweden)
Samia Bushnaq
2014-01-01
Full Text Available We present a new version of the reproducing kernel Hilbert space method (RKHSM for the solution of systems of fractional integrodifferential equations. In this approach, the solution is obtained as a convergent series with easily computable components. Several illustrative examples are given to demonstrate the effectiveness of the present method. The method described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.
Application of Variational Iteration Method to Fractional Hyperbolic Partial Differential Equations
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Fadime Dal
2009-01-01
Full Text Available The solution of the fractional hyperbolic partial differential equation is obtained by means of the variational iteration method. Our numerical results are compared with those obtained by the modified Gauss elimination method. Our results reveal that the technique introduced here is very effective, convenient, and quite accurate to one-dimensional fractional hyperbolic partial differential equations. Application of variational iteration technique to this problem has shown the rapid convergence of the sequence constructed by this method to the exact solution.
An Efficient Method for Performing Partial Fraction Expansion.
1980-02-01
Residues and Coefficients of High Order Poles," IRE Trans. Auto. Cont., AC-4, (1959). [2] Henrici , P., Applied and Computational Complex Analysis , Volume 1, John Wiley aind Sons, (1974). ... Henrici . A numerical example is provided. DD I Fhim3 1473 EDITIONO 01NOVSS1 OBSOLETE Unclassified /)’/, , SECURITY CLASSIFICATION OF THIS PAGE (*?Ion Data...the method of Henrici . A numerical example is provided. MAS (MOS) subject classificatiom (1970). Primary 65F99. Vi I A Introduction. At times it is
A Fractional Step Theta-Method for Viscoelastic Fluid Flow Using a UPG Approximation
2007-10-01
sphere) included in K, and h = maxk∈Th hK . Let Pk(A) denote the space of polynomials on A of degree no greater 5 than k and C(Ω̄)d́ the space of vector...t)− ∫ tθ t0 t utt(·, t) dt. =⇒ ∣∣∣∣∣u(θ) − u(0)θ∆t − u(θ)t ∣∣∣∣∣ = 1θ∆t ∣∣∣∣∫ θ∆t 0 tutt (·, t) dt ∣∣∣∣ ≤ 1 θ∆t (∫ tθ t0 t2 dt ) 1 2 (∫ tθ t0 |utt(·, t
DEFF Research Database (Denmark)
Wagner, Stephan; Legros, Samuel; Löschner, Katrin
2015-01-01
The applicability of a multi-step generic procedure to systematically develop sample preparation methods for the detection, characterization, and quantification of inorganic engineered nanoparticles (ENPs) in a complex matrix was successfully demonstrated. The research focused on the optimization...... content by asymmetric flow-field flow fractionation coupled to a multi-angle light scattering detector and an inductively coupled plasma mass spectrometer. Following the proposed generic procedure SiO2-ENPs were separated from a tomato soup. Two potential sample preparation methods were tested these being...
Solving Time-Fractional Advection-Dispersion Equation by Variable Weights Particle Tracking Method
Cao, Shaohua; Jiang, Jianguo; Wu, Jichun
2017-09-01
Particle tracking method is an efficient and reliable method to solve time-fractional advection-dispersion equation, which can describe anomalous transport in heterogeneous porous media. However, this method will lead to severe fluctuation or disappearance of solutions if the concentration value is small. A variable weights method is developed to conquer the shortcoming of particle tracking method. Then, one-dimensional and two-dimensional time-fractional advection-dispersion equations are solved by the variable weights particle tracking method. Compared to traditional particle tracking method, the variable weights version may eliminate the fluctuation and improve the accuracy by orders of magnitude without more computational cost.
Leydesdorff, Loet
2010-01-01
The ISI-Impact Factors suffer from a number of drawbacks, among them the statistics-why should one use the mean and not the median?-and the incomparability among fields of science because of systematic differences in citation behavior among fields. Can these drawbacks be counteracted by counting citation weights fractionally instead of using integers? (i) Fractional citation counts are normalized in terms of the citing papers and thus would take into account differences in citation behavior among fields of science. (ii) Differences in the resulting distributions can be tested statistically for their significance at different levels of aggregation. (iii) Fractional counting can be generalized to any document set including journals or groups of journals, and thus the significance of differences among both small and large sets can be tested. In addition to the Impact Factor, the Total Cites of the journals listed in the Science Citation Index (CD-Rom version) 2008 are analyzed in these terms. The between-group v...
A semi-analytical finite element method for a class of time-fractional diffusion equations
Sun, HongGuang; Sze, K Y
2011-01-01
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly employed in the related mathematical descriptions. These models usually involve long-time range computation, which is a critical obstacle for its application, improvement of the computational efficiency is of great significance. In this paper, a semi-analytical method is presented for solving a class of time-fractional diffusion equations which overcomes the critical long-time range computation problem of time fractional differential equations. In the procedure, the spatial domain is discretized by the finite element method which reduces the fractional diffusion equations into approximate fractional relaxation equations. As analytical solutions exist for the latter equations, the burden arising from long-time range computation can effectively be minimized. To illustrate its efficiency and simplicity, four...
Application of a four-step HMX kinetic model to an impact-induced fraction ignition problems
Energy Technology Data Exchange (ETDEWEB)
Perry, William L [Los Alamos National Laboratory; Gunderson, Jake A [Los Alamos National Laboratory; Dickson, Peter M [Los Alamos National Laboratory
2010-01-01
There has been a long history of interest in the decomposition kinetics of HMX and HMX-based formulations due to the widespread use of this explosive in high performance systems. The kinetics allow us to predict, or attempt to predict, the behavior of the explosive when subjected to thermal hazard scenarios that lead to ignition via impact, spark, friction or external heat. The latter, commonly referred to as 'cook off', has been widely studied and contemporary kinetic and transport models accurately predict time and location of ignition for simple geometries. However, there has been relatively little attention given to the problem of localized ignition that results from the first three ignition sources of impact, spark and friction. The use of a zero-order single-rate expression describing the exothermic decomposition of explosives dates to the early work of Frank-Kamanetskii in the late 1930s and continued through the 60's and 70's. This expression provides very general qualitative insight, but cannot provide accurate spatial or timing details of slow cook off ignition. In the 70s, Catalano, et al., noted that single step kinetics would not accurately predict time to ignition in the one-dimensional time to explosion apparatus (ODTX). In the early 80s, Tarver and McGuire published their well-known three step kinetic expression that included an endothermic decomposition step. This scheme significantly improved the accuracy of ignition time prediction for the ODTX. However, the Tarver/McGuire model could not produce the internal temperature profiles observed in the small-scale radial experiments nor could it accurately predict the location of ignition. Those factors are suspected to significantly affect the post-ignition behavior and better models were needed. Brill, et al. noted that the enthalpy change due to the beta-delta crystal phase transition was similar to the assumed endothermic decomposition step in the Tarver/McGuire model. Henson, et
Detection of protein concentrations using a pH-step titration method
Kruise, J.; Eijkel, J.C.T.; Bergveld, P.
1997-01-01
A stimulus-response method based on the application of a pH step is proposed for the detection of protein immobilized in a membrane on top of an ion-sensitive field-effect transistor (ISFET). The ISFET response to a step-wise change in pH, applied at the interface between the membrane and the surrou
Weighted Average Finite Difference Methods for Fractional Reaction-Subdiffusion Equation
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Nasser Hassen SWEILAM
2014-04-01
Full Text Available In this article, a numerical study for fractional reaction-subdiffusion equations is introduced using a class of finite difference methods. These methods are extensions of the weighted average methods for ordinary (non-fractional reaction-subdiffusion equations. A stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. Simple and accurate stability criterion valid for different discretization schemes of the fractional derivative, arbitrary weight factor, and arbitrary order of the fractional derivative, are given and checked numerically. Numerical test examples, figures, and comparisons have been presented for clarity.doi:10.14456/WJST.2014.50
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Ali Sevimlican
2010-01-01
Full Text Available He's variational iteration method (VIM is used for solving space and time fractional telegraph equations. Numerical examples are presented in this paper. The obtained results show that VIM is effective and convenient.
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.
Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.
2017-02-01
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.
Institute of Scientific and Technical Information of China (English)
HAN Shan-ling; ZHU Ping; LIN Zhong-qin
2005-01-01
The fractional volumetric lattice Boltzmann method with much better stability was used to simulate two dimensional cavity flows. Because the effective viscosity was reduced by the fraction factor, it is very effective forsimulating high Reynolds number flows. Simulations were carried out on a uniform grids system. The stream lines and the velocity profiles obtained from the simulations agree well with the standard lattice Boltzmann method simulations. Comparisons of detailed flow patterns with other studies via location of vortex centers are also satisfactory.
Apparatus and method for rapid separation and detection of hydrocarbon fractions in a fluid stream
Sluder, Charles S.; Storey, John M.; Lewis, Sr., Samuel A.
2013-01-22
An apparatus and method for rapid fractionation of hydrocarbon phases in a sample fluid stream are disclosed. Examples of the disclosed apparatus and method include an assembly of elements in fluid communication with one another including one or more valves and at least one sorbent chamber for removing certain classifications of hydrocarbons and detecting the remaining fractions using a detector. The respective ratios of hydrocarbons are determined by comparison with a non separated fluid stream.
Full-Newton step interior-point methods for conic optimization
Mansouri, H.
2008-01-01
In the theory of polynomial-time interior-point methods (IPMs) two important classes of methods are distinguished: small-update and large-update methods, respectively. Small-update IPMs have the best theoretical iteration bound and IPMs with full-Newton steps belong to this class of methods. Within
Noether's theorem and one-step corrections method for holonomic system
Institute of Scientific and Technical Information of China (English)
Shang Mei; Chen Xiang-Wei
2006-01-01
In this paper, a new computational method for improving the accuracy of numerically computed solutions is introduced. The computational method is based on the one-step method and conserved quantities of holonomic systems are considered as kinematical constraints in this method.
Constraint Stabilization and One-Step Correction Method for Dynamical Systems
Institute of Scientific and Technical Information of China (English)
SHANG Mei; CHEN Xiang-wei; MEI Feng-xiang
2007-01-01
A computational method of constraint stabilization and correction is introduced.The method is based on the Baumgart's one-step method.Constraint conditions are addressed to stabilize and correct the solution.Two examples are given to illustrate the results of the method.
Full-Newton step interior-point methods for conic optimization
Mansouri, H.
2008-01-01
In the theory of polynomial-time interior-point methods (IPMs) two important classes of methods are distinguished: small-update and large-update methods, respectively. Small-update IPMs have the best theoretical iteration bound and IPMs with full-Newton steps belong to this class of methods. Within
Development of a two-step touch method for website navigation on smartphones.
Jung, Kihyo; Jang, Jinah
2015-05-01
The touch method for hyperlink selection in smartphones can often create usability problems because a hyperlink is universally smaller than a finger contact area as well as visually occluded by a finger while pressing. In this study, we developed a two-step touch method (called Press and Flick method) and comprehensively examined its effectiveness using the goals, operators, methods, and selection rules (GOMS) model and user testing. The two-step touch method consisted of finger press and flick motions; a target hyperlink was selected by a finger press motion, and a finger flick method was subsequently conducted for error correction if the initial interaction (press) failed. We compared the two-step touch method with the current touch method through the GOMS model and user testing. As a result, the two-step touch method was significantly superior to the current touch method in terms of error rate and subjective satisfaction score; however, its superiority in terms of number of interactions and touch time was vulnerably affected by error rate. The two-step touch method developed in this study can improve the usability and user experience of website navigation using smartphones.
Directory of Open Access Journals (Sweden)
Süleyman Öğrekçi
2015-01-01
Full Text Available We propose an efficient analytic method for solving nonlinear differential equations of fractional order. The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. A new technique for calculating the generalized Taylor series coefficients (also known as “generalized differential transforms,” GDTs of nonlinear functions and a new approach of the generalized Taylor series method (GTSM are presented. This new method offers a simple algorithm for computing GDTs of nonlinear functions and avoids massive computational work that usually arises in the standard method. Several illustrative examples are demonstrated to show effectiveness of the proposed method.
Tian, Li-Ping; Liu, Lizhi; Wu, Fang-Xiang
2010-01-01
Derived from biochemical principles, molecular biological systems can be described by a group of differential equations. Generally these differential equations contain fractional functions plus polynomials (which we call improper fractional model) as reaction rates. As a result, molecular biological systems are nonlinear in both parameters and states. It is well known that it is challenging to estimate parameters nonlinear in a model. However, in fractional functions both the denominator and numerator are linear in the parameters while polynomials are also linear in parameters. Based on this observation, we develop an iterative linear least squares method for estimating parameters in biological systems modeled by improper fractional functions. The basic idea is to transfer optimizing a nonlinear least squares objective function into iteratively solving a sequence of linear least squares problems. The developed method is applied to the estimation of parameters in a metabolism system. The simulation results show the superior performance of the proposed method for estimating parameters in such molecular biological systems.
Inverse Scattering from a Sound-Hard Crack via Two-Step Method
Directory of Open Access Journals (Sweden)
Kuo-Ming Lee
2012-01-01
Full Text Available We present a two-step method for recovering an unknown sound-hard crack in ℝ2 from the measured far-field pattern. This method, based on a two-by-two system of nonlinear integral equations, splits the reconstruction into two consecutive steps which consists of a forward and an inverse problems. In this spirit, only the latter needs to be regularized.
DEFF Research Database (Denmark)
Guillaumie, Fanny; Justesen, Sune F. L.; Mutenda, Kudzai E.
2006-01-01
This work presents the optimized separation of pectin oligomers, their analysis by matrix-assisted laser desorption/ionization-time of flight mass spectrometry (MALDI-TOF MS), their subsequent immobilization to supports, and our initial steps towards solid-support assisted sequencing. The ambient...... pressure strong anion-exchange resin Source 15Q combined with ammonium formate buffer (AF) was used for the separation of unsaturated and saturated pectic oligogalacturonides (OGAs) derived from enzymatic digestion of pectin. Routinely, multi-milligram quantities of defined sizes OGAs with DPs from 5 to 19...
Nanowire-based polypyrrole hierarchical structures synthesized by a two-step electrochemical method.
Ge, Dongtao; Huang, Sanqing; Qi, Rucai; Mu, Jing; Shen, Yuqing; Shi, Wei
2009-08-03
A simple two-step electrochemical method is proposed for the synthesis of nanowire-based polypyrrole hierarchical structures. In the first step, microstructured polypyrrole films are prepared by electropolymerization. Then, polypyrrole nanowires are electrodeposited on the surface of the as-synthesized microstructured polypyrrole films. As a result, hierarchical structures of polypyrrole nanowires on polypyrrole microstructures are obtained. The surface wettabilities of the resulting nanowire-based polypyrrole hierarchical structures are examined. It is expected that this two-step method can be developed into a versatile route to produce nanowire-based polypyrrole hierarchical structures with different morphologies and surface properties.
Energy Technology Data Exchange (ETDEWEB)
Pettersson, Anita; Claesson, Frida
2009-07-01
Striving to improve the waste handling in an energy and environmental manner has led to an increased flow of waste fractions interesting for energy recovery by combustion, both for heat and power production. The increased flow of various waste fractions with varying chemical compositions results in new demands on the combustion plants. This because operational problems, such as bed sintering, corrosion and deposit formation resulting in expensive shut downs can be caused by relatively small changes in the fuel stream. It is primarily alkali metals in combination with chlorine that cause problems like fouling and corrosion. To avoid these problems, tools for characterization of these fuels to predict combustion processes are needed. Two such tools are the Aabo- and the CEN/TS 15105 methods which both are chemical characterization methods based on leaching. The Aabo-method is a more advanced method and also more time consuming compared to the CEN/TS 15105-method. These methods aim to dissolve and identify the compounds that are reactive during combustion and therefore able to cause combustion problems. Both these methods are developed for the characterization of biofuels but only the Aabo-method has been evaluated for waste fuels. The aim of this study was to evaluate the two methods by characterization of six waste fuels with different composition. In addition also four more homogeneous fuels: coal, straw, wood pellets and municipal sewage sludge. The analyses showed that the Aabo-method gave a more clear picture of the reactive elements in the waste fuel in comparison to the CEN/TS 15105-method. An advantage with the Aabo-method is also that the solid rest obtained after the leaching is analysed giving an element balance of the sample without having to make assumptions. The comparison of the methods showed that the CEN/TS 15105-method does not dissolve large parts of the available calcium in the waste fuel resulting in a large underestimation of the reactive
Comparison of fractionation methods for nitrogen and starch in maize and grass silages
Ali, M.; Jonge, de L.H.; Cone, J.W.; Duinkerken, van G.; Blok, M.C.; Bruinenberg, M.H.; Hendriks, W.H.
2016-01-01
In in situ nylon bag technique, many feed evaluation systems use a washing machine method (WMM) to determine the washout (W) fraction and to wash the rumen incubated nylon bags. As this method has some disadvantages, an alternate modified method (MM) was recently introduced. The aim of this study
Comparison of fractionation methods for nitrogen and starch in maize and grass silages
Ali, M; de Jonge, L H; Cone, J W; van Duinkerken, G; Blok, M C; Bruinenberg, M H; Hendriks, W H
2016-01-01
In in situ nylon bag technique, many feed evaluation systems use a washing machine method (WMM) to determine the washout (W) fraction and to wash the rumen incubated nylon bags. As this method has some disadvantages, an alternate modified method (MM) was recently introduced. The aim of this study wa
A Comparison of Three Methods of Teaching Fractions to Older Slow-Learners
Davies, Rhys Ll.; Williams, Phillip
1972-01-01
The author compared the relative efficiency of three methods of presenting and teaching fractions to slow learners in secondary school: formal-traditional method, cuisenaire (unimodel) material, and specially prepared multi-model materials; multi-model materials were found to be the most effective method. (Author/AN)
Comparison of fractionation methods for nitrogen and starch in maize and grass silages
Ali, M.; Jonge, de L.H.; Cone, J.W.; Duinkerken, van G.; Blok, M.C.; Bruinenberg, M.H.; Hendriks, W.H.
2016-01-01
In in situ nylon bag technique, many feed evaluation systems use a washing machine method (WMM) to determine the washout (W) fraction and to wash the rumen incubated nylon bags. As this method has some disadvantages, an alternate modified method (MM) was recently introduced. The aim of this study
Comparison of fractionation methods for nitrogen and starch in maize and grass silages
Ali, M; de Jonge, L H; Cone, J W; van Duinkerken, G; Blok, M C; Bruinenberg, M H; Hendriks, W H
2016-01-01
In in situ nylon bag technique, many feed evaluation systems use a washing machine method (WMM) to determine the washout (W) fraction and to wash the rumen incubated nylon bags. As this method has some disadvantages, an alternate modified method (MM) was recently introduced. The aim of this study wa
Time-Fractional KdV Equation for the plasma in auroral zone using Variational Methods
El-Wakil, El-Said A; Elshewy, Emad K; Mahmoud, Aber A
2010-01-01
The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. Numerical studies have been made using plasma parameters close to those values corresponding to the dayside auroral zone. The effects of the time fractional parameter on the electrostatic solitary structures are presented.
A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation
Directory of Open Access Journals (Sweden)
Yunying Zheng
2011-01-01
Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.
DEFF Research Database (Denmark)
Kristensen, Mette; Savorani, Francesco; Ravn-Haren, Gitte
2010-01-01
Risk of cardiovascular disease is related to cholesterol distribution in different lipoprotein fractions. Lipoproteins in rodent model studies can only reliably be measured by time- and plasma-consuming fractionation. An alternative method to measure cholesterol distribution in the lipoprotein...... fractions in rat plasma is presented in this paper. Plasma from two rat studies (n = 68) was used in determining the lipoprotein profile by an established ultracentrifugation method and proton nuclear magnetic resonance (NMR) spectra of replicate samples was obtained. From the ultracentrifugation reference...... data and the NMR spectra, an interval partial least-square (iPLS) regression model to predict the amount of cholesterol in the different lipoprotein fractions was developed. The relative errors of the prediction models were between 12 and 33% and had correlation coefficients (r) between 0.96 and 0...
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.
Byers, J A
1992-09-01
Studies of chemical ecology of an organism are founded on the isolation and identification of a semiochemical, often comprised of two or more synergistic compounds (each Synergist alone has little activity, but presented together they are bioactive). Chromatographie fractionation and bioassay methods of binary splitting, additive combination, and subtractive combination are compared for efficiency in isolating synergists. Formulas are derived for the latter two methods that calculate the expected number of bioassay tests required for isolation of from two to five synergists from biological extracts with any number of compounds, depending on the number of initial (major) Chromatographic fractions. A computer program based on the formulas demonstrates the superiority of the subtractive-combination method. Simulations with the program were used to determine the optimal number of initial fractions for the additive- and subtractive-combination methods when isolating two to five synergists from extracts of from 25 to 1200 compounds. Methods of bioassay, isolation, identification, and field testing of semiochemicals are discussed.
New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations
Directory of Open Access Journals (Sweden)
Mohamed S. Al-luhaibi
2015-01-01
Full Text Available This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.
Homotopy perturbation method for nonlinear partial differential equations of fractional order
Energy Technology Data Exchange (ETDEWEB)
Momani, Shaher [Department of Mathematics and Physics, Qatar University (Qatar)]. E-mail: shahermm@yahoo.com; Odibat, Zaid [Prince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa' Applied University, Salt (Jordan)]. E-mail: odibat@bau.edu.jo
2007-06-11
The aim of this Letter is to present an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative. The fractional derivative is described in the Caputo sense. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. The obtained results are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, efficient and easy to implement.
Directory of Open Access Journals (Sweden)
Asma Ali Elbeleze
2014-01-01
Full Text Available We are concerned here with singular partial differential equations of fractional order (FSPDEs. The variational iteration method (VIM is applied to obtain approximate solutions of this type of equations. Convergence analysis of the VIM is discussed. This analysis is used to estimate the maximum absolute truncated error of the series solution. A comparison between the results of VIM solutions and exact solution is given. The fractional derivatives are described in Caputo sense.
New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods
S Saha, Ray
2016-04-01
In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.
HIGH ORDER ONE-STEP A-STABLE EXPONENTIALLY FITTED METHODS
Institute of Scientific and Technical Information of China (English)
YangFengiian; ChenXinming; LuoYiping
1999-01-01
In this paper,the necessary and sutlicient conditions for general one-step methoos to be exponentially fitted at q0∈C are given, A class of multtderivative hybrid one-step methods of order at least s+1 is constructed with s+1 parameters,where s is the order of derivative. The necessary and sufficient conditions for these methods to be A-stable and exponentially fitted is proved, Furthermore,a class of A-stable 2 parameters hybrid one-step methods of order at least 8 are constructed,which use 4th order derivative,These methods are exponentially fitted at q0 if and only its fitted function f(q) satisfies f(q0)= 0, Finally,an A-stable exponentlally fitted method of order 8 is obtained.
An automatic fractional coefficient setting method of FODPSO for hyperspectral image segmentation
Xie, Weiying; Li, Yunsong
2015-05-01
In this paper, an automatic fractional coefficient setting method of fractional-order Darwinian particle swarm optimization (FODPSO) is proposed for hyperspectral image segmentation. The spectrum has been already taken into consideration by integrating various types of band selection algorithms, firstly. We provide a short overview of the hyperspectral image to select an appropriate set of bands by combining supervised, semi-supervised and unsupervised band selection algorithms. Some approaches are not limited in regards to their spectral dimension, but are limited with respect to their spatial dimension owing to low spatial resolution. The addition of spatial information will be focused on improving the performance of hyperspectral image segmentation for later fusion or classification. Many researchers have advocated that a large fractional coefficient should be in the exploration state while a small fractional coefficient should be in the exploitation, which does not mean the coefficient purely decrease with time. Due to such reasons, we propose an adaptive FODPSO by setting the fractional coefficient adaptively for the application of final hyperspectral image segmentation. In fact, the paper introduces an evolutionary factor to automatically control the fractional coefficient by using a sigmoid function. Therefore, fractional coefficient with large value will benefit the global search in the exploration state. Conversely, when the fractional coefficient has a small value, the exploitation state is detected. Hence, it can avoid optimization process get trapped into the local optima. Ultimately, the experimental segmentation results prove the validity and efficiency of our proposed automatic fractional coefficient setting method of FODPSO compared with traditional PSO, DPSO and FODPSO.
A novel approach for solving fractional Fisher equation using differential transform method
Indian Academy of Sciences (India)
MIRZAZADEH M
2016-05-01
In the present paper, an analytic solution of nonlinear fractional Fisher equation is deduced with the help of the powerful differential transform method (DTM). To illustrate the method, two examples have been prepared. The method for this equation has led to an exact solution. The reliability, simplicity and cost-effectiveness of the method are confirmed by applying this method on different forms of functional equations.
Directory of Open Access Journals (Sweden)
Gang Zhang
2017-07-01
Full Text Available The Sacramento model is widely utilized in hydrological forecast, of which the accuracy and performance are primarily determined by the model parameters, indicating the key role of parameter estimation. This paper presents a multi-step parameter estimation method, which divides the parameter estimation of Sacramento model into three steps and realizes optimization step by step. We firstly use the immune clonal selection algorithm (ICSA to solve the non-liner objective function of parameter estimation, and compare the parameter calibration result of ideal artificial data with Shuffled Complex Evolution (SCE-UA, Parallel Genetic Algorithm (PGA, and Serial Master-slaver Swarms Shuffling Evolution Algorithm Based on Particle Swarms Optimization (SMSE-PSO. The comparison result shows that ICSA has the best convergence, efficiency and precision. Then we apply ICSA to the parameter estimation of single-step and multi-step Sacramento model and simulate 32 floods based on application examples of Dongyang and Tantou river basins for validation. It is clearly shown that the results of multi-step method based on ICSA show higher accuracy and 100% qualified rate, indicating its higher precision and reliability, which has great potential to improve Sacramento model and hydrological forecast.
Bell, Benjamin; Fletcher, William; Ryan, Peter; Grant, Helen; Ilmen, Rachid
2016-04-01
Analysis of stable carbon isotopes can provide information on climate and the environmental conditions at different growth stages of the plant, both past and present. Carbon isotope discrimination in plant tissue is already well understood, and can be used as a drought stress indicator for semi-arid regions. Stable carbon isotope ratios measured directly on pollen provides the potential for the development of long-term environmental proxies (spanning thousands of years), as pollen is well preserved in the environment. Atlas Cedar (Cedrus atlantica Endl. Manetti ex Carrière), is an ideal test case to develop a pollen stable carbon isotope proxy. The tree grows across a wide altitudinal and climatic range and is extremely sensitive to moisture availability. The pollen is abundant, and easily identifiable to the species level in pollen analysis because different cedar species are geographically confined to different regions of the world. In 2015 we sampled 76 individual cedar trees across latitudinal, altitudinal and environmental gradients, highly focused on the Middle Atlas region of Morocco, with 25 additional samples from botanical gardens across Europe and the US to extend these gradients. Here, we report new stable carbon isotope data from pollen, leaf and stem wood from these samples with a view to assessing and quantifying species-specific fractionation effects associated with pollen production. The isotopic response of individual trees at local and wider geographical scales to altitude and climatic conditions is presented. This research forms part of an ongoing PhD project working to develop and calibrate a modern carbon isotope proxy in Atlas cedar pollen, which can ultimately be applied to fossil sequences and complement existing multi-proxy records (e.g. pollen analysis in lake sediments, tree-rings).
Directory of Open Access Journals (Sweden)
Jingjun Zhao
2013-01-01
Full Text Available A finite element method (FEM for multiterm fractional partial differential equations (MT-FPDEs is studied for obtaining a numerical solution effectively. The weak formulation for MT-FPDEs and the existence and uniqueness of the weak solutions are obtained by the well-known Lax-Milgram theorem. The Diethelm fractional backward difference method (DFBDM, based on quadrature for the time discretization, and FEM for the spatial discretization have been applied to MT-FPDEs. The stability and convergence for numerical methods are discussed. The numerical examples are given to match well with the main conclusions.
Directory of Open Access Journals (Sweden)
S. Das
2013-12-01
Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.
NON-EXISTENCE OF CONJUGATE-SYMPLECTIC MULTI-STEP METHODS OF ODD ORDER
Institute of Scientific and Technical Information of China (English)
Yandong Jiao; Guidong Dai; Quandong Feng; Yifa Tang
2007-01-01
We prove that any linear multi-step method Gτ1 of the form m∑k=0αkZk=τm∑k=0βkJ-1(△)H(Zk) with odd order u (u ≥ 3) cannot be conjugate to a symplectic method Gτ2 of order w(w ≥ u) via any generalized linear multi-step method Gτ3 of the form m∑k=0αkZk=τm∑k=0βkJ-1(△)H(m∑l=0γklZl).We also give a necessary condition for this kind of generalized linear multi-step methods to be conjugate-symplectic. We also demonstrate that these results can be easily extended to the case when Gτ3 is a more general operator.
An Alternative Method to Gauss-Jordan Elimination: Minimizing Fraction Arithmetic
Smith, Luke; Powell, Joan
2011-01-01
When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…
Explicit One-Step P-Stable Methods for Second Order Periodic Initial Value Problems
Institute of Scientific and Technical Information of China (English)
Qinghong Li; Yongzhong Song
2006-01-01
In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the efficiency of our methods.
Three-step relaxed hybrid steepest-descent methods for variational inequalities
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied.A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is establishe d under suitable assumptions imposed on the algorithm parameters.
Method for the single step introduction of a plurality of genes in microbial cells
Straat, van der L.; Graaff, de L.H.
2015-01-01
The invention provides a method for producing a vector for introducing a plurality of genes into a host cell, the method comprising the steps of: a) providing for each gene of the plurality of genes, a DNA fragment comprising an expression cassette for expression of the gene in the host cell, wherei
On the Hybrid Method with Three Off-Step Points for Initial Value Problems
Jator, S. N.
2010-01-01
A continuous representation of a hybrid method with three "off-step" points is developed via interpolation and collocation procedures, and used to obtain initial value methods (IVMs) for solving initial value problems. The IVMs are assembled into a single block matrix equation which is convergent and A-stable. We note that accuracy is improved by…
A novel auto-tuning method for fractional order PI/PD controllers.
De Keyser, Robin; Muresan, Cristina I; Ionescu, Clara M
2016-05-01
Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics.
Fractionation of sheep cheese whey by a scalable method to sequentially isolate bioactive proteins.
