WorldWideScience

Sample records for fractional step method

  1. The Fractional Step Method Applied to Simulations of Natural Convective Flows

    Science.gov (United States)

    Westra, Douglas G.; Heinrich, Juan C.; Saxon, Jeff (Technical Monitor)

    2002-01-01

    This paper describes research done to apply the Fractional Step Method to finite-element simulations of natural convective flows in pure liquids, permeable media, and in a directionally solidified metal alloy casting. The Fractional Step Method has been applied commonly to high Reynold's number flow simulations, but is less common for low Reynold's number flows, such as natural convection in liquids and in permeable media. The Fractional Step Method offers increased speed and reduced memory requirements by allowing non-coupled solution of the pressure and the velocity components. The Fractional Step Method has particular benefits for predicting flows in a directionally solidified alloy, since other methods presently employed are not very efficient. Previously, the most suitable method for predicting flows in a directionally solidified binary alloy was the penalty method. The penalty method requires direct matrix solvers, due to the penalty term. The Fractional Step Method allows iterative solution of the finite element stiffness matrices, thereby allowing more efficient solution of the matrices. The Fractional Step Method also lends itself to parallel processing, since the velocity component stiffness matrices can be built and solved independently of each other. The finite-element simulations of a directionally solidified casting are used to predict macrosegregation in directionally solidified castings. In particular, the finite-element simulations predict the existence of 'channels' within the processing mushy zone and subsequently 'freckles' within the fully processed solid, which are known to result from macrosegregation, or what is often referred to as thermo-solutal convection. These freckles cause material property non-uniformities in directionally solidified castings; therefore many of these castings are scrapped. The phenomenon of natural convection in an alloy under-going directional solidification, or thermo-solutal convection, will be explained. The

  2. Lagrangian fractional step method for the incompressible Navier--Stokes equations on a periodic domain

    International Nuclear Information System (INIS)

    Boergers, C.; Peskin, C.S.

    1987-01-01

    In the Lagrangian fractional step method introduced in this paper, the fluid velocity and pressure are defined on a collection of N fluid markers. At each time step, these markers are used to generate a Voronoi diagram, and this diagram is used to construct finite-difference operators corresponding to the divergence, gradient, and Laplacian. The splitting of the Navier--Stokes equations leads to discrete Helmholtz and Poisson problems, which we solve using a two-grid method. The nonlinear convection terms are modeled simply by the displacement of the fluid markers. We have implemented this method on a periodic domain in the plane. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams, and we report on numerical results which indicate the the fractional step method is convergent of first order. The overall work per time step is proportional to N log N. copyright 1987 Academic Press, Inc

  3. A GPU-accelerated semi-implicit fractional-step method for numerical solutions of incompressible Navier-Stokes equations

    Science.gov (United States)

    Ha, Sanghyun; Park, Junshin; You, Donghyun

    2018-01-01

    Utility of the computational power of Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. The Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution methods used in the semi-implicit fractional-step method take advantage of multiple tridiagonal matrices whose inversion is known as the major bottleneck for acceleration on a typical multi-core machine. A novel implementation of the semi-implicit fractional-step method designed for GPU acceleration of the incompressible Navier-Stokes equations is presented. Aspects of the programing model of Compute Unified Device Architecture (CUDA), which are critical to the bandwidth-bound nature of the present method are discussed in detail. A data layout for efficient use of CUDA libraries is proposed for acceleration of tridiagonal matrix inversion and fast Fourier transform. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while the Navier-Stokes equations are computed on a GPU. Performance of the present method using CUDA is assessed by comparing the speed of solving three tridiagonal matrices using ADI with the speed of solving one heptadiagonal matrix using a conjugate gradient method. An overall speedup of 20 times is achieved using a Tesla K40 GPU in comparison with a single-core Xeon E5-2660 v3 CPU in simulations of turbulent boundary-layer flow over a flat plate conducted on over 134 million grids. Enhanced performance of 48 times speedup is reached for the same problem using a Tesla P100 GPU.

  4. 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.

  5. Arsenic fractionation in agricultural soil using an automated three-step sequential extraction method coupled to hydride generation-atomic fluorescence spectrometry

    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

  6. A GPU-accelerated semi-implicit fractional step method for numerical solutions of incompressible Navier-Stokes equations

    Science.gov (United States)

    Ha, Sanghyun; Park, Junshin; You, Donghyun

    2017-11-01

    Utility of the computational power of modern Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. Due to its serial and bandwidth-bound nature, the present choice of numerical methods is considered to be a good candidate for evaluating the potential of GPUs for solving Navier-Stokes equations using non-explicit time integration. An efficient algorithm is presented for GPU acceleration of the Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution method used in the semi-implicit fractional-step method. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while Navier-Stokes equations are computed on a GPU. Extension to multiple NVIDIA GPUs is implemented using NVLink supported by the Pascal architecture. Performance of the present method is experimented on multiple Tesla P100 GPUs compared with a single-core Xeon E5-2650 v4 CPU in simulations of boundary-layer flow over a flat plate. Supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (Ministry of Science, ICT and Future Planning NRF-2016R1E1A2A01939553, NRF-2014R1A2A1A11049599, and Ministry of Trade, Industry and Energy 201611101000230).

  7. Discrete maximal regularity of time-stepping schemes for fractional evolution equations.

    Science.gov (United States)

    Jin, Bangti; Li, Buyang; Zhou, Zhi

    2018-01-01

    In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735-758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157-176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.

  8. Simulation of the two-fluid model on incompressible flow with Fractional Step method for both resolved and unresolved scale interfaces

    International Nuclear Information System (INIS)

    Hou, Xiaofei; Rigola, Joaquim; Lehmkuhl, Oriol; Oliva, Assensi

    2015-01-01

    Highlights: • Two phase flow with free surface is solved by means of two-fluid model (TFM). • Fractional Step method and finite volume technique is used to solve TFM. • Conservative Level Set method reduces interface sharpening diffusion problem. • Cases including high density ratios and high viscosities validate the models. - Abstract: In the present paper, the Fractional Step method usually used in single fluid flow is here extended and applied for the two-fluid model resolution using the finite volume discretization. The use of a projection method resolution instead of the usual pressure-correction method for multi-fluid flow, successfully avoids iteration processes. On the other hand, the main weakness of the two fluid model used for simulations of free surface flows, which is the numerical diffusion of the interface, is also solved by means of the conservative Level Set method (interface sharpening) (Strubelj et al., 2009). Moreover, the use of the algorithm proposed has allowed presenting different free-surface cases with or without Level Set implementation even under coarse meshes under a wide range of density ratios. Thus, the numerical results presented, numerically verified, experimentally validated and converged under high density ratios, shows the capability and reliability of this resolution method for both mixed and unmixed flows

  9. Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

    Science.gov (United States)

    Jain, Sonal

    2018-01-01

    In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

  10. A two-step leaching method designed based on chemical fraction distribution of the heavy metals for selective leaching of Cd, Zn, Cu, and Pb from metallurgical sludge.

    Science.gov (United States)

    Wang, Fen; Yu, Junxia; Xiong, Wanli; Xu, Yuanlai; Chi, Ru-An

    2018-01-01

    For selective leaching and highly effective recovery of heavy metals from a metallurgical sludge, a two-step leaching method was designed based on the distribution analysis of the chemical fractions of the loaded heavy metal. Hydrochloric acid (HCl) was used as a leaching agent in the first step to leach the relatively labile heavy metals and then ethylenediamine tetraacetic acid (EDTA) was applied to leach the residual metals according to their different fractional distribution. Using the two-step leaching method, 82.89% of Cd, 55.73% of Zn, 10.85% of Cu, and 0.25% of Pb were leached in the first step by 0.7 M HCl at a contact time of 240 min, and the leaching efficiencies for Cd, Zn, Cu, and Pb were elevated up to 99.76, 91.41, 71.85, and 94.06%, by subsequent treatment with 0.2 M EDTA at 480 min, respectively. Furthermore, HCl leaching induced fractional redistribution, which might increase the mobility of the remaining metals and then facilitate the following metal removal by EDTA. The facilitation was further confirmed by the comparison to the one-step leaching method with single HCl or single EDTA, respectively. These results suggested that the designed two-step leaching method by HCl and EDTA could be used for selective leaching and effective recovery of heavy metals from the metallurgical sludge or heavy metal-contaminated solid media.

  11. Closed-loop step response for tuning PID-fractional-order-filter controllers.

    Science.gov (United States)

    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. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  12. Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation

    International Nuclear Information System (INIS)

    Lim, S C; Teo, L P

    2009-01-01

    Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion

  13. Finite element method for time-space-fractional Schrodinger equation

    Directory of Open Access Journals (Sweden)

    Xiaogang Zhu

    2017-07-01

    Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.

  14. Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density

    KAUST Repository

    Guermond, J.-L.; Salgado, Abner J.

    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.

  15. An unstructured finite volume solver for two phase water/vapour flows based on an elliptic oriented fractional step method

    International Nuclear Information System (INIS)

    Mechitoua, N.; Boucker, M.; Lavieville, J.; Pigny, S.; Serre, G.

    2003-01-01

    Based on experience gained at EDF and Cea, a more general and robust 3-dimensional (3D) multiphase flow solver has been being currently developed for over three years. This solver, based on an elliptic oriented fractional step approach, is able to simulate multicomponent/multiphase flows. Discretization follows a 3D full unstructured finite volume approach, with a collocated arrangement of all variables. The non linear behaviour between pressure and volume fractions and a symmetric treatment of all fields are taken into account in the iterative procedure, within the time step. It greatly enforces the realizability of volume fractions (i.e 0 < α < 1), without artificial numerical needs. Applications to widespread test cases as static sedimentation, water hammer and phase separation are shown to assess the accuracy and the robustness of the flow solver in different flow conditions, encountered in nuclear reactors pipes. (authors)

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

    Directory of Open Access Journals (Sweden)

    Meriem Ait Mehdi

    2014-01-01

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

  17. Free Modal Algebras Revisited: The Step-by-Step Method

    NARCIS (Netherlands)

    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

  18. NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Yirang YUAN; Qing YANG; Changfeng LI; Tongjun SUN

    2017-01-01

    Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions.The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity.The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation.A mixed finite volume element approximation,keeping physical conservation law,is used to get numerical values of the electric potential and the accuracy is improved one order.Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences.This method can overcome numerical oscillation,dispersion and decreases computational complexity.Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened.An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations.This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.

  19. Fractional Step Like Schemes for Free Surface Problems with Thermal Coupling Using the Lagrangian PFEM

    Science.gov (United States)

    Aubry, R.; Oñate, E.; Idelsohn, S. R.

    2006-09-01

    The method presented in Aubry et al. (Comput Struc 83:1459-1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505-526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a Lagrangian description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. Numerical results are provided to assess the superiority of the modified algebraic splitting to the classical FS.

  20. A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting

    KAUST Repository

    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.

  1. A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting

    KAUST Repository

    Guermond, Jean-Luc; Minev, Peter D.

    2010-01-01

    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.

  2. The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations

    OpenAIRE

    Zhao, Jianping; Tang, Bo; Kumar, Sunil; Hou, Yanren

    2012-01-01

    An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powe...

  3. A finite difference method for space fractional differential equations with variable diffusivity coefficient

    KAUST Repository

    Mustapha, K.

    2017-06-03

    Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.

  4. A finite difference method for space fractional differential equations with variable diffusivity coefficient

    KAUST Repository

    Mustapha, K.; Furati, K.; Knio, Omar; Maitre, O. Le

    2017-01-01

    Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.

  5. Acoustic programming in step-split-flow lateral-transport thin fractionation.

    Science.gov (United States)

    Ratier, Claire; Hoyos, Mauricio

    2010-02-15

    We propose a new separation scheme for micrometer-sized particles combining acoustic forces and gravitational field in split-flow lateral-transport thin (SPLITT)-like fractionation channels. Acoustic forces are generated by ultrasonic standing waves set up in the channel thickness. We report on the separation of latex particles of two different sizes in a preliminary experiment using this proposed hydrodynamic acoustic sorter, HAS. Total binary separation of 5 and 10 microm diameter particles has been achieved. Numerical simulations of trajectories of particles flowing through a step-SPLITT under the conditions which combine acoustic standing waves and gravity show a very good agreement with the experiment. Calculations in order to compare separations obtained by the acoustic programming s-SPLITT fractionation and the conventional SPLITT fractionation show that the improvement in separation time is around 1 order of magnitude and could still be improved; this is the major finding of this work. This separation technique can be extended to biomimetic particles and blood cells.