Pilbrow, Jodi; Bekhit, Alaa El-din A; Carne, Alan
2016-07-15
This study reports a procedure for the simultaneous purification of glyco(caseino)macropeptide, immunoglobulin, lactoperoxidase, lactoferrin, α-lactalbumin and β-lactoglobulin from sheep cheese sweet whey, an under-utilized by-product of cheese manufacture generated by an emerging sheep dairy industry in New Zealand. These proteins have recognized value in the nutrition, biomedical and health-promoting supplements industries. A sequential fractionation procedure using economical anion and cation exchange chromatography on HiTrap resins was evaluated. The whey protein fractionation is performed under mild conditions, requires only the adjustment of pH between ion exchange chromatography steps, does not require buffer exchange and uses minimal amounts of chemicals. The purity of the whey protein fractions generated were analyzed by reversed phase-high performance liquid chromatography and the identity of the proteins was confirmed by mass spectrometry. This scalable procedure demonstrates that several proteins of recognized value can be fractionated in reasonable yield and purity from sheep cheese whey in one streamlined process.
Copot, Cosmin; Zhong, Yu; Ionescu, Clara; Keyser, Robin
2013-06-01
In this paper, two methods to tune a fractional-order PI λ D μ controller for a mechatronic system are presented. The first method is based on a genetic algorithm to obtain the parameter values for the fractionalorder PI λ D μ controller by global optimization. The second method used to design the fractional-order PI λ D μ controller relies on an auto-tuning approach by meeting some specifications in the frequency domain. The real-time experiments are conducted using a Steward platform which consists of a table tilted by six servo-motors with a ball on the top of the table. The considered system is a 6 degrees of freedom (d.o.f.) motion platform. The feedback on the position of the ball is obtained from images acquired by a visual sensor mounted above the platform. The fractional-order controllers were implemented and the performances of the steward platform are analyzed.
Buyukkilic, F.; Ok Bayrakdar, Z.; Demirhan, D.
2016-02-01
In this study, we investigate the cumulative diminution phenomenon for a physical quantity and a diminution process with a constant acquisition quantity in each step in a viscous medium. We analyze the existence of a dynamical mechanism that underlies the success of fractional calculus compared with standard mathematics for describing stochastic processes by proposing a Fibonacci approach, where we assume that the complex processes evolves cumulatively in fractal space and discrete time. Thus, when the differential-integral order α is attained, this indicates the involvement of the viscosity of the medium in the evolving process. The future value of the diminishing physical quantity is obtained in terms of the Mittag-Leffler function (MLF) and two rheological laws are inferred from the asymptotic limits. Thus, we conclude that the differential-integral calculus of fractional mathematics implicitly embodies the cumulative diminution mechanism that occurs in a viscous medium.
Comparison of fractionation methods for nitrogen and starch in maize and grass silages.
Ali, M; de Jonge, L H; Cone, J W; van Duinkerken, G; Blok, M C; Bruinenberg, M H; Hendriks, W H
2016-06-01
In in situ nylon bag technique, many feed evaluation systems use a washing machine method (WMM) to determine the washout (W) fraction and to wash the rumen incubated nylon bags. As this method has some disadvantages, an alternate modified method (MM) was recently introduced. The aim of this study was to determine and compare the W and non-washout (D+U) fractions of nitrogen (N) and/or starch of maize and grass silages, using the WMM and the MM. Ninety-nine maize silage and 99 grass silage samples were selected with a broad range in chemical composition. The results showed a large range in the W, soluble (S) and D+U fractions of N of maize and grass silages and the W, insoluble washout (W-S) and D+U fractions of starch of maize silages, determined by both methods, due to variation in their chemical composition. The values for N fractions of maize and grass silages obtained with both methods were found different (p silages which might be due to different methodological approaches, such as different rinsing procedures (washing vs. shaking), duration of rinsing (40 min vs. 60 min) and different solvents (water vs. buffer solution). The large differences (p < 0.001) in the W-S and D+U fractions of starch determined with both methods can led to different predicted values for the effective rumen starch degradability. In conclusion, the MM with one recommended shaking procedure, performed under identical and controlled experimental conditions, can give more reliable results compared to the WMM, using different washing programs and procedures.
One-step block method for solving Volterra integro-differential equations
Mohamed, Nurul Atikah binti; Majid, Zanariah Abdul
2015-10-01
One-step block method for solving linear Volterra integro-differential equations (VIDEs) is presented in this paper. In VIDEs, the unknown function appears in the form of derivative and under the integral sign. The popular methods for solving VIDEs are the method of quadrature or quadrature method combined with numerical method. The proposed block method will solve the ordinary differential equations (ODEs) part and Newton-Cotes quadrature rule is applied to calculate the integral part of VIDEs. Numerical problems are presented to illustrate the performance of the proposed method.
Huang, Zhongyi; Markowich, Peter; Sparber, Christof
2012-01-01
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\\"odinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by non-periodic potentials describing external electric fields. Our approach is based on the classical Bloch decomposition method which allows to diagonalize the periodic part of the Hamiltonian operator. Hence, the dominant effects from dispersion and periodic lattice potential are computed together, while the non-periodic potential acts only as a perturbation. Because the split-step communicator error between the periodic and non-periodic parts is relatively small, the step size can be chosen substantially larger than for the traditional splitting of the dispersion and potential operators. Indeed it is shown by the given examples, that our method is unconditionally stable and more efficient than the traditional split-step pseudo spectral schemes. To this end a particular fo...
Explicit local time-stepping methods for time-dependent wave propagation
Grote, Marcus
2012-01-01
Semi-discrete Galerkin formulations of transient wave equations, either with conforming or discontinuous Galerkin finite element discretizations, typically lead to large systems of ordinary differential equations. When explicit time integration is used, the time-step is constrained by the smallest elements in the mesh for numerical stability, possibly a high price to pay. To overcome that overly restrictive stability constraint on the time-step, yet without resorting to implicit methods, explicit local time-stepping schemes (LTS) are presented here for transient wave equations either with or without damping. In the undamped case, leap-frog based LTS methods lead to high-order explicit LTS schemes, which conserve the energy. In the damped case, when energy is no longer conserved, Adams-Bashforth based LTS methods also lead to explicit LTS schemes of arbitrarily high accuracy. When combined with a finite element discretization in space with an essentially diagonal mass matrix, the resulting time-marching scheme...
Directory of Open Access Journals (Sweden)
Petráš Ivo
2011-01-01
Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.
The modified simple equation method for solving some fractional-order nonlinear equations
Indian Academy of Sciences (India)
KAPLAN MELIKE; BEKIR AHMET
2016-07-01
Nonlinear fractional differential equations are encountered in various fields of mathematics, physics, chemistry, biology, engineering and in numerous other applications. Exact solutions of these equations play a crucial role in the proper understanding of the qualitative features of many phenomena and processes in various areas of natural science. Thus, many effective and powerful methods have been established and improved. In this study, we establish exact solutions of the time fractional biological population model equation and nonlinearfractional Klein–Gordon equation by using the modified simple equation method.
Optimal homotopy asymptotic method for solving fractional relaxation-oscillation equation
Directory of Open Access Journals (Sweden)
Mohammad Hamarsheh
2015-11-01
Full Text Available In this paper, an approximate analytical solution of linear fractional relaxation-oscillation equations in which the fractional derivatives are given in the Caputo sense, is obtained by the optimal homotopy asymptotic method (OHAM. The studied OHAM is based on minimizing the residual error. The results given by OHAM are compared with the exact solutions and the solutions obtained by generalized Taylor matrix method. The reliability and efficiency of the proposed approach are demonstrated in three examples with the aid of the symbolic algebra program Maple.
A fast method for the determination of fractional contributions to solvation in proteins
Talavera, David; Morreale, Antonio; Meyer, Tim; Hospital, Adam; Ferrer-Costa, Carles; Gelpi, Josep Lluis; de la Cruz, Xavier; Soliva, Robert; Luque, F. Javier; Orozco, Modesto
2006-01-01
A fast method for the calculation of residue contributions to protein solvation is presented. The approach uses the exposed polar and apolar surface of protein residues and has been parametrized from the fractional contributions to solvation determined from linear response theory coupled to molecular dynamics simulations. Application of the method to a large subset of proteins taken from the Protein Data Bank allowed us to compute the expected fractional solvation of residues. This information is used to discuss when a residue or a group of residues presents an uncommon solvation profile. PMID:17001031
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.
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso
2014-04-01
© 2014, Springer Science+Business Media Dordrecht. Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.
Comparison of Model Reliabilities from Single-Step and Bivariate Blending Methods
DEFF Research Database (Denmark)
Taskinen, Matti; Mäntysaari, Esa; Lidauer, Martin;
2013-01-01
Model based reliabilities in genetic evaluation are compared between three methods: animal model BLUP, single-step BLUP, and bivariate blending after genomic BLUP. The original bivariate blending is revised in this work to better account animal models. The study data is extracted from the product......Model based reliabilities in genetic evaluation are compared between three methods: animal model BLUP, single-step BLUP, and bivariate blending after genomic BLUP. The original bivariate blending is revised in this work to better account animal models. The study data is extracted from...... the production trait evaluation of Nordic Red dairy cattle. Genotyped bulls with daughters are used as training animals, and genotyped bulls and producing cows as candidate animals. For simplicity, size of the data is chosen so that the full inverses of the mixed model equation coefficient matrices can...... be calculated. Model reliabilities by the single-step and the bivariate blending methods were higher than by animal model due to genomic information. Compared to the single-step method, the bivariate blending method reliability estimates were, in general, lower. Computationally bivariate blending method was...
Photodiodes integration on a suspended ridge structure VOA using 2-step flip-chip bonding method
Kim, Seon Hoon; Kim, Tae Un; Ki, Hyun Chul; Kim, Doo Gun; Kim, Hwe Jong; Lim, Jung Woon; Lee, Dong Yeol; Park, Chul Hee
2015-01-01
In this works, we have demonstrated a VOA integrated with mPDs, based on silica-on-silicon PLC and flip-chip bonding technologies. The suspended ridge structure was applied to reduce the power consumption. It achieves the attenuation of 30dB in open loop operation with the power consumption of below 30W. We have applied two-step flipchip bonding method using passive alignment to perform high density multi-chip integration on a VOA with eutectic AuSn solder bumps. The average bonding strength of the two-step flip-chip bonding method was about 90gf.
Design of a Two-Step Calibration Method of Kinematic Parameters for Serial Robots
WANG, Wei; WANG, Lei; YUN, Chao
2017-03-01
Serial robots are used to handle workpieces with large dimensions, and calibrating kinematic parameters is one of the most efficient ways to upgrade their accuracy. Many models are set up to investigate how many kinematic parameters can be identified to meet the minimal principle, but the base frame and the kinematic parameter are indistinctly calibrated in a one-step way. A two-step method of calibrating kinematic parameters is proposed to improve the accuracy of the robot's base frame and kinematic parameters. The forward kinematics described with respect to the measuring coordinate frame are established based on the product-of-exponential (POE) formula. In the first step the robot's base coordinate frame is calibrated by the unit quaternion form. The errors of both the robot's reference configuration and the base coordinate frame's pose are equivalently transformed to the zero-position errors of the robot's joints. The simplified model of the robot's positioning error is established in second-power explicit expressions. Then the identification model is finished by the least square method, requiring measuring position coordinates only. The complete subtasks of calibrating the robot's 39 kinematic parameters are finished in the second step. It's proved by a group of calibration experiments that by the proposed two-step calibration method the average absolute accuracy of industrial robots is updated to 0.23 mm. This paper presents that the robot's base frame should be calibrated before its kinematic parameters in order to upgrade its absolute positioning accuracy.
Energy Technology Data Exchange (ETDEWEB)
Hajji, M., E-mail: mhajji2001@yahoo.fr [Laboratoire de Photovoltaïque, Centre de Recherche et des Technologies de l’Energie, Technopôle de Borj-Cédria BP 95, Hammam-Lif 2050 (Tunisia); Institut Supérieur d’Electronique et de Communication de Sfax, route Menzel Chaker Km 0.5, BP 868, Sfax 3018 (Tunisia); Khalifa, M.; Slama, S. Ben; Ezzaouia, H. [Laboratoire de Photovoltaïque, Centre de Recherche et des Technologies de l’Energie, Technopôle de Borj-Cédria BP 95, Hammam-Lif 2050 (Tunisia)
2013-11-01
This paper presents a new method to produce porous silicon which derived from the conventional stain etching (SE) method. But instead of one etching step that leads to formation of porous layer, the substrate is subjected to an initial etching step with a duration Δt{sub 0} followed by a number of supplementary short steps that differs from a layer to another. The duration of the initial step is just the necessary time to have a homogenous porous layer on the whole surface of the substrate. It was found that this duration is largely dependent of the doping type and level of the silicon substrate. The duration of supplementary steps was kept as short as possible to prevent the formation of bubbles on the silicon surface during silicon dissolution which leads generally to inhomogeneous porous layers. It is found from surface investigation by atomic force microscopy (AFM) that multistep stain etching (MS-SE) method allows to produce homogeneous porous silicon nanostructures compared to the conventional SE method. The chemical composition of the obtained porous layers has been evaluated using Fourier transform infrared spectroscopy (FTIR). Photoluminescence (PL) measurement shows that porous layers produced by SE and MS-SE methods have comparable spectra indicating that those layers are composed of nanocrystallites with comparable sizes. But the intensity of photoluminescence of layer elaborated by MS-SE method is higher than that elaborated by the SE method. Total reflectance characteristics show that the presented method allows the production of porous silicon layers with controllable thicknesses and optical properties. Results for porous silicon layers elaborated on heavily doped n-type silicon show that the reflectance can be reduced to values less than 3% in the major part of the spectrum.
A simple three step method for selective placement of organic groups in mesoporous silica thin films
Energy Technology Data Exchange (ETDEWEB)
Franceschini, Esteban A. [Gerencia Química, Centro Atómico Constituyentes, Comisión Nacional de Energía Atómica, Av. Gral Paz 1499 (B1650KNA) San Martín, Buenos Aires (Argentina); Llave, Ezequiel de la; Williams, Federico J. [Departamento de Química Inorgánica, Analítica y Química Física and INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, C1428EHA Buenos Aires (Argentina); Soler-Illia, Galo J.A.A., E-mail: galo.soler.illia@gmail.com [Departamento de Química Inorgánica, Analítica y Química Física and INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, C1428EHA Buenos Aires (Argentina); Instituto de Nanosistemas, Universidad Nacional de General San Martín, 25 de Mayo y Francia (1650) San Martín, Buenos Aires (Argentina)
2016-02-01
Selective functionalization of mesoporous silica thin films was achieved using a three step method. The first step consists in an outer surface functionalization, followed by washing off the structuring agent (second step), leaving the inner surface of the pores free to be functionalized in the third step. This reproducible method permits to anchor a volatile silane group in the outer film surface, and a second type of silane group in the inner surface of the pores. As a concept test we modified the outer surface of a mesoporous silica film with trimethylsilane (–Si–(CH{sub 3}){sub 3}) groups and the inner pore surface with propylamino (–Si–(CH{sub 2}){sub 3}–NH{sub 2}) groups. The obtained silica films were characterized by Environmental Ellipsometric Porosimetry (EEP), EDS, XPS, contact angle and electron microscopy. The selectively functionalized silica (SF) shows an amount of surface amino functions 4.3 times lower than the one-step functionalized (OSF) silica samples. The method presented here can be extended to a combination of silane chlorides and alkoxides as functional groups, opening up a new route toward the synthesis of multifunctional mesoporous thin films with precisely localized organic functions. - Highlights: • Selective functionalization of mesoporous silica thin films was achieved using a three step method. • A volatile silane group is anchored by evaporation on the outer film surface. • A second silane is deposited in the inner surface of the pores by post-grafting. • Contact angle, EDS and XPS measurements show different proportions of amino groups on both surfaces. • This method can be extended to a combination of silane chlorides and alkoxides functional groups.
Three-step iterative methods with eighth-order convergence for solving nonlinear equations
Directory of Open Access Journals (Sweden)
Mashallah Matinfar
2013-01-01
Full Text Available A family of eighth-order iterative methods for solution of nonlinear equations is presented. We propose an optimal three-step method with eight-order convergence for finding the simple roots of nonlinear equations by Hermite interpolation method. Per iteration of this method requires two evaluations of the function and two evaluations of its first derivative, which implies that the efficiency index of the developed methods is 1.682. Some numerical examples illustrate that the algorithms are more efficient and performs better than the other methods.
2013-01-01
This thesis focuses on the determination of fractional snow cover (FSC) from optical data provided by satellite instruments. It describes the method development, starting from a simple regionally applicable linear interpolation method and ending at a globally applicable, semi-empirical modeling approach. The development work was motivated by the need for an easily implementable and feasible snow mapping method that could provide reliable information particularly for forested areas. The con...
2013-01-01
This thesis focuses on the determination of fractional snow cover (FSC) from optical data provided by satellite instruments. It describes the method development, starting from a simple regionally applicable linear interpolation method and ending at a globally applicable, semi-empirical modeling approach. The development work was motivated by the need for an easily implementable and feasible snow mapping method that could provide reliable information particularly for forested areas. The co...
Methods for growth of relatively large step-free SiC crystal surfaces
Neudeck, Philip G. (Inventor); Powell, J. Anthony (Inventor)
2002-01-01
A method for growing arrays of large-area device-size films of step-free (i.e., atomically flat) SiC surfaces for semiconductor electronic device applications is disclosed. This method utilizes a lateral growth process that better overcomes the effect of extended defects in the seed crystal substrate that limited the obtainable step-free area achievable by prior art processes. The step-free SiC surface is particularly suited for the heteroepitaxial growth of 3C (cubic) SiC, AlN, and GaN films used for the fabrication of both surface-sensitive devices (i.e., surface channel field effect transistors such as HEMT's and MOSFET's) as well as high-electric field devices (pn diodes and other solid-state power switching devices) that are sensitive to extended crystal defects.
Antimutagenic activity of major fractions of Zataria multiflora Boiss by Ames method
Directory of Open Access Journals (Sweden)
Fariba Sharififar
2015-01-01
Full Text Available Zataria multiflora is a medicinal plant that has been interested in antimutagenicity effect because of its high antioxidant activity and richness of flavonoids. Antimutagenicity effect of total extract of the plant has been reported previously. Aerial parts of Z. multiflora were extracted by petroleum ether, chloroform and 80% methanol by liquid-liquid extraction method consequently. The fractions were concentrated in vacuum and dried at 40°C in oven. The genotype of two standard strains of Salmonella typhimurium (TA98, TA100 was confirmed by the evaluation of two important factors of histidine requirement and the presence of R factor. The minimum inhibition concentration (MIC of the fractions against these two strains was determined by agar dilution method. From each fraction, various concentrations less than MIC were studied for anti-mutagenic test. The sample along with bacterial strain and mutagen agent were incubated at 37°C for 48 h. The number of revertant colonies was counted and compared with control plates. Our results showed that all fractions especially petroleum ether and chloroform ones maintain the number of colonies in the standard range in control plates and prevent from the growth of many strains of bacteria and increase of revertant colonies enhancement in a concentration-dependent manner. This effect was prominent against TA100 starin. Methanolic fraction exhibited anti-mutagen activity just in the highest used concentration in the presence of TA98.
Optimal q-homotopy analysis method for time-space fractional gas dynamics equation
Saad, K. M.; AL-Shareef, E. H.; Mohamed, Mohamed S.; Yang, Xiao-Jun
2017-01-01
It is well known that the homotopy analysis method is one of the most efficient methods for obtaining analytical or approximate semi-analytical solutions of both linear and non-linear partial differential equations. A more general form of HAM is introduced in this paper, which is called Optimal q-Homotopy Analysis Method (Oq-HAM). It has better convergence properties as compared with the usual HAM, due to the presence of fraction factor associated with the solution. The convergence of q-HAM is studied in details elsewhere (M.A. El-Tawil, Int. J. Contemp. Math. Sci. 8, 481 (2013)). Oq-HAM is applied to the non-linear homogeneous and non-homogeneous time and space fractional gas dynamics equations with initial condition. An optimal convergence region is determined through the residual error. By minimizing the square residual error, the optimal convergence control parameters can be obtained. The accuracy and efficiency of the proposed method are verified by comparison with the exact solution of the fractional gas dynamics equation. Also, it is shown that the Oq-HAM for the fractional gas dynamics equation is equivalent to the exact solution. We obtain graphical representations of the solutions using MATHEMATICA.
A new computational method for fractal heat-diffusion via local fractional derivative
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Liu Geng-Yuan
2016-01-01
Full Text Available The fractal heat-conduction problem via local fractional derivative is investigated in this paper. The solution of the fractal heat-diffusion equation is obtained. The characteristic equation method is proposed to find the analytical solution of the partial differential equation in fractal heat-conduction problem.
Characteristic equation method for fractal heat-transfer problem via local fractional calculus
Directory of Open Access Journals (Sweden)
Liu Geng-Yuan
2016-01-01
Full Text Available In this paper the fractal heat-transfer problem described by the theory of local fractional calculus is considered. The non-differentiable-type solution of the heat-transfer equation is obtained. The characteristic equation method is proposed as a powerful technology to illustrate the analytical solution of the partial differential equation in fractal heat transfer.
DEFF Research Database (Denmark)
de Tomás, Alberto; Nieto, Héctor; Guzinski, Radoslaw;
2014-01-01
Remote sensing has proved to be a consistent tool for monitoring water fluxes at regional scales. The triangle method, in particular, estimates the evaporative fraction (EF), defined as the ratio of latent heat flux (LE) to available energy, based on the relationship between satellite observation...
Strang-type preconditioners for solving fractional diffusion equations by boundary value methods
Gu, Xian-Ming; Huang, Ting-Zhu; Zhao, Xi-Le; Li, Hou-Biao; Li, Liang
2015-01-01
The finite difference scheme with the shifted Grünwarld formula is employed to semi-discrete the fractional diffusion equations. This spatial discretization can reduce to the large system of ordinary differential equations (ODEs) with initial values. Recently, boundary value method (BVM) was develop
A novel method for estimating solid fraction of roller-compacted ribbons.
Nkansah, Paul; Wu, Sy-Juen; Sobotka, Stephanie; Yamamoto, Ken; Shao, Zezhi J
2008-02-01
A simple method has been developed to estimate solid fraction or relative density of compacts using the weight of ribbons produced during roller compaction. The method provides an alternative to the commonly used dimensional measurement, especially for formulations not amenable to forming quality ribbons. Surface texture of the compaction rolls has been taken into consideration in our mathematical treatment along with correction for ribbon relaxation. Ribbon relaxation occurring upon ribbon exiting the compaction zone is estimated using roll geometry, roll gap, and ribbon thickness. Detailed experimental runs have been carried out to confirm the validity of the proposed theory. The predicted solid fraction was found comparable to that from actual dimensional measurement by caliper. In the case of the microcrystalline cellulose/dicalcium phosphate one:one formulation, the predicted solid fraction had an error sum of squares (SSE) of 2.64E-03 when compared to the dimensional method. When relaxation was included, the SSE decreased by four folds. Similarly, for the microcrystalline cellulose/lactose monohydrate 2:1 formulation, the SSE decreased twelfth folds when relaxation was taken into consideration. These results further confirm the utility of the proposed throughput method for estimating the solid fraction of ribbons.
Medunić, Gordana; Juranović Cindrić, Iva; Lovrenčić Mikelić, Ivanka; Tomašić, Nenad; Balen, Dražen; Oreščanin, Višnja; Kampić, Štefica; Ivković, Ivana
2013-12-01
The aim of this study was to establish the fractionation of copper and zinc in a small apple orchard using the revised (four-step) Bureau Communautaire de Référence (BCR) sequential extraction procedure and assess their potential mobility in soil. Soil samples were collected at the depth of 10 cm to 25 cm, sixteen from the orchard and five control samples from a meadow located some 200 m away from the orchard. As the distribution of trace-element concentrations in the control samples was normal, they were used for comparison as background levels. We also determined soil mineralogical composition, carbonate content, soil pH, cation exchange capacity, and soil organic matter. The extraction yields of Cu and Zn from the control soil were lower than from the orchard soil (25% vs. 34% and 47% vs. 52%, respectively), which pointed to natural processes behind metal bonding in the control soil and greater influence of man-made activities in the orchard soil. Compared to control, the orchard soil had significantly higher concentrations of total Cu (P=0.0009), possibly due to the application of Cu-based fungicides. This assumption was further supported by greater speciation variability of Cu than of zinc, which points to different origins of the two, Cu from pesticides and Zn from the parent bedrock. Copper levels significantly better (P=0.01) correlated with the oxidisable fraction of the orchard soil than of control soil. Residual and organically bound copper and zinc constituted the most important fractions in the studied soils. However, the use of Cu-based fungicides in the apple orchard did not impose environmental and health risk from Cu exposure.
Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEs
Hadjimichael, Yiannis
2017-09-30
A plethora of physical phenomena are modelled by hyperbolic partial differential equations, for which the exact solution is usually not known. Numerical methods are employed to approximate the solution to hyperbolic problems; however, in many cases it is difficult to satisfy certain physical properties while maintaining high order of accuracy. In this thesis, we develop high-order time-stepping methods that are capable of maintaining stability constraints of the solution, when coupled with suitable spatial discretizations. Such methods are called strong stability preserving (SSP) time integrators, and we mainly focus on perturbed methods that use both upwind- and downwind-biased spatial discretizations. Firstly, we introduce a new family of third-order implicit Runge–Kuttas methods with arbitrarily large SSP coefficient. We investigate the stability and accuracy of these methods and we show that they perform well on hyperbolic problems with large CFL numbers. Moreover, we extend the analysis of SSP linear multistep methods to semi-discretized problems for which different terms on the right-hand side of the initial value problem satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain augmented monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding non-additive SSP linear multistep methods. Furthermore, we develop the first SSP linear multistep methods of order two and three with variable step size, and study their optimality. We describe an optimal step-size strategy and demonstrate the effectiveness of these methods on various one- and multi-dimensional problems. Finally, we establish necessary conditions
Ion-step method for surface potential sensing of silicon nanowires
Chen, Songyue; Nieuwkasteele, van Jan W.; Berg, van den Albert; Eijkel, Jan C.T.
2016-01-01
This paper presents a novel stimulus-response method for surface potential sensing of silicon nanowire (Si NW) field-effect transistors. When an "ion-step" from low to high ionic strength is given as a stimulus to the gate oxide surface, an increase of double layer capacitance is therefore expected.
The Galerkin finite element method for a multi-term time-fractional diffusion equation
Jin, Bangti
2015-01-01
© 2014 The Authors. We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.
Directory of Open Access Journals (Sweden)
S. C. Lim
2012-01-01
Full Text Available A new direct operational inversion method is introduced for solving coupled linear systems of ordinary fractional differential equations. The solutions so-obtained can be expressed explicitly in terms of multivariate Mittag-Leffler functions. In the case where the multiorders are multiples of a common real positive number, the solutions can be reduced to linear combinations of Mittag-Leffler functions of a single variable. The solutions can be shown to be asymptotically oscillatory under certain conditions. This technique is illustrated in detail by two concrete examples, namely, the coupled harmonic oscillator and the fractional Wien bridge circuit. Stability conditions and simulations of the corresponding solutions are given.
The Modified Adomian Decomposition Method for Nonlinear Fractional Boundary Value Problems
Institute of Scientific and Technical Information of China (English)
WANG Jie
2012-01-01
We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem Dα0+u(x)=f(x,u(x)), 0＜x＜1, 3＜α≤4u(0) =α0, u″(0) =α2 (1)u(1) =β0, u″(1) =β2where Dα0+u is Caputo fractional derivative and α0,α2,β0,β2 is not zero at all,and f:[0,1] x R → R is continuous.The calculated numerical results show reliability and efficiency of the algorithm given.The numerical procedure is tested on linear and nonlinear problems.
Method and apparatus for separating a non-ferrous metal-comprising fraction from ferrous scrap
Rem, P.C.; Berkhout, S.P.M.
2010-01-01
Method for separating a non-ferrous metal-comprising fraction from ferrous scrap, wherein the ferrous scrap is conveyed to a processing device for separating the non-ferrous metal-comprising fraction from the remainder of the ferrous scrap. The processing device supplies a beam of water, and the ferrous scrap is conveyed and released into the waterbeam so as to cause that the ferrous scrap is allowed to fall and move further, subject to the forces of gravity and the waterbeam.
Institute of Scientific and Technical Information of China (English)
黄果; 蒲亦非; 陈庆利; 周激流
2011-01-01
为了改善图像增强的效果,根据图像具有高度自相关性的特性(越接近目标像素的像素点其两者的相似性越高),构造了基于非整数步长的分数阶微分滤波器,打破了Grümwald-Letnikov定义中分数阶微分数值计算取单位步长的思想,即在传统的分数阶微分的基础上再增加一个自由度参量步长.在一定范围内适当调节v和n的大小来构造相应的掩模算子,并利用线性加权的拉格朗日多项式的分段插值方法来确定非整数步长像素点的灰度值,在一定程度上起到降噪的作用.实验结果表明,提出的方法在增强图像细节和抗噪方面取得了较好的平衡点.%In order to improve the effect of image enhancement, the fractional order differential filter based on non-integer step was constructed according to the image with the characteristics of high autocorrelation, which broke the idea that the step in the numerical calculation based on Grtlmwald-Letnikov definition was taken unit one. This method added a parameter named step on the basis of the traditional fractional order differential definitions. A good performance mask operator was attained by appropriately adjusting the size of step and order. The gray value of non-integer step pixel was got by the linear weighted method based on Lagrange interpolation polynomial, so it could play a role of denoising in the process of image enhancement. The experimental results showed that the method can make a better balance between enhancing image details and denoising.
An Improved Split-Step Wavelet Transform Method for Anomalous Radio Wave Propagation Modelling
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A. Iqbal
2014-12-01
Full Text Available Anomalous tropospheric propagation caused by ducting phenomenon is a major problem in wireless communication. Thus, it is important to study the behavior of radio wave propagation in tropospheric ducts. The Parabolic Wave Equation (PWE method is considered most reliable to model anomalous radio wave propagation. In this work, an improved Split Step Wavelet transform Method (SSWM is presented to solve PWE for the modeling of tropospheric propagation over finite and infinite conductive surfaces. A large number of numerical experiments are carried out to validate the performance of the proposed algorithm. Developed algorithm is compared with previously published techniques; Wavelet Galerkin Method (WGM and Split-Step Fourier transform Method (SSFM. A very good agreement is found between SSWM and published techniques. It is also observed that the proposed algorithm is about 18 times faster than WGM and provide more details of propagation effects as compared to SSFM.