  6. Two-step extraction method for lead isotope fractionation to reveal anthropogenic lead pollution.

    Science.gov (United States)

    Katahira, Kenshi; Moriwaki, Hiroshi; Kamura, Kazuo; Yamazaki, Hideo

    2018-05-28

    This study developed the 2-step extraction method which eluted the Pb adsorbing on the surface of sediments in the first solution by aqua regia and extracted the Pb absorbed inside particles into the second solution by mixed acid of nitric acid, hydrofluoric acid and hydrogen peroxide solution. We applied the method to sediments in the enclosed water area and found out that the isotope ratios of Pb in the second solution represented those of natural origin. This advantage of the method makes it possible to distinguish the Pb between natural origin and anthropogenic source on the basis of the isotope ratios. The results showed that the method was useful to discuss the Pb sources and that anthropogenic Pb in the sediment samples analysed was mainly derived from China because of transboundary air pollution.

  7. Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Ahmet Bekir

    2013-01-01

    Full Text Available The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

  8. 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.

  9. A matrix-free, implicit, incompressible fractional-step algorithm for fluid–structure interaction applications

    CSIR Research Space (South Africa)

    Oxtoby, Oliver F

    2012-05-01

    Full Text Available In this paper we detail a fast, fully-coupled, partitioned fluid–structure interaction (FSI) scheme. For the incompressible fluid, new fractional-step algorithms are proposed which make possible the fully implicit, but matrixfree, parallel solution...

  10. A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

    International Nuclear Information System (INIS)

    Feng Qing-Hua

    2014-01-01

    In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

  11. Integral transform method for solving time fractional systems and fractional heat equation

    Directory of Open Access Journals (Sweden)

    Arman Aghili

    2014-01-01

    Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.

  12. A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

    Directory of Open Access Journals (Sweden)

    Pezza L.

    2018-03-01

    Full Text Available The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

  13. Valve cam design using numerical step-by-step method

    OpenAIRE

    Vasilyev, Aleksandr; Bakhracheva, Yuliya; Kabore, Ousman; Zelenskiy, Yuriy

    2014-01-01

    This article studies the numerical step-by-step method of cam profile design. The results of the study are used for designing the internal combustion engine valve gear. This method allows to profile the peak efficiency of cams in view of many restrictions, connected with valve gear serviceability and reliability.

  14. A generalized fractional sub-equation method for fractional differential equations with variable coefficients

    International Nuclear Information System (INIS)

    Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

    2012-01-01

    In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.

  15. New method dynamically models hydrocarbon fractionation

    Energy Technology Data Exchange (ETDEWEB)

    Kesler, M.G.; Weissbrod, J.M.; Sheth, B.V. [Kesler Engineering, East Brunswick, NJ (United States)

    1995-10-01

    A new method for calculating distillation column dynamics can be used to model time-dependent effects of independent disturbances for a range of hydrocarbon fractionation. It can model crude atmospheric and vacuum columns, with relatively few equilibrium stages and a large number of components, to C{sub 3} splitters, with few components and up to 300 equilibrium stages. Simulation results are useful for operations analysis, process-control applications and closed-loop control in petroleum, petrochemical and gas processing plants. The method is based on an implicit approach, where the time-dependent variations of inventory, temperatures, liquid and vapor flows and compositions are superimposed at each time step on the steady-state solution. Newton-Raphson (N-R) techniques are then used to simultaneously solve the resulting finite-difference equations of material, equilibrium and enthalpy balances that characterize distillation dynamics. The important innovation is component-aggregation and tray-aggregation to contract the equations without compromising accuracy. This contraction increases the N-R calculations` stability. It also significantly increases calculational speed, which is particularly important in dynamic simulations. This method provides a sound basis for closed-loop, supervisory control of distillation--directly or via multivariable controllers--based on a rigorous, phenomenological column model.

  16. Exact Solutions of Fractional Burgers and Cahn-Hilliard Equations Using Extended Fractional Riccati Expansion Method

    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.

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

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2014-01-01

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

  18. On varitional iteration method for fractional calculus

    Directory of Open Access Journals (Sweden)

    Wu Hai-Gen

    2017-01-01

    Full Text Available Modification of the Das’ variational iteration method for fractional differential equations is discussed, and its main shortcoming involved in the solution process is pointed out and overcome by using fractional power series. The suggested computational procedure is simple and reliable for fractional calculus.

  19. The effect of DNA extraction methods on observed microbial communities from fibrous and liquid rumen fractions of dairy cows

    NARCIS (Netherlands)

    Vaidya, Jueeli D.; Bogert, van den Bartholomeus; Boekhorst, Jos; Saccenti, Edoardo; Plugge, Caroline M.; Smidt, Hauke

    2018-01-01

    DNA based methods have been widely used to study the complexity of the rumen microbiota, and it is well known that the method of DNA extraction is a critical step in enabling accurate assessment of this complexity. Rumen fluid (RF) and fibrous content (FC) fractions differ substantially in terms of

  20. Regularization by fractional filter methods and data smoothing

    International Nuclear Information System (INIS)

    Klann, E; Ramlau, R

    2008-01-01

    This paper is concerned with the regularization of linear ill-posed problems by a combination of data smoothing and fractional filter methods. For the data smoothing, a wavelet shrinkage denoising is applied to the noisy data with known error level δ. For the reconstruction, an approximation to the solution of the operator equation is computed from the data estimate by fractional filter methods. These fractional methods are based on the classical Tikhonov and Landweber method, but avoid, at least partially, the well-known drawback of oversmoothing. Convergence rates as well as numerical examples are presented

  1. Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers.

    Science.gov (United States)

    Merrikh-Bayat, Farshad

    2011-04-01

    One main approach for time-domain simulation of the linear output-feedback systems containing fractional-order controllers is to approximate the transfer function of the controller with an integer-order transfer function and then perform the simulation. In general, this approach suffers from two main disadvantages: first, the internal stability of the resulting feedback system is not guaranteed, and second, the amount of error caused by this approximation is not exactly known. The aim of this paper is to propose an efficient method for time-domain simulation of such systems without facing the above mentioned drawbacks. For this purpose, the fractional-order controller is approximated with an integer-order transfer function (possibly in combination with the delay term) such that the internal stability of the closed-loop system is guaranteed, and then the simulation is performed. It is also shown that the resulting approximate controller can effectively be realized by using the proposed method. Some formulas for estimating and correcting the simulation error, when the feedback system under consideration is subjected to the unit step command or the unit step disturbance, are also presented. Finally, three numerical examples are studied and the results are compared with the Oustaloup continuous approximation method. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

  2. Chebyshev Finite Difference Method for Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    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

  3. Current lipid extraction methods are significantly enhanced adding a water treatment step in Chlorella protothecoides.

    Science.gov (United States)

    Ren, Xiaojie; Zhao, Xinhe; Turcotte, François; Deschênes, Jean-Sébastien; Tremblay, Réjean; Jolicoeur, Mario

    2017-02-11

    Microalgae have the potential to rapidly accumulate lipids of high interest for the food, cosmetics, pharmaceutical and energy (e.g. biodiesel) industries. However, current lipid extraction methods show efficiency limitation and until now, extraction protocols have not been fully optimized for specific lipid compounds. The present study thus presents a novel lipid extraction method, consisting in the addition of a water treatment of biomass between the two-stage solvent extraction steps of current extraction methods. The resulting modified method not only enhances lipid extraction efficiency, but also yields a higher triacylglycerols (TAG) ratio, which is highly desirable for biodiesel production. Modification of four existing methods using acetone, chloroform/methanol (Chl/Met), chloroform/methanol/H 2 O (Chl/Met/H 2 O) and dichloromethane/methanol (Dic/Met) showed respective lipid extraction yield enhancement of 72.3, 35.8, 60.3 and 60.9%. The modified acetone method resulted in the highest extraction yield, with 68.9 ± 0.2% DW total lipids. Extraction of TAG was particularly improved with the water treatment, especially for the Chl/Met/H 2 O and Dic/Met methods. The acetone method with the water treatment led to the highest extraction level of TAG with 73.7 ± 7.3 µg/mg DW, which is 130.8 ± 10.6% higher than the maximum value obtained for the four classical methods (31.9 ± 4.6 µg/mg DW). Interestingly, the water treatment preferentially improved the extraction of intracellular fractions, i.e. TAG, sterols, and free fatty acids, compared to the lipid fractions of the cell membranes, which are constituted of phospholipids (PL), acetone mobile polar lipids and hydrocarbons. Finally, from the 32 fatty acids analyzed for both neutral lipids (NL) and polar lipids (PL) fractions, it is clear that the water treatment greatly improves NL-to-PL ratio for the four standard methods assessed. Water treatment of biomass after the first solvent extraction step

  4. Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators

    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.

  5. Step by step parallel programming method for molecular dynamics code

    International Nuclear Information System (INIS)

    Orii, Shigeo; Ohta, Toshio

    1996-07-01

    Parallel programming for a numerical simulation program of molecular dynamics is carried out with a step-by-step programming technique using the two phase method. As a result, within the range of a certain computing parameters, it is found to obtain parallel performance by using the level of parallel programming which decomposes the calculation according to indices of do-loops into each processor on the vector parallel computer VPP500 and the scalar parallel computer Paragon. It is also found that VPP500 shows parallel performance in wider range computing parameters. The reason is that the time cost of the program parts, which can not be reduced by the do-loop level of the parallel programming, can be reduced to the negligible level by the vectorization. After that, the time consuming parts of the program are concentrated on less parts that can be accelerated by the do-loop level of the parallel programming. This report shows the step-by-step parallel programming method and the parallel performance of the molecular dynamics code on VPP500 and Paragon. (author)

  6. Shutdown Dose Rate Analysis Using the Multi-Step CADIS Method

    International Nuclear Information System (INIS)

    Ibrahim, Ahmad M.; Peplow, Douglas E.; Peterson, Joshua L.; Grove, Robert E.

    2015-01-01

    The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) hybrid Monte Carlo (MC)/deterministic radiation transport method was proposed to speed up the shutdown dose rate (SDDR) neutron MC calculation using an importance function that represents the neutron importance to the final SDDR. This work applied the MS-CADIS method to the ITER SDDR benchmark problem. The MS-CADIS method was also used to calculate the SDDR uncertainty resulting from uncertainties in the MC neutron calculation and to determine the degree of undersampling in SDDR calculations because of the limited ability of the MC method to tally detailed spatial and energy distributions. The analysis that used the ITER benchmark problem compared the efficiency of the MS-CADIS method to the traditional approach of using global MC variance reduction techniques for speeding up SDDR neutron MC calculation. Compared to the standard Forward-Weighted-CADIS (FW-CADIS) method, the MS-CADIS method increased the efficiency of the SDDR neutron MC calculation by 69%. The MS-CADIS method also increased the fraction of nonzero scoring mesh tally elements in the space-energy regions of high importance to the final SDDR

  7. Exp-function method for solving fractional partial differential equations.

    Science.gov (United States)

    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.

  8. Identification of fractional order systems using modulating functions method

    KAUST Repository

    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.

  9. Detection of questionable occlusal carious lesions using an electrical bioimpedance method with fractional electrical model

    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.

  10. Detection of questionable occlusal carious lesions using an electrical bioimpedance method with fractional electrical model

    International Nuclear Information System (INIS)

    Morais, A. P.; Pino, A. V.; Souza, M. N.

    2016-01-01

    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.

  11. Direct nuclear magnetic resonance identification and quantification of geometric isomers of conjugated linoleic acid in milk lipid fraction without derivatization steps: Overcoming sensitivity and resolution barriers

    International Nuclear Information System (INIS)

    Tsiafoulis, Constantinos G.; Skarlas, Theodore; Tzamaloukas, Ouranios; Miltiadou, Despoina; Gerothanassis, Ioannis P.

    2014-01-01

    Highlights: • The first NMR quantification of four geometric 18:2 CLA isomers has been achieved. • Sensitivity and resolution NMR barriers have been overcome. • Selective suppression and reduced 13 C spectral width have been utilized. • The method is applied in the milk lipid fraction without derivatization steps. • The method is selective, sensitive with very good analytical characteristics. - Abstract: We report the first successful direct and unequivocal identification and quantification of four minor geometric (9-cis, 11-trans) 18:2, (9-trans, 11-cis) 18:2, (9-cis, 11-cis) 18:2 and (9-trans, 11-trans) 18:2 conjugated linoleic acid (CLA) isomers in lipid fractions of lyophilized milk samples with the combined use of 1D 1 H-NMR, 2D 1 H- 1 H TOCSY and 2D 1 H- 13 C HSQC NMR. The significant sensitivity barrier has been successfully overcome under selective suppression of the major resonances, with over 10 4 greater equilibrium magnetization of the -(CH 2 ) n - 1 H spins compared to that of the 1 H spins of the conjugated bonds of the CLA isomers. The resolution barrier has been significantly increased using reduced 13 C spectral width in the 2D 1 H- 13 C HSQC experiment. The assignment was confirmed with spiking experiments with CLA standard compounds and the method does not require any derivatization steps for the lipid fraction. The proposed method is selective, sensitive and compares favorably with the GS-MS method of analysis

  12. A Fast O(N log N Finite Difference Method for the One-Dimensional Space-Fractional Diffusion Equation

    Directory of Open Access Journals (Sweden)

    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.

  13. Homogenization versus homogenization-free method to measure muscle glycogen fractions.

    Science.gov (United States)

    Mojibi, N; Rasouli, M

    2016-12-01

    The glycogen is extracted from animal tissues with or without homogenization using cold perchloric acid. Three methods were compared for determination of glycogen in rat muscle at different physiological states. Two groups of five rats were kept at rest or 45 minutes muscular activity. The glycogen fractions were extracted and measured by using three methods. The data of homogenization method shows that total glycogen decreased following 45 min physical activity and the change occurred entirely in acid soluble glycogen (ASG), while AIG did not change significantly. Similar results were obtained by using "total-glycogen-fractionation methods". The findings of "homogenization-free method" indicate that the acid insoluble fraction (AIG) was the main portion of muscle glycogen and the majority of changes occurred in AIG fraction. The results of "homogenization method" are identical with "total glycogen fractionation", but differ with "homogenization-free" protocol. The ASG fraction is the major portion of muscle glycogen and is more metabolically active form.

  14. s-Step Krylov Subspace Methods as Bottom Solvers for Geometric Multigrid

    Energy Technology Data Exchange (ETDEWEB)

    Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lijewski, Mike [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Almgren, Ann [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Straalen, Brian Van [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Carson, Erin [Univ. of California, Berkeley, CA (United States); Knight, Nicholas [Univ. of California, Berkeley, CA (United States); Demmel, James [Univ. of California, Berkeley, CA (United States)

    2014-08-14

    Geometric multigrid solvers within adaptive mesh refinement (AMR) applications often reach a point where further coarsening of the grid becomes impractical as individual sub domain sizes approach unity. At this point the most common solution is to use a bottom solver, such as BiCGStab, to reduce the residual by a fixed factor at the coarsest level. Each iteration of BiCGStab requires multiple global reductions (MPI collectives). As the number of BiCGStab iterations required for convergence grows with problem size, and the time for each collective operation increases with machine scale, bottom solves in large-scale applications can constitute a significant fraction of the overall multigrid solve time. In this paper, we implement, evaluate, and optimize a communication-avoiding s-step formulation of BiCGStab (CABiCGStab for short) as a high-performance, distributed-memory bottom solver for geometric multigrid solvers. This is the first time s-step Krylov subspace methods have been leveraged to improve multigrid bottom solver performance. We use a synthetic benchmark for detailed analysis and integrate the best implementation into BoxLib in order to evaluate the benefit of a s-step Krylov subspace method on the multigrid solves found in the applications LMC and Nyx on up to 32,768 cores on the Cray XE6 at NERSC. Overall, we see bottom solver improvements of up to 4.2x on synthetic problems and up to 2.7x in real applications. This results in as much as a 1.5x improvement in solver performance in real applications.

  15. One step beyond: Different step-to-step transitions exist during continuous contact brachiation in siamangs

    Directory of Open Access Journals (Sweden)

    Fana Michilsens

    2012-02-01

    In brachiation, two main gaits are distinguished, ricochetal brachiation and continuous contact brachiation. During ricochetal brachiation, a flight phase exists and the body centre of mass (bCOM describes a parabolic trajectory. For continuous contact brachiation, where at least one hand is always in contact with the substrate, we showed in an earlier paper that four step-to-step transition types occur. We referred to these as a ‘point’, a ‘loop’, a ‘backward pendulum’ and a ‘parabolic’ transition. Only the first two transition types have previously been mentioned in the existing literature on gibbon brachiation. In the current study, we used three-dimensional video and force analysis to describe and characterize these four step-to-step transition types. Results show that, although individual preference occurs, the brachiation strides characterized by each transition type are mainly associated with speed. Yet, these four transitions seem to form a continuum rather than four distinct types. Energy recovery and collision fraction are used as estimators of mechanical efficiency of brachiation and, remarkably, these parameters do not differ between strides with different transition types. All strides show high energy recoveries (mean  = 70±11.4% and low collision fractions (mean  = 0.2±0.13, regardless of the step-to-step transition type used. We conclude that siamangs have efficient means of modifying locomotor speed during continuous contact brachiation by choosing particular step-to-step transition types, which all minimize collision fraction and enhance energy recovery.

  16. The improved fractional sub-equation method and its applications to the space–time fractional differential equations in fluid mechanics

    International Nuclear Information System (INIS)

    Guo, Shimin; Mei, Liquan; Li, Ying; Sun, Youfa

    2012-01-01

    By introducing a new general ansätz, the improved fractional sub-equation method is proposed to construct analytical solutions of nonlinear evolution equations involving Jumarie's modified Riemann–Liouville derivative. By means of this method, the space–time fractional Whitham–Broer–Kaup and generalized Hirota–Satsuma coupled KdV equations are successfully solved. The obtained results show that the proposed method is quite effective, promising and convenient for solving nonlinear fractional differential equations. -- Highlights: ► We propose a novel method for nonlinear fractional differential equations. ► Two important fractional differential equations in fluid mechanics are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained. ► These solutions will advance the understanding of nonlinear physical phenomena.

  17. A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

    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(Klog⁡K. 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.

  18. Topologically induced fractional Hall steps in the integer quantum Hall regime of MoS 2

    Science.gov (United States)

    Firoz Islam, SK; Benjamin, Colin

    2016-09-01

    The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. In particular, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivitity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms.

  19. Two-step Raman spectroscopy method for tumor diagnosis

    Science.gov (United States)

    Zakharov, V. P.; Bratchenko, I. A.; Kozlov, S. V.; Moryatov, A. A.; Myakinin, O. O.; Artemyev, D. N.

    2014-05-01

    Two-step Raman spectroscopy phase method was proposed for differential diagnosis of malignant tumor in skin and lung tissue. It includes detection of malignant tumor in healthy tissue on first step with identification of concrete cancer type on the second step. Proposed phase method analyze spectral intensity alteration in 1300-1340 and 1640-1680 cm-1 Raman bands in relation to the intensity of the 1450 cm-1 band on first step, and relative differences between RS intensities for tumor area and healthy skin closely adjacent to the lesion on the second step. It was tested more than 40 ex vivo samples of lung tissue and more than 50 in vivo skin tumors. Linear Discriminant Analysis, Quadratic Discriminant Analysis and Support Vector Machine were used for tumors type classification on phase planes. It is shown that two-step phase method allows to reach 88.9% sensitivity and 87.8% specificity for malignant melanoma diagnosis (skin cancer); 100% sensitivity and 81.5% specificity for adenocarcinoma diagnosis (lung cancer); 90.9% sensitivity and 77.8% specificity for squamous cell carcinoma diagnosis (lung cancer).

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

    KAUST Repository

    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.

  1. Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation

    OpenAIRE

    Choe, Hui-Chol; Kang, Yong-Suk

    2013-01-01

    We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial conditions and boundary conditions to nonlinear fractional integral equations and consider the relations between them. We present a Spline Collocation Method and prove the existence, uniqueness and convergence of approximate solution as well as error estimatio...

  2. Robust fractional order differentiators using generalized modulating functions method

    KAUST Repository

    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.

  3. Robust fractional order differentiators using generalized modulating functions method

    KAUST Repository

    Liu, Dayan; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

  4. Lipoprotein metabolism in familial hypercholesterolemia: Serial assessment using a one-step ultracentrifugation method

    Directory of Open Access Journals (Sweden)

    Hayato Tada

    2015-04-01

    Full Text Available Objectives: It is well known that familial hypercholesterolemia (FH is a common inherited disorder that can markedly elevate the level of plasma LDL cholesterol. However, little data exists regarding the clinical impact of the plasma triglyceride (TG-rich lipoprotein fraction, including VLDL and IDL, in FH. Thus, we assessed the hypothesis that the mutations in the LDL receptor modulate lipoprotein metabolism other than the LDL fraction. Design and methods: We investigated plasma lipoprotein with a one-step ultracentrifugation method for 146 controls (mean age=61.4±17.1 yr, mean LDL cholesterol=92.7±61.2 mg/dl, 213 heterozygous mutation-determined FH subjects (mean age=46.0±18.0 yr, mean LDL cholesterol=225.1±61.2 mg/dl, and 16 homozygous/compound heterozygous mutation-determined FH subjects (mean age=26.9±17.1 yr, mean LDL cholesterol=428.6±86.1 mg/dl. In addition, we evaluated cholesterol/TG ratio in each lipoprotein fraction separated by ultracentrifugation. Results: In addition to total cholesterol and LDL cholesterol levels, VLDL cholesterol (19.5±10.4, 25.2±19.3, 29.5±21.4 mg/dl, respectively and IDL cholesterol (8.3±3.7, 16.8±11.5, 40.0±37.3 mg/dl, respectively exhibited a tri-model distribution according to their status in LDL receptor mutation(s. Moreover, the ratios of cholesterol/TG of each lipoprotein fraction increased significantly in heterozygous FH and homozygous/compound heterozygous FH groups, compared with that of controls, suggesting that the abnormality in LDL receptor modulates the quality as well as the quantity of each lipoprotein fraction. Conclusions: Our results indicate that cholesterol in TG-rich lipoproteins, including VLDL and IDL, are significantly higher in FH subjects, revealing a tri-modal distribution according to the number of LDL receptor mutations. Keywords: LDL cholesterol, Familial hypercholesterolemia, Ultracentrifugation, Lipoprotein

  5. An efficient method for solving fractional Sturm-Liouville problems

    International Nuclear Information System (INIS)

    Al-Mdallal, Qasem M.

    2009-01-01

    The numerical approximation of the eigenvalues and the eigenfunctions of the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, is considered. The present results can be implemented on the numerical solution of the fractional diffusion-wave equation. The results show the simplicity and efficiency of the numerical method.

  6. Discrete adjoint of fractional step Navier-Stokes solver in generalized coordinates

    Science.gov (United States)

    Wang, Mengze; Mons, Vincent; Zaki, Tamer

    2017-11-01

    Optimization and control in transitional and turbulent flows require evaluation of gradients of the flow state with respect to the problem parameters. Using adjoint approaches, these high-dimensional gradients can be evaluated with a similar computational cost as the forward Navier-Stokes simulations. The adjoint algorithm can be obtained by discretizing the continuous adjoint Navier-Stokes equations or by deriving the adjoint to the discretized Navier-Stokes equations directly. The latter algorithm is necessary when the forward-adjoint relations must be satisfied to machine precision. In this work, our forward model is the fractional step solution to the Navier-Stokes equations in generalized coordinates, proposed by Rosenfeld, Kwak & Vinokur. We derive the corresponding discrete adjoint equations. We also demonstrate the accuracy of the combined forward-adjoint model, and its application to unsteady wall-bounded flows. This work has been partially funded by the Office of Naval Research (Grant N00014-16-1-2542).

  7. Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

    Science.gov (United States)

    Abuasad, Salah; Hashim, Ishak

    2018-04-01

    In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

  8. Improved perovskite phototransistor prepared using multi-step annealing method

    Science.gov (United States)

    Cao, Mingxuan; Zhang, Yating; Yu, Yu; Yao, Jianquan

    2018-02-01

    Organic-inorganic hybrid perovskites with good intrinsic physical properties have received substantial interest for solar cell and optoelectronic applications. However, perovskite film always suffers from a low carrier mobility due to its structural imperfection including sharp grain boundaries and pinholes, restricting their device performance and application potential. Here we demonstrate a straightforward strategy based on multi-step annealing process to improve the performance of perovskite photodetector. Annealing temperature and duration greatly affects the surface morphology and optoelectrical properties of perovskites which determines the device property of phototransistor. The perovskite films treated with multi-step annealing method tend to form highly uniform, well-crystallized and high surface coverage perovskite film, which exhibit stronger ultraviolet-visible absorption and photoluminescence spectrum compare to the perovskites prepared by conventional one-step annealing process. The field-effect mobilities of perovskite photodetector treated by one-step direct annealing method shows mobility as 0.121 (0.062) cm2V-1s-1 for holes (electrons), which increases to 1.01 (0.54) cm2V-1s-1 for that treated with muti-step slow annealing method. Moreover, the perovskite phototransistors exhibit a fast photoresponse speed of 78 μs. In general, this work focuses on the influence of annealing methods on perovskite phototransistor, instead of obtains best parameters of it. These findings prove that Multi-step annealing methods is feasible to prepared high performance based photodetector.

  9. Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators

    Directory of Open Access Journals (Sweden)

    Dumitru Baleanu

    2014-01-01

    Full Text Available We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. 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.