Design of Retarded Fractional Delay Differential Systems Using the Method of Inequalities
Institute of Scientific and Technical Information of China (English)
Suchin Arunsawatwong; Van Quang Nguyen
2009-01-01
Methods based on numerical optimization are useful and effective in the design of control systems.This paper describes the design of retarded fractional delay differential systems (RFDDSs) by the method of inequalities,in which the design problem is formulated so that it is suitable for solution by numerical methods. Zakian's original formulation,which was first proposed in connection with rational systems,is extended to the case of RFDDSs.In making the use of this formulation possible for RFDDSs,the associated stability problems are resolved by using the stability test and the numerical algorithm for computing the abscissa of stability recently developed by the authors.During the design process,the time responses are obtained by a known method for the numerical inversion of Laplace transforms.Two numerical examples are given,where fractional controllers are designed for a time-delay and a heat-conduction plants.
Joo, H
1999-01-01
Recent test results indicated drawbacks associated with the simple exponential attenuation method (SEAM) as currently applied to neutron radiography measurements to determine vapor fractions in a hydrogenous two-phase flow in a metallic conduit. The scattering component of the neutron beam intensity exiting the flow system is not adequately accounted for by SEAM, and this leads to inaccurate results. To properly account for the scattering effect, a neutron scattering probability method (SPM) is developed. The method applies a neutron-hydrogen scattering kernel to scattered thermal neutrons that leave the incident beam in narrow conduits but eventually show up elsewhere in the measurements. The SPM has been tested with known vapor (void) distributions within an acrylic disk and a water/vapor channel. The vapor (void) fractions deduced by SPM are in good agreement with the known exact values. Details of the scattering correction method and the test results are discussed.
Dietary fibre fractions in cereal foods measured by a new integrated AOAC method.
Hollmann, Juergen; Themeier, Heinz; Neese, Ursula; Lindhauer, Meinolf G
2013-10-01
The reliable determination of soluble, insoluble and total dietary fibre in baked goods and cereal flours is an important issue for research, nutritional labelling and marketing. We compared total dietary fibre (TDF) contents of selected cereal based foods determined by AOAC Method 991.43 and the new AOAC Method 2009.01. Fifteen bread and bakery products were included in the study. Our results showed that TDF values of cereal products determined by AOAC Method 2009.01 were always significantly higher than those determined by AOAC Method 991.43. This was explained by the inclusion of low molecular weight soluble fibre fractions and resistant starch fractions in the TDF measurement by AOAC 2009.01. This documents that nutritional labelling of cereal products poses the challenge how to update TDF data in nutrient databases in a reasonable time with an acceptable expenditure. Copyright © 2013. Published by Elsevier Ltd.
Institute of Scientific and Technical Information of China (English)
ZHENG Bin
2012-01-01
In this paper, the ( G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.
A new MC-based method to evaluate the fission fraction uncertainty at reactor neutrino experiment
Ma, X B; Chen, Y X
2016-01-01
Uncertainties of fission fraction is an important uncertainty source for the antineutrino flux prediction in a reactor antineutrino experiment. A new MC-based method of evaluating the covariance coefficients between isotopes was proposed. It was found that the covariance coefficients will varying with reactor burnup and which may change from positive to negative because of fissioning balance effect, for example, the covariance coefficient between $^{235}$U and $^{239}$Pu changes from 0.15 to -0.13. Using the equation between fission fraction and atomic density, the consistent of uncertainty of fission fraction and the covariance matrix were obtained. The antineutrino flux uncertainty is 0.55\\% which does not vary with reactor burnup, and the new value is about 8.3\\% smaller.
Ma, X. B.; Qiu, R. M.; Chen, Y. X.
2017-02-01
Uncertainties regarding fission fractions are essential in understanding antineutrino flux predictions in reactor antineutrino experiments. A new Monte Carlo-based method to evaluate the covariance coefficients between isotopes is proposed. The covariance coefficients are found to vary with reactor burnup and may change from positive to negative because of balance effects in fissioning. For example, between 235U and 239Pu, the covariance coefficient changes from 0.15 to -0.13. Using the equation relating fission fraction and atomic density, consistent uncertainties in the fission fraction and covariance matrix were obtained. The antineutrino flux uncertainty is 0.55%, which does not vary with reactor burnup. The new value is about 8.3% smaller.
TwoStep: An Authentication Method Combining Text and Graphical Passwords
van Oorschot, P. C.; Wan, Tao
Text-based passwords alone are subject to dictionary attacks as users tend to choose weak passwords in favor of memorability, as well as phishing attacks. Many recognition-based graphical password schemes alone, in order to offer sufficient security, require a number of rounds of verification, introducing usability issues. We suggest a hybrid user authentication approach combining text passwords, recognition-based graphical passwords, and a two-step process, to provide increased security with fewer rounds than such graphical passwords alone. A variation of this two-step authentication method, which we have implemented and deployed, is in use in the real world.
A phase retrieval method of interferograms add-subtracting based on two-step phase shifting.
Xu, Yuanyuan; Wang, Yawei; Ji, Ying; Jin, Weifeng; Bu, Min; Shang, Xuefu
2014-01-01
A phase retrieval method is introduced in quantitative phase imaging (QPI) based on two-step phase-shifting technique. By acquiring two measured interferograms and calculating the addition and subtraction between them, the quantitative phase information can be directly retrieved. This method is illustrated by both theory and simulation experiments of a ball. The results of the simulation and the experiment of the red blood cell show a good agreement, demonstrating its application for studying cells.
Directory of Open Access Journals (Sweden)
Syed Tauseef Mohyud-Din
2015-01-01
Full Text Available This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractional Drinfeld-Sokolov equations, and system of coupled fractional Sine-Gordon equations subject to the appropriate initial conditions which arise frequently in mathematical physics. The derivatives are defined in Jumarie’s sense. The accuracy, efficiency, and convergence of the proposed technique are demonstrated through the numerical examples. It is observed that the presented coupling is an alternative approach to overcome the demerit of complex calculation of fractional differential equations. The proposed technique is independent of complexities arising in the calculation of Lagrange multipliers, Adomian’s polynomials, linearization, discretization, perturbation, and unrealistic assumptions and hence gives the solution in the form of convergent power series with elegantly computed components. All the examples show that the proposed combination is a powerful mathematical tool to solve other nonlinear equations also.
SOLUTION OF SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS BY ADOMIAN DECOMPOSITION METHOD
Institute of Scientific and Technical Information of China (English)
Duan Junsheng; An Jianye; Xu Mingyu
2007-01-01
The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solutions are expressed in terms of Mittag-Leffier functions of matric argument. The Adomian decomposition method is straightforward, applicable for broader problems and avoids the difficulties in applying integral transforms. As the order is 1,the result here is simplified to that of first order differential equation.
Variable step direct block multistep method for general second order ODEs
Waeleh, Nazreen; Majid, Zanariah Abdul
2014-10-01
Direct block multistep method is developed for the numerical solution of second order ordinary differential equations (ODEs). This method was designed for computing the solution at four points simultaneously using variable step size. The development of this method based on numerical integration and using interpolation approach which are similar to the Adams method. In order to gain an efficient and reliable numerical approximation, this developed block method is implemented in the predictor corrector mode using simple iteration technique. This method has also been proven as a convergence method under suitable conditions of stability and consistency. Several tested problems are taken into account in the numerical experiments and were compared with the existing method. The results obtained showed that this developed block method managed to produce good results.
Abbasbandy, S.
2007-10-01
In this article, an application of He's variational iteration method is proposed to approximate the solution of a nonlinear fractional differential equation with Riemann-Liouville's fractional derivatives. Also, the results are compared with those obtained by Adomian's decomposition method and truncated series method. The results reveal that the method is very effective and simple.
A simple two-step method to fabricate highly transparent ITO/polymer nanocomposite films
Energy Technology Data Exchange (ETDEWEB)
Liu, Haitao [State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029 (China); Zeng, Xiaofei, E-mail: zengxf@mail.buct.edu.cn [State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029 (China); Kong, Xiangrong [State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029 (China); Bian, Shuguang [The High Technology Research and Development Center, The Ministry of Science and Technology, Beijing 100044 (China); Chen, Jianfeng [Research Center of the Ministry of Education for High Gravity Engineering and Technology, Beijing University of Chemical Technology, Beijing 100029 (China)
2012-09-01
Highlights: Black-Right-Pointing-Pointer A simple two-step method without further surface modification step was employed. Black-Right-Pointing-Pointer ITO nanoparticles were easily to be uniformly dispersed in polymer matrix. Black-Right-Pointing-Pointer ITO/polymer nanocomposite film had high transparency and UV/IR blocking properties. - Abstract: Transparent functional indium tin oxide (ITO)/polymer nanocomposite films were fabricated via a simple approach with two steps. Firstly, the functional monodisperse ITO nanoparticles were synthesized via a facile nonaqueous solvothermal method using bifunctional chemical agent (N-methyl-pyrrolidone, NMP) as the reaction solvent and surface modifier. Secondly, the ITO/acrylics polyurethane (PUA) nanocomposite films were fabricated by a simple sol-solution mixing method without any further surface modification step as often employed traditionally. Flower-like ITO nanoclusters with about 45 nm in diameter were mono-dispersed in ethyl acetate and each nanocluster was assembled by nearly spherical nanoparticles with primary size of 7-9 nm in diameter. The ITO nanoclusters exhibited an excellent dispersibility in polymer matrix of PUA, remaining their original size without any further agglomeration. When the loading content of ITO nanoclusters reached to 5 wt%, the transparent functional nanocomposite film featured a high transparency more than 85% in the visible light region (at 550 nm), meanwhile cutting off near-infrared radiation about 50% at 1500 nm and blocking UV ray about 45% at 350 nm. It could be potential for transparent functional coating materials applications.
Different methods evaluation of antioxidant properties of Myrtus communis extract and its fractions
Directory of Open Access Journals (Sweden)
Soheila Moein
2015-09-01
Full Text Available Myrtus communis L. is a plant traditionally used as an antiseptic and disinfectant drug. In this research, the antioxidant activity of Myrtus communis was assayed by evaluating radical scavenging activity, reducing power, FRAP method and determination of phenolic compounds. The methanolic extract of leaves of Myrtus communis was fractionated by using petroleum ether, chloroform, ethyl acetate and buthanol. In reducing power, different concentrations of samples were mixed with phosphate buffer, ferrocyanate, TCA and ferric chloride. Different concentrations of samples were mixed with DPPH and after 30 min the absorbances were measured. For determination of phenolic content, 500 μl of sample was mixed with Folin-Ciocalteu and sodium carbonate. For determination of flavonoids, 500 μl of sample was mixed with 2 ml of distilled water, NaNO2 and NaOH. In reducing power method, chloroform fraction showed the highest reducing capacity. In the DPPH radical scavenging method, the highest antioxidant capacity was found in buthanol fraction (IC50=84.42±1.8 μg/ml. In FRAP method, the highest antioxidant capacity was found in crude extract (5.4±0.3 mg/ml and buthanol fractions (5.51±0.4 mg/ml, respectively. The highest amount of phenolic compounds was detected in ethyl acetate fraction of Myrtus communis (17.5±0.001 μg/g. The highest amount of flavonoids was found in crude extract of Myrtus communis (171.9±7.3 μg/ml. Overall, we can suggest that the leaves of Myrtus communis can be used as antioxidant and as a food additives to avoid oxidative degradation of foods.
Time-step limits for a Monte Carlo Compton-scattering method
Energy Technology Data Exchange (ETDEWEB)
Densmore, Jeffery D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Lowrie, Robert B [Los Alamos National Laboratory
2008-01-01
Compton scattering is an important aspect of radiative transfer in high energy density applications. In this process, the frequency and direction of a photon are altered by colliding with a free electron. The change in frequency of a scattered photon results in an energy exchange between the photon and target electron and energy coupling between radiation and matter. Canfield, Howard, and Liang have presented a Monte Carlo method for simulating Compton scattering that models the photon-electron collision kinematics exactly. However, implementing their technique in multiphysics problems that include the effects of radiation-matter energy coupling typically requires evaluating the material temperature at its beginning-of-time-step value. This explicit evaluation can lead to unstable and oscillatory solutions. In this paper, we perform a stability analysis of this Monte Carlo method and present time-step limits that avoid instabilities and nonphysical oscillations by considering a spatially independent, purely scattering radiative-transfer problem. Examining a simplified problem is justified because it isolates the effects of Compton scattering, and existing Monte Carlo techniques can robustly model other physics (such as absorption, emission, sources, and photon streaming). Our analysis begins by simplifying the equations that are solved via Monte Carlo within each time step using the Fokker-Planck approximation. Next, we linearize these approximate equations about an equilibrium solution such that the resulting linearized equations describe perturbations about this equilibrium. We then solve these linearized equations over a time step and determine the corresponding eigenvalues, quantities that can predict the behavior of solutions generated by a Monte Carlo simulation as a function of time-step size and other physical parameters. With these results, we develop our time-step limits. This approach is similar to our recent investigation of time discretizations for the
An efficient two-step Monte Carlo method for heat conduction in nanostructures
Hua, Yu-Chao; Cao, Bing-Yang
2017-08-01
Research on the heat conduction in nanostructures has drawn much attention due to their potential applications in thermoelectric devices. Although the phonon tracing Monte Carlo (MC) technique, where the trajectories of individual phonons are simulated independently, has been extensively used for simulating the heat conduction in nanomaterials, it cannot efficiently simulate the phonon transport in the large area periodic nanostructures yet, due to the demand of absorbing boundaries. In the present work, we develop a two-step phonon tracing MC method to solve this problem. At the first step, the initial phonon transmittance and the phonon emission distributions at the internal virtual boundary are obtained by simulating phonon transport in the initial simulation unit that is directly in contact with the phonon bath. At the second step, the internal phonon transmittance is calculated for the internal simulation units according to the internal boundary phonon emission distributions. Since the whole structure can be simplified as a one-dimensional phonon transport system, the total phonon transmittance can be readily calculated via the combination of initial and internal phonon transmittances, and the effective thermal conductivity is then derived. Furthermore, for verification, we calculate the effective thermal conductivities of three typical nanostructures, that is, the cross-plane and in-plane nanofilms and the periodic nanoporous structures, by using the theoretical models, the standard and the two-step MC simulations, respectively. The two-step MC method well predicts the results calculated by the standard MC simulations and the theoretical models. More importantly, the computation time of the two-step MC simulation is at least one order of magnitude less than that of the standard MC simulation, while its under-prediction can be less than 10% even 5%.
A Method of MPPT Control Based on Power Variable Step-size in Photovoltaic Converter System
Directory of Open Access Journals (Sweden)
Xu Hui-xiang
2016-01-01
Full Text Available Since the disadvantage of traditional MPPT algorithms of variable step-size, proposed power tracking based on variable step-size with the advantage method of the constant-voltage and the perturb-observe (P&O[1-3]. The control strategy modify the problem of voltage fluctuation caused by perturb-observe method, at the same time, introducing the advantage of constant-voltage method and simplify the circuit topology. With the theoretical derivation, control the output power of photovoltaic modules to change the duty cycle of main switch. Achieve the maximum power stabilization output, reduce the volatility of energy loss effectively, and improve the inversion efficiency[3,4]. Given the result of experimental test based theoretical derivation and the curve of MPPT when the prototype work.
LiLEDDA: A Six-Step Forum-Based Netnographic Research Method for Nursing Science
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MARTIN SALZMANN-ERIKSON
2012-01-01
Full Text Available Internet research methods in nursing science are less developed than in other sciences. We choose to present an approach to conducting nursing research on an internet-based forum. This paper presents LiLEDDA, a six-step forum-based netnographic research method for nursing science. The steps consist of: 1. Literature review and identification of the research question(s; 2. Locating the field(s online; 3. Ethical considerations; 4. Data gathering; 5. Data analysis and interpretation; and 6. Abstractions and trustworthiness. Traditional research approaches are limiting when studying non-normative and non-mainstream life-worlds and their cultures. We argue that it is timely to develop more up-to-date research methods and study designs applicable to nursing science that reflect social developments and human living conditions that tend to be increasingly online-based.
Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation
Jin, Bangti
2014-01-01
© 2014 Society for Industrial and Applied Mathematics We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann-Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2 (D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.
Zhang, Dawei
2017-03-01
Molecular fractionation with conjugate caps (MFCC) method is introduced for the efficient estimation of quantum mechanical (QM) interaction energies between nanomaterial (carbon nanotube, fullerene, and graphene surface) and ligand (charged and neutral). In the calculations, nanomaterials are partitioned into small fragments and conjugated caps that are properly capped, and the interaction energies can be obtained through the summation of QM calculations of the fragments from which the contribution of the conjugated caps is removed. All the calculations were performed by density functional theory (DFT) and dispersion contributions for the attractive interactions were investigated by dispersion corrected DFT method. The predicted interaction energies by MFCC at each computational level are found to give excellent agreement with full system (FS) calculations with the mean energy deviation just a fractional kcal/mol. The accurate determination of nanomaterial-ligand interaction energies by MFCC suggests that it is an effective method for performing QM calculations on nanomaterial-ligand systems.
Zhang, Dawei
2017-01-01
Molecular fractionation with conjugate caps (MFCC) method is introduced for the efficient estimation of quantum mechanical (QM) interaction energies between nanomaterial (carbon nanotube, fullerene, and graphene surface) and ligand (charged and neutral). In the calculations, nanomaterials are partitioned into small fragments and conjugated caps that are properly capped, and the interaction energies can be obtained through the summation of QM calculations of the fragments from which the contribution of the conjugated caps is removed. All the calculations were performed by density functional theory (DFT) and dispersion contributions for the attractive interactions were investigated by dispersion corrected DFT method. The predicted interaction energies by MFCC at each computational level are found to give excellent agreement with full system (FS) calculations with the mean energy deviation just a fractional kcal/mol. The accurate determination of nanomaterial-ligand interaction energies by MFCC suggests that it is an effective method for performing QM calculations on nanomaterial-ligand systems. PMID:28300179
Locke, Jonathan; White, Paul R
2011-10-01
The analysis of cetacean vocalizations is considered using Fourier-based techniques that employ chirp functions in their decomposition. In particular, the paper considers a short-time methods based on the fractional Fourier transform for detecting frequency modulated narrow-band signals, such as dolphin whistles, and compares this to the classical short-time Fourier methods. The fractional Fourier technique explored computes transforms associated with a range of chirp rates and automatically selects the rate for the final analysis. This avoids the need for prior knowledge of signal's chirp rate. An analysis is presented that details the performance of both methods as signal detectors and allows one to determine their detection thresholds. These thresholds are then used to measure the detectability of synthetic signals. This principle is then extended to measure performance on a set of recordings of narrow-band vocalizations from a range of cetacean species.
Application of He's homotopy perturbation method for solving fractional Fokker-Planck equations
Energy Technology Data Exchange (ETDEWEB)
Mousa, Mohamed M. [Dept. of Basic Science, Benha Higher Inst. of Tech., Benha Univ. (Egypt); Dept. of Mechanics, al-Farabi Kazakh National Univ., Almaty (Kazakhstan); Kaltayev, Aidarkhan [Dept. of Mechanics, al-Farabi Kazakh National Univ., Almaty (Kazakhstan)
2009-12-15
The fractional Fokker-Planck equation (FFPE) has been used in many physical transport problems which take place under the influence of an external force field and other important applications in various areas of engineering and physics. In this paper, by means of the homotopy perturbation method (HPM), exact and approximate solutions are obtained for two classes of the FFPE initial value problems. The method gives an analytic solution in the form of a convergent series with easily computed components. The obtained results show that the HPM is easy to implement, accurate and reliable for solving FFPEs. The method introduces a promising tool for solving other types of differential equation with fractional order derivatives. (orig.)
Numerical Methods for Pricing American Options with Time-Fractional PDE Models
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Zhiqiang Zhou
2016-01-01
Full Text Available In this paper we develop a Laplace transform method and a finite difference method for solving American option pricing problem when the change of the option price with time is considered as a fractal transmission system. In this scenario, the option price is governed by a time-fractional partial differential equation (PDE with free boundary. The Laplace transform method is applied to the time-fractional PDE. It then leads to a nonlinear equation for the free boundary (i.e., optimal early exercise boundary function in Laplace space. After numerically finding the solution of the nonlinear equation, the Laplace inversion is used to transform the approximate early exercise boundary into the time space. Finally the approximate price of the American option is obtained. A boundary-searching finite difference method is also proposed to solve the free-boundary time-fractional PDEs for pricing the American options. Numerical examples are carried out to compare the Laplace approach with the finite difference method and it is confirmed that the former approach is much faster than the latter one.
Energy Technology Data Exchange (ETDEWEB)
Hussein, Mahir S. [DCTA, Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, SP (Brazil); Universidade de Sao Paulo, Instituto de Estudos Avancados, C. P. 72012, Sao Paulo, SP (Brazil); Universidade de Sao Paulo, Instituto de Fisica, C. P. 66318, Sao Paulo, SP (Brazil)
2017-05-15
In this Letter I argue that the Surrogate Method, used to extract the fast neutron capture cross section on actinide target nuclei, which has important practical application for the next generation of breeder reactors, and the Trojan Horse Method employed to extract reactions of importance to nuclear astrophysics, have a common foundation, the Inclusive Non-Elastic Breakup (INEB) Theory. Whereas the Surrogate Method relies on the premise that the extracted neutron cross section in a (d, p) reaction is predominantly a compound-nucleus one, the Trojan Horse Method assumes a predominantly direct process for the secondary reaction induced by the surrogate fragment. In general, both methods contain both direct and compound contributions, and I show how these seemingly distinct methods are in fact the same but at different energies and different kinematic regions. The unifying theory is the rather well developed INEB theory. (orig.)
Hussein, Mahir S.
2017-05-01
In this Letter I argue that the Surrogate Method, used to extract the fast neutron capture cross section on actinide target nuclei, which has important practical application for the next generation of breeder reactors, and the Trojan Horse Method employed to extract reactions of importance to nuclear astrophysics, have a common foundation, the Inclusive Non-Elastic Breakup (INEB) Theory. Whereas the Surrogate Method relies on the premise that the extracted neutron cross section in a ( d, p) reaction is predominantly a compound-nucleus one, the Trojan Horse Method assumes a predominantly direct process for the secondary reaction induced by the surrogate fragment. In general, both methods contain both direct and compound contributions, and I show how these seemingly distinct methods are in fact the same but at different energies and different kinematic regions. The unifying theory is the rather well developed INEB theory.
Developing Methods for Fraction Cover Estimation Toward Global Mapping of Ecosystem Composition
Roberts, D. A.; Thompson, D. R.; Dennison, P. E.; Green, R. O.; Kokaly, R. F.; Pavlick, R.; Schimel, D.; Stavros, E. N.
2016-12-01
Terrestrial vegetation seldom covers an entire pixel due to spatial mixing at many scales. Estimating the fractional contributions of photosynthetic green vegetation (GV), non-photosynthetic vegetation (NPV), and substrate (soil, rock, etc.) to mixed spectra can significantly improve quantitative remote measurement of terrestrial ecosystems. Traditional methods for estimating fractional vegetation cover rely on vegetation indices that are sensitive to variable substrate brightness, NPV and sun-sensor geometry. Spectral mixture analysis (SMA) is an alternate framework that provides estimates of fractional cover. However, simple SMA, in which the same set of endmembers is used for an entire image, fails to account for natural spectral variability within a cover class. Multiple Endmember Spectral Mixture Analysis (MESMA) is a variant of SMA that allows the number and types of pure spectra to vary on a per-pixel basis, thereby accounting for endmember variability and generating more accurate cover estimates, but at a higher computational cost. Routine generation and delivery of GV, NPV, and substrate (S) fractions using MESMA is currently in development for large, diverse datasets acquired by the Airborne Visible Infrared Imaging Spectrometer (AVIRIS). We present initial results, including our methodology for ensuring consistency and generalizability of fractional cover estimates across a wide range of regions, seasons, and biomes. We also assess uncertainty and provide a strategy for validation. GV, NPV, and S fractions are an important precursor for deriving consistent measurements of ecosystem parameters such as plant stress and mortality, functional trait assessment, disturbance susceptibility and recovery, and biomass and carbon stock assessment. Copyright 2016 California Institute of Technology. All Rights Reserved. We acknowledge support of the US Government, NASA, the Earth Science Division and Terrestrial Ecology program.
A single-step method for rapid extraction of total lipids from green microalgae.
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Martin Axelsson
Full Text Available Microalgae produce a wide range of lipid compounds of potential commercial interest. Total lipid extraction performed by conventional extraction methods, relying on the chloroform-methanol solvent system are too laborious and time consuming for screening large numbers of samples. In this study, three previous extraction methods devised by Folch et al. (1957, Bligh and Dyer (1959 and Selstam and Öquist (1985 were compared and a faster single-step procedure was developed for extraction of total lipids from green microalgae. In the single-step procedure, 8 ml of a 2∶1 chloroform-methanol (v/v mixture was added to fresh or frozen microalgal paste or pulverized dry algal biomass contained in a glass centrifuge tube. The biomass was manually suspended by vigorously shaking the tube for a few seconds and 2 ml of a 0.73% NaCl water solution was added. Phase separation was facilitated by 2 min of centrifugation at 350 g and the lower phase was recovered for analysis. An uncharacterized microalgal polyculture and the green microalgae Scenedesmus dimorphus, Selenastrum minutum, and Chlorella protothecoides were subjected to the different extraction methods and various techniques of biomass homogenization. The less labour intensive single-step procedure presented here allowed simultaneous recovery of total lipid extracts from multiple samples of green microalgae with quantitative yields and fatty acid profiles comparable to those of the previous methods. While the single-step procedure is highly correlated in lipid extractability (r² = 0.985 to the previous method of Folch et al. (1957, it allowed at least five times higher sample throughput.
Taroncher, Mariam; Vidal-Pantaleoni, Ana; Boria, Vicente E.; Marini, Stephan; Soto, Pablo; Cogollos, Santiago
2004-04-01
This paper describes a novel technique for the very efficient and accurate commputation of the coupling integrals of waveguide step discontinuities between arbitrary cross section waveguides. This new technique relies on solving the Integral Equation (IE) that provides the well-known Boundary Integral -- Resonant Mode Expansion (Bi-RME) method by the Nystrom approach, instead of using the traditional Galerkin version of the Method of Moments (MoM), thus providing large savings on computational costs. Comparative benchmarks between the results provided by the new technique and the original BI-RME method are successfully presented.
Canine distemper virus detection by different methods of One-Step RT-qPCR
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Claudia de Camargo Tozato
2016-01-01
Full Text Available ABSTRACT: Three commercial kits of One-Step RT-qPCR were evaluated for the molecular diagnosis of Canine Distemper Virus. Using the kit that showed better performance, two systems of Real-time RT-PCR (RT-qPCR assays were tested and compared for analytical sensitivity to Canine Distemper Virus RNA detection: a One-Step RT-qPCR (system A and a One-Step RT-qPCR combined with NESTED-qPCR (system B. Limits of detection for both systems were determined using a serial dilution of Canine Distemper Virus synthetic RNA or a positive urine sample. In addition, the same urine sample was tested using samples with prior centrifugation or ultracentrifugation. Commercial kits of One-Step RT-qPCR assays detected canine distemper virus RNA in 10 (100% urine samples from symptomatic animals tested. The One-Step RT-qPCR kit that showed better results was used to evaluate the analytical sensitivity of the A and B systems. Limit of detection using synthetic RNA for the system A was 11 RNA copies µL-1 and 110 RNA copies µl-1 for first round System B. The second round of the NESTED-qPCR for System B had a limit of detection of 11 copies µl-1. Relationship between Ct values and RNA concentration was linear. The RNA extracted from the urine dilutions was detected in dilutions of 10-3 and10-2 by System A and B respectively. Urine centrifugation increased the analytical sensitivity of the test and proved to be useful for routine diagnostics. The One-Step RT-qPCR is a fast, sensitive and speciﬁc method for canine distemper routine diagnosis and research projects that require sensitive and quantitative methodology.
Investigating the Effectiveness of Teaching Methods Based on a Four-Step Constructivist Strategy
Çalik, Muammer; Ayas, Alipaşa; Coll, Richard K.
2010-02-01
This paper reports on an investigation of the effectiveness an intervention using several different methods for teaching solution chemistry. The teaching strategy comprised a four-step approach derived from a constructivist view of learning. A sample consisting of 44 students (18 boys and 26 girls) was selected purposively from two different Grade 9 classes in the city of Trabzon, Turkey. Data collection employed a purpose-designed `solution chemistry concept test', consisting of 17 items, with the quantitative data from the survey supported by qualitative interview data. The findings suggest that using different methods embedded within the four-step constructivist-based teaching strategy enables students to refute some alternative conceptions, but does not completely eliminate student alternative conceptions for solution chemistry.
Zhong, Zhaopeng; Talamo, Alberto; Gohar, Yousry
2013-07-01
The effective delayed neutron fraction β plays an important role in kinetics and static analysis of the reactor physics experiments. It is used as reactivity unit referred to as "dollar". Usually, it is obtained by computer simulation due to the difficulty in measuring it experimentally. In 1965, Keepin proposed a method, widely used in the literature, for the calculation of the effective delayed neutron fraction β. This method requires calculation of the adjoint neutron flux as a weighting function of the phase space inner products and is easy to implement by deterministic codes. With Monte Carlo codes, the solution of the adjoint neutron transport equation is much more difficult because of the continuous-energy treatment of nuclear data. Consequently, alternative methods, which do not require the explicit calculation of the adjoint neutron flux, have been proposed. In 1997, Bretscher introduced the k-ratio method for calculating the effective delayed neutron fraction; this method is based on calculating the multiplication factor of a nuclear reactor core with and without the contribution of delayed neutrons. The multiplication factor set by the delayed neutrons (the delayed multiplication factor) is obtained as the difference between the total and the prompt multiplication factors. Using Monte Carlo calculation Bretscher evaluated the β as the ratio between the delayed and total multiplication factors (therefore the method is often referred to as the k-ratio method). In the present work, the k-ratio method is applied by Monte Carlo (MCNPX) and deterministic (PARTISN) codes. In the latter case, the ENDF/B nuclear data library of the fuel isotopes (235U and 238U) has been processed by the NJOY code with and without the delayed neutron data to prepare multi-group WIMSD neutron libraries for the lattice physics code DRAGON, which was used to generate the PARTISN macroscopic cross sections. In recent years Meulekamp and van der Marck in 2006 and Nauchi and Kameyama
Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations
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B. A. Jacobs
2014-01-01
Full Text Available A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time-marching to a particular point in time.
Energy Technology Data Exchange (ETDEWEB)
Mahoney, Lenna A.