  10. A novel fractional technique for the modified point kinetics equations

    Directory of Open Access Journals (Sweden)

    Ahmed E. Aboanber

    2016-10-01

    Full Text Available A fractional model for the modified point kinetics equations is derived and analyzed. An analytical method is used to solve the fractional model for the modified point kinetics equations. This methodical technique is based on the representation of the neutron density as a power series of the relaxation time as a small parameter. The validity of the fractional model is tested for different cases of step, ramp and sinusoidal reactivity. The results show that the fractional model for the modified point kinetics equations is the best representation of neutron density for subcritical and supercritical reactors.

  11. On Solution of a Fractional Diffusion Equation by Homotopy Transform Method

    International Nuclear Information System (INIS)

    Salah, A.; Hassan, S.S.A.

    2012-01-01

    The homotopy analysis transform method (HATM) is applied in this work in order to find the analytical solution of fractional diffusion equations (FDE). These equations are obtained from standard diffusion equations by replacing a second-order space derivative by a fractional derivative of order α and a first order time derivative by a fractional derivative. Furthermore, some examples are given. Numerical results show that the homotopy analysis transform method is easy to implement and accurate when applied to a fractional diffusion equations.

  12. Solving point reactor kinetic equations by time step-size adaptable numerical methods

    International Nuclear Information System (INIS)

    Liao Chaqing

    2007-01-01

    Based on the analysis of effects of time step-size on numerical solutions, this paper showed the necessity of step-size adaptation. Based on the relationship between error and step-size, two-step adaptation methods for solving initial value problems (IVPs) were introduced. They are Two-Step Method and Embedded Runge-Kutta Method. PRKEs were solved by implicit Euler method with step-sizes optimized by using Two-Step Method. It was observed that the control error has important influence on the step-size and the accuracy of solutions. With suitable control errors, the solutions of PRKEs computed by the above mentioned method are accurate reasonably. The accuracy and usage of MATLAB built-in ODE solvers ode23 and ode45, both of which adopt Runge-Kutta-Fehlberg method, were also studied and discussed. (authors)

  13. Residual power series method for fractional Sharma-Tasso-Olever equation

    Directory of Open Access Journals (Sweden)

    Amit Kumar

    2016-02-01

    Full Text Available In this paper, we introduce a modified analytical approximate technique to obtain solution of time fractional Sharma-Tasso-Olever equation. First, we present an alternative framework of the Residual power series method (RPSM which can be used simply and effectively to handle nonlinear fractional differential equations arising in several physical phenomena. This method is basically based on the generalized Taylor series formula and residual error function. A good result is found between our solution and the given solution. It is shown that the proposed method is reliable, efficient and easy to implement on all kinds of fractional nonlinear problems arising in science and technology.

  14. The Effect of DNA Extraction Methods on Observed Microbial Communities from Fibrous and Liquid Rumen Fractions of Dairy Cows

    Directory of Open Access Journals (Sweden)

    Jueeli D. Vaidya

    2018-01-01

    Full Text Available DNA based methods have been widely used to study the complexity of the rumen microbiota, and it is well known that the method of DNA extraction is a critical step in enabling accurate assessment of this complexity. Rumen fluid (RF and fibrous content (FC fractions differ substantially in terms of their physical nature and associated microorganisms. The aim of this study was therefore to assess the effect of four DNA extraction methods (RBB, PBB, FDSS, PQIAmini differing in cell lysis and/or DNA recovery methods on the observed microbial diversity in RF and FC fractions using samples from four rumen cannulated dairy cows fed 100% grass silage (GS100, 67% GS and 33% maize silage (GS67MS33, 33% GS and 67% MS (GS33MS67, or 100% MS (MS100. An ANOVA statistical test was applied on DNA quality and yield measurements, and it was found that the DNA yield was significantly affected by extraction method (p < 0.001 and fraction (p < 0.001. The 260/280 ratio was not affected by extraction (p = 0.08 but was affected by fraction (p = 0.03. On the other hand, the 260/230 ratio was affected by extraction method (p < 0.001 but not affected by fraction (p = 0.8. However, all four extraction procedures yielded DNA suitable for further analysis of bacterial, archaeal and anaerobic fungal communities using quantitative PCR and pyrosequencing of relevant taxonomic markers. Redundancy analysis (RDA of bacterial 16S rRNA gene sequence data at the family level showed that there was a significant effect of rumen fraction (p = 0.012, and that PBB (p = 0.012 and FDSS (p = 0.024 also significantly contributed to explaining the observed variation in bacterial community composition. Whilst the DNA extraction method affected the apparent bacterial community composition, no single extraction method could be concluded to be ineffective. No obvious effect of DNA extraction method on the anaerobic fungi or archaea was observed, although fraction effects were evident for both. In

  15. Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method

    International Nuclear Information System (INIS)

    Bekir Ahmet; Güner Özkan

    2013-01-01

    In this paper, we use the fractional complex transform and the (G′/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann—Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations

  16. Influence of multi-step washing using Na2EDTA, oxalic acid and phosphoric acid on metal fractionation and spectroscopy characteristics from contaminated soil.

    Science.gov (United States)

    Wei, Meng; Chen, Jiajun

    2016-11-01

    A multi-step soil washing test using a typical chelating agent (Na 2 EDTA), 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 Na 2 EDTA-phosphoric-oxalic acid (EPO) and phosphoric-oxalic acid-Na 2 EDTA (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]).

  17. 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...... 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......, on the other hand, lighter than the single-step method....

  18. Strong Stability Preserving Two-step Runge–Kutta Methods

    KAUST Repository

    Ketcheson, David I.; Gottlieb, Sigal; Macdonald, Colin B.

    2011-01-01

    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.

  19. Strong Stability Preserving Two-step Runge–Kutta Methods

    KAUST Repository

    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.

  20. Wavelet Methods for Solving Fractional Order Differential Equations

    OpenAIRE

    A. K. Gupta; S. Saha Ray

    2014-01-01

    Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linea...

  1. Bio-oil fractionation and condensation

    Science.gov (United States)

    Brown, Robert C; Jones, Samuel T; Pollard, Anthony

    2013-07-02

    A method of fractionating bio-oil vapors which involves providing bio-oil vapors comprising bio-oil constituents is described. The bio-oil vapors are cooled in a first stage which comprises a condenser having passages for the bio-oil separated by a heat conducting wall from passages for a coolant. The coolant in the condenser of the first stage is maintained at a substantially constant temperature, set at a temperature in the range of 75 to 100.degree. C., to condense a first liquid fraction of liquefied bio-oil constituents in the condenser of the first stage. The first liquid fraction of liquified bio-oil constituents from the condenser in the first stage is collected. Also described are steps for subsequently recovering further liquid fractions of liquefied bio-oil constituents. Particular compositions of bio-oil condensation products are also described.

  2. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

    Science.gov (United States)

    Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

    2013-03-01

    In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

  3. Intelligent numerical methods applications to fractional calculus

    CERN Document Server

    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.

  4. Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

    Science.gov (United States)

    Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.

    2013-06-01

    In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.

  5. Stable multi-domain spectral penalty methods for fractional partial differential equations

    Science.gov (United States)

    Xu, Qinwu; Hesthaven, Jan S.

    2014-01-01

    We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

  6. Non-asymptotic fractional order differentiators via an algebraic parametric method

    KAUST Repository

    Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid

    2012-01-01

    Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

  7. Non-asymptotic fractional order differentiators via an algebraic parametric method

    KAUST Repository

    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.

  8. The Effect of DNA Extraction Methods on Observed Microbial Communities from Fibrous and Liquid Rumen Fractions of Dairy Cows.

    Science.gov (United States)

    Vaidya, Jueeli D; van den Bogert, Bartholomeus; Edwards, Joan E; Boekhorst, Jos; van Gastelen, Sanne; Saccenti, Edoardo; Plugge, Caroline M; Smidt, Hauke

    2018-01-01

    DNA based methods have been widely used to study the complexity of the rumen microbiota, and it is well known that the method of DNA extraction is a critical step in enabling accurate assessment of this complexity. Rumen fluid (RF) and fibrous content (FC) fractions differ substantially in terms of their physical nature and associated microorganisms. The aim of this study was therefore to assess the effect of four DNA extraction methods (RBB, PBB, FDSS, PQIAmini) differing in cell lysis and/or DNA recovery methods on the observed microbial diversity in RF and FC fractions using samples from four rumen cannulated dairy cows fed 100% grass silage (GS100), 67% GS and 33% maize silage (GS67MS33), 33% GS and 67% MS (GS33MS67), or 100% MS (MS100). An ANOVA statistical test was applied on DNA quality and yield measurements, and it was found that the DNA yield was significantly affected by extraction method ( p anaerobic fungal communities using quantitative PCR and pyrosequencing of relevant taxonomic markers. Redundancy analysis (RDA) of bacterial 16S rRNA gene sequence data at the family level showed that there was a significant effect of rumen fraction ( p = 0.012), and that PBB ( p = 0.012) and FDSS ( p = 0.024) also significantly contributed to explaining the observed variation in bacterial community composition. Whilst the DNA extraction method affected the apparent bacterial community composition, no single extraction method could be concluded to be ineffective. No obvious effect of DNA extraction method on the anaerobic fungi or archaea was observed, although fraction effects were evident for both. In summary, the comprehensive assessment of observed communities of bacteria, archaea and anaerobic fungi described here provides insight into a rational basis for selecting an optimal methodology to obtain a representative picture of the rumen microbiota.

  9. Khater method for nonlinear Sharma Tasso-Olever (STO) equation of fractional order

    Science.gov (United States)

    Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Khan, Umar; Ahmed, Naveed

    In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations of fractional order. Number of solutions provided by this method is greater than other traditional methods. Exact solutions of nonlinear fractional order Sharma Tasso-Olever (STO) equation are expressed in terms of kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative and Fractional complex transform have been used for compatibility with fractional order sense. Solutions have been graphically simulated for understanding the physical aspects and importance of the method. A comparative discussion between our established results and the results obtained by existing ones is also presented. Our results clearly reveal that the proposed method is an effective, powerful and straightforward technique to work out new solutions of various types of differential equations of non-integer order in the fields of applied sciences and engineering.

  10. Generalized characteristic ratios assignment for commensurate fractional order systems with one zero.

    Science.gov (United States)

    Tabatabaei, Mohammad

    2017-07-01

    In this paper, a new method for determination of the desired characteristic equation and zero location of commensurate fractional order systems is presented. The concept of the characteristic ratio is extended for zero-including commensurate fractional order systems. The generalized version of characteristic ratios is defined such that the time-scaling property of characteristic ratios is also preserved. The monotonicity of the magnitude frequency response is employed to assign the generalized characteristic ratios for commensurate fractional order transfer functions with one zero. A simple pattern for characteristic ratios is proposed to reach a non-overshooting step response. Then, the proposed pattern is revisited to reach a low overshoot (say for example 2%) step response. Finally, zero-including controllers such as fractional order PI or lag (lead) controllers are designed using generalized characteristic ratios assignment method. Numerical simulations are provided to show the efficiency of the so designed controllers. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  11. Methods And Apparatus For Acoustic Fiber Fractionation

    Science.gov (United States)

    Brodeur, Pierre

    1999-11-09

    Methods and apparatus for acoustic fiber fractionation using a plane ultrasonic wave field interacting with water suspended fibers circulating in a channel flow using acoustic radiation forces to separate fibers into two or more fractions based on fiber radius, with applications of the separation concept in the pulp and paper industry. The continuous process relies on the use of a wall-mounted, rectangular cross-section piezoelectric ceramic transducer to selectively deflect flowing fibers as they penetrate the ultrasonic field. The described embodiment uses a transducer frequency of approximately 150 kHz. Depending upon the amount of dissolved gas in water, separation is obtained using a standing or a traveling wave field.

  12. A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

    Science.gov (United States)

    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.

  13. 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....

  14. A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Mehmet Ali Akinlar

    2013-01-01

    Full Text Available A new solution technique for analytical solutions of fractional partial differential equations (FPDEs is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as well as a more general fractional differential equation.

  15. Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schroedinger Equations

    International Nuclear Information System (INIS)

    Tang Chen; Zhang Fang; Yan Haiqing; Luo Tao; Chen Zhanqing

    2005-01-01

    We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three-step 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 Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.

  16. A multi-domain spectral method for time-fractional differential equations

    Science.gov (United States)

    Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

    2015-07-01

    This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

  17. Method for fractional solid-waste sampling and chemical analysis

    DEFF Research Database (Denmark)

    Riber, Christian; Rodushkin, I.; Spliid, Henrik

    2007-01-01

    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...... of variance (20-85% of the overall variation). Only by increasing the sample size significantly can this variance be reduced. The accuracy and short-term reproducibility of the chemical characterization were good, as determined by the analysis of several relevant certified reference materials. Typically, six...... to eight different certified reference materials representing a range of concentrations levels and matrix characteristics were included. Based on the documentation provided, the methods introduced were considered satisfactory for characterization of the chemical composition of waste-material fractions...