2006-10-18
The toxicological source terms used for potential accident assessment in the Hanford Tank Farms DSA are based on toxicological sums-of-fractions (SOFs) that were calculated based on the Best Basis Inventory (BBI) from May 2002, using a method that depended on thermodynamic equilibrium calculations of the compositions of liquid and solid phases. The present report describes a simplified SOF-calculation method that is to be used in future toxicological updates and assessments and compares its results (for the 2002 BBI) to those of the old method.
Comparison of Two Methods for the Extraction of Fractionated Rice Bran Protein
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Changyuan Wang
2014-01-01
Full Text Available Two different methods for extracting fractionated rice bran protein (FRBP from defatted rice bran were investigated according to the solubility of protein in different extraction solvents. The yields of the obtained proteins and their purity were first compared. Sodium dodecyl sulfate polyacrylamide gel electrophoresis, differential scanning calorimetry, protein surface hydrophobicity, and protein secondary molecular structure analyses were subsequently applied to identify and compare the compositional, structural, and functional characteristics of the obtained proteins. The highest yield (13.8%, w/w and purity (45–47% of FRBP products were obtained using 0.4 M NaCl, 80% ethanol, and 0.01 M NaOH as extraction solvents to fractionate albumin, globulin, prolamin, and glutelin. Several good properties were exhibited, including good functionality, specific denaturation temperature, and enthalpy values, for FRBP products prepared by the above method.
Power Grid De-icing Optimal Plan Based on Fractional Sieve Method
Xie, Guangbin; Lin, Meihan; Li, Huaqiang
2017-05-01
Aiming at the problem that the reliability of system was reduced and the security risk was increased during the DC de-icing period, a decision-making model based on the fractional sieve method was proposed. This model introduced risk assessment theory, and took into account the comprehensive failure probability model of protection action and ice cover. Considering the de-icing condition, a DC de-icing strategy model, which was with the objective function of minimizing the load of shedding and minimizing the operating risk, was proposed. The objective function was optimized by particle swarm optimization algorithm and fractional sieve method. The simulative results of IEEE30-bus system indicated that the load loss caused by de-icing and the operational risk of the system could be effectively reduced by the proposed model. It provided a reference for power department to make a de-icing plan.
Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)
2002-01-01
Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.
Papacharalampous, Georgia; Tyralis, Hristos; Koutsoyiannis, Demetris
2017-04-01
Machine learning (ML) is considered to be a promising approach to hydrological processes forecasting. We conduct a comparison between several stochastic and ML point estimation methods by performing large-scale computational experiments based on simulations. The purpose is to provide generalized results, while the respective comparisons in the literature are usually based on case studies. The stochastic methods used include simple methods, models from the frequently used families of Autoregressive Moving Average (ARMA), Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Exponential Smoothing models. The ML methods used are Random Forests (RF), Support Vector Machines (SVM) and Neural Networks (NN). The comparison refers to the multi-step ahead forecasting properties of the methods. A total of 20 methods are used, among which 9 are the ML methods. 12 simulation experiments are performed, while each of them uses 2 000 simulated time series of 310 observations. The time series are simulated using stochastic processes from the families of ARMA and ARFIMA models. Each time series is split into a fitting (first 300 observations) and a testing set (last 10 observations). The comparative assessment of the methods is based on 18 metrics, that quantify the methods' performance according to several criteria related to the accurate forecasting of the testing set, the capturing of its variation and the correlation between the testing and forecasted values. The most important outcome of this study is that there is not a uniformly better or worse method. However, there are methods that are regularly better or worse than others with respect to specific metrics. It appears that, although a general ranking of the methods is not possible, their classification based on their similar or contrasting performance in the various metrics is possible to some extent. Another important conclusion is that more sophisticated methods do not necessarily provide better forecasts
PBL and Computer Programming — The Seven Steps Method with Adaptations
Nuutila, Esko; Törmä, Seppo; Malmi, Lauri
2005-06-01
Problem-Based Learning (PBL) method emphasizes students' own activity in learning about problems, setting up their own learning goals and actively searching for and analyzing information. In this paper, we describe and discuss our experiences on applying PBL, especially the seven steps method widely used in medical faculties, in an introductory computer programming course. We explain how the method is implemented, give examples and identify different kinds of PBL cases, and describe how the method is supplemented by other learning methods in our course. According to our experience, the PBL method increases the commitment of the students which results in a significantly lower drop-out rate: the average is 17% versus 45% in our traditional programming courses. In addition to computer programming, students also learn generic skills related to group work, collaborative design work, independent studying, and externalization of their knowledge.
Different methods evaluation of antioxidant properties of Myrtus communis extract and its fractions
Soheila Moein; Mahmoodreza Moein; Fatemeh Farmani
2015-01-01
Myrtus communis L. is a plant traditionally used as an antiseptic and disinfectant drug. In this research, the antioxidant activity of Myrtus communis was assayed by evaluating radical scavenging activity, reducing power, FRAP method and determination of phenolic compounds. The methanolic extract of leaves of Myrtus communis was fractionated by using petroleum ether, chloroform, ethyl acetate and buthanol. In reducing power, different concentrations of samples were mixed with phosphate buffer...
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D. Baleanu
2013-01-01
fractional derivatives is based on modified generalized Laguerre polynomials Li(α,β(x with x∈Λ=(0,∞, α>−1, and β>0, and i is the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre-Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.
Stepping Control Method of Linear Displacement Mechanism Driven by TRUM Based on PSoC
Institute of Scientific and Technical Information of China (English)
Wang Junping; Liu Weidong; Zhu Hua; Li Yijun; Li Jianjun
2015-01-01
A method based on programmable system-on-chip (PSoC) is proposed to realize high resolution stepping motion control of liner displacement mechanism driven by traveling wave rotary ultrasonic motors (TRUM ) .Intel-ligent controller of stepping ultrasonic motor consists of PSoC microprocessor .Continuous square wave signal is sent out by the pulse width modulator (PWM) module inside PSoC ,and converted into sinusoidal signal which is essential to the motor′s normal working by power amplifier circuit .Subsequently ,signal impulse transmission is realized by the counter control break ,and the stepping motion of linear displacement mechanism based on TRUM is achieved .Running status of the ultrasonic motor is controlled by an upper computer .Control command is sent to PSoC through serial communication circuit of RS-232 .Relative program and control interface are written in Lab-View .Finally the mechanism is tested by XL-80 laser interferometer .Test results show that the mechanism can provide a stable motion and a fixed step pitch with the displacement resolution of 6 nm .
Directory of Open Access Journals (Sweden)
Ahmet Bekir
2014-09-01
Full Text Available In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then G′G-expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers’ equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation.
Hydrogen Solubility in Heavy Undefined Petroleum Fractions Using Group Contributions Methods
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Aguilar-Cisneros Humberto
2017-01-01
Full Text Available Hydrogen solubility in heavy undefined petroleum fractions is estimated by taking as starting point a method of characterization based on functional groups [ Carreón-Calderón et al. (2012 Ind. Eng. Chem. Res. 51, 14188-14198 ]. Such method provides properties entering into equations of states and molecular pseudostructures formed by non-integer numbers of functional groups. Using Vapor-Liquid Equilibria (VLE data from binary mixtures of known compounds, interaction parameters between hydrogen and the calculated functional groups were estimated. Besides, the incorporation of the hydrogen-carbon ratio of the undefined petroleum fractions into the method allows the corresponding hydrogen solubility to be properly estimated. This procedure was tested with seven undefined petroleum fractions from 27 to 6 API over wide ranges of pressure and temperature (323.15 to 623.15 K. The results seem to be in good agreement with experimental data (overall Relative Average Deviation, RAD < 15%.
A NOVEL IMAGING METHOD IN STEPPED FREQUENCY RADAR WITHOUT SPURIOUS PEAKS
Institute of Scientific and Technical Information of China (English)
Lei Wen; Long Teng; Han Yueqiu
2001-01-01
Stepped frequency signal is often used to synthesize high-resolution range profile,but redundant high-resolution range profile exists before synthesis. Two methods have been given to extract target from overlapped high-resolution range profile and analyzed to show how spurious peaks appear. This paper provides a reverse-count algorithm to resolve the problem of spurious peaks for moving target. This proposed method selects the peak with maximum amplitude as the extracted target and gets its position by using the number of samples prceding before the present sample position and the number of high-resolution range cell of the target. This proposed method is compared with the already given method and the result shows the ability of the proposed method to remove spurious peaks, it provides the foundation for high-resolution range profile.
Photon strength functions studied with the method of two-step cascades
Tomandl, I.; Honzátko, J.; Bečvář, F.; Krtička, M.; Cejnar, P.
2000-07-01
The method of two-step γ cascades, following the thermal neutron capture, has proved to be a promising tool for investigation of photon strength functions in the region of transition energies near 3 MeV. Using this method we studied behavior of photon strength functions in 108Ag, 116In, 125Te, 144,146Nd, 150Sm, 156,158Gd, 163Dy and 168Er. Besides the detailed information for individual nuclei a large amount of experimental data allows us to look for general trends in the mass region incorporating spherical, transitional and deformed nuclei. Despite continuing systematic study on other nuclei, some general conclusions could already be done.
Two-Step Robust Diagnostic Method for Identification of Multiple High Leverage Points
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Arezoo Bagheri
2009-01-01
Full Text Available Problem statement: High leverage points are extreme outliers in the X-direction. In regression analysis, the detection of these leverage points becomes important due to their arbitrary large effects on the estimations as well as multicollinearity problems. Mahalanobis Distance (MD has been used as a diagnostic tool for identification of outliers in multivariate analysis where it finds the distance between normal and abnormal groups of the data. Since the computation of MD relies on non-robust classical estimations, the classical MD can hardly detect outliers accurately. As an alternative, Robust MD (RMD methods such as Minimum Covariance Determinant (MCD and Minimum Volume Ellipsoid (MVE estimators had been used to identify the existence of high leverage points in the data set. However, these methods tended to swamp some low leverage points even though they can identify high leverage points correctly. Since, the detection of leverage points is one of the most important issues in regression analysis, it is imperative to introduce a novel detection method of high leverage points. Approach: In this study, we proposed a relatively new two-step method for detection of high leverage points by utilizing the RMD (MVE and RMD (MCD in the first step to identify the suspected outlier points. Then, in the second step the MD was used based on the mean and covariance of the clean data set. We called this method two-step Robust Diagnostic Mahalanobis Distance (RDMDTS which could identify high leverage points correctly and also swamps less low leverage points. Results: The merit of the newly proposed method was investigated extensively by real data sets and Monte Carlo Simulations study. The results of this study indicated that, for small sample sizes, the best detection method is (RDMDTS (MVE-mad while there was not much difference between (RDMDTS (MVE-mad and (RDMDTS (MCD-mad for large sample sizes. Conclusion/Recommendations: In order to swamp less low
[Study on the identification of ganoderma by multi-steps infrared macro-fingerprint method].
Chen, Xiao-kang; Huang, Dong-lan; Sun, Su-qin; Cao, Jia-jia; Wang, Shao-ling
2010-01-01
Ganoderma lucidum, ganoderma atrum, ganderma tsugae Murr. and ganoderma lipsiense can be discriminated and identified by using multi-steps infrared macro-fingerprint method. The 1D-1R spectra, based on the peaks intensity at 1153 and 1078 cm(-1), which are the fingerprint characteristic peaks of glucoside compounds, show that the content of glucoside compounds of them was in the order of: ganoderma lucidum>ganoderma atrum>ganderma tsugae Murr. >ganoderma lipsiense. Generally, the second derivative IR spectra can clearly enhance the spectra resolution. In the range of 1600-1720 cm(-1), the position and sharpness of characteristics peaks were very different, and it's proved that amino acid peptide compounds of them were different. In the 2D-IR spectra, four of them have the same autopeak at 1100 cm(-1), which is the autopeaks of glucoside, but the number of autopeaks of ganoderma lucidum was 4 and its strongest autopeak was 1040 cm(-1), while 5 autopeaks, 4 autopeaks and 5 autopeaks were for ganoderma atrum, ganderma tsugae Murr. and ganoderma lipsiense respectively, and their strongest autopeaks were 1040, 1139, 1140 and 1134 cm(-1) respectively. The multi-steps infrared maro-fingerprint identification testified that the contents of glucoside compounds and amino acid peptide compounds in these four kinds of ganoderma are different. It's proved that multi-steps infrared maro-fingerprint method can be used to analyze and distinguish ganoderma lucidum, ganoderma atrum, ganderma tsugae Murr. and ganoderma lipsiense.
Institute of Scientific and Technical Information of China (English)
SONG AiJing; WANG JianHua; LIU ChunDong; DENG LinHong
2009-01-01
We report a simple "one pot" single step method to synthesize sulfoalkyl ether β-cyclodextrin (β-CD)derivatives in aqueous solution,which avoids the limitations associated with commonly used organic synthesis of such derivatives including multi-step reactions,use of expensive,toxic,and often environmentally hazardous organic solvents and/or reagents. Using this method,we obtained sulfopropyl and sulfobutyl ethyl β-CDs. We characterized these two derivatives and evaluated their ability to enhance solubility of fluconazole,s commonly used antifungal drug with poor water solubility. Experimental results indicate that these derivatives are structurally analogous to some of the commercially available β-CD derivatives. More importantly,when they formed supramolecular inclusion complexes with fluconazole,they demonstrated similar,if not better,capacity to enhance fluconazole solubility compared with commercially available β-CD derivatives,suggesting that the simple "one pot" single step synthesis may provide an effective alternative approach to produce large quantity of β-CD derivatives as pharmaceutical biomaterials for medicinal applications.
Koshak, William; Solakiewicz, Richard
2013-01-01
An analytic perturbation method is introduced for estimating the lightning ground flash fraction in a set of N lightning flashes observed by a satellite lightning mapper. The value of N is large, typically in the thousands, and the observations consist of the maximum optical group area produced by each flash. The method is tested using simulated observations that are based on Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) data. National Lightning Detection NetworkTM (NLDN) data is used to determine the flash-type (ground or cloud) of the satellite-observed flashes, and provides the ground flash fraction truth for the simulation runs. It is found that the mean ground flash fraction retrieval errors are below 0.04 across the full range 0-1 under certain simulation conditions. In general, it is demonstrated that the retrieval errors depend on many factors (i.e., the number, N, of satellite observations, the magnitude of random and systematic measurement errors, and the number of samples used to form certain climate distributions employed in the model).
Directory of Open Access Journals (Sweden)
Chunye Gong
2014-01-01
Full Text Available It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE with iterative implicit finite difference method is O(MxMyN2. In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16–4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.
A method for detecting the presence of organic fraction in nucleation mode sized particles
Directory of Open Access Journals (Sweden)
P. Vaattovaara
2005-01-01
Full Text Available New particle formation and growth has a very important role in many climate processes. However, the overall knowlegde of the chemical composition of atmospheric nucleation mode (particle diameter, d<20 nm and the lower end of Aitken mode particles (d≤50 nm is still insufficient. In this work, we have applied the UFO-TDMA (ultrafine organic tandem differential mobility analyzer method to shed light on the presence of an organic fraction in the nucleation mode size class in different atmospheric environments. The basic principle of the organic fraction detection is based on our laboratory UFO-TDMA measurements with organic and inorganic compounds. Our laboratory measurements indicate that the usefulness of the UFO-TDMA in the field experiments would arise especially from the fact that atmospherically the most relevant inorganic compounds do not grow in subsaturated ethanol vapor, when particle size is 10 nm in diameter and saturation ratio is about 86% or below it. Furthermore, internally mixed particles composed of ammonium bisulfate and sulfuric acid with sulfuric acid mass fraction ≤33% show no growth at 85% saturation ratio. In contrast, 10 nm particles composed of various oxidized organic compounds of atmospheric relevance are able to grow in those conditions. These discoveries indicate that it is possible to detect the presence of organics in atmospheric nucleation mode sized particles using the UFO-TDMA method. In the future, the UFO-TDMA is expected to be an important aid to describe the composition of atmospheric newly-formed particles.
A method for detecting the presence of organic fraction in nucleation mode sized particles
Directory of Open Access Journals (Sweden)
P. Vaattovaara
2005-06-01
Full Text Available New particle formation and growth has a very important role in many climate processes. However, the overall knowlegde of the chemical composition of atmospheric nucleation mode (particle diameter, d<20 nm and the lower end of Aitken mode particles (d≤50 nm is still insufficient. In this work, we have applied the UFO-TDMA (ultrafine organic tandem differential mobility analyzer method to shed light on the presence of organic fraction in the nucleation mode size class in different atmospheric environments. The basic principle of the organic fraction detection is based on our laboratory UFO-TDMA measurements with organic and inorganic compounds. Our laboratory measurements indicate that the usefulness of the UFO-TDMA in the field experiments would arise especially from the fact that atmospherically the most relevant inorganic compounds do not grow in subsaturated ethanol vapor, when particle size is 10nm in diameter and saturation ratio is about 86% or below it. Furthermore, internally mixed particles composed of ammonium bisulfate and sulfuric acid with sulfuric acid mass fraction ≤33% show no growth at 85% saturation ratio. In contrast, 10 nm particles composed of various organic compounds of atmospheric relevance are able to grow in those conditions. These discoveries indicate that it is possible to detect the presence of organics in atmospheric nucleation mode sized particles using the UFO-TDMA method. In the future, the UFO-TDMA is expected to be an important aid to describe the composition of atmospheric newly-formed particles.
Energy Technology Data Exchange (ETDEWEB)
Yang, Xiao-Jun, E-mail: dyangxiaojun@hotmail.com [Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou, Jiangsu, 221008 (China); Institute of Applied Mathematics, Qujing Normal University, Qujing 655011 (China); Srivastava, H.M., E-mail: harimsri@math.uvic.ca [Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4 (Canada); He, Ji-Huan, E-mail: hejihuan@suda.edu.cn [National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123 (China); Baleanu, Dumitru, E-mail: dumitru@cankaya.edu.tr [Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530 (Turkey); Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589 (Saudi Arabia); Institute of Space Sciences, Magurele-Bucharest (Romania)
2013-10-15
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.
The Step Method - Battling Identity Theft Using E-Retailers' Websites
Schulze, Marion; Shah, Mahmood H.
Identity theft is the fastest growing crime in the 21st century. This paper investigates firstly what well-known e-commerce organizations are communicating on their websites to address this issue. For this purpose we analyze secondary data (literature and websites of ten organizations). Secondly we investigate the good practice in this area and recommend practical steps. The key findings are that some organizations only publish minimum security information to comply with legal requirements. Others inform consumers on how they actively try to prevent identity theft, how consumers can protect themselves, and about supporting actions when identity theft related fraud actually happens. From these findings we developed the Support - Trust - Empowerment -Prevention (STEP) method. It is aimed at helping to prevent identity theft and dealing with consequences when it occurs. It can help organizations on gaining and keeping consumers’ trust which is so essential for e-retailers in a climate of rising fraud.
Well-Posedness of Equations with Fractional Derivative via the Method of Sum
Institute of Scientific and Technical Information of China (English)
Shang Quan BU
2012-01-01
We study the well-posedness of the equations with fractional derivative Dαu(t) =Au(t)+f(t) (0 ≤ t≤ 2π),where A is a closed operator in a Banach space X,0 ＜ α ＜ 1 and Dα is the fractional derivative in the sense of Weyl.Although this problem is not always well-posed in Lp(0,2π;(X)) or periodic continuous function spaces Cper([0,2π];(X）),we show by using the method of sum that it is well-posed in some subspaces of Lp(0,2π; X) or Cper([0,2π]; X).
Method of increasing anhydrosugars, pyroligneous fractions and esterified bio-oil
Steele, Philip H; Yu, Fei; Li, Qi; Mitchell, Brian
2014-12-30
The device and method are provided to increase anhydrosugars yield during pyrolysis of biomass. This increase is achieved by injection of a liquid or gas into the vapor stream of any pyrolysis reactor prior to the reactor condensers. A second feature of our technology is the utilization of sonication, microwave excitation, or shear mixing of the biomass to increase the acid catalyst rate for demineralization or removal of hemicellulose prior to pyrolysis. The increased reactivity of these treatments reduces reaction time as well as the required amount of catalyst to less than half of that otherwise required. A fractional condensation system employed by our pyrolysis reactor is another feature of our technology. This system condenses bio-oil pyrolysis vapors to various desired fractions by differential temperature manipulation of individual condensers comprising a condenser chain.
Wang, Jianwen; An, Qi
2008-02-01
A new method for measuring void fraction in lubricating oils is presented based on the image processing technique. The problem here differs from the bubbles detection problem in two-phase fluids in that our interest lies in the gross amount of gas voids in oils. Our method is based on an observation that gas voids in oils change the color of the mixed gas-oil material. Therefore, a measurement technique was established based on the change in color. In particular, the relationship between the change in color and amount of voids was established experimentally. The experiment and testing were performed on a particular setup which consists of a pipe, oil, and air. The test result has shown that this method is effective. The method is the simplest and most accurate one among the existing methods.
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)
Developing intake fraction estimates with limited data: Comparison of methods in Mexico City
Stevens, Gretchen; de Foy, Benjamin; West, J. Jason; Levy, Jonathan I.
In order to estimate the health benefits of reducing mobile source emissions, analysts typically use detailed atmospheric models to estimate the change in population exposure that results from a given change in emissions. However, this may not be feasible in settings where data are limited or policy decisions are needed in the short term. Intake fraction (iF), defined as the fraction of emissions of a pollutant or its precursor that is inhaled by the population, is a metric that can be used to compare exposure assessment methods in a health benefits analysis context. To clarify the utility of rapid-assessment methods, we calculate particulate matter iFs for the Mexico City Metropolitan Area using five methods, some more resource intensive than others. First, we create two simple box models to describe dispersion of primary fine particulate matter (PM 2.5) in the Mexico City basin. Second, we extrapolate iFs for primary PM 2.5, ammonium sulfate, and ammonium nitrate from US values using a regression model. Third, we calculate iFs by assuming a linear relationship between emissions and population-weighted concentrations of primary PM 2.5, ammonium nitrate, and ammonium sulfate (a particle composition method). Finally, we estimate PM iFs from detailed atmospheric dispersion and chemistry models run for only a short period of time. Intake fractions vary by up to a factor of five, from 23 to 120 per million for primary PM 2.5. Estimates of 60, 7, and 0.7 per million for primary PM, secondary ammonium sulfate, and secondary ammonium nitrate, respectively, represent credible central estimates, with an approximate factor of two uncertainty surrounding each estimate. Our results emphasize that multiple rapid-assessment methods can provide meaningful estimates of iFs in resource-limited environments, and that formal uncertainty analysis, with special attention to model biases and uncertainty, would be important for health benefits analyses.
An Online Non-Invasive Condition Monitoring Method for Stepping Motor CRDM in HTGR
Directory of Open Access Journals (Sweden)
S. Bakhri
2016-12-01
Full Text Available Control Rod Drive Mechanism (CRDM based on stepping motor is one of the components applied in High Temperature Gas Coold Reactor (HTGR to control the reactivity as well as to maintain the safety of reactor. The stepping motor requires a unique condition monitoring to avoid any failures especially due to the specific environments of CRDM in HTGR such as the allowable of high temperature, high radiation and the location of stepper motor inside a pressure shell. This research aims to demonstrate an online non-invasive condition monitoring method without direct access to the CRDM of HTGR based on voltage and stator current measurements. A simple stepping motor CRDM simulator is employed. The online condition monitoring is carried out by direct pattern matching of the output signals of logic generator block and the output signals of motor driver. The online method utilizes signature patterns of voltage and stator current signals of the healthy motor as a baseline for healthy motor. In addition, the method is applied to detect high-resistance problem on the connector between the motor driver block and the stepper motor to show the effectiveness and the applicability of this method. The online condition monitoring system demonstrates a capability to identify a minimum detectable simulated high-resistance for about 2.9% which decreases the measured stator current and motor’s torque for around 5.1% and 3.3%, respectively. The paper also points out signatures of healthy motor, including mutual inductions of the motor’s winding in voltage and current measurement which can be used as the fault symptom indicators for online monitoring purposes.
Hydrogen production from lignocellulosic biomass by two-step gasification method
Energy Technology Data Exchange (ETDEWEB)
Lee, In-Gu [Korea Institute of Energy Research (Korea, Republic of)
2010-07-01
Hydrogen can be produced from woody biomass by conventional gasification methods such as partial oxidation or steam gasification. Since these methods produce gas products with low content of hydrogen as well as high content of tar from gasification reactors, posttreatment processes including tar cracker and water-gas shift reaction process are usually necessary for obtaining clean hydrogen-rich gas from woody biomass. In this work, a twostep gasification method was experimentally studied as an alternative to the conventional methods. The first step of the gasification is the fast pyrolysis of biomass to obtain liquid-phase product (bio-oil) and the second step is to gasify the bio-oil to hydrogen-rich gas in supercritical water. The fast pyrolysis of woody biomass was carried out using a bench-scale fluidized-bed reactor. The gasification of bio-oil in supercritical water was performed using a continuous-flow reactor packed with catalyst. The effect of major reaction conditions such as temperature and catalyst on hydrogen yield will be discussed. (orig.)
Influence of application methods of one-step self-etching adhesives on microtensile bond strength
Directory of Open Access Journals (Sweden)
Chul-Kyu Choi,
2011-05-01
Full Text Available Objectives The purpose of this study was to evaluate the effect of various application methods of one-step self-etch adhesives to microtensile resin-dentin bond strength. Materials and Methods Thirty-six extracted human molars were used. The teeth were assigned randomly to twelve groups (n = 15, according to the three different adhesive systems (Clearfil Tri-S Bond, Adper Prompt L-Pop, G-Bond and application methods. The adhesive systems were applied on the dentin as follows: 1 The single coating, 2 The double coating, 3 Manual agitation, 4 Ultrasonic agitation. Following the adhesive application, light-cure composite resin was constructed. The restored teeth were stored in distilled water at room temperature for 24 hours, and prepared 15 specimens per groups. Then microtensile bond strength was measured and the failure mode was examined. Results Manual agitation and ultrasonic agitation of adhesive significantly increased the microtensile bond strength than single coating and double coating did. Double coating of adhesive significantly increased the microtensile bond strength than single coating did and there was no significant difference between the manual agitation and ultrasonic agitation group. There was significant difference in microtensile bonding strength among all adhesives and Clearfil Tri-S Bond showed the highest bond strength. Conclusions In one-step self-etching adhesives, there was significant difference according to application methods and type of adhesives. No matter of the material, the manual or ultrasonic agitation of the adhesive showed significantly higher microtensile bond strength.
Diaby, Vakaramoko; Goeree, Ron
2014-02-01
In recent years, the quest for more comprehensiveness, structure and transparency in reimbursement decision-making in healthcare has prompted the research into alternative decision-making frameworks. In this environment, multi-criteria decision analysis (MCDA) is arising as a valuable tool to support healthcare decision-making. In this paper, we present the main MCDA decision support methods (elementary methods, value-based measurement models, goal programming models and outranking models) using a case study approach. For each family of methods, an example of how an MCDA model would operate in a real decision-making context is presented from a critical perspective, highlighting the parameters setting, the selection of the appropriate evaluation model as well as the role of sensitivity and robustness analyses. This study aims to provide a step-by-step guide on how to use MCDA methods for reimbursement decision-making in healthcare.
Institute of Scientific and Technical Information of China (English)
Dong Wang; Steven J. Ruuth
2008-01-01
Implicit-explicit (IMEX) linear multistep methods are popular techniques for solving partial differential equations (PDEs) with terms of different types. While fixed time-step versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit (VSIMEX) linear multistep methods for time-dependent PDEs. Families of order-p, p-step VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers' equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.
Second round robin for plasma hepcidin methods: first steps toward harmonization.
Kroot, Joyce J C; van Herwaarden, Antonius E; Tjalsma, Harold; Jansen, Rob T P; Hendriks, Jan C M; Swinkels, Dorine W
2012-10-01
Measurements of the iron regulatory hormone hepcidin by various methodologies and laboratories are not harmonized. As a result different numeric results are obtained for the same clinical sample. We investigated whether better agreement between plasma hepcidin methods can be achieved by harmonization. Native plasma pools (n = 11) of a variety of hepcidin concentrations and blank plasma spiked with three different quantities of synthetic hepcidin-25 purchased from two different commercial sources (n = 6), were distributed in duplicate among 21 methods worldwide. We assessed commutability by comparing results from synthetic hepcidin with those from native samples in various method couples by Bland-Altman plots. Methods differed substantially in absolute values and reproducibility. For the majority of methods we found that samples with synthetic hepcidin-25 were noncommutable with the native samples. In an attempt to harmonize by using native hepcidin results, we selected two methods that showed good mutual agreement of native results and calculated consensus values as the medians for the 11 duplicate native samples obtained by these two methods. Finally, we constructed algorithms enabling the laboratories to calculate the hepcidin consensus (HEPCON) value using their own native hepcidin results. We found that the use of these algorithms substantially reduced the between-method CV. Until commutable materials are defined, hepcidin harmonization can be achieved by exploiting specific algorithms, allowing each lab to report their native hepcidin concentrations in HEPCON values. This study represents the first step toward harmonization of plasma hepcidin methods and facilitates aggregation of hepcidin data from different research investigations.
Yoshida, K; Sekiguchi, K; Mizuno, N; Kasai, K; Sakai, I; Sato, H; Seta, S
1995-03-21
This investigation was undertaken as an efficient method for isolating sperm DNA from a mixed fluid sample which contains vaginal epithelial cells in a greater amount. The modified method of the two-step differential extraction procedure was found to be suitable for separating sperm DNA and vaginal epithelial cell DNA from the mixed stains. As the first step of digestion, vaginal epithelial cells in the mixed stains were lysed with Proteinase K and SDS, and sperm heads remaining in the lysed solution were collected by centrifugation. As the second step digestion, the sperm heads were lysed with the buffer containing Proteinase K, SDS and DTT as reducing agent. DNA fractions extracted from the two lysed solutions were enriched, one with sperm DNA and the other with vaginal epithelial cell DNA. MCT118(D1S80), ApoB VNTR and HLADQ alpha types of sperm DNA were detected and were confirmed by matching with corresponding male blood DNA. In the case of vaginal secretion mixed with semen of two males, the mixture of MCT118 types of the two males was detected in sperm DNA fraction.
Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schr(o)dinger Equations
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the threestep explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schr(o)dinger equation and the nonlinear Schr(o)dinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.