  18. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

    OpenAIRE

    Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

    2013-01-01

    In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and technique...

  19. Computational Challenge of Fractional Differential Equations and the Potential Solutions: A Survey

    Directory of Open Access Journals (Sweden)

    Chunye Gong

    2015-01-01

    Full Text Available We present a survey of fractional differential equations and in particular of the computational cost for their numerical solutions from the view of computer science. The computational complexities of time fractional, space fractional, and space-time fractional equations are O(N2M, O(NM2, and O(NM(M + N compared with O(MN for the classical partial differential equations with finite difference methods, where M, N are the number of space grid points and time steps. The potential solutions for this challenge include, but are not limited to, parallel computing, memory access optimization (fractional precomputing operator, short memory principle, fast Fourier transform (FFT based solutions, alternating direction implicit method, multigrid method, and preconditioner technology. The relationships of these solutions for both space fractional derivative and time fractional derivative are discussed. The authors pointed out that the technologies of parallel computing should be regarded as a basic method to overcome this challenge, and some attention should be paid to the fractional killer applications, high performance iteration methods, high order schemes, and Monte Carlo methods. Since the computation of fractional equations with high dimension and variable order is even heavier, the researchers from the area of mathematics and computer science have opportunity to invent cornerstones in the area of fractional calculus.

  20. Stability and delay sensitivity of neutral fractional-delay systems.

    Science.gov (United States)

    Xu, Qi; Shi, Min; Wang, Zaihua

    2016-08-01

    This paper generalizes the stability test method via integral estimation for integer-order neutral time-delay systems to neutral fractional-delay systems. The key step in stability test is the calculation of the number of unstable characteristic roots that is described by a definite integral over an interval from zero to a sufficient large upper limit. Algorithms for correctly estimating the upper limits of the integral are given in two concise ways, parameter dependent or independent. A special feature of the proposed method is that it judges the stability of fractional-delay systems simply by using rough integral estimation. Meanwhile, the paper shows that for some neutral fractional-delay systems, the stability is extremely sensitive to the change of time delays. Examples are given for demonstrating the proposed method as well as the delay sensitivity.

  1. [Soil organic carbon fractionation methods and their applications in farmland ecosystem research: a review].

    Science.gov (United States)

    Zhang, Guo; Cao, Zhi-ping; Hu, Chan-juan

    2011-07-01

    Soil organic carbon is of heterogeneity in components. The active components are sensitive to agricultural management, while the inert components play an important role in carbon fixation. Soil organic carbon fractionation mainly includes physical, chemical, and biological fractionations. Physical fractionation is to separate the organic carbon into active and inert components based on the density, particle size, and its spatial distribution; chemical fractionation is to separate the organic carbon into various components based on the solubility, hydrolizability, and chemical reactivity of organic carbon in a variety of extracting agents. In chemical fractionation, the dissolved organic carbon is bio-available, including organic acids, phenols, and carbohydrates, and the acid-hydrolyzed organic carbon can be divided into active and inert organic carbons. Simulated enzymatic oxidation by using KMnO4 can separate organic carbon into active and non-active carbon. Biological fractionation can differentiate microbial biomass carbon and potential mineralizable carbon. Under different farmland management practices, the chemical composition and pool capacity of soil organic carbon fractions will have different variations, giving different effects on soil quality. To identify the qualitative or quantitative relationships between soil organic carbon components and carbon deposition, we should strengthen the standardization study of various fractionation methods, explore the integrated application of different fractionation methods, and sum up the most appropriate organic carbon fractionation method or the appropriate combined fractionation methods for different farmland management practices.

  2. Solving Fokker-Planck Equations on Cantor Sets Using Local Fractional Decomposition Method

    Directory of Open Access Journals (Sweden)

    Shao-Hong Yan

    2014-01-01

    Full Text Available The local fractional decomposition method is applied to approximate the solutions for Fokker-Planck equations on Cantor sets with local fractional derivative. The obtained results give the present method that is very effective and simple for solving the differential equations on Cantor set.

  3. Fourier spectral methods for fractional-in-space reaction-diffusion equations

    KAUST Repository

    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.

  4. Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method

    Directory of Open Access Journals (Sweden)

    A. A. Hemeda

    2013-01-01

    Full Text Available An extension of the so-called new iterative method (NIM has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM and the variational iteration method (VIM reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.

  5. Recurrence of random walks with long-range steps generated by fractional Laplacian matrices on regular networks and simple cubic lattices

    Science.gov (United States)

    Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.

    2017-12-01

    We analyze a Markovian random walk strategy on undirected regular networks involving power matrix functions of the type L\\frac{α{2}} where L indicates a ‘simple’ Laplacian matrix. We refer to such walks as ‘fractional random walks’ with admissible interval 0walk. From these analytical results we establish a generalization of Polya’s recurrence theorem for fractional random walks on d-dimensional infinite lattices: The fractional random walk is transient for dimensions d > α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0walk is transient for all lattice dimensions d=1, 2, .. and in the range 1≤slantα walk is transient only for lattice dimensions d≥slant 3 . The generalization of Polya’s recurrence theorem remains valid for the class of random walks with Lévy flight asymptotics for long-range steps. We also analyze the mean first passage probabilities, mean residence times, mean first passage times and global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0walk is generated by the non-diagonality of the fractional Laplacian matrix with Lévy-type heavy tailed inverse power law decay for the probability of long-range moves. This non-local and asymptotic behavior of the fractional random walk introduces small-world properties with the emergence of Lévy flights on large (infinite) lattices.

  6. Doubly labeled water method: in vivo oxygen and hydrogen isotope fractionation

    International Nuclear Information System (INIS)

    Schoeller, D.A.; Leitch, C.A.; Brown, C.

    1986-01-01

    The accuracy and precision of the doubly labeled water method for measuring energy expenditure are influenced by isotope fractionation during evaporative water loss and CO 2 excretion. To characterize in vivo isotope fractionation, we collected and isotopically analyzed physiological fluids and gases. Breath and transcutaneous water vapor were isotopically fractionated. The degree of fractionation indicated that the former was fractionated under equilibrium control at 37 0 C, and the latter was kinetically fractionated. Sweat and urine were unfractionated. By use of isotopic balance models, the fraction of water lost via fractionating routes was estimated from the isotopic abundances of body water, local drinking water, and dietary solids. Fractionated water loss averaged 23% (SD = 10%) of water turnover, which agreed with our previous estimates based on metabolic rate, but there was a systematic difference between the results based on O 2 and hydrogen. Corrections for isotopic fractionation of water lost in breath and (nonsweat) transcutaneous loss should be made when using labeled water to measure water turnover or CO 2 production

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

    KAUST Repository

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

    2016-01-01

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

  8. Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEs

    KAUST Repository

    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

  9. MIDPOINT TWO- STEPS RULE FOR THE SQUARE ROOT METHOD

    African Journals Online (AJOL)

    DR S.E UWAMUSI

    Aberth third order method for finding zeros of a polynomial in interval ... KEY WORDS: Square root iteration, midpoint two steps Method, ...... A New set of Methods for the simultaneous determination of zeros of polynomial equation and iterative ...

  10. Solution of fractional differential equations by using differential transform method

    International Nuclear Information System (INIS)

    Arikoglu, Aytac; Ozkol, Ibrahim

    2007-01-01

    In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply

  11. Solution of fractional differential equations by using differential transform method

    Energy Technology Data Exchange (ETDEWEB)

    Arikoglu, Aytac [Istanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Maslak, TR-34469 Istanbul (Turkey); Ozkol, Ibrahim [Istanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Maslak, TR-34469 Istanbul (Turkey)]. E-mail: ozkol@itu.edu.tr

    2007-12-15

    In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply.

  12. 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.

  13. New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

    Science.gov (United States)

    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.

  14. Analysis of a time fractional wave-like equation with the homotopy analysis method

    International Nuclear Information System (INIS)

    Xu Hang; Cang Jie

    2008-01-01

    The time fractional wave-like differential equation with a variable coefficient is studied analytically. By using a simple transformation, the governing equation is reduced to two fractional ordinary differential equations. Then the homotopy analysis method is employed to derive the solutions of these equations. The accurate series solutions are obtained. Especially, when h f =h g =-1, these solutions are exactly the same as those results given by the Adomian decomposition method. The present work shows the validity and great potential of the homotopy analysis method for solving nonlinear fractional differential equations. The basic idea described in this Letter is expected to be further employed to solve other similar nonlinear problems in fractional calculus

  15. Numerical Methods for Pricing American Options with Time-Fractional PDE Models

    Directory of Open Access Journals (Sweden)

    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.

  16. Considerations for the independent reaction times and step-by-step methods for radiation chemistry simulations

    Science.gov (United States)

    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.

  17. Vitrification and Devitrification of Rigid Amorphous Fraction of PET during Quasi-isothermal Cooling and Heating

    Science.gov (United States)

    Cebe, Peggy; Chen, Huipeng

    2009-03-01

    Poly(ethylene terephthalate), PET, was studied by quasi-isothermal (QI) Temperature Modulated Differential Scanning Calorimetry (TMDSC). For the first time, both the temperature dependent crystalline fraction and rigid amorphous fraction (RAF) were quantitatively analyzed during QI cooling and reheating. Specific reversing heat capacity measurements show that most RAF vitrifies step by step during QI cooling after completion of crystallization. Upon subsequent QI reheating, the RAF devitrifies also step by step and only a small RAF of 0.04 remains at 470K, while melting starts above 473K. To obtain the exact temperature of the start of melting, heat capacity measurements were made using subsequent standard DSC heating, after QI cooling. By combining this method with the QI results, the temperature dependent phase fractions were obtained during standard DSC heating. We conclude that RAF completely devitrifies before the temperature reaches the crystal melting endotherm under the conditions used in this work.

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

    Science.gov (United States)

    Narayanamoorthy, S; Kalyani, S

    2015-01-01

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

  19. Exact Solutions for Fractional Differential-Difference Equations by an Extended Riccati Sub-ODE Method

    International Nuclear Information System (INIS)

    Feng Qinghua

    2013-01-01

    In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann—Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established. (general)

  20. A Spiral Step-by-Step Educational Method for Cultivating Competent Embedded System Engineers to Meet Industry Demands

    Science.gov (United States)

    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…

  1. Influence of intra-fractional breathing movement in step-and-shoot IMRT

    International Nuclear Information System (INIS)

    Schaefer, M; Muenter, M W; Thilmann, C; Sterzing, F; Haering, P; Combs, S E; Debus, J

    2004-01-01

    Efforts have been made to extend the application of intensity-modulated radiotherapy to a variety of organs. One of the unanswered questions is whether breathing-induced organ motion may lead to a relevant over- or underdosage, e.g., in treatment plans for the irradiation of lung cancer. Theoretical considerations have been made concerning the different kinds of IMRT but there is still a lack of experimental data. We examined 18 points in a fraction of a clinical treatment plan of a NSCLC delivered in static IMRT with a new phantom and nine ionization chambers. Measurements were performed at a speed of 12 and 16 breathing cycles per minute. The dose differences between static points and moving target points ranged between -2.4% and +5.5% (mean: +0.2%, median: -0.1%) when moving with 12 cycles min -1 and between -3.6% and +5.0% (mean: -0.4%, median: -0.6%) when moving with 16 cycles min -1 . All differences of measurements with and without movements were below 5%, with one exception. In conclusion, our results underline that at least in static IMRT breathing effects (concerning target dose coverage) due to interplay effects between collimator leaf movement and target movement are of secondary importance and will not reduce the clinical value of IMRT in the step-and-shoot technique for irradiation of thoracic targets. (note)

  2. 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

  3. A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

    OpenAIRE

    Mehmet Ali Akinlar; Muhammet Kurulay

    2013-01-01

    A new solution technique for analytical solutions of fractional partial differential equations (FPDEs) is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as...

  4. A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

    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.

  5. New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods

    International Nuclear Information System (INIS)

    Saha Ray, S

    2016-01-01

    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. (paper)

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

    Directory of Open Access Journals (Sweden)

    S. Narayanamoorthy

    2015-01-01

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

  7. The Technique of Changing the Drive Method of Micro Step Drive and Sensorless Drive for Hybrid Stepping Motor

    Science.gov (United States)

    Yoneda, Makoto; Dohmeki, Hideo

    The position control system with the advantage large torque, low vibration, and high resolution can be obtained by the constant current micro step drive applied to hybrid stepping motor. However loss is large, in order not to be concerned with load torque but to control current uniformly. As the one technique of a position control system in which high efficiency is realizable, the same sensorless control as a permanent magnet motor is effective. But, it was the purpose that the control method proposed until now controls speed. Then, this paper proposed changing the drive method of micro step drive and sensorless drive. The change of the drive method was verified from the simulation and the experiment. On no load, it was checked not producing change of a large speed at the time of a change by making electrical angle and carrying out zero reset of the integrator. On load, it was checked that a large speed change arose. The proposed system could change drive method by setting up the initial value of an integrator using the estimated result, without producing speed change. With this technique, the low loss position control system, which employed the advantage of the hybrid stepping motor, has been built.

  8. Improved Full-Newton Step O(nL) Infeasible Interior-Point Method for Linear Optimization

    NARCIS (Netherlands)

    Gu, G.; Mansouri, H.; Zangiabadi, M.; Bai, Y.Q.; Roos, C.

    2009-01-01

    We present several improvements of the full-Newton step infeasible interior-point method for linear optimization introduced by Roos (SIAM J. Optim. 16(4):1110–1136, 2006). Each main step of the method consists of a feasibility step and several centering steps. We use a more natural feasibility step,

  9. Analysis of polymeric phenolics in red wines using different techniques combined with gel permeation chromatography fractionation.

    Science.gov (United States)

    Guadalupe, Zenaida; Soldevilla, Alberto; Sáenz-Navajas, María-Pilar; Ayestarán, Belén

    2006-04-21

    A multiple-step analytical method was developed to improve the analysis of polymeric phenolics in red wines. With a common initial step based on the fractionation of wine phenolics by gel permeation chromatography (GPC), different analytical techniques were used: high-performance liquid chromatography-diode array detection (HPLC-DAD), HPLC-mass spectrometry (MS), capillary zone electrophoresis (CZE) and spectrophotometry. This method proved to be valid for analyzing different families of phenolic compounds, such as monomeric phenolics and their derivatives, polymeric pigments and proanthocyanidins. The analytical characteristics of fractionation by GPC were studied and the method was fully validated, yielding satisfactory statistical results. GPC fractionation substantially improved the analysis of polymeric pigments by CZE, in terms of response, repeatability and reproducibility. It also represented an improvement in the traditional vanillin assay used for proanthocyanidin (PA) quantification. Astringent proanthocyanidins were also analyzed using a simple combined method that allowed these compounds, for which only general indexes were available, to be quantified.

  10. Hydrogen Solubility in Heavy Undefined Petroleum Fractions Using Group Contributions Methods

    Directory of Open Access Journals (Sweden)

    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%.

  11. Enriched reproducing kernel particle method for fractional advection-diffusion equation

    Science.gov (United States)

    Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam

    2018-06-01

    The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

  12. Comparing Multi-Step IMAC and Multi-Step TiO2 Methods for Phosphopeptide Enrichment

    Science.gov (United States)

    Yue, Xiaoshan; Schunter, Alissa; Hummon, Amanda B.

    2016-01-01

    Phosphopeptide enrichment from complicated peptide mixtures is an essential step for mass spectrometry-based phosphoproteomic studies to reduce sample complexity and ionization suppression effects. Typical methods for enriching phosphopeptides include immobilized metal affinity chromatography (IMAC) or titanium dioxide (TiO2) beads, which have selective affinity and can interact with phosphopeptides. In this study, the IMAC enrichment method was compared with the TiO2 enrichment method, using a multi-step enrichment strategy from whole cell lysate, to evaluate their abilities to enrich for different types of phosphopeptides. The peptide-to-beads ratios were optimized for both IMAC and TiO2 beads. Both IMAC and TiO2 enrichments were performed for three rounds to enable the maximum extraction of phosphopeptides from the whole cell lysates. The phosphopeptides that are unique to IMAC enrichment, unique to TiO2 enrichment, and identified with both IMAC and TiO2 enrichment were analyzed for their characteristics. Both IMAC and TiO2 enriched similar amounts of phosphopeptides with comparable enrichment efficiency. However, phosphopeptides that are unique to IMAC enrichment showed a higher percentage of multi-phosphopeptides, as well as a higher percentage of longer, basic, and hydrophilic phosphopeptides. Also, the IMAC and TiO2 procedures clearly enriched phosphopeptides with different motifs. Finally, further enriching with two rounds of TiO2 from the supernatant after IMAC enrichment, or further enriching with two rounds of IMAC from the supernatant TiO2 enrichment does not fully recover the phosphopeptides that are not identified with the corresponding multi-step enrichment. PMID:26237447

  13. Development of measurement method of void fraction distribution on subcooled flow boiling using neutron radiography

    International Nuclear Information System (INIS)

    Kureta, Masatoshi; Matsubayashi, Masahito; Akimoto, Hajime

    1999-03-01

    In relation to the development of a solid target of high intensity neutron source, plasma-facing components of fusion reactor and so forth, it is indispensable to estimate the void fraction for high-heat-load subcooled flow boiling of water. Since the existing prediction method of void fraction is based on the database for tubes, it is necessary to investigate extendibility of the existing prediction method to narrow-gap rectangular channels that is used in the high-heat-load devices. However, measurement method of void fraction in the narrow-gap rectangular channel has not been established yet because of the difficulty of measurement. The objectives of this investigation are development of a new system for bubble visualization and void fraction measurement on subcooled flow boiling in narrow-gap rectangular channels using the neutron radiography, and establishment of void fraction database by using this measurement system. This report describes the void fraction measurement method by the neutron radiography technique, and summarizes the measured void fraction data in one-side heated narrow-gap rectangular channels at subcooled boiling condition. (author)

  14. The response analysis of fractional-order stochastic system via generalized cell mapping method.

    Science.gov (United States)

    Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei

    2018-01-01

    This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.

  15. A two-step Hilbert transform method for 2D image reconstruction

    International Nuclear Information System (INIS)

    Noo, Frederic; Clackdoyle, Rolf; Pack, Jed D

    2004-01-01

    The paper describes a new accurate two-dimensional (2D) image reconstruction method consisting of two steps. In the first step, the backprojected image is formed after taking the derivative of the parallel projection data. In the second step, a Hilbert filtering is applied along certain lines in the differentiated backprojection (DBP) image. Formulae for performing the DBP step in fan-beam geometry are also presented. The advantage of this two-step Hilbert transform approach is that in certain situations, regions of interest (ROIs) can be reconstructed from truncated projection data. Simulation results are presented that illustrate very similar reconstructed image quality using the new method compared to standard filtered backprojection, and that show the capability to correctly handle truncated projections. In particular, a simulation is presented of a wide patient whose projections are truncated laterally yet for which highly accurate ROI reconstruction is obtained

  16. Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

    Directory of Open Access Journals (Sweden)

    Rahmatullah

    2018-03-01

    Full Text Available We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation

  17. The functional variable method for solving the fractional Korteweg ...

    Indian Academy of Sciences (India)

    The physical and engineering processes have been modelled by means of fractional ... very important role in various fields such as economics, chemistry, notably control the- .... In §3, the functional variable method is applied for finding exact.

  18. SU-F-J-66: Anatomy Deformation Based Comparison Between One-Step and Two-Step Optimization for Online ART

    International Nuclear Information System (INIS)

    Feng, Z; Yu, G; Qin, S; Li, D; Ma, C; Zhu, J; Yin, Y

    2016-01-01

    Purpose: This study investigated that how the quality of adapted plan was affected by inter-fractional anatomy deformation by using one-step and two-step optimization for on line adaptive radiotherapy (ART) procedure. Methods: 10 lung carcinoma patients were chosen randomly to produce IMRT plan by one-step and two-step algorithms respectively, and the prescribed dose was set as 60 Gy on the planning target volume (PTV) for all patients. To simulate inter-fractional target deformation, four specific cases were created by systematic anatomy variation; including target superior shift 0.5 cm, 0.3cm contraction, 0.3 cm expansion and 45-degree rotation. Based on these four anatomy deformation, adapted plan, regenerated plan and non-adapted plan were created to evaluate quality of adaptation. Adapted plans were generated automatically by using one-step and two-step algorithms respectively to optimize original plans, and regenerated plans were manually created by experience physicists. Non-adapted plans were produced by recalculating the dose distribution based on corresponding original plans. The deviations among these three plans were statistically analyzed by paired T-test. Results: In PTV superior shift case, adapted plans had significantly better PTV coverage by using two-step algorithm compared with one-step one, and meanwhile there was a significant difference of V95 by comparison with adapted and non-adapted plans (p=0.0025). In target contraction deformation, with almost same PTV coverage, the total lung received lower dose using one-step algorithm than two-step algorithm (p=0.0143,0.0126 for V20, Dmean respectively). In other two deformation cases, there were no significant differences observed by both two optimized algorithms. Conclusion: In geometry deformation such as target contraction, with comparable PTV coverage, one-step algorithm gave better OAR sparing than two-step algorithm. Reversely, the adaptation by using two-step algorithm had higher efficiency

  19. SU-F-J-66: Anatomy Deformation Based Comparison Between One-Step and Two-Step Optimization for Online ART

    Energy Technology Data Exchange (ETDEWEB)

    Feng, Z; Yu, G; Qin, S; Li, D [Shandong Normal University, Jinan, Shandong (China); Ma, C; Zhu, J; Yin, Y [Shandong Cancer Hospital and Institute, Jinan, Shandong (China)

    2016-06-15

    Purpose: This study investigated that how the quality of adapted plan was affected by inter-fractional anatomy deformation by using one-step and two-step optimization for on line adaptive radiotherapy (ART) procedure. Methods: 10 lung carcinoma patients were chosen randomly to produce IMRT plan by one-step and two-step algorithms respectively, and the prescribed dose was set as 60 Gy on the planning target volume (PTV) for all patients. To simulate inter-fractional target deformation, four specific cases were created by systematic anatomy variation; including target superior shift 0.5 cm, 0.3cm contraction, 0.3 cm expansion and 45-degree rotation. Based on these four anatomy deformation, adapted plan, regenerated plan and non-adapted plan were created to evaluate quality of adaptation. Adapted plans were generated automatically by using one-step and two-step algorithms respectively to optimize original plans, and regenerated plans were manually created by experience physicists. Non-adapted plans were produced by recalculating the dose distribution based on corresponding original plans. The deviations among these three plans were statistically analyzed by paired T-test. Results: In PTV superior shift case, adapted plans had significantly better PTV coverage by using two-step algorithm compared with one-step one, and meanwhile there was a significant difference of V95 by comparison with adapted and non-adapted plans (p=0.0025). In target contraction deformation, with almost same PTV coverage, the total lung received lower dose using one-step algorithm than two-step algorithm (p=0.0143,0.0126 for V20, Dmean respectively). In other two deformation cases, there were no significant differences observed by both two optimized algorithms. Conclusion: In geometry deformation such as target contraction, with comparable PTV coverage, one-step algorithm gave better OAR sparing than two-step algorithm. Reversely, the adaptation by using two-step algorithm had higher efficiency

  20. Assessing SOC labile fractions through respiration test, density-size fractionation and thermal analysis - A comparison of methods

    Science.gov (United States)

    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

  1. Stability of one-step methods in transient nonlinear heat conduction

    International Nuclear Information System (INIS)

    Hughes, J.R.

    1977-01-01

    The purpose of the present work is to ascertain practical stability conditions for one-step methods commonly used in transient nonlinear heat conduction analyses. The class of problems considered is governed by a temporally continuous, spatially discrete system involving the capacity matrix C, conductivity matrix K, heat supply vector, temperature vector and time differenciation. In the linear case, in which K and C are constant, the stability behavior of one-step methods is well known. But in this paper the concepts of stability, appropriate to the nonlinear problem, are thoroughly discussed. They of course reduce to the usual stability criterion for the linear, constant coefficient case. However, for nonlinear problems there are differences and these ideas are of key importance in obtaining practical stability conditions. Of particular importance is a recent result which indicates that, in a sense, the trapezoidal and midpoint families are quivalent. Thus, stability results for one family may be translated into a result for the other. The main results obtained are summarized as follows. The stability behavior of the explicit Euler method in the nonlinear regime is analogous to that for linear problems. In particular, an a priori step size restriction may be determined for each time step. The precise time step restriction on implicit conditionally stable members of the trapezoidal and midpoint families is shown not to be determinable a priori. Of considerable practical significance, unconditionally stable members of the trapezoidal and midpoint families are identified

  2. Nondestructive Determination of Reinforcement Volume Fractions in Particulate Composites : Ultrasonic Method

    International Nuclear Information System (INIS)

    Jeong, Hyun Jo

    1998-01-01

    A nondestructive ultrasonic technique is presented for estimating the reinforcement volume fractions of particulate composites. The proposed technique employs a theoretical model which accounts for composite microstructures, together with a measurement of ultrasonic velocity to determine the reinforcement volume fractions. The approach is used for a wide range of SiC particulate reinforced Al matrix (SiC p /AI) composites. The method is considered to be reliable in determining the reinforcement volume fractions. The technique could be adopted in a production unit for the quality assessment of the metal matrix particulate composite extrusions

  3. Dietary fibre enrichment from defatted rice bran by dry fractionation

    NARCIS (Netherlands)

    Wang, Jue; Suo, Geng; Wit, de Martin; Boom, Remko M.; Schutyser, Maarten A.I.