Single step deposition method for nearly stoichiometric CuInSe{sub 2} thin films
Energy Technology Data Exchange (ETDEWEB)
Karthikeyan, Sreejith, E-mail: s.karthikeyan@edu.salford.ac.u [Materials and Physics Research Centre, University of Salford, Salford, M5 4WT (United Kingdom); Hill, Arthur E.; Pilkington, Richard D.; Cowpe, John S. [Materials and Physics Research Centre, University of Salford, Salford, M5 4WT (United Kingdom); Hisek, Joerg [Technische Universitaet Braunschweig, Hannover (Germany); Bagnall, Darren M. [School of Electronics and Computer Science, University of Southampton, SO17 1BJ (United Kingdom)
2011-03-01
This paper reports the production of high quality copper indium diselenide thin films using pulsed DC magnetron sputtering from a powder target. As-grown thin films consisted of pin-hole free, densely packed grains. X-ray diffraction showed that films were highly orientated in the (112) and/or (204)/(220) direction with no secondary phases present. The most surprising and exciting outcome of this study was that the as-grown films were of near stoichiometric composition, almost independent of the composition of the starting material. No additional steps or substrate heating were necessary to incorporate selenium and create single phase CuInSe{sub 2}. Electrical properties obtained by hot point probe and four point probe gave values of low resistivity and showed that the films were all p-type. The physical and structural properties of these films were analyzed using X-ray diffraction, scanning electron microscopy and atomic force microscopy. Resistivity measurements were carried out using the four point probe and hot probe methods. The single step deposition process can cut down the cost of the complex multi step processes involved in the traditional vacuum based deposition techniques.
DEVELOPMENT OF AN ITERATIVE METHOD TO SOLVE THE DIFFUSION PROBLEM IN THE PREDESIGN STEP
Abouali Sanchez, Said
2014-01-01
One of the most important and difficult steps in the design process is the predesign. In this step, the main goal is to obtain the geometry characteristics and some other features to solve the problem we want to solve. Thus, reducing the duration of this phase is one of the challenging objectives in the actual engineering design process. As regards our study, following the energy deposition calculations with the means of the FLUKA code, a heat diffusion code is usually needed to calculate the evolution in time of the temperature distributions as well the associated stresses on the object under study. As a preliminary optimization step in the object design process, in this project we are proposing thedevelopment of a new method implemented in a code which allows us to obtain the solution for this equation in a complex geometry by using the information given by the FLUKA code for a simple geometry. By this way, we will be able to reduce the predesign phase duration.
A New Void Fraction Measurement Method for Gas-Liquid Two-Phase Flow in Small Channels.
Li, Huajun; Ji, Haifeng; Huang, Zhiyao; Wang, Baoliang; Li, Haiqing; Wu, Guohua
2016-01-27
Based on a laser diode, a 12 × 6 photodiode array sensor, and machine learning techniques, a new void fraction measurement method for gas-liquid two-phase flow in small channels is proposed. To overcome the influence of flow pattern on the void fraction measurement, the flow pattern of the two-phase flow is firstly identified by Fisher Discriminant Analysis (FDA). Then, according to the identification result, a relevant void fraction measurement model which is developed by Support Vector Machine (SVM) is selected to implement the void fraction measurement. A void fraction measurement system for the two-phase flow is developed and experiments are carried out in four different small channels. Four typical flow patterns (including bubble flow, slug flow, stratified flow and annular flow) are investigated. The experimental results show that the development of the measurement system is successful. The proposed void fraction measurement method is effective and the void fraction measurement accuracy is satisfactory. Compared with the conventional laser measurement systems using standard laser sources, the developed measurement system has the advantages of low cost and simple structure. Compared with the conventional void fraction measurement methods, the proposed method overcomes the influence of flow pattern on the void fraction measurement. This work also provides a good example of using low-cost laser diode as a competent replacement of the expensive standard laser source and hence implementing the parameter measurement of gas-liquid two-phase flow. The research results can be a useful reference for other researchers' works.
Two regularization methods for solving a Riesz-Feller space-fractional backward diffusion problem
Zheng, G. H.; Wei, T.
2010-11-01
In this paper, a backward diffusion problem for a space-fractional diffusion equation (SFDE) in a strip is investigated. Such a problem is obtained from the classical diffusion equation in which the second-order space derivative is replaced with a Riesz-Feller derivative of order β in (0, 2]. We show that such a problem is severely ill-posed and further propose a new regularization method and apply a spectral regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under a priori bound assumptions for the exact solution. Finally, numerical examples are given to show that the proposed numerical methods are effective.
Gravitational Field-Flow Fractionation Devices Fabricated via a Hot Embossing/Thermal Bonding Method
Directory of Open Access Journals (Sweden)
Kaijun Yang
2014-04-01
Full Text Available A novel hot embossing/low temperature ethanol solvent bonding method for the fabrication of polymethylmethacrylate (PMMA field flow fractionation devices has been developed. The separation channel on a PMMA substrate was generated by a hot embossing process without vacuum. Special temperature-pressure profiles were used to analyze the influence of the hot embossing parameters. After the hot embossing process, ethanol solvent bonding was used to seal the separation channel on the PMMA substrate. The experimental results show that the bonding strength with ethanol solvent bonding at 35 °C (aspect ratio (depth/width: 0.043 is 3.05 MPa, and the deformation percentage is very low (0.54%. A burst pressure test indicated that the as-prepared PMMA gravitational field flow fractionation device has a very high burst pressure. Furthermore, the higher resolution of the as-prepared PMMA gravitational field flow fractionation device in the separation of wheat and starch particles shows that the hot embossing/low temperature ethanol solvent bonding technique will have potential commercial value.
Kassa, Semu Mitiku; Tsegay, Teklay Hailay
2017-08-01
Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.
Graham, Ken; Rea, Rosemary; Simpson, Paul; Stack, Helena
2017-01-01
Enterococci show higher proteolytic activities than other lactic acid bacteria and thus have received considerable attention in scientific literature in recent years. Proteolytic enzymes of enterococci have warranted the use of some species as starter, adjuncts or protective cultures and as probiotics, while in some strains they have also been linked with virulence. Consequently, the isolation and identification of proteolytic enterococci is becoming of increasing interest and importance. However, current screening methods for proteolytic enterococci can be time consuming, requiring a two-step procedure which may take up to 96h. This study describes a method, utilising Kanamycin Skim Milk Aesculin Azide (KSMEA) agar, for the isolation of proteolytic enterococci in one-step, thereby significantly reducing screening time. KSMEA combines the selective properties of Kanamycin Aesculin Azide Agar (KAA) with skim milk powder for the detection of proteolytic enterococci. Enterococci produced colonies with a black halo on KSMEA which were accompanied by a zone of clearing in the media when enterococci were proteolytic. KSMEA medium retained the selectivity of KAA, while proteolytic enterococci were easily distinguished from non-proteolytic enterococci when two known strains were propagated on KSMEA. KSMEA also proved effective at isolating and detecting enterococci in raw milk, faeces and soil. Isolates recovered from the screen were confirmed as enterococci using genus-specific primers. Proteolytic enterococci were present in the raw milk sample only and were easily distinguishable from non-proteolytic enterococci and other microorganisms. Therefore, KSMEA provides a rapid, one-step screening method for the isolation of presumptive proteolytic enterococci.
Rapid expansion method (REM) for time‐stepping in reverse time migration (RTM)
Pestana, Reynam C.
2009-01-01
We show that the wave equation solution using a conventional finite‐difference scheme, derived commonly by the Taylor series approach, can be derived directly from the rapid expansion method (REM). After some mathematical manipulation we consider an analytical approximation for the Bessel function where we assume that the time step is sufficiently small. From this derivation we find that if we consider only the first two Chebyshev polynomials terms in the rapid expansion method we can obtain the second order time finite‐difference scheme that is frequently used in more conventional finite‐difference implementations. We then show that if we use more terms from the REM we can obtain a more accurate time integration of the wave field. Consequently, we have demonstrated that the REM is more accurate than the usual finite‐difference schemes and it provides a wave equation solution which allows us to march in large time steps without numerical dispersion and is numerically stable. We illustrate the method with post and pre stack migration results.
A novel cognitive ISAR imaging method with random stepped frequency chirp signal
Institute of Scientific and Technical Information of China (English)
ZHU Feng; ZHANG Qun; LUO Ying; LI KaiMing; GU FuFei
2012-01-01
The random stepped frequency chirp signal (RSFCS） has better performance in anti-jamming than that of conventional stepped frequency chirp signal (SFCS).In combination with the theory of compressing sensing (CS),a novel ISAR imaging method is proposed based on RSFCS,in which the high resolution range profile (HRRP） is reconstructed by using the conventional OMP algorithm,whereas the cognitive approach is introduced to further reduce the number of sub-pulse in RSFCS.In the proposed method,via cognizing the characteristics of moving targets,the number of sub-pulse in each burst can be adjusted adaptively.Finally,in the cross-range direction,the accurate reconstruction of ISAR image by using CS theory is implemented,which can effectively accomplish unwrapping.With the proposed method,high quality HRRP and ISAR image can be achieved with fewer sub-pulses of RSFCS and lower burst repetition frequency (BRF).Some simulation results are given to validate the effectiveness and robustness of the proposed algorithm.
A three-step method of self-reflection using reflective journal writing.
Riley-Doucet, C; Wilson, S
1997-05-01
Fiscal and financial constraints present a challenge for nurse educators to broaden the diversity and scope of teaching/learning methodologies. One method designed to promote autonomy and self-direction of nursing students is self-reflection combined with reflective journal writing. This paper describes a three-step process of self-reflection encompassing critical appraisal, peer group discussion and self-awareness. This process of self-reflection was initiated with one group of clinical nursing students. Using student and teacher feedback, implications for employing this teaching/learning strategy in clinical practice are suggested.
Institute of Scientific and Technical Information of China (English)
FENG Yu-zhong; QI Sheng-li; LIU Jing-jing; WU Zhan-peng; YANG Xiao-ping; JIN Ri-guang; WU De-zhen
2011-01-01
Soluble and ordered ladder like polyphenylsilsesquioxane was synthesized by a two-step sol-gel method including hydrolysis and polycondensation. The procedure was monitored by Fourier transform infrared spectroscopy and the presence of the ladder like structure was confirmed by X-ray techniques. 29Si NMR analysis shows a very narrow half peak width(δ＜4) at δ-78.866 of the main chain unit C6H5SiO3/2 of polyphenylsilsesquioxane, indicating that the polyphenylsilsesquioxane has ordered ladder like structures rather than the branched ones. The relationship between molecular weight and the time of polycondensation was also discussed.
A modified split—step fourier method for optical pulse propagation with polarization mode dispersion
Institute of Scientific and Technical Information of China (English)
RaoMin; SunXiao-Han; ZhangMing-De
2003-01-01
A modified split-step Fourier method (SSFM) is presented to solve the coupled nonlinear Schroedinger equation (CNLS) that can be used to model high-speed pulse propagation in optical fibres with polarization mode dispersion (PMD). We compare our approach with the SSFM and demonstrate that our approach is much faster with no loss of pre-chirped RZ(CRZ) formats in the presence of high PMD through this approach. The simulation results show that CRZ pulses are the most tolerant to high PMD values and the extinct ratio has a great impact on the transmission performance.
Variable catchment sizes for the two-step floating catchment area (2SFCA) method.
Luo, Wei; Whippo, Tara
2012-07-01
Government efforts designed to help improve healthcare access rely on accurate measures of accessibility so that resources can be allocated to truly needy areas. In order to capture the interaction between physicians and populations, various access measures have been utilized, including the popular two-step floating catchment area (2SFCA) method. However, despite the many advantages of 2SFCA, the problems associated with using fixed catchment sizes have not been satisfactorily addressed. We propose a new method to dynamically determine physician and population catchment sizes by incrementally increasing the catchment until a base population and a physician-to-population ratio are met. Preliminary application to the ten-county region in northern Illinois has demonstrated that the new method is effective in determining the appropriate catchment sizes across the urban to suburban/rural continuum and has revealed greater detail in spatial variation of accessibility compared to results using fixed catchment sizes. Copyright © 2012 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Song Fu
2015-01-01
Full Text Available Although the uniform theory of diffraction (UTD could be theoretically applied to arbitrarilyshaped convex objects modeled by nonuniform rational B-splines (NURBS, one of the great challenges in calculation of the UTD surface diffracted fields is the difficulty in determining the geodesic paths along which the creeping waves propagate on arbitrarilyshaped NURBS surfaces. In differential geometry, geodesic paths satisfy geodesic differential equation (GDE. Hence, in this paper, a general and efficient adaptive variable step Euler method is introduced for solving the GDE on arbitrarilyshaped NURBS surfaces. In contrast with conventional Euler method, the proposed method employs a shape factor (SF ξ to efficiently enhance the accuracy of tracing and extends the application of UTD for practical engineering. The validity and usefulness of the algorithm can be verified by the numerical results.
A two-step iterative method and its acceleration for outer inverses
Indian Academy of Sciences (India)
SHWETABH SRIVASTAVA; DHARMENDRA K GUPTA
2016-10-01
A two-step iterative method and its accelerated version for approximating outer inverse A2 T,S of an arbitrary matrix A are proposed. A convergence theorem for its existence is established. The rigorous error bounds are derived. Numerical experiments involving singular square, rectangular, random matrices and a sparse matrix obtained by discretization of the Poisson’s equation are solved. Iterations count, computational time and the error bounds are used to measure the performance of our method. On comparing our results with those of other iterative methods, it is seen that significantly better performance is achieved. Thus, enhanced speed and accuracy from the computational points of view has resulted for our methodology.
Institute of Scientific and Technical Information of China (English)
XU; Mingyu; TAN; Wenchang
2006-01-01
From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equations) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern mechanics. Some authors' researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.
A New Void Fraction Measurement Method for Gas-Liquid Two-Phase Flow in Small Channels
Huajun Li; Haifeng Ji; Zhiyao Huang; Baoliang Wang; Haiqing Li; Guohua Wu
2016-01-01
Based on a laser diode, a 12 × 6 photodiode array sensor, and machine learning techniques, a new void fraction measurement method for gas-liquid two-phase flow in small channels is proposed. To overcome the influence of flow pattern on the void fraction measurement, the flow pattern of the two-phase flow is firstly identified by Fisher Discriminant Analysis (FDA). Then, according to the identification result, a relevant void fraction measurement model which is developed by Support Vector Mach...
Methods and Algorithms for Solving Inverse Problems for Fractional Advection-Dispersion Equations
Aldoghaither, Abeer
2015-11-12
Fractional calculus has been introduced as an e cient tool for modeling physical phenomena, thanks to its memory and hereditary properties. For example, fractional models have been successfully used to describe anomalous di↵usion processes such as contaminant transport in soil, oil flow in porous media, and groundwater flow. These models capture important features of particle transport such as particles with velocity variations and long-rest periods. Mathematical modeling of physical phenomena requires the identification of pa- rameters and variables from available measurements. This is referred to as an inverse problem. In this work, we are interested in studying theoretically and numerically inverse problems for space Fractional Advection-Dispersion Equation (FADE), which is used to model solute transport in porous media. Identifying parameters for such an equa- tion is important to understand how chemical or biological contaminants are trans- ported throughout surface aquifer systems. For instance, an estimate of the di↵eren- tiation order in groundwater contaminant transport model can provide information about soil properties, such as the heterogeneity of the medium. Our main contribution is to propose a novel e cient algorithm based on modulat-ing functions to estimate the coe cients and the di↵erentiation order for space FADE, which can be extended to general fractional Partial Di↵erential Equation (PDE). We also show how the method can be applied to the source inverse problem. This work is divided into two parts: In part I, the proposed method is described and studied through an extensive numerical analysis. The local convergence of the proposed two-stage algorithm is proven for 1D space FADE. The properties of this method are studied along with its limitations. Then, the algorithm is generalized to the 2D FADE. In part II, we analyze direct and inverse source problems for a space FADE. The problem consists of recovering the source term using final
Patil-Gadhe, Arpana; Pokharkar, Varsha
2014-04-01
Quality by Design (QbD) is a systematic approach to develop drug products which includes evaluation of formulation parameters to achieve defined final product quality. In the present study principles of QbD were extended to the preparation, in-vitro and in-vivo performance of rifapentine-loaded proliposomes for pulmonary inhalation where final product needs to comply with specific properties. The rifapentine-loaded proliposomes for the treatment of tuberculosis were prepared in single step by spray drying method and independent variables were optimized using factorial design approach. Contour plots and multiple regression analysis were used to study the effect of selected independent variables on dependent variables. The effect of presence of drug: hydrogenated soya phosphatidylcholine (HSPC) and type of charged lipid in the formulation at three levels were studied on mass median diameter (MMD), liposomal vesicle size, % encapsulation efficiency (% EE), mass median aerodynamic diameter (MMAD) and fine particle fraction (FPF) as critical quality attributes. Optimized formulation (R-LDPI-7) with drug: HSPC ratio of 1:2 and stearyl amine as charged lipid were found to give respirable proliposomes with MMAD of 1.56 ± 0.16 μm and FPF of 92.5 ± 1.5%. Sustained drug release with Higuchi diffusion kinetics was achieved from liposomally encapsulated rifapentine. Pulmonary pharmacokinetics of optimized batch R-LDPI-7 revealed longer retention of drug in lungs with 7 fold increase in both, the mean residence time and t1/2 as compared to R-DPI-0. The study results demonstrated the application of QbD principles and design of experiment (DOE) approach to develop drug encapsulated proliposomes for inhalation by spray drying in single step.
Directory of Open Access Journals (Sweden)
Jinfeng Wang
2014-01-01
Full Text Available We discuss and analyze an H1-Galerkin mixed finite element (H1-GMFE method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H1-GMFE method. Based on the discussion on the theoretical error analysis in L2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H1-norm. Moreover, we derive and analyze the stability of H1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure.
Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong
2014-01-01
We discuss and analyze an H(1)-Galerkin mixed finite element (H(1)-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H(1)-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H(1)-GMFE method. Based on the discussion on the theoretical error analysis in L(2)-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H(1)-norm. Moreover, we derive and analyze the stability of H(1)-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure.
Wang, Xianghong; Liu, Xinyu; Wang, Nanshuo; Yu, Xiaojun; Bo, En; Chen, Si; Liu, Linbo
2017-02-01
Optical coherence tomography (OCT) provides high resolution and cross-sectional images of biological tissue and is widely used for diagnosis of ocular diseases. However, OCT images suffer from speckle noise, which typically considered as multiplicative noise in nature, reducing the image resolution and contrast. In this study, we propose a two-step iteration (TSI) method to suppress those noises. We first utilize augmented Lagrange method to recover a low-rank OCT image and remove additive Gaussian noise, and then employ the simple and efficient split Bregman method to solve the Total-Variation Denoising model. We validated such proposed method using images of swine, rabbit and human retina. Results demonstrate that our TSI method outperforms the other popular methods in achieving higher peak signal-to-noise ratio (PSNR) and structure similarity (SSIM) while preserving important structural details, such as tiny capillaries and thin layers in retinal OCT images. In addition, the results of our TSI method show clearer boundaries and maintains high image contrast, which facilitates better image interpretations and analyses.
A Novel Two-Step Method for Screening Shade Tolerant Mutant Plants via Dwarfism
Li, Wei; Katin-Grazzini, Lorenzo; Krishnan, Sanalkumar; Thammina, Chandra; El-Tanbouly, Rania; Yer, Huseyin; Merewitz, Emily; Guillard, Karl; Inguagiato, John; McAvoy, Richard J.; Liu, Zongrang; Li, Yi
2016-01-01
When subjected to shade, plants undergo rapid shoot elongation, which often makes them more prone to disease and mechanical damage. Shade-tolerant plants can be difficult to breed; however, they offer a substantial benefit over other varieties in low-light areas. Although perennial ryegrass (Lolium perenne L.) is a popular species of turf grasses because of their good appearance and fast establishment, the plant normally does not perform well under shade conditions. It has been reported that, in turfgrass, induced dwarfism can enhance shade tolerance. Here we describe a two-step procedure for isolating shade tolerant mutants of perennial ryegrass by first screening for dominant dwarf mutants, and then screening dwarf plants for shade tolerance. The two-step screening process to isolate shade tolerant mutants can be done efficiently with limited space at early seedling stages, which enables quick and efficient isolation of shade tolerant mutants, and thus facilitates development of shade tolerant new cultivars of turfgrasses. Using the method, we isolated 136 dwarf mutants from 300,000 mutagenized seeds, with 65 being shade tolerant (0.022%). When screened directly for shade tolerance, we recovered only four mutants from a population of 150,000 (0.003%) mutagenized seeds. One shade tolerant mutant, shadow-1, was characterized in detail. In addition to dwarfism, shadow-1 and its sexual progeny displayed high degrees of tolerance to both natural and artificial shade. We showed that endogenous gibberellin (GA) content in shadow-1 was higher than wild-type controls, and shadow-1 was also partially GA insensitive. Our novel, simple and effective two-step screening method should be applicable to breeding shade tolerant cultivars of turfgrasses, ground covers, and other economically important crop plants that can be used under canopies of existing vegetation to increase productivity per unit area of land. PMID:27752260
A Novel Two-Step Method for Screening Shade Tolerant Mutant Plants via Dwarfism.
Li, Wei; Katin-Grazzini, Lorenzo; Krishnan, Sanalkumar; Thammina, Chandra; El-Tanbouly, Rania; Yer, Huseyin; Merewitz, Emily; Guillard, Karl; Inguagiato, John; McAvoy, Richard J; Liu, Zongrang; Li, Yi
2016-01-01
When subjected to shade, plants undergo rapid shoot elongation, which often makes them more prone to disease and mechanical damage. Shade-tolerant plants can be difficult to breed; however, they offer a substantial benefit over other varieties in low-light areas. Although perennial ryegrass (Lolium perenne L.) is a popular species of turf grasses because of their good appearance and fast establishment, the plant normally does not perform well under shade conditions. It has been reported that, in turfgrass, induced dwarfism can enhance shade tolerance. Here we describe a two-step procedure for isolating shade tolerant mutants of perennial ryegrass by first screening for dominant dwarf mutants, and then screening dwarf plants for shade tolerance. The two-step screening process to isolate shade tolerant mutants can be done efficiently with limited space at early seedling stages, which enables quick and efficient isolation of shade tolerant mutants, and thus facilitates development of shade tolerant new cultivars of turfgrasses. Using the method, we isolated 136 dwarf mutants from 300,000 mutagenized seeds, with 65 being shade tolerant (0.022%). When screened directly for shade tolerance, we recovered only four mutants from a population of 150,000 (0.003%) mutagenized seeds. One shade tolerant mutant, shadow-1, was characterized in detail. In addition to dwarfism, shadow-1 and its sexual progeny displayed high degrees of tolerance to both natural and artificial shade. We showed that endogenous gibberellin (GA) content in shadow-1 was higher than wild-type controls, and shadow-1 was also partially GA insensitive. Our novel, simple and effective two-step screening method should be applicable to breeding shade tolerant cultivars of turfgrasses, ground covers, and other economically important crop plants that can be used under canopies of existing vegetation to increase productivity per unit area of land.
A two-step semiparametric method to accommodate sampling weights in multiple imputation.
Zhou, Hanzhi; Elliott, Michael R; Raghunathan, Trviellore E
2016-03-01
Multiple imputation (MI) is a well-established method to handle item-nonresponse in sample surveys. Survey data obtained from complex sampling designs often involve features that include unequal probability of selection. MI requires imputation to be congenial, that is, for the imputations to come from a Bayesian predictive distribution and for the observed and complete data estimator to equal the posterior mean given the observed or complete data, and similarly for the observed and complete variance estimator to equal the posterior variance given the observed or complete data; more colloquially, the analyst and imputer make similar modeling assumptions. Yet multiply imputed data sets from complex sample designs with unequal sampling weights are typically imputed under simple random sampling assumptions and then analyzed using methods that account for the sampling weights. This is a setting in which the analyst assumes more than the imputer, which can led to biased estimates and anti-conservative inference. Less commonly used alternatives such as including case weights as predictors in the imputation model typically require interaction terms for more complex estimators such as regression coefficients, and can be vulnerable to model misspecification and difficult to implement. We develop a simple two-step MI framework that accounts for sampling weights using a weighted finite population Bayesian bootstrap method to validly impute the whole population (including item nonresponse) from the observed data. In the second step, having generated posterior predictive distributions of the entire population, we use standard IID imputation to handle the item nonresponse. Simulation results show that the proposed method has good frequentist properties and is robust to model misspecification compared to alternative approaches. We apply the proposed method to accommodate missing data in the Behavioral Risk Factor Surveillance System when estimating means and parameters of
Directory of Open Access Journals (Sweden)
Zhiqiang Zhou
2017-01-01
Full Text Available We study the pricing of the American options with fractal transmission system under two-state regime switching models. This pricing problem can be formulated as a free boundary problem of time-fractional partial differential equation (FPDE system. Firstly, applying Laplace transform to the governing FPDEs with respect to the time variable results in second-order ordinary differential equations (ODEs with two free boundaries. Then, the solutions of ODEs are expressed in an explicit form. Consequently the early exercise boundaries and the values for the American option are recovered using the Gaver-Stehfest formula. Numerical comparisons of the methods with the finite difference methods are carried out to verify the efficiency of the methods.
Sweilam, N. H.; Abou Hasan, M. M.
2016-08-01
This paper reports a new spectral algorithm for obtaining an approximate solution for the Lévy-Feller diffusion equation depending on Legendre polynomials and Chebyshev collocation points. The Lévy-Feller diffusion equation is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative. A new formula expressing explicitly any fractional-order derivatives, in the sense of Riesz-Feller operator, of Legendre polynomials of any degree in terms of Jacobi polynomials is proved. Moreover, the Chebyshev-Legendre collocation method together with the implicit Euler method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical results with comparisons are given to confirm the reliability of the proposed method for the Lévy-Feller diffusion equation.
Efficient Recursive Methods for Partial Fraction Expansion of General Rational Functions
Directory of Open Access Journals (Sweden)
Youneng Ma
2014-01-01
Full Text Available Partial fraction expansion (pfe is a classic technique used in many fields of pure or applied mathematics. The paper focuses on the pfe of general rational functions in both factorized and expanded form. Novel, simple, and recursive formulas for the computation of residues and residual polynomial coefficients are derived. The proposed pfe methods require only simple pure-algebraic operations in the whole computation process. They do not involve derivatives when tackling proper functions and require no polynomial division when dealing with improper functions. The methods are efficient and very easy to apply for both computer and manual calculation. Various numerical experiments confirm that the proposed methods can achieve quite desirable accuracy even for pfe of rational functions with multiple high-order poles or some tricky ill-conditioned poles.
A simple two-step method to fabricate highly transparent ITO/polymer nanocomposite films
Liu, Haitao; Zeng, Xiaofei; Kong, Xiangrong; Bian, Shuguang; Chen, Jianfeng
2012-09-01
Transparent functional indium tin oxide (ITO)/polymer nanocomposite films were fabricated via a simple approach with two steps. Firstly, the functional monodisperse ITO nanoparticles were synthesized via a facile nonaqueous solvothermal method using bifunctional chemical agent (N-methyl-pyrrolidone, NMP) as the reaction solvent and surface modifier. Secondly, the ITO/acrylics polyurethane (PUA) nanocomposite films were fabricated by a simple sol-solution mixing method without any further surface modification step as often employed traditionally. Flower-like ITO nanoclusters with about 45 nm in diameter were mono-dispersed in ethyl acetate and each nanocluster was assembled by nearly spherical nanoparticles with primary size of 7-9 nm in diameter. The ITO nanoclusters exhibited an excellent dispersibility in polymer matrix of PUA, remaining their original size without any further agglomeration. When the loading content of ITO nanoclusters reached to 5 wt%, the transparent functional nanocomposite film featured a high transparency more than 85% in the visible light region (at 550 nm), meanwhile cutting off near-infrared radiation about 50% at 1500 nm and blocking UV ray about 45% at 350 nm. It could be potential for transparent functional coating materials applications.
Indian Academy of Sciences (India)
EMRULLAH YA¸SAR; ILKER BURAK GIRESUNLU
2016-08-01
In this work, we present ($G' /G, 1/G$)-expansion method for solving fractional differential equations based on a fractional complex transform. We apply this method for solving space–time fractional Cahn--Allen equation and space--time fractional Klein–Gordon equation. The fractional derivatives are described in the sense of modified Riemann--Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced. The obtained solutions may be used for explaining of some physical problems.The($G' /G, 1/G$)-expansion method has a wider applicability for nonlinear equations. We have verified all the obtained solutions with the aid of Maple.
Two-step adaptive extraction method for ground points and breaklines from lidar point clouds
Yang, Bisheng; Huang, Ronggang; Dong, Zhen; Zang, Yufu; Li, Jianping
2016-09-01
The extraction of ground points and breaklines is a crucial step during generation of high quality digital elevation models (DEMs) from airborne LiDAR point clouds. In this study, we propose a novel automated method for this task. To overcome the disadvantages of applying a single filtering method in areas with various types of terrain, the proposed method first classifies the points into a set of segments and one set of individual points, which are filtered by segment-based filtering and multi-scale morphological filtering, respectively. In the process of multi-scale morphological filtering, the proposed method removes amorphous objects from the set of individual points to decrease the effect of the maximum scale on the filtering result. The proposed method then extracts the breaklines from the ground points, which provide a good foundation for generation of a high quality DEM. Finally, the experimental results demonstrate that the proposed method extracts ground points in a robust manner while preserving the breaklines.
Rodríguez-Alleres, María; de Blas, Esther; Benito, Elena
2007-05-25
The water repellency of soils with different texture under different types of plant cover was determined by applying the WDPT and MED methods to both whole samples and the following size fractions: 2-1, 1-0.5, 0.5-0.25, 0.25-0.05 and water repellency in the finest fraction (<0.05 mm) as a result of its higher organic carbon content. On the other hand, all fractions in the forest soils, which were extremely water repellent, contributed to the overall repellency; in any case, the MED test revealed that the finest fraction was strongly repellent in the forest soils as well.
Directory of Open Access Journals (Sweden)
Somayeh Nemati
2016-11-01
Full Text Available In this paper, we consider the second-kind Chebyshev polynomials (SKCPs for the numerical solution of the fractional optimal control problems (FOCPs. Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature formula to reduce the fractional optimal control problem to solving a system of nonlinear algebraic equations that greatly simplifies the problem. Finally, some examples are included to confirm the efficiency and accuracy of the proposed method.
One-step Double-layer Thermal Evaporation Method for Organic Light Emitting Diodes
Kee, Y. Y.; Yong, T. K.; Ong, D. S.; Tou, T. Y.
2011-03-01
A new one-step double-layer thermal evaporation method was used to fabricate organic light emitting diodes (OLEDs) with device structure of: ITO (anode)/N,N_-diphenyl-N,N_-bis(3-methylphenyl)-1,1_-diphenyl-4,4_-diamine (TPD) /tris-(8-hydroxyquinoline)aluminum(3) (Alq3)/Al (cathode). These OLEDs were fabricated in cleanroom on the ITO-coated glass with a sheet resistivity of 20Ω/sq and an optical transmittance of 90%. The I-V and brightness characteristic showed that the new method could produce better performance achieving lower turn-on voltage (-2V), higher peak current efficiency (+29%) and higher brightness (+36%).