    2016-01-01

    Defatted rice bran is excellent source of dietary fibre. The mostly used lab-scale method to extract dietary fibre is not very efficient; dry fractionation is a more energy efficient alternative at larger scale. Three separation routes were studied: two-step electrostatic separation, sieving and

  4. Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods

    Directory of Open Access Journals (Sweden)

    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.

  5. Modified random hinge transport mechanics and multiple scattering step-size selection in EGS5

    International Nuclear Information System (INIS)

    Wilderman, S.J.; Bielajew, A.F.

    2005-01-01

    The new transport mechanics in EGS5 allows for significantly longer electron transport step sizes and hence shorter computation times than required for identical problems in EGS4. But as with all Monte Carlo electron transport algorithms, certain classes of problems exhibit step-size dependencies even when operating within recommended ranges, sometimes making selection of step-sizes a daunting task for novice users. Further contributing to this problem, because of the decoupling of multiple scattering and continuous energy loss in the dual random hinge transport mechanics of EGS5, there are two independent step sizes in EGS5, one for multiple scattering and one for continuous energy loss, each of which influences speed and accuracy in a different manner. Further, whereas EGS4 used a single value of fractional energy loss (ESTEPE) to determine step sizes at all energies, to increase performance by decreasing the amount of effort expended simulating lower energy particles, EGS5 permits the fractional energy loss values which are used to determine both the multiple scattering and continuous energy loss step sizes to vary with energy. This results in requiring the user to specify four fractional energy loss values when optimizing computations for speed. Thus, in order to simplify step-size selection and to mitigate step-size dependencies, a method has been devised to automatically optimize step-size selection based on a single material dependent input related to the size of problem tally region. In this paper we discuss the new transport mechanics in EGS5 and describe the automatic step-size optimization algorithm. (author)

  6. Doubled Shapiro steps in a topological Josephson junction

    Science.gov (United States)

    Li, Yu-Hang; Song, Juntao; Liu, Jie; Jiang, Hua; Sun, Qing-Feng; Xie, X. C.

    2018-01-01

    We study the transport properties of a superconductor-quantum spin Hall insulator-superconductor hybrid system in the presence of microwave radiation. Instead of adiabatic analysis or use of the resistively shunted junction model, we start from the microscopic Hamiltonian and calculate the d.c. current directly with the help of the nonequilibrium Green's function method. The numerical results show that (i) the I-V curves of background current due to multiple Andreev reflections exhibit a different structure from those in the conventional junctions, and (ii) all Shapiro steps are visible and appear one by one at high frequencies, while at low frequencies, the steps evolve exactly as the Bessel functions and the odd steps are completely suppressed, implying a fractional Josephson effect.

  7. Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

    Science.gov (United States)

    Agarwal, P.; El-Sayed, A. A.

    2018-06-01

    In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

  8. Comparison of the Screening Tests for Gestational Diabetes Mellitus between "One-Step" and "Two-Step" Methods among Thai Pregnant Women.

    Science.gov (United States)

    Luewan, Suchaya; Bootchaingam, Phenphan; Tongsong, Theera

    2018-01-01

    To compare the prevalence and pregnancy outcomes of GDM between those screened by the "one-step" (75 gm GTT) and "two-step" (100 gm GTT) methods. A prospective study was conducted on singleton pregnancies at low or average risk of GDM. All were screened between 24 and 28 weeks, using the one-step or two-step method based on patients' preference. The primary outcome was prevalence of GDM, and secondary outcomes included birthweight, gestational age, rates of preterm birth, small/large-for-gestational age, low Apgar scores, cesarean section, and pregnancy-induced hypertension. A total of 648 women were screened: 278 in the one-step group and 370 in the two-step group. The prevalence of GDM was significantly higher in the one-step group; 32.0% versus 10.3%. Baseline characteristics and pregnancy outcomes in both groups were comparable. However, mean birthweight was significantly higher among pregnancies with GDM diagnosed by the two-step approach (3204 ± 555 versus 3009 ± 666 g; p =0.022). Likewise, the rate of large-for-date tended to be higher in the two-step group, but was not significant. The one-step approach is associated with very high prevalence of GDM among Thai population, without clear evidence of better outcomes. Thus, this approach may not be appropriate for screening in a busy antenatal care clinic like our setting or other centers in developing countries.

  9. Improved Full-Newton Step O(nL) Infeasible Interior-Point Method for Linear Optimization

    OpenAIRE

    Gu, G.; Mansouri, H.; Zangiabadi, M.; Bai, Y.Q.; Roos, C.

    2009-01-01

    We present several improvements of the full-Newton step infeasible interior-point method for linear optimization introduced by Roos (SIAM J. Optim. 16(4):1110–1136, 2006). Each main step of the method consists of a feasibility step and several centering steps. We use a more natural feasibility step, which targets the ?+-center of the next pair of perturbed problems. As for the centering steps, we apply a sharper quadratic convergence result, which leads to a slightly wider neighborhood for th...

  10. Comparison of methods for the quantification of the different carbon fractions in atmospheric aerosol samples

    Science.gov (United States)

    Nunes, Teresa; Mirante, Fátima; Almeida, Elza; Pio, Casimiro

    2010-05-01

    Atmospheric carbon consists of: organic carbon (OC, including various organic compounds), elemental carbon (EC, or black carbon [BC]/soot, a non-volatile/light-absorbing carbon), and a small quantity of carbonate carbon. Thermal/optical methods (TOM) have been widely used for quantifying total carbon (TC), OC, and EC in ambient and source particulate samples. Unfortunately, the different thermal evolution protocols in use can result in a wide elemental carbon-to-total carbon variation. Temperature evolution in thermal carbon analysis is critical to the allocation of carbon fractions. Another critical point in OC and EC quantification by TOM is the interference of carbonate carbon (CC) that could be present in the particulate samples, mainly in the coarse fraction of atmospheric aerosol. One of the methods used to minimize this interference consists on the use of a sample pre-treatment with acid to eliminate CC prior to thermal analysis (Chow et al., 2001; Pio et al., 1994). In Europe, there is currently no standard procedure for determining the carbonaceous aerosol fraction, which implies that data from different laboratories at various sites are of unknown accuracy and cannot be considered comparable. In the framework of the EU-project EUSAAR, a comprehensive study has been carried out to identify the causes of differences in the EC measured using different thermal evolution protocols. From this study an optimised protocol, the EUSAAR-2 protocol, was defined (Cavali et al., 2009). During the last two decades thousands of aerosol samples have been taken over quartz filters at urban, industrial, rural and background sites, and also from plume forest fires and biomass burning in a domestic closed stove. These samples were analysed for OC and EC, by a TOM, similar to that in use in the IMPROVE network (Pio et al., 2007). More recently we reduced the number of steps in thermal evolution protocols, without significant repercussions in the OC/EC quantifications. In order

  11. SPAR-H Step-by-Step Guidance

    Energy Technology Data Exchange (ETDEWEB)

    W. J. Galyean; A. M. Whaley; D. L. Kelly; R. L. Boring

    2011-05-01

    This guide provides step-by-step guidance on the use of the SPAR-H method for quantifying Human Failure Events (HFEs). This guide is intended to be used with the worksheets provided in: 'The SPAR-H Human Reliability Analysis Method,' NUREG/CR-6883, dated August 2005. Each step in the process of producing a Human Error Probability (HEP) is discussed. These steps are: Step-1, Categorizing the HFE as Diagnosis and/or Action; Step-2, Rate the Performance Shaping Factors; Step-3, Calculate PSF-Modified HEP; Step-4, Accounting for Dependence, and; Step-5, Minimum Value Cutoff. The discussions on dependence are extensive and include an appendix that describes insights obtained from the psychology literature.

  12. SPAR-H Step-by-Step Guidance

    International Nuclear Information System (INIS)

    Galyean, W.J.; Whaley, A.M.; Kelly, D.L.; Boring, R.L.

    2011-01-01

    This guide provides step-by-step guidance on the use of the SPAR-H method for quantifying Human Failure Events (HFEs). This guide is intended to be used with the worksheets provided in: 'The SPAR-H Human Reliability Analysis Method,' NUREG/CR-6883, dated August 2005. Each step in the process of producing a Human Error Probability (HEP) is discussed. These steps are: Step-1, Categorizing the HFE as Diagnosis and/or Action; Step-2, Rate the Performance Shaping Factors; Step-3, Calculate PSF-Modified HEP; Step-4, Accounting for Dependence, and; Step-5, Minimum Value Cutoff. The discussions on dependence are extensive and include an appendix that describes insights obtained from the psychology literature.

  13. 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)

  14. Q-Step methods for Newton-Jacobi operator equation | Uwasmusi ...

    African Journals Online (AJOL)

    The paper considers the Newton-Jacobi operator equation for the solution of nonlinear systems of equations. Special attention is paid to the computational part of this method with particular reference to the q-step methods. Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 237-241 ...

  15. An Alternative Method to Gauss-Jordan Elimination: Minimizing Fraction Arithmetic

    Science.gov (United States)

    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…

  16. Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2013-01-01

    Full Text Available We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

  17. some generalized two-step block hybrid numerov method for solving ...

    African Journals Online (AJOL)

    Nwokem et al.

    ABSTRACT. This paper proposes a class of generalized two-step Numerov methods, a block hybrid type for the direct solution of general second order ordinary differential equations. Both the main method and additional methods were derived via interpolation and collocation procedures. The basic properties of zero ...

  18. The modified simple equation method for solving some fractional ...

    Indian Academy of Sciences (India)

    ... 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 ...

  19. 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.

  20. A New Void Fraction Measurement Method for Gas-Liquid Two-Phase Flow in Small Channels.

    Science.gov (United States)

    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.

  1. A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D Methods

    Directory of Open Access Journals (Sweden)

    Tamer Ahmed El-Sayed

    2017-01-01

    Full Text Available The exact solution for multistepped Timoshenko beam is derived using a set of fundamental solutions. This set of solutions is derived to normalize the solution at the origin of the coordinates. The start, end, and intermediate boundary conditions involve concentrated masses and linear and rotational elastic supports. The beam start, end, and intermediate equations are assembled using the present normalized transfer matrix (NTM. The advantage of this method is that it is quicker than the standard method because the size of the complete system coefficient matrix is 4 × 4. In addition, during the assembly of this matrix, there are no inverse matrix steps required. The validity of this method is tested by comparing the results of the current method with the literature. Then the validity of the exact stepped analysis is checked using experimental and FE(3D methods. The experimental results for stepped beams with single step and two steps, for sixteen different test samples, are in excellent agreement with those of the three-dimensional finite element FE(3D. The comparison between the NTM method and the finite element method results shows that the modal percentage deviation is increased when a beam step location coincides with a peak point in the mode shape. Meanwhile, the deviation decreases when a beam step location coincides with a straight portion in the mode shape.

  2. A modification of \\mathsf {WKB} method for fractional differential operators of Schrödinger's type

    Science.gov (United States)

    Sayevand, K.; Pichaghchi, K.

    2017-09-01

    In this paper, we were concerned with the description of the singularly perturbed differential equations within the scope of fractional calculus. However, we shall note that one of the main methods used to solve these problems is the so-called WKB method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the WKB to the scope of fractional derivative, we proposed a relatively new derivative called the local fractional derivative. By use of properties of local fractional derivative, we extend the WKB method in the scope of the fractional differential equation. By means of this extension, the WKB analysis based on the Borel resummation, for fractional differential operators of WKB type are investigated. The convergence and the Mittag-Leffler stability of the proposed approach is proven. The obtained results are in excellent agreement with the existing ones in open literature and it is shown that the present approach is very effective and accurate. Furthermore, we are mainly interested to construct the solution of fractional Schrödinger equation in the Mittag-Leffler form and how it leads naturally to this semi-classical approximation namely modified WKB.

  3. 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.

  4. A connection between the asymptotic iteration method and the continued fractions formalism

    International Nuclear Information System (INIS)

    Matamala, A.R.; Gutierrez, F.A.; Diaz-Valdes, J.

    2007-01-01

    In this work, we show that there is a connection between the asymptotic iteration method (a method to solve second order linear ordinary differential equations) and the older method of continued fractions to solve differential equations

  5. Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G-Expansion Method

    Directory of Open Access Journals (Sweden)

    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.

  6. Using a Three-Step Method in a Calculus Class: Extending the Worked Example

    Science.gov (United States)

    Miller, David

    2010-01-01

    This article discusses a three-step method that was used in a college calculus course. The three-step method was developed to help students understand the course material and transition to be more independent learners. In addition, the method helped students to transfer concepts from short-term to long-term memory while lowering cognitive load.…

  7. Fourier spectral methods for fractional-in-space reaction-diffusion equations

    KAUST Repository

    Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin

    2014-01-01

    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

  8. Gas phase fractionation method using porous ceramic membrane

    Science.gov (United States)

    Peterson, Reid A.; Hill, Jr., Charles G.; Anderson, Marc A.