Industrial Process Identification and Control Design Step-test and Relay-experiment-based Methods
Liu, Tao
2012-01-01
Industrial Process Identification and Control Design is devoted to advanced identification and control methods for the operation of continuous-time processes both with and without time delay, in industrial and chemical engineering practice. The simple and practical step- or relay-feedback test is employed when applying the proposed identification techniques, which are classified in terms of common industrial process type: open-loop stable; integrating; and unstable, respectively. Correspondingly, control system design and tuning models that follow are presented for single-input-single-output processes. Furthermore, new two-degree-of-freedom control strategies and cascade control system design methods are explored with reference to independently-improving, set-point tracking and load disturbance rejection. Decoupling, multi-loop, and decentralized control techniques for the operation of multiple-input-multiple-output processes are also detailed. Perfect tracking of a desire output trajectory is realiz...
A step beyond the Monte Carlo method in economics: Application of multivariate normal distribution
Kabaivanov, S.; Malechkova, A.; Marchev, A.; Milev, M.; Markovska, V.; Nikolova, K.
2015-11-01
In this paper we discuss the numerical algorithm of Milev-Tagliani [25] used for pricing of discrete double barrier options. The problem can be reduced to accurate valuation of an n-dimensional path integral with probability density function of a multivariate normal distribution. The efficient solution of this problem with the Milev-Tagliani algorithm is a step beyond the classical application of Monte Carlo for option pricing. We explore continuous and discrete monitoring of asset path pricing, compare the error of frequently applied quantitative methods such as the Monte Carlo method and finally analyze the accuracy of the Milev-Tagliani algorithm by presenting the profound research and important results of Honga, S. Leeb and T. Li [16].
One-Step Method for Preparation of Magnetic Nanoparticles Coated with Chitosan
Directory of Open Access Journals (Sweden)
Karla M. Gregorio-Jauregui
2012-01-01
Full Text Available Preparation of magnetic nanoparticles coated with chitosan in one step by the coprecipitation method in the presence of different chitosan concentrations is reported here. Obtaining of magnetic superparamagnetic nanoparticles was confirmed by X-ray diffraction and magnetic measurements. Scanning transmission electron microscopy allowed to identify spheroidal nanoparticles with around 10-11 nm in average diameter. Characterization of the products by Fourier transform infrared spectroscopy demonstrated that composite chitosan-magnetic nanoparticles were obtained. Chitosan content in obtained nanocomposites was estimated by thermogravimetric analysis. The nanocomposites were tested in Pb2+ removal from a PbCl2 aqueous solution, showing a removal efficacy up to 53.6%. This work provides a simple method for chitosan-coated nanoparticles obtaining, which could be useful for heavy metal ions removal from water.
A high order single step-β method for nonlinear structural dynamic analysis
Institute of Scientific and Technical Information of China (English)
王焕定; 张永山; 王伟
2003-01-01
A high order single step-β algorithm, a new direct integration algorithm is proposed for solution ofequations of motion. Whenβ = 0. 5, the accuracy of displacement, velocity and acceleration is of forth order (atruncation error of △t5 ), and the algorithm is unconditionally stable and has no arithmetic damping and noovershooting. When ＞ 0. 5, and an arithmetic damping is adopted, the algorithm is again unconditionally stablewith a third order accuracy (a truncation error of △t4). The analyses run with typical examples show that thealgorithm proposed has higher speed, higher precision and better properties than other direct integrationmethods, such as Wilson-θ method and Newmark-β method in analysing linear elastic responses and nonlinearearthquake responses.
Guo, Wei; Jia, Kebin; Tian, Jie; Han, Dong; Liu, Xueyan; Wu, Ping; Feng, Jinchao; Yang, Xin
2012-03-01
Among many molecular imaging modalities, Bioluminescence tomography (BLT) is an important optical molecular imaging modality. Due to its unique advantages in specificity, sensitivity, cost-effectiveness and low background noise, BLT is widely studied for live small animal imaging. Since only the photon distribution over the surface is measurable and the photo propagation with biological tissue is highly diffusive, BLT is often an ill-posed problem and may bear multiple solutions and aberrant reconstruction in the presence of measurement noise and optical parameter mismatches. For many BLT practical applications, such as early detection of tumors, the volumes of the light sources are very small compared with the whole body. Therefore, the L1-norm sparsity regularization has been used to take advantage of the sparsity prior knowledge and alleviate the ill-posedness of the problem. Iterative shrinkage (IST) algorithm is an important research achievement in a field of compressed sensing and widely applied in sparse signal reconstruction. However, the convergence rate of IST algorithm depends heavily on the linear operator. When the problem is ill-posed, it becomes very slow. In this paper, we present a sparsity regularization reconstruction method for BLT based on the two-step iterated shrinkage approach. By employing Two-step strategy of iterative reweighted shrinkage (IRS) to improve IST, the proposed method shows faster convergence rate and better adaptability for BLT. The simulation experiments with mouse atlas were conducted to evaluate the performance of proposed method. By contrast, the proposed method can obtain the stable and comparable reconstruction solution with less number of iterations.
Institute of Scientific and Technical Information of China (English)
Ke Xiao; Shang-Bo Zhou; Wei-Wei Zhang
2008-01-01
For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method arediscussed.
Institute of Scientific and Technical Information of China (English)
Liu Jin-Cun; Hou Guo-Lin
2010-01-01
In this paper, the generalised two-dimensional differential transform method (DTM) of solving the time-fractional coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the generalised two-dimensional DTM is effective for the coupled equations.
Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G-Expansion Method
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Muhammad Shakeel
2014-01-01
Full Text Available The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method.
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Ravi Shanker Dubey
2015-01-01
Full Text Available An efficient approach based on homotopy perturbation method by using Sumudu transform is proposed to solve some linear and nonlinear space-time fractional Fokker-Planck equations (FPEs in closed form. The space and time fractional derivatives are considered in Caputo sense. The homotopy perturbation Sumudu transform method (HPSTM is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. Some examples show that the HPSTM is an effective tool for solving many space time fractional partial differential equations.
Deniz, Furkan Nur; Alagoz, Baris Baykant; Tan, Nusret; Atherton, Derek P
2016-05-01
This paper introduces an integer order approximation method for numerical implementation of fractional order derivative/integrator operators in control systems. The proposed method is based on fitting the stability boundary locus (SBL) of fractional order derivative/integrator operators and SBL of integer order transfer functions. SBL defines a boundary in the parametric design plane of controller, which separates stable and unstable regions of a feedback control system and SBL analysis is mainly employed to graphically indicate the choice of controller parameters which result in stable operation of the feedback systems. This study reveals that the SBL curves of fractional order operators can be matched with integer order models in a limited frequency range. SBL fitting method provides straightforward solutions to obtain an integer order model approximation of fractional order operators and systems according to matching points from SBL of fractional order systems in desired frequency ranges. Thus, the proposed method can effectively deal with stability preservation problems of approximate models. Illustrative examples are given to show performance of the proposed method and results are compared with the well-known approximation methods developed for fractional order systems. The integer-order approximate modeling of fractional order PID controllers is also illustrated for control applications.
Jin, Xinsheng; Zhang, John Z H; He, Xiao
2017-03-30
In this study, the electrostatically embedded generalized molecular fractionation with conjugate caps (concaps) method (EE-GMFCC) was employed for efficient linear-scaling quantum mechanical (QM) calculation of total energies of RNAs. In the EE-GMFCC approach, the total energy of RNA is calculated by taking a proper combination of the QM energy of each nucleotide-centric fragment with large caps or small caps (termed EE-GMFCC-LC and EE-GMFCC-SC, respectively) deducted by the energies of concaps. The two-body QM interaction energy between non-neighboring ribonucleotides which are spatially in close contact are also taken into account for the energy calculation. Numerical studies were carried out to calculate the total energies of a number of RNAs using the EE-GMFCC-LC and EE-GMFCC-SC methods at levels of the Hartree-Fock (HF) method, density functional theory (DFT), and second-order many-body perturbation theory (MP2), respectively. The results show that the efficiency of the EE-GMFCC-SC method is about 3 times faster than the EE-GMFCC-LC method with minimal accuracy sacrifice. The EE-GMFCC-SC method is also applied for relative energy calculations of 20 different conformers of two RNA systems using HF and DFT, respectively. Both single-point and relative energy calculations demonstrate that the EE-GMFCC method has deviations from the full system results of only a few kcal/mol.
2012-01-01
Nanochannel arrays were fabricated by the self-organized multi-electrolyte-step anodic aluminum oxide [AAO] method in this study. The anodization conditions used in the multi-electrolyte-step AAO method included a phosphoric acid solution as the electrolyte and an applied high voltage. There was a change in the phosphoric acid by the oxalic acid solution as the electrolyte and the applied low voltage. This method was used to produce self-organized nanochannel arrays with good regularity and circularity, meaning less power loss and processing time than with the multi-step AAO method. PMID:22333268
Cod Fractions - Methods of Measurement and Use in Wastewater Treatment Technology
Myszograj, Sylwia; Płuciennik-Koropczuk, Ewelina; Jakubaszek, Anita
2017-03-01
The paper presents the results of studies concerning the designation of COD fraction in raw wastewater. The research was conducted in four municipal mechanical-biological sewage treatment plants and one industrial sewage treatment plant. The following fractions of COD were determined: non-biodegradable (inert) soluble SI, biodegradable soluble fraction SS, particulate slowly degradable XS and particulate non-biodegradable XI. The methodology for determining the COD fraction was based on the ATV-A131 guidelines and Łomotowski-Szpindor methodology. The real concentration of fractions in raw wastewater and the percentage of each fraction in total COD are different from data reported in the literature.
Cod Fractions - Methods of Measurement and Use in Wastewater Treatment Technology
Directory of Open Access Journals (Sweden)
Myszograj Sylwia
2017-03-01
Full Text Available The paper presents the results of studies concerning the designation of COD fraction in raw wastewater. The research was conducted in four municipal mechanical-biological sewage treatment plants and one industrial sewage treatment plant. The following fractions of COD were determined: non-biodegradable (inert soluble SI, biodegradable soluble fraction SS, particulate slowly degradable XS and particulate non-biodegradable XI. The methodology for determining the COD fraction was based on the ATV-A131 guidelines and Łomotowski-Szpindor methodology. The real concentration of fractions in raw wastewater and the percentage of each fraction in total COD are different from data reported in the literature.
Two-Step Injection Method for Collecting Digital Evidence in Digital Forensics
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Nana Rachmana Syambas
2015-01-01
Full Text Available In digital forensic investigations, the investigators take digital evidence from computers, laptops or other electronic goods. There are many complications when a suspect or related person does not want to cooperate or has removed digital evidence. A lot of research has been done with the goal of retrieving data from flash memory or other digital storage media from which the content has been deleted. Unfortunately, such methods cannot guarantee that all data will be recovered. Most data can only be recovered partially and sometimes not perfectly, so that some or all files cannot be opened. This paper proposes the development of a new method for the retrieval of digital evidence called the Two-Step Injection method (TSI. It focuses on the prevention of the loss of digital evidence through the deletion of data by suspects or other parties. The advantage of this method is that the system works in secret and can be combined with other digital evidence applications that already exist, so that the accuracy and completeness of the resulting digital evidence can be improved. An experiment to test the effectiveness of the method was set up. The developed TSI system worked properly and had a 100% success rate.
Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
Jin, B.
2014-05-30
© 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞ (0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.
Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations
Jin, Bangti
2013-01-01
We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition ν(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., ν ∈ H2(Ω) ∩ H0 1(Ω) and ν ∈ L2(Ω). For the lumped mass method, the optimal L2-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. © 2013 Society for Industrial and Applied Mathematics.
Method of computation of energies in the fractional quantum Hall effect regime
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M.A. Ammar
2016-09-01
Full Text Available In a previous work, we reported exact results of energies of the ground state in the fractional quantum Hall effect (FQHE regime for systems with up to N_{e}=6 electrons at the filling factor ν=1/3 by using the method of complex polar coordinates. In this work, we display interesting computational details of the previous calculation and extend the calculation to N_{e}=7 electrons at ν=1/3. Moreover, similar exact results are derived at the filling ν=1/5 for systems with up to N_{e}=6 electrons. The results that we obtained by analytical calculation are in good agreement with their analogues ones derived by the method of Monte Carlo in a precedent work.
Assessment of New Calculation Method for Toxicological Sums-of-Fractions for Hanford Tank Wastes
Energy Technology Data Exchange (ETDEWEB)
Mahoney, Lenna A.
2006-09-26
The toxicological source terms used for potential accident assessment in the Tank Farms DSA are based on toxicological sums-of-fractions (SOFs) that were calculated in fiscal years 2002 and 2003 based on the Best Basis Inventory (BBI) from May 2002, using the method described by Cowley et al. (2003). The present report describes a modified SOF-calculation method that is to be used in future toxicological updates and assessments and compares its results (for the 2002 BBI) to those of the old method. The new method generally calculated different (usually larger) SOFs than the old. The dominant reason was the more conservative way in which the new method represents concentration variability, in that it uses the waste layer with the maximum SOF to represent the tank SOF. The old method had used a tank-average waste composition and SOF. Differences between thermodynamically modeled and BBI solubilities were the next most common reason for differences between old (modeled) and new (BBI) SOFs, particularly in the liquid phase. The solubility-related changes in SOF were roughly equally distributed between increases and decreases. Changes in the effective toxicities of TOC and lead, which resulted from changes in the compounds in which these analytes were considered to be present, were the third most common reason. These toxicity changes increased SOFs and therefore were in a conservative direction.
Raslan, K. R.; EL-Danaf, Talaat S.; Ali, Khalid K.
2017-07-01
In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.
Directory of Open Access Journals (Sweden)
Nina Ching Y. Wang
2012-01-01
Full Text Available Both the Massachusetts Department of Environmental Protection (MADEP and the Total Petroleum Hydrocarbon Criteria Working Group (TPHCWG developed fraction-based approaches for assessing human health risks posed by total petroleum hydrocarbon (TPH mixtures in the environment. Both organizations defined TPH fractions based on their expected environmental fate and by analytical chemical methods. They derived toxicity values for selected compounds within each fraction and used these as surrogates to assess hazard or risk of exposure to the whole fractions. Membership in a TPH fraction is generally defined by the number of carbon atoms in a compound and by a compound's equivalent carbon (EC number index, which can predict its environmental fate. Here, we systematically and objectively re-evaluate the assignment of TPH to specific fractions using comparative molecular field analysis and hierarchical clustering. The approach is transparent and reproducible, reducing inherent reliance on judgment when toxicity information is limited. Our evaluation of membership in these fractions is highly consistent (̃80% on average across various fractions with the empirical approach of MADEP and TPHCWG. Furthermore, the results support the general methodology of mixture risk assessment to assess both cancer and noncancer risk values after the application of fractionation.
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Kirsch Lee E
2008-07-01
Full Text Available Abstract Background Glucagon is a peptide hormone with many uses as a therapeutic agent, including the emergency treatment of hypoglycemia. Physical instability of glucagon in solution leads to problems with the manufacture, formulation, and delivery of this pharmaceutical product. Glucagon has been shown to aggregate and form fibrils and gels in vitro. Small oligomeric precursors serve to initiate and nucleate the aggregation process. In this study, these initial aggregates, or seed nuclei, are characterized in bulk solution using light scattering methods and field-flow fractionation. Results High molecular weight aggregates of glucagon were detected in otherwise monomeric solutions using light scattering techniques. These aggregates were detected upon initial mixing of glucagon powder in dilute HCl and NaOH. In the pharmaceutically relevant case of acidic glucagon, the removal of aggregates by filtration significantly slowed the aggregation process. Field-flow fractionation was used to separate aggregates from monomeric glucagon and determine relative mass. The molar mass of the large aggregates was shown to grow appreciably over time as the glucagon solutions gelled. Conclusion The results of this study indicate that initial glucagon solutions are predominantly monomeric, but contain small quantities of large aggregates. These results suggest that the initial aggregates are seed nuclei, or intermediates which catalyze the aggregation process, even at low concentrations.
Fast Measurement of Methanol Concentration in Ionic Liquids by Potential Step Method
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Michael L. Hainstock
2015-01-01
Full Text Available The development of direct methanol fuel cells required the attention to the electrolyte. A good electrolyte should not only be ionic conductive but also be crossover resistant. Ionic liquids could be a promising electrolyte for fuel cells. Monitoring methanol was critical in several locations in a direct methanol fuel cell. Conductivity could be used to monitor the methanol content in ionic liquids. The conductivity of 1-butyl-3-methylimidazolium tetrafluoroborate had a linear relationship with the methanol concentration. However, the conductivity was significantly affected by the moisture or water content in the ionic liquid. On the contrary, potential step could be used in sensing methanol in ionic liquids. This method was not affected by the water content. The sampling current at a properly selected sampling time was proportional to the concentration of methanol in 1-butyl-3-methylimidazolium tetrafluoroborate. The linearity still stood even when there was 2.4 M water present in the ionic liquid.
Suleimanov, Yury V
2015-01-01
We present a simple protocol which allows fully automated discovery of elementary chemical reaction steps using in cooperation single- and double-ended transition-state optimization algorithms - the freezing string and Berny optimization methods, respectively. To demonstrate the utility of the proposed approach, the reactivity of several systems of combustion and atmospheric chemistry importance is investigated. The proposed algorithm allowed us to detect without any human intervention not only "known" reaction pathways, manually detected in the previous studies, but also new, previously "unknown", reaction pathways which involve significant atom rearrangements. We believe that applying such a systematic approach to elementary reaction path finding will greatly accelerate the possibility of discovery of new chemistry and will lead to more accurate computer simulations of various chemical processes.
Superlinear/Quadratic One-step Smoothing Newton Method for P0-NCP
Institute of Scientific and Technical Information of China (English)
Li Ping ZHANG; Ji Ye HAN; Zheng Hai HUANG
2005-01-01
We propose a one-step smoothing Newton method for solving the non-linear complementarity problem with P0-function (P0-NCP) based on the smoothing symmetric perturbed Fisher function (for short, denoted as the SSPF-function). The proposed algorithm has to solve only one linear system of equations and performs only one line search per iteration. Without requiring any strict complementarity assumption at the P0-NCP solution, we show that the proposed algorithm converges globally and superlinearly under mild conditions. Furthermore, the algorithm has local quadratic convergence under suitable conditions. The main feature of our global convergence results is that we do not assume a priori the existence of an accumulation point. Compared to the previous literatures, our algorithm has stronger convergence results under weaker conditions.
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Shulin Wu
2009-01-01
Full Text Available We propose a new idea to construct an effective algorithm to compute the minimal positive solution of the nonsymmetric algebraic Riccati equations arising from transport theory. For a class of these equations, an important feature is that the minimal positive solution can be obtained by computing the minimal positive solution of a couple of fixed-point equations with vector form. Based on the fixed-point vector equations, we introduce a new algorithm, namely, two-step relaxation Newton, derived by combining two different relaxation Newton methods to compute the minimal positive solution. The monotone convergence of the solution sequence generated by this new algorithm is established. Numerical results are given to show the advantages of the new algorithm for the nonsymmetric algebraic Riccati equations in vector form.
Ionic liquid-stabilized non-spherical gold nanofluids synthesized using a one-step method.
Zhang, Hao; Cui, Hua; Yao, Shiwei; Zhang, Kelong; Tao, Haikun; Meng, Haibo
2012-10-23
Ionic liquid (IL)-stabilized non-spherical gold nanofluids have been synthesized by a one-step method in aqueous solution. The whole reaction proceeded in room temperature. In the presence of amino-functionalized ionic liquids, gold nanofluids with long-wave surface plasmon resonance (SPR) absorption (>600 nm) could be obtained by adopting tannic acid as the reductant. The specific SPR absorption was related to the non-spherical gold nanoparticles including gold triangle, decahedra, and icosahedra nanocrystals. All the nanocrystals were observed by transmission electron microscopy. It was deduced that the formation of non-spherical gold nanofluids was related to the hydroxyls in tannic acid while IL acted as the synthesis template.
Suleimanov, Yury V; Green, William H
2015-09-08
We present a simple protocol which allows fully automated discovery of elementary chemical reaction steps using in cooperation double- and single-ended transition-state optimization algorithms--the freezing string and Berny optimization methods, respectively. To demonstrate the utility of the proposed approach, the reactivity of several single-molecule systems of combustion and atmospheric chemistry importance is investigated. The proposed algorithm allowed us to detect without any human intervention not only "known" reaction pathways, manually detected in the previous studies, but also new, previously "unknown", reaction pathways which involve significant atom rearrangements. We believe that applying such a systematic approach to elementary reaction path finding will greatly accelerate the discovery of new chemistry and will lead to more accurate computer simulations of various chemical processes.
A modified split-step Fourier method for optical pulse propagation with polarization mode dispersion
Institute of Scientific and Technical Information of China (English)
饶敏; 孙小菡; 张明德
2003-01-01
A modified split-step Fourier method (SSFM) is presented to solve the coupled nonlinear Schrǒdinger equation (CNLS) that can be used to model high-speed pulse propagation in optical fibres with polarization mode dispersion (PMD). We compare our approach with the SSFM and démonstrate that our approach is much faster with no loss of accuracy. We discuss the pulse distortion and system Q-factor of non-return-to-zero (NRZ), return-to-zero (RZ) and pre-chirped RZ (CRZ) formats in the presence of high PMD through this approach. The simulation results show that CRZ pulses are the most tolerant to high PMD wlues and the extinct ratio has a great impact on the transmission performance.
Distribution of photon strength in nuclei by a method of two-step cascades
Energy Technology Data Exchange (ETDEWEB)
Becvar, F.; Cejnar, P. (Karlova Univ., Prague (Czechoslovakia). Fakulta Matematicko-Fyzikalni); Chrien, R.E. (Brookhaven National Lab., Upton, NY (USA)); Kopecky, J. (Netherlands Energy Research Foundation, Petten (Netherlands))
1990-01-01
The applicability of sum-coincidence measurements of two-step cascade {gamma}-ray spectra to the determination of photon strength functions at intermediate {gamma}-ray energies (3 or 4 MeV) is discussed. An experiment based on thermal neutron capture in Nd was undertaken at the Brookhaven National Laboratory High Flux Beam Reactor to test this model. To understand the role of various uncertainties in similar experiments a series of model calculations was performed. We present an analysis of our experimental data which demonstrates the high sensitivity of the method to E1 and M1 photon strength functions. Our experimental data are in sharp contradiction to those expected from an E1 photon strength distributed according to the classical Lorentzian form with an energy invariant damping width. An alternative distribution of Kadmenskij et al., which violates Brink's Hypothesis, is strongly preferred. 13 refs., 5 figs.
Improved morphology control using a modified two-step method for efficient perovskite solar cells.
Bi, Dongqin; El-Zohry, Ahmed M; Hagfeldt, Anders; Boschloo, Gerrit
2014-11-12
A two-step wet chemical synthesis method for methylammonium lead(II) triiodide (CH3NH3PbI3) perovskite is further developed for the preparation of highly reproducible solar cells, with the following structure: fluorine-doped tin oxide (FTO)/TiO2 (compact)/TiO2 (mesoporous)/CH3NH3PbI3/spiro-OMeTAD/Ag. The morphology of the perovskite layer could be controlled by careful variation of the processing conditions. Specifically, by modifying the drying process and inclusion of a dichloromethane treatment, more uniform films could be prepared, with longer emission lifetime in the perovskite material and longer electron lifetime in solar cell devices, as well as faster electron transport and enhanced charge collection at the selective contacts. Solar cell efficiencies up to 13.5% were obtained.
Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise.
Liu, Yingjun; Liu, Yong; Wang, Kun; Jiang, Tianzi; Yang, Lihua
2009-12-01
Fractional Gaussian noise (fGn) is an important and widely used self-similar process, which is mainly parametrized by its Hurst exponent (H) . Many researchers have proposed methods for estimating the Hurst exponent of fGn. In this paper we put forward a modified periodogram method for estimating the Hurst exponent based on a refined approximation of the spectral density function. Generalizing the spectral exponent from a linear function to a piecewise polynomial, we obtained a closer approximation of the fGn's spectral density function. This procedure is significant because it reduced the bias in the estimation of H . Furthermore, the averaging technique that we used markedly reduced the variance of estimates. We also considered the asymptotical unbiasedness of the method and derived the upper bound of its variance and confidence interval. Monte Carlo simulations showed that the proposed estimator was superior to a wavelet maximum likelihood estimator in terms of mean-squared error and was comparable to Whittle's estimator. In addition, a real data set of Nile river minima was employed to evaluate the efficiency of our proposed method. These tests confirmed that our proposed method was computationally simpler and faster than Whittle's estimator.
Yang, Qingxia; Xu, Jun; Cao, Binggang; Li, Xiuqing
2017-01-01
Identification of internal parameters of lithium-ion batteries is a useful tool to evaluate battery performance, and requires an effective model and algorithm. Based on the least square genetic algorithm, a simplified fractional order impedance model for lithium-ion batteries and the corresponding parameter identification method were developed. The simplified model was derived from the analysis of the electrochemical impedance spectroscopy data and the transient response of lithium-ion batteries with different states of charge. In order to identify the parameters of the model, an equivalent tracking system was established, and the method of least square genetic algorithm was applied using the time-domain test data. Experiments and computer simulations were carried out to verify the effectiveness and accuracy of the proposed model and parameter identification method. Compared with a second-order resistance-capacitance (2-RC) model and recursive least squares method, small tracing voltage fluctuations were observed. The maximum battery voltage tracing error for the proposed model and parameter identification method is within 0.5%; this demonstrates the good performance of the model and the efficiency of the least square genetic algorithm to estimate the internal parameters of lithium-ion batteries. PMID:28212405
Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise
Liu, Yingjun; Liu, Yong; Wang, Kun; Jiang, Tianzi; Yang, Lihua
2009-12-01
Fractional Gaussian noise (fGn) is an important and widely used self-similar process, which is mainly parametrized by its Hurst exponent (H) . Many researchers have proposed methods for estimating the Hurst exponent of fGn. In this paper we put forward a modified periodogram method for estimating the Hurst exponent based on a refined approximation of the spectral density function. Generalizing the spectral exponent from a linear function to a piecewise polynomial, we obtained a closer approximation of the fGn’s spectral density function. This procedure is significant because it reduced the bias in the estimation of H . Furthermore, the averaging technique that we used markedly reduced the variance of estimates. We also considered the asymptotical unbiasedness of the method and derived the upper bound of its variance and confidence interval. Monte Carlo simulations showed that the proposed estimator was superior to a wavelet maximum likelihood estimator in terms of mean-squared error and was comparable to Whittle’s estimator. In addition, a real data set of Nile river minima was employed to evaluate the efficiency of our proposed method. These tests confirmed that our proposed method was computationally simpler and faster than Whittle’s estimator.
Yang, Qingxia; Xu, Jun; Cao, Binggang; Li, Xiuqing
2017-01-01
Identification of internal parameters of lithium-ion batteries is a useful tool to evaluate battery performance, and requires an effective model and algorithm. Based on the least square genetic algorithm, a simplified fractional order impedance model for lithium-ion batteries and the corresponding parameter identification method were developed. The simplified model was derived from the analysis of the electrochemical impedance spectroscopy data and the transient response of lithium-ion batteries with different states of charge. In order to identify the parameters of the model, an equivalent tracking system was established, and the method of least square genetic algorithm was applied using the time-domain test data. Experiments and computer simulations were carried out to verify the effectiveness and accuracy of the proposed model and parameter identification method. Compared with a second-order resistance-capacitance (2-RC) model and recursive least squares method, small tracing voltage fluctuations were observed. The maximum battery voltage tracing error for the proposed model and parameter identification method is within 0.5%; this demonstrates the good performance of the model and the efficiency of the least square genetic algorithm to estimate the internal parameters of lithium-ion batteries.
Method for six-legged robot stepping on obstacles by indirect force estimation
Xu, Yilin; Gao, Feng; Pan, Yang; Chai, Xun
2016-07-01
Adaptive gaits for legged robots often requires force sensors installed on foot-tips, however impact, temperature or humidity can affect or even damage those sensors. Efforts have been made to realize indirect force estimation on the legged robots using leg structures based on planar mechanisms. Robot Octopus III is a six-legged robot using spatial parallel mechanism(UP-2UPS) legs. This paper proposed a novel method to realize indirect force estimation on walking robot based on a spatial parallel mechanism. The direct kinematics model and the inverse kinematics model are established. The force Jacobian matrix is derived based on the kinematics model. Thus, the indirect force estimation model is established. Then, the relation between the output torques of the three motors installed on one leg to the external force exerted on the foot tip is described. Furthermore, an adaptive tripod static gait is designed. The robot alters its leg trajectory to step on obstacles by using the proposed adaptive gait. Both the indirect force estimation model and the adaptive gait are implemented and optimized in a real time control system. An experiment is carried out to validate the indirect force estimation model. The adaptive gait is tested in another experiment. Experiment results show that the robot can successfully step on a 0.2 m-high obstacle. This paper proposes a novel method to overcome obstacles for the six-legged robot using spatial parallel mechanism legs and to avoid installing the electric force sensors in harsh environment of the robot's foot tips.
Method for Six-Legged Robot Stepping on Obstacles by Indirect Force Estimation
Institute of Scientific and Technical Information of China (English)
XU Yilin; GAO Feng; PAN Yang; CHAI Xun
2016-01-01
Adaptive gaits for legged robots often requires force sensors installed on foot-tips, however impact, temperature or humidity can affect or even damage those sensors. Efforts have been made to realize indirect force estimation on the legged robots using leg structures based on planar mechanisms. Robot Octopus III is a six-legged robot using spatial parallel mechanism(UP-2UPS) legs. This paper proposed a novel method to realize indirect force estimation on walking robot based on a spatial parallel mechanism. The direct kinematics model and the inverse kinematics model are established. The force Jacobian matrix is derived based on the kinematics model. Thus, the indirect force estimation model is established. Then, the relation between the output torques of the three motors installed on one leg to the external force exerted on the foot tip is described. Furthermore, an adaptive tripod static gait is designed. The robot alters its leg trajectory to step on obstacles by using the proposed adaptive gait. Both the indirect force estimation model and the adaptive gait are implemented and optimized in a real time control system. An experiment is carried out to validate the indirect force estimation model. The adaptive gait is tested in another experiment. Experiment results show that the robot can successfully step on a 0.2 m-high obstacle. This paper proposes a novel method to overcome obstacles for the six-legged robot using spatial parallel mechanism legs and to avoid installing the electric force sensors in harsh environment of the robot’s foot tips.
Institute of Scientific and Technical Information of China (English)
Wang Zhao-Kui; Lin Kui-Xun; Lin Xuan-Ying; Qiu Gui-Ming; Zhu Zu-Song
2005-01-01
A newly established movable sampling apparatus of mass spectrometer is used to measure the spatial distribution of depletion fraction of silane plasma. A straight-line fit method of deducing the depletion fraction of silane is proposed.Theoretical analysis and test results demonstrate that the proposed new method is universal and more accurate than the existing one. There exist a largest peak near the middle of two electrodes and two peaks near the electrodes in the spatial distribution of silane depletion fraction, which are related to the distribution of electric field and the silane plasma sheaths.
Single-step blood direct PCR: A robust and rapid method to diagnose triplet repeat disorders.
Singh, Inder; Swarup, Vishnu; Shakya, Sunil; Goyal, Vinay; Faruq, Mohammed; Srivastava, Achal Kumar
2017-08-15
DNA extraction prior to polymerase chain reaction (PCR) amplification in genetic diagnoses of triplet repeat disorders (TRDs) is tedious and labour-intensive and has the limitations of sample contamination with foreign DNA, including that from preceding samples. Therefore, we aimed to develop a rapid, robust, and cost-effective method for expeditious genetic investigation of TRDs from whole blood as a DNA template. Peripheral blood samples were collected from 70 clinically suspected patients of progressive ataxia. The conventional method using genomic DNA and single-step Blood-Direct PCR (BD-PCR) method with just 2μl of whole blood sample were tested to amplify triplet repeat expansion in genes related to spinocerebellar ataxia (SCA) types 1, 2, 3, 12 and Friedreich's ataxia (FRDA). Post-PCR, the allele sizes were mapped and repeat numbers were calculated using GeneMapper and macros run in Microsoft Excel programmes. Successful amplification of target regions was achieved in all samples by both methods. The frequency of the normal and mutated allele was concordant between both methods, diagnosing 37% positive for a mutation in either of the candidate genes. The BD-PCR resulted in higher intensities of product peaks of normal and pathogenic alleles. The nearly-accurate sizing of the normal and expanded allele was achieved in a shorter time (4-5h), without DNA extraction and any risk of cross contamination, which suggests the BD-PCR to be a reliable, inexpensive, and rapid method to confirm TRDs. This technique can be introduced in routine diagnostic procedures of other tandem repeat disorders. Copyright © 2017 Elsevier B.V. All rights reserved.
Series Solution for the Time-Fractional Coupled mKdV Equation Using the Homotopy Analysis Method
Directory of Open Access Journals (Sweden)
J. F. Gómez-Aguilar
2016-01-01
Full Text Available We present new analytical approximated solutions for the space-time fractional nonlinear partial differential coupled mKdV equation. A homotopy analysis method is considered to obtain an infinite series solution. The effectiveness of this method is demonstrated by finding exact solutions of the fractional equation proposed, for the special case when the limit of the integral order of the time derivative is considered. The comparison shows a precise agreement between these solutions.
ZnO micro-nano composite hydrophobic film prepared by the three-step method
Institute of Scientific and Technical Information of China (English)
Ma Kai; Li Hua; Zhang Han; Xu Xiao-Liang; Gong Mao-Gang; Yang Zhou
2009-01-01
The hydrophobicity of the lotus leaf is mainly due to its surface micro-nano composite structure. In order to mimic the lotus structure, ZnO micro-nano composite hydrophobic films were prcpared via the three-step method. On thin buffer films of SiO2, which were first fabricated on glass substrates by the sol gel dip-coating method, a ZnO seed layer was deposited via RF magnetron sputtering. Then two different ZnO films, micro-nano and micro-only flower-like structures, were grown by the hydrothermal method. The prepared films have different hydrophobic properties after surface modification. The structures of the obtained ZnO films were characterized using x-ray diffraction and field-emission scanning electron microscopy. A conclusion that a micro-nano composite structure is more beneficial to hydrophobicity than a micro-only structure was obtained through research into the effect of structure on hydrophobic properties.
ZnO micro-nano composite hydrophobic film prepared by the three-step method
Ma, Kai; Li, Hua; Zhang, Han; Xu, Xiao-Liang; Gong, Mao-Gang; Yang, Zhou
2009-05-01
The hydrophobicity of the lotus leaf is mainly due to its surface micro-nano composite structure. In order to mimic the lotus structure, ZnO micro-nano composite hydrophobic films were prepared via the three-step method. On thin buffer films of SiO2, which were first fabricated on glass substrates by the sol-gel dip-coating method, a ZnO seed layer was deposited via RF magnetron sputtering. Then two different ZnO films, micro-nano and micro-only flower-like structures, were grown by the hydrothermal method. The prepared films have different hydrophobic properties after surface modification. The structures of the obtained ZnO films were characterized using x-ray diffraction and field-emission scanning electron microscopy. A conclusion that a micro-nano composite structure is more beneficial to hydrophobicity than a micro-only structure was obtained through research into the effect of structure on hydrophobic properties.
A method for detecting the presence of organic fraction in nucleation mode sized particles
Vaattovaara, P.; Räsänen, M.; Kühn, T.; Joutsensaari, J.; Laaksonen, A.
2005-12-01
New particle formation and growth has a very important role in many climate processes. However, the overall knowlegde of the chemical composition of atmospheric nucleation mode (particle diameter, dammonium bisulfate and sulfuric acid with sulfuric acid mass fraction ≤33% show no growth at 85% saturation ratio. In contrast, 10 nm particles composed of various oxidized organic compounds of atmospheric relevance are able to grow in those conditions. These discoveries indicate that it is possible to detect the presence of organics in atmospheric nucleation mode sized particles using the UFO-TDMA method. In the future, the UFO-TDMA is expected to be an important aid to describe the composition of atmospheric newly-formed particles.
Dynamic Flow-through Methods for Metal Fractionation in Environmental Solid Samples
DEFF Research Database (Denmark)
Miró, Manuel; Hansen, Elo Harald; Petersen, Roongrat
occurring processes always take place under dynamic conditions, recent trends have been focused on the development of alternative flow-through dynamic methods aimed at mimicking environmental events more correctly than their classical extraction counterparts. In this lecture particular emphasis is paid......Accummulation of metal ions in different compartments of the biosphere and their possible mobilization under changing environmental conditions induce a pertubation of the ecosystem and may cause adverse health effects. Nowadays, it is widely recognized that the information on total content...... the ecotoxicological significance of metal ions in solid environmental samples. The background of end-over-end fractionation for releasing metal species bound to particular soil phases is initially discussed, its relevant features and limitations being thoroughly described. However, taking into account that naturally...
Fractional complex transform for fractional differential equations
National Research Council Canada - National Science Library
Lİ, Zheng Biao; HE, Ji Huan
2010-01-01
Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily...
Directory of Open Access Journals (Sweden)
Huitzilin Yépez-Martínez
2015-01-01
Full Text Available The fractional derivatives in the sense of the modified Riemann-Liouville derivative and Feng’s first integral method are employed to obtain the exact solutions of the nonlinear space-time fractional ZKBBM equation and the nonlinear space-time fractional generalized Fisher equation. The power of this manageable method is presented by applying it to the above equations. Our approach provides first integrals in polynomial form with high accuracy. Exact analytical solutions are obtained through establishing first integrals. The present method is efficient and reliable, and it can be used as an alternative to establish new solutions of different types of fractional differential equations applied in mathematical physics.
Institute of Scientific and Technical Information of China (English)
Si Gang-Quan; Sun Zhi-Yong; Zhang Yan-Bin
2011-01-01
This paper investigates the synchronization between integer-order and fractional-order chaotic systems.By introducing fractional-order operators into the controllers,the addressed problem is transformed into a synchronization one among integer-order systems.A novel general method is presented in the paper with rigorous proof.Based on this method,effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order,and for the synchronization between an integer-order Chen system and a fractional-order Liu system.Numerical results,which agree well with the theoretical analyses,are also given to show the effectiveness of this method.
Wei, Yuquan; Zhao, Yue; Wang, Huan; Lu, Qian; Cao, Zhenyu; Cui, Hongyang; Zhu, Longji; Wei, Zimin
2016-12-01
The study was conducted to investigate the influence of biochar and/or phosphate-solubilizing bacteria (PSB) inoculants on microbial biomass, bacterial community composition and phosphorus (P) fractions during kitchen waste composting amended with rock phosphate (RP). There were distinct differences in the physic-chemical parameters, the proportion of P fractions and bacterial diversity in different treatments. The contribution of available P fractions increased during composting especially in the treatment with the addition of PSB and biochar. Redundancy analysis showed that bacterial compositions were significantly influenced by P content, inoculation and biochar. Variance partitioning further showed that synergy of inoculated PSB and indigenous bacterial communities and the joint effect between biochar and bacteria explained the largest two proportion of the variation in P fractions. Therefore, the combined application of PSB and biochar to improve the inoculation effect and an optimized regulating method were suggested based on the distribution of P fractions.
Heidenreich, J. E., III; Thiemens, M. H.
1985-01-01
A non-mass dependent (NoMaD) oxygen isotope effect is demonstrated in the dissociation of CO2 similar to that observed in the electrosynthesis of ozone. The molecular oxygen produced carries the signature of two separate isotopic fractionation processes; a mass-dependent fractionation probably due to CO2 + O isotopic exchange, and a secondary NoMaD fractionation (delta O-17 = 0.97 + or - 0.09 delta O-18, with the O2 depleted in O-17 and O-18). It is suggested that the effect is due to either the formation or relaxation of ozone in an excited electronic state. This represents the latest advance in the understanding of chemical NoMaD effects which may be essential to the explanation of non-mass-dependent fractionations observed in meteorites.
A New Void Fraction Measurement Method for Gas-Liquid Two-Phase Flow in Small Channels
Directory of Open Access Journals (Sweden)
Huajun Li
2016-01-01
Full Text Available Based on a laser diode, a 12 × 6 photodiode array sensor, and machine learning techniques, a new void fraction measurement method for gas-liquid two-phase flow in small channels is proposed. To overcome the influence of flow pattern on the void fraction measurement, the flow pattern of the two-phase flow is firstly identified by Fisher Discriminant Analysis (FDA. Then, according to the identification result, a relevant void fraction measurement model which is developed by Support Vector Machine (SVM is selected to implement the void fraction measurement. A void fraction measurement system for the two-phase flow is developed and experiments are carried out in four different small channels. Four typical flow patterns (including bubble flow, slug flow, stratified flow and annular flow are investigated. The experimental results show that the development of the measurement system is successful. The proposed void fraction measurement method is effective and the void fraction measurement accuracy is satisfactory. Compared with the conventional laser measurement systems using standard laser sources, the developed measurement system has the advantages of low cost and simple structure. Compared with the conventional void fraction measurement methods, the proposed method overcomes the influence of flow pattern on the void fraction measurement. This work also provides a good example of using low-cost laser diode as a competent replacement of the expensive standard laser source and hence implementing the parameter measurement of gas-liquid two-phase flow. The research results can be a useful reference for other researchers’ works.
Directory of Open Access Journals (Sweden)
Zongqi Liang
2009-01-01
Full Text Available We analyze a class of large time-stepping Fourier spectral methods for the semiclassical limit of the defocusing Nonlinear Schrödinger equation and provide highly stable methods which allow much larger time step than for a standard implicit-explicit approach. An extra term, which is consistent with the order of the time discretization, is added to stabilize the numerical schemes. Meanwhile, the first-order and second-order semi-implicit schemes are constructed and analyzed. Finally the numerical experiments are performed to demonstrate the effectiveness of the large time-stepping approaches.
Ag-doped ZnO nanorods synthesized by two-step method
Institute of Scientific and Technical Information of China (English)
Chen Xian-Mei; Ji Yong; Gao Xiao-Yong; Zhao Xian-Wei
2012-01-01
A two-step method is adopted to synthesize Ag-doped ZnO nanorods.A ZnO seed layer is first prepared on a glass substrate by thermal decomposition of zinc acetate.Ag-doped ZnO nanorods are then assembled on the ZnO seed layer using the hydrothermal method.The influences of the molar percentage of Ag ions to Zn ions (RAg/Zn) on the structural and optical properties of the ZnO nanorods obtained are carefully studied using X-ray diffractometry,scanning electron microscopy and spectrophotometry.Results indicate that Ag ions enter into the crystal lattice through the substitution of Zn ions.The 〈002〉 c-axis-preferred orientation of the ZnO nanorods decreases as RAg/Zn increases.At RAg/Zn ＞ 1.0％,ZnO nanorods lose their c-axis-preferred orientation and generate Ag precipitates from the ZnO crystal lattice.The average transmissivity in the visible region first increases and then decreases as RAg/Zn increases.The absorption edge is first blue shifted and then red shifted.The influence of Ag doping on the average head face,and axial dimensions of the ZnO nanorods may be optimized to improve the average transmissivity at RAg/Zn ＜ 1.0％.
Improved adhesion of superhydrophobic layer on metal surfaces via one step spraying method
Directory of Open Access Journals (Sweden)
Wael I. El Dessouky
2017-03-01
Full Text Available Superhydrophobic metal substrates have been fabricated by a simple spraying method. The processes of decreasing surface free energy and increasing surface roughness have been accomplished in one step via the addition of functionalized silica (silica nano particles with octyltriethoxysilane to adhesive polymer. The method is simple, cost-effective and can be applied on the large industrial scale. Scanning electron microscopy (SEM was used for surface morphology analysis, showing the roughness produced by surface treatment. The wettability of the micro-nano silica film varied from hydrophilicity (water contact angle 88° to superhydrophobicity (water contact angle 156.9°, while sliding contact angles dramatically decreased (<5° by adding Functionalized silica and/or adhesive polymer. Roughness increased with silica increment which improves the wettability. The coatings were electrochemically characterized by electrochemical impedance spectroscopy (EIS and Tafel polarization curves; it was found that both systems had good performance against corrosion in 3.5% sodium chloride solution. Furthermore, the stability of the coated layer on copper substrate was investigated.
Application of the Taguchi method to the analysis of the deposition step in microarray production.
Severgnini, Marco; Pattini, Linda; Consolandi, Clarissa; Rizzi, Ermanno; Battaglia, Cristina; De Bellis, Gianluca; Cerutti, Sergio
2006-09-01
Every microarray experiment is affected by many possible sources of variability that may even corrupt biological evidence on analyzed sequences. We applied a "Taguchi method" strategy, based on the use of orthogonal arrays to optimize the deposition step of oligonucleotide sequences on glass slides. We chose three critical deposition parameters (humidity, surface, and buffer) at two levels each, in order to establish optimum settings. A L8 orthogonal array was used in order to monitor both the main effects and interactions on the deposition of a 25 mer oligonucleotide hybridized to its fluorescent-labeled complementary. Signal-background ratio and deposition homogeneity in terms of mean intensity and spot diameter were considered as significant outputs. An analysis of variance (ANOVA) was applied to raw data and to mean results for each slide and experimental run. Finally we calculated an overall evaluation coefficient to group together important outputs in one number. Environmental humidity and surface-buffer interaction were recognized as the most critical factors, for which a 50% humidity, associated to a chitosan-covered slide and a sodium phosphate + 25% dimethyl sulfoxide (DMSO) buffer gave best performances. Our results also suggested that Taguchi methods can be efficiently applied in optimization of microarray procedures.
Numerical simulation of flow over backward-facing step using parallel multi-block compact method
Energy Technology Data Exchange (ETDEWEB)
Esfahanian, V.; Torabi, F.; Khajavi Rad, A.; Babaee, H. [Univ. of Tehran, Mechanical Engineering Dept., Tehran (Iran, Islamic Republic of)]. E-mail: evahid@ut.ac.ir
2005-07-01
In this study the accurate location of separation and reattachment points in the flow over backward-facing step have been determined for 100
Zavarzina, A. G.; Vanifatova, N. G.; Stepanov, A. A.
2008-12-01
Humic acids (HAs) represent heterogeneous and polydisperse mixture of molecules that differ in their chemical structure, composition, and functional properties. Fractionation of HAs is of key importance for understanding their interactions with various organic and inorganic compounds, for studying their physiological activity, and for predicting their behavior in natural environments and agroecosystems. Existing fractionation methods are rather laborious and time consuming, which limits their application in fundamental science and industry. It is shown that fractionation of humic acids with ammonium sulfate ensures their preparative separation with respect to (a) hydrophobicity, (b) molecular size, and (c) charge dependent on the amount of functional groups. Salting out at the lowest and highest degrees of saturation with ammonium sulfate, upon which precipitation of the molecules occurs, makes it possible to separate humic acids into functionally different high-molecular-weight/hydrophobic and low-molecular-weight/hydrophilic fractions. The first fraction is characterized by a lower electrophoretic mobility than the second fraction. The weight percentage of the components coagulated at the lowest degree of salt saturation can be used as a quantitative parameter for comparing hydrophobic properties of humic acids. Salting out is recommended as a fast, simple, and cheap alternative to chromatographic methods for preparative separation of humic acids if large amounts of functionally different fractions need to be obtained.
Institute of Scientific and Technical Information of China (English)
Xiao-Bing LI; Yun-Hao CHEN; Hua YANG; Yun-Xia ZHANG
2005-01-01
As one of the important vegetation parameters, vegetation fractional coverage (VFC) is more difficult to measure accurately among a good many parameters of plant communities. The temperate typical steppe in the north of China was chosen for investigation in the present study and a digital camera was used to measure herb community coverage in the field, adopting methods of ocular estimation, gridding measurement, visual interpretation, supervised classification, and information extraction of color spatial transformation to calculate the VFC of images captured by the digital camera. In addition VFC calculated by various methods was analyzed and compared VFC, enabling us to propose an effective method for measuring VFC using a digital camera. The results of the present study indicate that: (i) as two common useful and effective methods of measuring VFC with a digital camera, not only does the error of estimated values of visual estimation and supervised classification vary considerably, but the degree of automatization is very low and depends, to a great extent, on the manipulator; (ii) although the method of visual interpretation may assure the precision of the calculated VFC and enable the precision of results obtained using other methods to be determined, as far as large quantities of data are concerned, this method has the disadvantages of wasting time and energy, and the applications of this method are limited; (iii) the precision and stability of VFC calculated using the grid and node method are superior to those of visual estimation and supervised classification and inferior to those of visual interpretation, but, as for visual interpretation and supervised classification, gridding measurements are difficult to apply in practice because they are not time efficient;and (iv) in terms of the precision of calculation of the VFC, an information-extracting model based on an intensity, hue, saturation (IHS) color space-multi-component series segmentation strategy is
Bahşı, Ayşe Kurt; Yalçınbaş, Salih
2016-01-01
In this study, the Fibonacci collocation method based on the Fibonacci polynomials are presented to solve for the fractional diffusion equations with variable coefficients. The fractional derivatives are described in the Caputo sense. This method is derived by expanding the approximate solution with Fibonacci polynomials. Using this method of the fractional derivative this equation can be reduced to a set of linear algebraic equations. Also, an error estimation algorithm which is based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation algorithm. If the exact solution of the problem is not known, the absolute error function of the problems can be approximately computed by using the Fibonacci polynomial solution. By using this error estimation function, we can find improved solutions which are more efficient than direct numerical solutions. Numerical examples, figures, tables are comparisons have been presented to show efficiency and usable of proposed method.
Directory of Open Access Journals (Sweden)
Caroline Morito Pereira
2016-11-01
Full Text Available Storage processes have acquired great importance in the modern supply chain, which demands better performance by warehouses in organizing goods in order to achieve high utilization of physical space and to facilitate the movement of materials. Sizing the storage area and organizing items strategically in storage positions ensures better efficiency in picking processes and customer service. In this context, this study aims to propose a method for defining the positions of pallets assigned to fractioned picking orders in a warehouse according to criteria based on popularity and turnover of the products. This method will be presented in a case study, and the pallets will be positioned in the warehouse in accordance with the results obtained. The gains in terms of order picking productivity and optimization of storage positions will then be measured. Research in this area has grown rapidly in recent years, but the combination of sizing items and classifying these items has not been closely explored. Thus, it is believed that the results could contribute to future research, bridging academic researchers and warehouse professionals.
Analysis of transpression within contractional fault steps using finite-element method
Nabavi, Seyed Tohid; Alavi, Seyed Ahmad; Mohammadi, Soheil; Ghassemi, Mohammad Reza; Frehner, Marcel
2017-03-01
Two-dimensional finite-element modelling of elastic Newtonian rheology is used to compute stress distribution and strain localization patterns in a transpression zone between two pre-existing right-stepping, left-lateral strike-slip fault segments. Three representative fault segment interactions are modelled: underlapping, neutral, and overlapping. The numerical results indicate that at the onset of deformation, displacement vectors are oblique to the regional compression direction (20-90°). The orientations of the local σ1 (the maximum compressive stress) and σ3 (the minimum compressive stress) directions strongly depend on the structural position within the transpression zone. For neutral and overlapping fault steps, there is a contractional linking damage zone between the fault segments. For overlapping faults, the σ1 trajectories within the transpression zone deflects significantly forming a sigmoidal pattern, which is created by two rotational flow patterns close to the fault tips. These flow patterns are related to friction effects and different shear deformation, from pure shear outside of the fault steps toward simple shear along the fault segments. Interaction between the two fault segments perturbs the stress field and reflects the heterogeneous nature of deformation. A lozenge- (for underlapping steps), rhomboidal- (for neutral steps), and sigmoidal-shaped (for overlapping steps) transpression zone developed between the two segments. The modelled mean stress pattern shows a similar pattern to that of the contractional steps, and decrease and increase in underlapping and overlapping fault steps, respectively. Comparison of the Kuh-e-Hori transpression zone, between the Esmail-abad and West Neh left-stepping right-lateral strike-slip fault segments in SE Iran, with the modelling results shows strong similarities with the neutral step configuration.
A new method to reconstruct intra-fractional prostate motion in volumetric modulated arc therapy
Chi, Y.; Rezaeian, N. H.; Shen, C.; Zhou, Y.; Lu, W.; Yang, M.; Hannan, R.; Jia, X.
2017-07-01
Intra-fractional motion is a concern during prostate radiation therapy, as it may cause deviations between planned and delivered radiation doses. Because accurate motion information during treatment delivery is critical to address dose deviation, we developed the projection marker matching method (PM3), a novel method for prostate motion reconstruction in volumetric modulated arc therapy. The purpose of this method is to reconstruct in-treatment prostate motion trajectory using projected positions of implanted fiducial markers measured in kV x-ray projection images acquired during treatment delivery. We formulated this task as a quadratic optimization problem. The objective function penalized the distance from the reconstructed 3D position of each fiducial marker to the corresponding straight line, defined by the x-ray projection of the marker. Rigid translational motion of the prostate and motion smoothness along the temporal dimension were assumed and incorporated into the optimization model. We tested the motion reconstruction method in both simulation and phantom experimental studies. We quantified the accuracy using 3D normalized root-mean-square (RMS) error defined as the norm of a vector containing ratios between the absolute RMS errors and corresponding motion ranges in three dimensions. In the simulation study with realistic prostate motion trajectories, the 3D normalized RMS error was on average ~0.164 (range from 0.097 to 0.333 ). In an experimental study, a prostate phantom was driven to move along a realistic prostate motion trajectory. The 3D normalized RMS error was ~0.172 . We also examined the impact of the model parameters on reconstruction accuracy, and found that a single set of parameters can be used for all the tested cases to accurately reconstruct the motion trajectories. The motion trajectory derived by PM3 may be incorporated into novel strategies, including 4D dose reconstruction and adaptive treatment replanning to address motion
Cao, X.; Hayles, J. A.; Bao, H.
2015-12-01
The equilibrium isotope fractionation factor α is a fundamental parameter in stable isotope geochemistry. Although equilibrium α can be determined by theoretical calculation or by measurement of natural samples, direct laboratory experiments are ultimately required to verify those results. The attainment of a true exchange equilibrium in experiments is often difficult, but three methods have been devised and used to ensure that an equilibrium α has been obtained in an isotope exchange experiment. These are the two-directional method, partial-exchange method, and three-isotope method. Of these, the three-isotope method is thought to be the most rigorous. Using water-water exchange as a basic unit, we have developed a set of complex exchange models to study when and why the three-isotope method may work well or not. We found that the method cannot promise to lead to an equilibrium α before the kinetic complexity of the specific exchange experiment is known. An equilibrium point in δ17O-δ18O space can be reached only when all of the isotope exchange pathways are fully reversible, i.e. there is no mass loss at any instant, and the forward and backward reactions share the same pathway. If the exchange pathways are not fully reversible, steady state may be reached, but a steady state α can be very different from the equilibrium α. Our results validated the earlier warning that the trajectory for three-isotope evolution in δ17O-δ18O space may be a distinctly curved line or contain more than one straight line due to the non-fully reversible isotope exchange reactions. The three-isotope method for equilibrium α determination is not as rigorous or as promising as it may seem. Instead, the trajectory of three-isotope evolution provides detailed insights into the kinetics of isotope exchange between compounds. If multiple components exist in the exchange system, the δ17O-δ18O evolving trajectory would be more complex.
Flood profiles of the Alafia River, west-central Florida, computed by step-backwater method
Robertson, A.F.
1977-01-01
The Alafia River is a coastal stream that discharges into Hillsborough Bay. The river and its two principal tributaries, North Prong Alafia River and South Prong Alafia River, drain an area of 420 sq mi of predominantly rural land. However, near the coast, urban residential developments are increasing. The flood plain of the river is subject to flooding, particularly during large regional storms. Peak-discharge frequencies have been determined for data available at two gaging stations in the basin. The flood profiles for peak discharges of recurrence intervals of 2.33, 5, 10, 25, 50, 100, and 200 years have been determined using the step-backwater method. These profiles can be used in conjunction with topographic maps to delineate the area of flooding. Flood profiles were not determined for the tidally affected area near the mouth of the river. Flood marks were located that can be associated with the 1960 flood which occurred when Hurricane Donna passed over the area. (Woodard-USGS)
Preparation and Photocatalytic of Nanoneedle Bi/ZnWO₄by Two-Step Hydrothermal Method.
Chen, Haifeng; Guo, Lingmei; Zhang, Dandan; Li, Jingxin; Liu, Shipin; Li, Bin
2016-01-01
Nanoneedle Bi/ZnWO₄ photocatalysts were successfully synthesized using a two-step hydrothermal method. In the first hydrothermal experiment ZnO/ZnWO₄ nanoneedle crystals were synthesized from NaWO₄· 2H₂O and Zn(NO₃)₂· 6H₂O, using polyacrylamide (PAM) as a template in a hydrothermal environment. Bi cations were then reduced by t-BuONa in a second hydrothermal experiment, adding nanoneedle ZnO/ZnWO₄. The catalysts were then characterized by powder X-ray diffraction (XRD), scanning electron microcopy (SEM), energy dispersive spectrometer (EDS) and UV-vis diffuse reflectance spectrum (DRS). The results show that by adding Bi nanoparticles, the composition of the mixture gradually changed from that of ZnO/ZnWO₄ to Bi/ZnWO₄. The nanoneedle Bi/ZnWO₄samples displayed better UV light photocatalysis than the nanoneedle ZnO/ZnWO₄ samples. The optimum concentration of Bi was investigated using a photocatalytic experiment. A "blue shift" was observed when the molar ratio of Bi was increased.
A one pot, one step, precision cloning method with high throughput capability.
Directory of Open Access Journals (Sweden)
Carola Engler
Full Text Available Current cloning technologies based on site-specific recombination are efficient, simple to use, and flexible, but have the drawback of leaving recombination site sequences in the final construct, adding an extra 8 to 13 amino acids to the expressed protein. We have devised a simple and rapid subcloning strategy to transfer any DNA fragment of interest from an entry clone into an expression vector, without this shortcoming. The strategy is based on the use of type IIs restriction enzymes, which cut outside of their recognition sequence. With proper design of the cleavage sites, two fragments cut by type IIs restriction enzymes can be ligated into a product lacking the original restriction site. Based on this property, a cloning strategy called 'Golden Gate' cloning was devised that allows to obtain in one tube and one step close to one hundred percent correct recombinant plasmids after just a 5 minute restriction-ligation. This method is therefore as efficient as currently used recombination-based cloning technologies but yields recombinant plasmids that do not contain unwanted sequences in the final construct, thus providing precision for this fundamental process of genetic manipulation.
Forming mechanism of radial V-shaped microgrooves on plate using step punching method
Directory of Open Access Journals (Sweden)
Xiang Jian-hua
2015-02-01
Full Text Available The finned surface can increase the specific surface area, which could enhance the boiling efficiency of the working medium to realize the enhancement of heat transfer performance. This research adopted a step punching method to form a radial microgroove structure on the surface of a copper plate. The scanning electron microscopy analysis indicates that when the pressed metal is in the deformation range, it will flow under extrusion and is subject to the reaction force from the metal outside the deformation range, so a micro-finned structure nearby the punching tool is formed. And the deformation area of the formed microgroove is higher than the workpiece’s primitive surface. The relationships of the punching interference length Li with θc, ac, and αpt are analyzed; and the influence of forming parameters on the groove surface morphology as well as the relationships among these parameters are discussed. When the punching depth ac is 0.3 mm and the punching feeding angle θc is 2°–4°, the finned surface of the radial V-shaped microgrooves can be obtained.
A Novel Two-Step Method for Fabricating Silver Plating Cotton Fabrics
Directory of Open Access Journals (Sweden)
Hao Liu
2016-01-01
Full Text Available A novel two-step method was presented for fabricating silver plating cotton fabrics (SPCFs with high electrical conductivity and excellent washing fastness. First, polydopamine (PDA film was coated on the surface of cotton fabrics by in situ polymerization of dopamine, the silver ions in silver nitrate solution were reduced by the catechol groups of polydopamine, and silver nanoparticles were combined with polydopamine by covalent bond on the surface of cotton fabrics. Second, silver ions were reduced by glucose, and silver plating was coated on the surface. Subsequently, the properties of SPCFs were characterized by field emission scanning electron microscopy (FESEM, X-ray photoelectron spectroscopy (XPS and thermogravimetric analysis (TGA, and so forth. With the increasing of silver-ammonia solution concentration or dopamine concentration, the surface resistivity of SPCFs decreases and gradually stabilized. The surface resistivity of the SPCFs can reach 0.12±0.02 Ω, and electromagnetic shielding effectiveness (ESE of the SPCFs can reach 58.5±4.5 dB. Conductive fabrics have wide application prospect in many of fields, such as antibacterial, intelligent textiles, smart garments, electromagnetic shielding, and flexible sensors.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Gametophytes of Laminaria japonica were cryopreserved in liquid nitrogen using encapsulation-dehydration with two-step cooling method. Gametophytes cultured at 10℃ and under continuous irradiance of 30 μmol m-2 s-1 for 3 weeks were encapsulated in calcium alginate beads. The beads were dehydrated in 0.4 molL-1 sucrose prepared with seawater for 6 h, desiccated in an incubator set at 10℃ and 70% relative humidity for 4 h, pre-frozen at either -40℃ or -60℃ for 30 min, and stored in liquid nitrogen for ＞24 h. As high as 43% of survival rate was observed when gametophytes were thawed by placing the beads in 40℃seawater and re-hydrated in 0.05 molL-1 citrate sodium prepared using 30‰ NaC1 7 d later. More cells of male gametophytes survived the whole procedure in comparison with female gametophytes. The cells of gametophytes surviving the preservation were able to grow asexually and produce morphologically normal sporophytes.
An Investigation of Fraction Models in Early Elementary Grades: A Mixed-Methods Approach
Wilkerson, Trena L.; Cooper, Susan; Gupta, Dittika; Montgomery, Mark; Mechell, Sara; Arterbury, Kristin; Moore, Sherrie; Baker, Betty Ruth; Sharp, Pat T.
2015-01-01
This study examines the effect varying models have on student understanding of fractions. The study addressed the question of what students know and understand about fractional concepts through the use of discrete and continuous models. A sample of 54 students in kindergarten and 3rd grade were given an interview pretest, participated in…
Fractional calculus in bioengineering.
Magin, Richard L
2004-01-01
Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub
Duan, Beiping; Zheng, Zhoushun; Cao, Wen
2016-08-01
In this paper, we revisit two spectral approximations, including truncated approximation and interpolation for Caputo fractional derivative. The two approaches have been studied to approximate Riemann-Liouville (R-L) fractional derivative by Chen et al. and Zayernouri et al. respectively in their most recent work. For truncated approximation the reconsideration partly arises from the difference between fractional derivative in R-L sense and Caputo sense: Caputo fractional derivative requires higher regularity of the unknown than R-L version. Another reason for the reconsideration is that we distinguish the differential order of the unknown with the index of Jacobi polynomials, which is not presented in the previous work. Also we provide a way to choose the index when facing multi-order problems. By using generalized Hardy's inequality, the gap between the weighted Sobolev space involving Caputo fractional derivative and the classical weighted space is bridged, then the optimal projection error is derived in the non-uniformly Jacobi-weighted Sobolev space and the maximum absolute error is presented as well. For the interpolation, analysis of interpolation error was not given in their work. In this paper we build the interpolation error in non-uniformly Jacobi-weighted Sobolev space by constructing fractional inverse inequality. With combining collocation method, the approximation technique is applied to solve fractional initial-value problems (FIVPs). Numerical examples are also provided to illustrate the effectiveness of this algorithm.
a Three-Step Spatial-Temporal Clustering Method for Human Activity Pattern Analysis
Huang, W.; Li, S.; Xu, S.
2016-06-01
How people move in cities and what they do in various locations at different times form human activity patterns. Human activity pattern plays a key role in in urban planning, traffic forecasting, public health and safety, emergency response, friend recommendation, and so on. Therefore, scholars from different fields, such as social science, geography, transportation, physics and computer science, have made great efforts in modelling and analysing human activity patterns or human mobility patterns. One of the essential tasks in such studies is to find the locations or places where individuals stay to perform some kind of activities before further activity pattern analysis. In the era of Big Data, the emerging of social media along with wearable devices enables human activity data to be collected more easily and efficiently. Furthermore, the dimension of the accessible human activity data has been extended from two to three (space or space-time) to four dimensions (space, time and semantics). More specifically, not only a location and time that people stay and spend are collected, but also what people "say" for in a location at a time can be obtained. The characteristics of these datasets shed new light on the analysis of human mobility, where some of new methodologies should be accordingly developed to handle them. Traditional methods such as neural networks, statistics and clustering have been applied to study human activity patterns using geosocial media data. Among them, clustering methods have been widely used to analyse spatiotemporal patterns. However, to our best knowledge, few of clustering algorithms are specifically developed for handling the datasets that contain spatial, temporal and semantic aspects all together. In this work, we propose a three-step human activity clustering method based on space, time and semantics to fill this gap. One-year Twitter data, posted in Toronto, Canada, is used to test the clustering-based method. The results show that the
A THREE-STEP SPATIAL-TEMPORAL-SEMANTIC CLUSTERING METHOD FOR HUMAN ACTIVITY PATTERN ANALYSIS
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W. Huang
2016-06-01
Full Text Available How people move in cities and what they do in various locations at different times form human activity patterns. Human activity pattern plays a key role in in urban planning, traffic forecasting, public health and safety, emergency response, friend recommendation, and so on. Therefore, scholars from different fields, such as social science, geography, transportation, physics and computer science, have made great efforts in modelling and analysing human activity patterns or human mobility patterns. One of the essential tasks in such studies is to find the locations or places where individuals stay to perform some kind of activities before further activity pattern analysis. In the era of Big Data, the emerging of social media along with wearable devices enables human activity data to be collected more easily and efficiently. Furthermore, the dimension of the accessible human activity data has been extended from two to three (space or space-time to four dimensions (space, time and semantics. More specifically, not only a location and time that people stay and spend are collected, but also what people “say” for in a location at a time can be obtained. The characteristics of these datasets shed new light on the analysis of human mobility, where some of new methodologies should be accordingly developed to handle them. Traditional methods such as neural networks, statistics and clustering have been applied to study human activity patterns using geosocial media data. Among them, clustering methods have been widely used to analyse spatiotemporal patterns. However, to our best knowledge, few of clustering algorithms are specifically developed for handling the datasets that contain spatial, temporal and semantic aspects all together. In this work, we propose a three-step human activity clustering method based on space, time and semantics to fill this gap. One-year Twitter data, posted in Toronto, Canada, is used to test the clustering-based method. The
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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.
Energy Technology Data Exchange (ETDEWEB)
Huthmacher, Klaus [Department of Physics and OPTIMAS Research Center, University of Kaiserslautern (Germany); Molberg, Andreas K. [Department of Chemistry and OPTIMAS Research Center, University of Kaiserslautern (Germany); Rethfeld, Bärbel [Department of Physics and OPTIMAS Research Center, University of Kaiserslautern (Germany); Gulley, Jeremy R., E-mail: jgulley@kennesaw.edu [Department of Physics, Kennesaw State University, Kennesaw, GA 30144 (United States)
2016-10-01
A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron–phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron–electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron–electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.
Huthmacher, Klaus; Molberg, Andreas K.; Rethfeld, Bärbel; Gulley, Jeremy R.
2016-10-01
A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron-phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron-electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron-electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.
Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei
2015-12-01
In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.
Carels, Nicolas; Frías, Diego
2013-01-01
phenotypes in rice, maize, and humans. We discuss the error rate and the interference of noisy sequences such as pseudogenes, transposons, and retrotransposons. This method is suitable for rapid cORF extraction from transcriptome data and allows correct description of the genome phenotypes of plant genomes without prior knowledge. Additional care is necessary when addressing the human transcriptome due to the interference caused by large amounts of noisy sequences. UFM can be regarded as a low complexity tool for prior knowledge extraction concerning the coding fraction of the transcriptome of any eukaryote. Due to its low level of complexity, UFM is also very robust to variations of codon usage.
Zhou, Hao-Jun; Fan, Xiao-Qiang; Li, Zheng-Hong; Pu, Yi-Kang
2015-01-01
The perturbation method is proposed to obtain the effective delayed neutron fraction (\\b{eta}eff) of a cylindrical highly enriched uranium reactor. Based on the reactivity measurements with and without a sample at a designable position using the positive periodic technique, the reactor reactivity perturbation {\\Delta}\\r{ho} of the sample in \\b{eta}eff units is measured. The simulation of the perturbation experiments are performed by MCNP program. The PERT card is used to provide the difference dk of effective neutron multiplication factors with and without the sample inside the reactor. Based on the relationship between the effective multiplication factor and the reactivity, the equation \\b{eta}eff =dk/{\\Delta}\\r{ho} is derived. In this paper, the reactivity perturbations of 13 metal samples at the designable position of the reactor are measured and calculated. The average \\b{eta}eff value of the reactor is given as 0.00645, and the standard uncertainty is 3.0%. Additionally, the perturbation experiments for ...
Zhou, Hao-Jun; Yin, Yan-Peng; Fan, Xiao-Qiang; Li, Zheng-Hong; Pu, Yi-Kang
2016-06-01
A perturbation method is proposed to obtain the effective delayed neutron fraction β eff of a cylindrical highly enriched uranium reactor. Based on reactivity measurements with and without a sample at a specified position using the positive period technique, the reactor reactivity perturbation Δρ of the sample in β eff units is measured. Simulations of the perturbation experiments are performed using the MCNP program. The PERT card is used to provide the difference dk of effective neutron multiplication factors with and without the sample inside the reactor. Based on the relationship between the effective multiplication factor and the reactivity, the equation β eff = dk/Δρ is derived. In this paper, the reactivity perturbations of 13 metal samples at the designable position of the reactor are measured and calculated. The average β eff value of the reactor is given as 0.00645, and the standard uncertainty is 3.0%. Additionally, the perturbation experiments for β eff can be used to evaluate the reliabilities of the delayed neutron parameters. This work shows that the delayed neutron data of 235U and 238U from G.R. Keepin’s publication are more reliable than those from ENDF-B6.0, ENDF-B7.0, JENDL3.3 and CENDL2.2. Supported by Foundation of Key Laboratory of Neutron Physics, China Academy of Engineering Physics (2012AA01, 2014AA01), National Natural Science Foundation (11375158, 91326104)
Indian Academy of Sciences (India)
M Matinfar; M Eslami; M Kordy
2015-10-01
This paper presents the exact solutions for the fractional Korteweg–de Vries equations and the coupled Korteweg–de Vries equations with time-fractional derivatives using the functional variable method. The fractional derivatives are described in the modified Riemann–Liouville derivative sense. It is demonstrated that the calculations involved in the functional variable method are extremely simple and straightforward and this method is very effective for handling nonlinear fractional equations.
Multi-step polynomial regression method to model and forecast malaria incidence.
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Chandrajit Chatterjee
Full Text Available Malaria is one of the most severe problems faced by the world even today. Understanding the causative factors such as age, sex, social factors, environmental variability etc. as well as underlying transmission dynamics of the disease is important for epidemiological research on malaria and its eradication. Thus, development of suitable modeling approach and methodology, based on the available data on the incidence of the disease and other related factors is of utmost importance. In this study, we developed a simple non-linear regression methodology in modeling and forecasting malaria incidence in Chennai city, India, and predicted future disease incidence with high confidence level. We considered three types of data to develop the regression methodology: a longer time series data of Slide Positivity Rates (SPR of malaria; a smaller time series data (deaths due to Plasmodium vivax of one year; and spatial data (zonal distribution of P. vivax deaths for the city along with the climatic factors, population and previous incidence of the disease. We performed variable selection by simple correlation study, identification of the initial relationship between variables through non-linear curve fitting and used multi-step methods for induction of variables in the non-linear regression analysis along with applied Gauss-Markov models, and ANOVA for testing the prediction, validity and constructing the confidence intervals. The results execute the applicability of our method for different types of data, the autoregressive nature of forecasting, and show high prediction power for both SPR and P. vivax deaths, where the one-lag SPR values plays an influential role and proves useful for better prediction. Different climatic factors are identified as playing crucial role on shaping the disease curve. Further, disease incidence at zonal level and the effect of causative factors on different zonal clusters indicate the pattern of malaria prevalence in the city
Agachev, J. R.; Galimyanov, A. F.
2016-11-01
In this paper the method of mechanical quadrature solutions fractional integral equation. Computational scheme quadrature method is based on the quadrature formula of rectangles with equidistant nodes, which is the formula of the highest trigonometric degree of accuracy, using a regularizing parameter. This decision is taken for the approximate trigonometric interpolation polynomial constructed from the values that make up the solution of the quadrature method. The substantiation of the method in Holder spaces.
Febriani, K.; Wahyuni, I.; Setiasih, S.; Hudiyono, S.
2017-07-01
The enzyme can be purified by fractional precipitation. This can be done by salt or organic solvent. In this research, purification of bromelain from pineapple core by fractional precipitation was done by 2 compounds, ammonium sulfate, and ethanol. Fractional precipitation by ammonium sulfate proved to be more effective as it yielded a higher specific activity. Specific activity by ethanol and ammonium sulfate is 4.6480 U/mg at 0-60 % saturation and 8.2243 U/mg at 50-80 % saturation.
Porous plasmonic nanocomposites for SERS substrates fabricated by two-step laser method
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Koleva, M.E., E-mail: mihaela_ek@yahoo.com [Institute of Electronics, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee blvd., Sofia 1784 (Bulgaria); International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044 (Japan); Nedyalkov, N.N.; Atanasov, P.A. [Institute of Electronics, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee blvd., Sofia 1784 (Bulgaria); Gerlach, J.W.; Hirsch, D.; Prager, A.; Rauschenbach, B. [Leibniz Institute of Surface Modification (IOM), Permoserstrasse 15, D-04318 Leipzig (Germany); Fukata, N.; Jevasuwan, W. [International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044 (Japan)
2016-04-25
This research is focused on investigation of coupled plasmonic/metal-semiconductor nanomaterials. A two-step laser-assisted method is demonstrated for formation of plasmonic Ag nanoparticles (NPs) distributed into porous metal–oxide semiconductors. The mosaic Ag-ZnO target is used for laser ablation and, subsequently, laser annealing of the deposited layer is applied. The plasmon resonance properties of the nanostructures produced are confirmed by optical transmission spectroscopy. The wurtzite structure of ZnO is formed with tilted c-axis orientation and, respectively, a mixed Raman mode appears at 580 cm{sup −1}. The oxygen pressure applied during a deposition process has impact on the morphology and thickness of the porous nanostructures, but not on the size and size distribution of AgNPs. The porous nanocomposites exhibited potential for SERS applications, most pronounced for the oxygen deficient sample, grown at lower oxygen pressure. The observed considerable SERS enhancement of R6G molecules on AgNP/ZnO can be attributed to the ZnO-to-molecule charge transfer contribution, enhanced by the additional electrons from the local surface plasmon resonance (LSPR) of AgNPs to the ZnO through the conduction band. - Highlights: • Porous AgNPs/ZnO composites are obtained by laser deposition and laser annealing. • Morphology and properties depend on growth oxygen pressure. • The emergence of mixed-symmetry Raman mode at 580 cm{sup −1} is registered. • The AgNPs/ZnO porous nanocomposites are suitable for SERS-active substrates. • The charge transfer enhanced by LSPR has a contribution to SERS effect.
Distant exchange interactions in Cd1-xMnxS from magnetization steps method
Gratens, X.; Chitta, V.
2017-07-01
Three new distant neighbor (DN) antiferromagnetic exchange constants have been measured in wurtzite Cd1-xMnxS (x = 0.0087 and x = 0.0278) using the magnetization steps method in the millikelvin regime. The second (J(2)), third (J(3)), and fourth (J(4)) largest exchange constants (after the two first neighbor exchange interactions J1 and J1' ) have been measured. The results are J(2) = 300 ± 10 mK, J(3) = 173 ± 10 mK, and J(4) = 55 ± 10 mK. No significant change of the exchange constant values has been observed as a function of the Mn concentration. The mapping of the DN exchange interactions has been investigated within a sphere of radius 2 times the nearest neighbors distance. The only way to identify the J constants was using the number coordination Zn of the different DN classes: J(2) is associated to DN classes with Zn = 6, J(3) with Zn = 12, and J(4) is ascribed to a group of three DN classes with J values around J(4). The magnitude of the J constants is not in agreement with theoretical predictions of the monotonic decrease of the exchange constant with increasing distance. The present results are similar to those obtained for Cd1-xMnxSe but are different from the ones obtained for Zn1-xMnxO. The present work confirms the long-range character of the DN exchange interactions in the wurtzite type Mn-based II-VI diluted magnetic semiconductors.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A noninterior continuation method is proposed for semidefinite complementarity problem (SDCP). This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are: (i)it is well defined for the monotones SDCP; (ii) it has to solve just one linear system of equations at each step; (iii) it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.
Mucientes, A. E.; de la Pena, M. A.
2009-01-01
The concentration-time integrals method has been used to solve kinetic equations of parallel-consecutive first-order reactions with a reversible step. This method involves the determination of the area under the curve for the concentration of a given species against time. Computer techniques are used to integrate experimental curves and the method…
Directory of Open Access Journals (Sweden)
Deepak Kumar
2012-10-01
Full Text Available Objective: To investigate the effect and evaluation of Anti-hyperlipidemic activity guided subfraction isolated from total methanolic extract of Bauhinia variegata (Linn. leaves on Triton WR-1339 induced hyperlipidemic rats. Methods: Column chromatographic fractionation of butanol fraction of total methanol extract of leaves of Bauhinia variegata (Linn. yields four subfractions (sub-fraction A-D. All sub-fractions tested for their anti-hyperlipidemic activity. Subfractions administered at a dose of 65 mg/kg (oral to the Triton WR-1339 induced hyperlipidemic rats and total cholesterol, triglycerides, HDL, LDL and VLDL level in the blood were checked. Results: Sub-fraction D showed significant reduction (P<0.05 among four sub-fraction in comparison with standard drug fenofibrate. Conclusions: From the above study it could be concluded that butanol sub-fraction D of Bauhinia variegata (Linn. not only have resulted in significant reduction in cholesterol, triglyceride, LDL, VLDL level but also increases the HDL level at a reduced dose level.
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.
Mönkäre, Tiina J; Palmroth, Marja R T; Rintala, Jukka A
2017-02-01
Increasing interest for the landfill mining and the amount of fine fraction (FF) in landfills (40-70% (w/w) of landfill content) mean that sustainable treatment and utilization methods for FF are needed. For this study FF (mined from a municipal solid waste (MSW) landfill operated from 1967 to 1989. FF, which resembles soil, was stabilized in laboratory scale reactors in two phases: first, anaerobically for 101days and second, for 72days using four different methods: anaerobic with the addition of moisture (water) or inoculum (sewage sludge) and aerobic with continuous water washing, with, or without, bulking material. The aim was to evaluate the effect on the stability of mined FF, which has been rarely reported, and to study the quality and quantity of gas and leachate produced during the stabilization experiment. The study showed that aerobic treatment reduced respiration activity (final values 0.9-1.1mgO2/gTS) and residual methane potential (1.1LCH4/kgTS) better than anaerobic methods (1.8-2.3mg O2/g TS and 1.3-2.4L CH4/kg TS, respectively). Bulking material mixed in FF in one aerobic reactor had no effect on the stability of FF. The benefit of anaerobic treatment was the production of methane, which could be utilized as energy. Even though the inoculum addition increased methane production from FF about 30%, but the methane production was still relatively low (in total 1.5-1.7L CH4/kg TS). Continuous water washing was essential to remove leachable organic matter and soluble nutrients from FF, while increasing the volume of leachate collected. In the aerobic treatment, nitrogen was oxidized into nitrite and nitrate and then washed out in the leachate. Both anaerobic and aerobic methods could be used for FF stabilization. The use of FF, in landscaping for example, is possible because its nutrient content (4gN/kg TS and 1g P/kg TS) can increase the nutrient content of soil, but this may have limitations due to the possible presence of heavy metal and other
A New Method to Improve the Electrical Properties of KNN-based Ceramics: Tailoring Phase Fraction
Lv, Xiang
2017-08-18
Although both the phase type and fraction of multi-phase coexistence can affect the electrical properties of (K,Na)NbO3 (KNN)-based ceramics, effects of phase fraction on their electrical properties were few concerned. In this work, through changing the calcination temperature of CaZrO3 powders, we successfully developed the 0.96K0.5Na0.5Nb0.96Sb0.04O3-0.01CaZrO3-0.03Bi0.5Na0.5HfO3 ceramics containing a wide rhombohedral-tetragonal (R-T) phase coexistence with the variations of T (or R) phase fractions. It was found that higher T phase fraction can warrant a larger piezoelectric constant (d33) and d33 also showed a linear variation with respect to tetragonality ratio (c/a). More importantly, a number of domain patterns were observed due to high T phase fraction and large c/a ratio, greatly benefiting the piezoelectricity. In addition, the improved ferroelectric fatigue behavior and thermal stability were also shown in the ceramics containing high T phase fraction. Therefore, this work can bring a new viewpoint into the physical mechanism of KNN-based ceramics behind R-T phase coexistence.
Yang, Yongping; Sharan, Shyam K
2003-08-01
The bacteriophage lambda recombination system has proven to be a valuable tool for engineering bacterial artificial chromosomes (BAC). Due to its high efficiency, subtle alterations in the BACs can be generated using oligonucleotides as targeting vectors. Since no selection marker is used, recombinant clones are identified utilizing a selective PCR screening method. However, occasionally the selective PCR screening is not feasible. We describe here a two-step 'hit and fix' method that can be reliably used for generating any subtle alteration in BACs using short denatured PCR fragments as targeting vectors. In the first step of this method, 6-20 nucleotides are changed around the base where the mutation has to be generated. In the second step, these altered nucleotides are reverted to the original sequence and simultaneously a subtle alteration is introduced. Since in each step several nucleotides are changed, PCR primers specific for such alterations can be designed. This two-step method provides a simple and efficient tool for generating subtle alterations in BACs that can be very valuable for functional analysis of genes.
Directory of Open Access Journals (Sweden)
Vercier P.
2006-11-01
Full Text Available Après avoir défini les termes fractions lourdes et pétroles bruts lourds, et avoir souligné l'intérêt économique qu'il y a à utiliser ces matériaux, on passera en revue les techniques analytiques disponibles pour aborder les difficiles problèmes technologiques que soulève l'emploi des équipements et des méthodes conventionnels. On montrera que les analystes auront besoin de techniques améliorées ou même entièrement nouvelles pour séparer ces produits en des fractions plus simples, susceptibles d'être alors analysées par les méthodes plus traditionnelles : distillation à haute température (jusqu'à 650 °C ; séparation en asphaltènes, résines et huile ; séparation en acides, bases, neutres, saturés, mono-, di-, poly-aromatiques ; analyses structurales (analyses élémentaires, détermination des masses moléculaires, spectrométrie de masse, RMN, pyrolyse et détection à l'aide de détecteurs spécifiques pour le soufre et l'azote. Comme le facteur temps est important dans les études pilote, il sera montré que la mise au point des méthodes rapides et modernes de chromatographie liquide sera l'objectif prioritaire de la recherche analytique dans le futur proche. After defining the terms heavy fractionsand heavy crudesand then stressing the economic interest there is in using such materials, a survey is made of the analytical techniques available for tackling the difficult technological problems arising from the use of conventional equipment and methods. It is shown that analysts will need improved or even completely new techniques for separating such products into simpler fractions so that they can be analyzed by more traditional methods, i. e. high-temperature distillation (up to 650°C; separation into asphaltenes, resins and oils; structural analyses (elemental analyses, determining molecular weights, mass spectrometry, NMR, pyrolysis and detection with specific sulfur and nitrogen detectors. Since the time
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Xiaowei Wang
2014-01-01
Full Text Available This paper proposes a stepped selection method based on spectral kurtosis relative energy entropy. Firstly, the length and type of window function are set; then when fault occurs, enter step 1: the polarity of first half-wave extremes is analyzed; if the ratios of extremes between neighboring lines are positive, the bus bar is the fault line, else, the SK relative energy entropies are calculated, and then enter step 2: if the obtained entropy multiple is bigger than the threshold or equal to the threshold, the overhead line of max entropy corresponding is the fault line, if not, enter step 3: the line of max entropy corresponding is the fault line. At last, the applicability of the proposed algorithm is presented, and the comparison results are discussed.
Simple One-Step Method to Synthesize Polypyrrole-Indigo Carmine-Silver Nanocomposite
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Lara Fernandes Loguercio
2016-01-01
Full Text Available A nanocomposite of indigo carmine doped polypyrrole/silver nanoparticles was obtained by a one-step electrochemical process. The nanocomposite was characterized by scanning electron microscopy, infrared spectroscopy, ultraviolet-visible-near infrared spectroscopy, and cyclic voltammetry. The simple one-step process allowed the growth of silver nanoparticles during the polymerization of polypyrrole, resulting in films with electrochromic behavior and improved electroactivity. In addition, polypyrrole chains in the nanocomposite were found to present longer conjugation length than pristine polypyrrole films.
Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping
Bonito, Andrea
2014-10-31
© Springer International Publishing Switzerland 2015. In this paper, we design and study two modifications of the first order standard pressure increment projection scheme for the Stokes system. The first scheme improves the existing schemes in the case of open boundary condition by modifying the pressure increment boundary condition, thereby minimizing the pressure boundary layer and recovering the optimal first order decay. The second scheme allows for variable time stepping. It turns out that the straightforward modification to variable time stepping leads to unstable schemes. The proposed scheme is not only stable but also exhibits the optimal first order decay. Numerical computations illustrating the theoretical estimates are provided for both new schemes.
Diagnostic Performance of a Lattice Boltzmann-Based Method for Fast CT-Fractional Flow Reserve.
Giannopoulos, Andreas; Tang, Anji; Ge, Yin; Cheezum, Michael; Steigner, Michael; Fujimoto, Shinichiro; Kumamaru, Kanako; Chiappino, Dante; Della Latta, Daniele; Berti, Sergio; Chiappino, Sara; Rybicki, Frank; Melchionna, Simone; Mitsouras, Dimitrios
2017-06-27
Fractional flow reserve (FFR) estimated from coronary computed tomography angiography (CT-FFR) offers non-invasive detection of lesion-specific ischemia. We developed and validated a fast CT-FFR algorithm utilizing the Lattice-Boltzmann Method for blood flow simulation (LBM CT-FFR). 64 patients from 3 institutions with clinically-indicated CTA and invasive FFR measurement were retrospectively analyzed. CT-FFR was performed using an on-site tool interfacing with a commercial Lattice-Boltzmann fluid dynamics cloud-based platform. Diagnostic accuracy of LBM CT-FFR≤0.8 and percent diameter stenosis >50% by CTA to detect invasive FFR≤0.8 were compared using area under the receiver operating characteristic curve (AUC). 60 patients successfully underwent LBM CT-FFR analysis; 29 of 73 lesions in 69 vessels had invasive FFR≤0.8. Total time to perform LBM CT-FFR was 40±10 min. Compared to invasive FFR, LBM CT-FFR had good correlation (r=0.64), small bias (0.009) and good limits of agreement (-0.223 to 0.206). The AUC of LBM CT-FFR (AUC=0.894, 95% confidence interval [CI]: 0.792- 0.996) was significantly higher than CTA (AUC=0.685, 95% CI: 0.576-0.794) to detect FFR≤0.8 (p=0.0021). Per-lesion specificity, sensitivity, accuracy of LBM CT-FFR were 97.7%, 79.3%, and 90.4%, respectively. LBM CT-FFR has very good diagnostic accuracy to detect lesion-specific ischemia (FFR≤0.8) and can be performed in less than 1 hour.
Energy Technology Data Exchange (ETDEWEB)
Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)
2016-02-15
We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.
Angstmann, C. N.; Donnelly, I. C.; Henry, B. I.; Jacobs, B. A.; Langlands, T. A. M.; Nichols, J. A.
2016-02-01
We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction-diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.
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Ryu, E. K.; Choi, Y. S.; Kim, D. H.; Ko, B. H.; Lee, K. H.; Choi, Y.; Kim, B. T. [Samsung Medical Center, Seoul (Korea, Republic of)
2005-07-01
Metabolism studies are prerequisite for characterization of novel radiotracers. In this study, in vitro metabolism method using mouse liver S9 fraction was established and evaluated using model radiotracers, and the results were compared with those of in vivo method and in vitro method using liver microsomes. 1-(4-[F-18] fluoro methylbenzyl)- ([F-18]1) and 1-(4-[F-18]fluorobenzyl)-4-phen ylpiperazine ([F-18]2) were synthesized and purified by HPLC. Liver S9 fraction and microsomes were prepared from mice. In the in vivo method, mice were injected with the radiotracer, and the bone and blood were collected at 1, 5, 15, 30 and 60 min postinjection. In the in vitro method, the radiotracer was incubated with either S9 fraction or microsomes in the presence of NADPH. The metabolites were analyzed by radio-TLC. Metabolic defluorination was also measured from the incubation of the metabolites with calcium phosphate. [F-18]1 and [F-18]2 were synthesized in 25-35% yield. In the in vivo method, [F-18]1 underwent severe metabolic defluorination based on the increase of bone uptake with time and appearance of [F-18]fluoride ion on radio-TLC in the blood samples. This result was consistent with the in vitro metabolism using either S9 fraction or microsomes, which showed a significant uptake by calcium phosphate. [F-18]2 was converted into unidentified polar metabolites both in vivo and in vitro. There was no increasing uptake by either bone or calcium phosphate with time. The in vitro metabolism of these radiotracers using S9 fraction gave the similar patterns to those using the blood as well as microsomes. This result demonstrated that liver S9 fraction can be used in place of microsomes as well as the blood for the metabolism studies of radiotracers. Moreover, the use of liver S9 fraction has advantages in that it is easily obtained during the early stage of liver microsomal preparation and contains both microsomal and cytosolic fractions.
A novel two-step method for screening shade tolerant mutant plants via dwarfism
When subjected to shade, plants undergo rapid shoot elongation, which often makes them more prone to disease and mechanical damage. It has been reported that, in turfgrass, induced dwarfism can enhance shade tolerance. Here, we describe a two-step procedure for isolating shade tolerant mutants of ...
Photon strength function in the Hf-181 nucleus by method of two-step cascade
Le Hong Khiem
2003-01-01
The applicability of sum-coincidence measurements of two-step cascade gamma ray spectra determining Photon Strength Function (PSF) of Hf-181 induced from Hf-180 (n,2 gamma) Hf-181 reaction is presented. Up to 80% intensity of the primary gamma ray transitions in a wide energy range have been deduced and compared to model calculation.
The Mixing of Methods: a three-step process for improving rigour in impact evaluations
Ton, G.
2012-01-01
This article describes a systematic process that is helpful in improving impact evaluation assignments, within restricted budgets and timelines. It involves three steps: a rethink of the key questions of the evaluation to develop more relevant, specific questions; a way of designing a mix of