    1996-01-01

    Flaw-free porous ceramic membranes fabricated from metal sols and coated onto a porous support are advantageously used in gas phase fractionation methods. Mean pore diameters of less than 40 .ANG., preferably 5-20 .ANG. and most preferably about 15 .ANG., are permeable at lower pressures than existing membranes. Condensation of gases in small pores and non-Knudsen membrane transport mechanisms are employed to facilitate and increase membrane permeability and permselectivity.

  9. Fractionation, solid-phase immobilization and chemical degradation of long pectin oligogalacturonides. Initial steps towards sequencing of oligosaccharides

    DEFF Research Database (Denmark)

    Guillaumie, Fanny; Justesen, Sune Frederik Lamdahl; Mutenda, K.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...... were produced in excellent purity (> 95%). Elution of OGAs followed by direct analysis of the peak fractions by MALDI-TOF MS. Purified OGAs (DP 5-7) were chemoselectively immobilized onto aminooxy-terminated polyethylene glycol polyacrylamide (PEGA) supports. Solid-phase anchoring took place...... at the reducing end of the oligosaccharide and resulted in the formation of an oxime linkage. The very high coupling yields confirmed the general suitability of aminooxy-PEGA resins for the immobilization of OGAs of different lengths. The OGA-functionalized PEGA supports were subsequently treated with aq TFA...

  10. Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

    Science.gov (United States)

    Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

    2018-03-01

    We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

  11. Stability of one-step methods in transient nonlinear heat conduction

    International Nuclear Information System (INIS)

    Hughes, J.R.

    1977-01-01

    The purpose of the present work is to ascertain practical stability conditions for one-step methods commonly used in transient nonlinear heat conduction analyses. In this paper the concepts of stability, appropriate to the nonlinear problem, are thoroughly discussed. They of course reduce to the usual stability critierion for the linear, constant coefficient case. However, for nonlinear problems there are differences and theses ideas are of key importance in obtaining practical stability conditions. Of particular importance is a recent result which indicates that, in a sense, the trapezoidal and midpoint families are equivalent. Thus, stability results for one family may be translated into a result for the other. The main results obtained are: The stability behaviour of the explicit Euler method in the nonlinear regime is analogous to that for linear problems. In particular, an a priori step size restriction may be determined for each time step. The precise time step restriction on implicit conditionally stable members of the trapezoidal and midpoint families is shown not to be determinable a priori. Of considerable practical significance, unconditionally stable members of the trapezoidal and midpoint families are identified. All notions of stability employed are motivated and defined, and their interpretations in practical computing are indicated. (Auth.)

  12. Development of evaluation method of fuel failure fraction during the High Temperature Engineering Test Reactor operation

    Energy Technology Data Exchange (ETDEWEB)

    Sawa, Kazuhiro; Yoshimuta, Shigeharu; Tobita, Tsutomu; Sato, Masashi [Japan Atomic Energy Research Inst., Oarai, Ibaraki (Japan). Oarai Research Establishment

    1997-05-01

    The High Temperature Engineering Test Reactor (HTTR) uses coated particles as fuel. During normal operation, short-lived noble gases are mainly released by diffusion from fuel particles with defects in their coating layers (i.e., failed particle). Since noble gases do not plate out on the inner surfaces of primary cooling system, their activities in primary coolant reflect fuel failure fraction in the core. An evaluation method was developed to predict failure fraction of coated fuel particles during normal operation of the HTTR. The method predicts core-average and hot plenum regionwise failure fractions based on the fractional releases, (R/B)s, of noble gases. The (R/B)s are calculated by fission gas concentration measurements in the primary cooling system of the HTTR. Recent fabrication data show that through-coatings failure fraction is extremely low. Then, fractional release from matrix contamination uranium, which is background for accurate evaluation of the fuel failure fraction, should be precisely predicted. This report describes an evaluation method of fuel failure fraction from measurements in the HTTR together with a fission gas release model from fuel compact containing failed particles and matrix contamination uranium. (author)

  13. Nonlinear Conservation Laws and Finite Volume Methods

    Science.gov (United States)

    Leveque, Randall J.

    Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

  14. 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)

  15. Mass fractionation processes of transition metal isotopes

    Science.gov (United States)

    Zhu, X. K.; Guo, Y.; Williams, R. J. P.; O'Nions, R. K.; Matthews, A.; Belshaw, N. S.; Canters, G. W.; de Waal, E. C.; Weser, U.; Burgess, B. K.; Salvato, B.

    2002-06-01

    Recent advances in mass spectrometry make it possible to utilise isotope variations of transition metals to address some important issues in solar system and biological sciences. Realisation of the potential offered by these new isotope systems however requires an adequate understanding of the factors controlling their isotope fractionation. Here we show the results of a broadly based study on copper and iron isotope fractionation during various inorganic and biological processes. These results demonstrate that: (1) naturally occurring inorganic processes can fractionate Fe isotope to a detectable level even at temperature ˜1000°C, which challenges the previous view that Fe isotope variations in natural system are unique biosignatures; (2) multiple-step equilibrium processes at low temperatures may cause large mass fractionation of transition metal isotopes even when the fractionation per single step is small; (3) oxidation-reduction is an importation controlling factor of isotope fractionation of transition metal elements with multiple valences, which opens a wide range of applications of these new isotope systems, ranging from metal-silicate fractionation in the solar system to uptake pathways of these elements in biological systems; (4) organisms incorporate lighter isotopes of transition metals preferentially, and transition metal isotope fractionation occurs stepwise along their pathways within biological systems during their uptake.

  16. Detection of protein concentrations using a pH-step titration method

    NARCIS (Netherlands)

    Kruise, J.; Kruise, J.; Eijkel, Jan C.T.; Bergveld, Piet

    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

  17. Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods

    International Nuclear Information System (INIS)

    Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang

    2014-01-01

    In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same

  18. 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.

  19. An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    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.

  20. N-terminus of Cardiac Myosin Essential Light Chain Modulates Myosin Step-Size

    Science.gov (United States)

    Wang, Yihua; Ajtai, Katalin; Kazmierczak, Katarzyna; Szczesna-Cordary, Danuta; Burghardt, Thomas P.

    2016-01-01

    Muscle myosin cyclically hydrolyzes ATP to translate actin. Ventricular cardiac myosin (βmys) moves actin with three distinct unitary step-sizes resulting from its lever-arm rotation and with step-frequencies that are modulated in a myosin regulation mechanism. The lever-arm associated essential light chain (vELC) binds actin by its 43 residue N-terminal extension. Unitary steps were proposed to involve the vELC N-terminal extension with the 8 nm step engaging the vELC/actin bond facilitating an extra ~19 degrees of lever-arm rotation while the predominant 5 nm step forgoes vELC/actin binding. A minor 3 nm step is the unlikely conversion of the completed 5 to the 8 nm step. This hypothesis was tested using a 17 residue N-terminal truncated vELC in porcine βmys (Δ17βmys) and a 43 residue N-terminal truncated human vELC expressed in transgenic mouse heart (Δ43αmys). Step-size and step-frequency were measured using the Qdot motility assay. Both Δ17βmys and Δ43αmys had significantly increased 5 nm step-frequency and coincident loss in the 8 nm step-frequency compared to native proteins suggesting the vELC/actin interaction drives step-size preference. Step-size and step-frequency probability densities depend on the relative fraction of truncated vELC and relate linearly to pure myosin species concentrations in a mixture containing native vELC homodimer, two truncated vELCs in the modified homodimer, and one native and one truncated vELC in the heterodimer. Step-size and step-frequency, measured for native homodimer and at two or more known relative fractions of truncated vELC, are surmised for each pure species by using a new analytical method. PMID:26671638

  1. Exact Solution of Space-Time Fractional Coupled EW and Coupled MEW Equations Using Modified Kudryashov Method

    International Nuclear Information System (INIS)

    Raslan, K. R.; Ali, Khalid K.; EL-Danaf, Talaat S.

    2017-01-01

    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. (paper)

  2. 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.

  3. Numerical approximations of nonlinear fractional differential difference equations by using modified He-Laplace method

    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.

  4. The G′G-expansion method using modified Riemann–Liouville derivative for some space-time fractional differential equations

    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.

  5. 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.

  6. Validation of DRAGON side-step method for Bruce-A restart Phase-B physics tests

    International Nuclear Information System (INIS)

    Shen, W.; Ngo-Trong, C.; Davis, R.S.

    2004-01-01

    The DRAGON side-step method, developed at AECL, has a number of advantages over the all-DRAGON method that was used before. It is now the qualified method for reactivity-device calculations. Although the side-step-method-generated incremental cross sections have been validated against those previously calculated with the all-DRAGON method, it is highly desirable to validate the side-step method against device-worth measurements in power reactors directly. In this paper, the DRAGON side-step method was validated by comparison with the device-calibration measurements made in Bruce-A NGS Unit 4 restart Phase-B commissioning in 2003. The validation exercise showed excellent results, with the DRAGON code overestimating the measured ZCR worth by ∼5%. A sensitivity study was also performed in this paper to assess the effect of various DRAGON modelling techniques on the incremental cross sections. The assessment shows that the refinement of meshes in 3-D and the use of the side-step method are two major reasons contributing to the improved agreement between the calculated ZCR worths and the measurements. Use of different DRAGON versions, DRAGON libraries, local-parameter core conditions, and weighting techniques for the homogenization of tube clusters inside the ZCR have a very small effect on the ZCR incremental thermal absorption cross section and ZCR reactivity worth. (author)

  7. One-step isolation of γ-oryzanol from rice bran oil by non-aqueous hydrostatic countercurrent chromatography.

    Science.gov (United States)

    Angelis, Apostolis; Urbain, Aurélie; Halabalaki, Maria; Aligiannis, Nektarios; Skaltsounis, Alexios-Leandros

    2011-09-01

    The value-added γ-oryzanol was purified in one step from crude rice bran oil (RBO) using a preparative hydrostatic countercurrent chromatography (hydrostatic CCC) method, operating in the dual mode. The fractionation was performed using a non-aqueous biphasic solvent system consisting of heptane-acetonitrile-butanol (1.8:1.4:0.7, v/v/v), leading rapidly to the target compounds. Transfer of the analytical CCC method to large-scale isolation was also carried out yielding a high quantity-high purity fraction of γ-oryzanol. In addition, a fraction of hydroxylated triterpene alcohol ferulates (polar γ-oryzanol) was clearly separated and obtained. Furthermore, a fast HPLC-APCI(±)-HRMS method was developed and applied for the identification of γ-oryzanol as well as the polar γ-oryzanol in RBO and the resulting fractions. The purity of γ-oryzanol fraction was estimated as 97% based on HPLC-APCI-HRMS analysis. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  8. Design of quadrature mirror filter bank using Lagrange multiplier method based on fractional derivative constraints

    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.

  9. Stepping stability: effects of sensory perturbation

    Directory of Open Access Journals (Sweden)

    Krebs David E

    2005-05-01

    Full Text Available Abstract Background Few tools exist for quantifying locomotor stability in balance impaired populations. The objective of this study was to develop and evaluate a technique for quantifying stability of stepping in healthy people and people with peripheral (vestibular hypofunction, VH and central (cerebellar pathology, CB balance dysfunction by means a sensory (auditory perturbation test. Methods Balance impaired and healthy subjects performed a repeated bench stepping task. The perturbation was applied by suddenly changing the cadence of the metronome (100 beat/min to 80 beat/min at a predetermined time (but unpredictable by the subject during the trial. Perturbation response was quantified by computing the Euclidian distance, expressed as a fractional error, between the anterior-posterior center of gravity attractor trajectory before and after the perturbation was applied. The error immediately after the perturbation (Emax, error after recovery (Emin and the recovery response (Edif were documented for each participant, and groups were compared with ANOVA. Results Both balance impaired groups exhibited significantly higher Emax (p = .019 and Emin (p = .028 fractional errors compared to the healthy (HE subjects, but there were no significant differences between CB and VH groups. Although response recovery was slower for CB and VH groups compared to the HE group, the difference was not significant (p = .051. Conclusion The findings suggest that individuals with balance impairment have reduced ability to stabilize locomotor patterns following perturbation, revealing the fragility of their impairment adaptations and compensations. These data suggest that auditory perturbations applied during a challenging stepping task may be useful for measuring rehabilitation outcomes.

  10. A higher order numerical method for time fractional partial differential equations with nonsmooth data

    Science.gov (United States)

    Xing, Yanyuan; Yan, Yubin

    2018-03-01

    Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

  11. Fractional Resonance-Based RLβCα Filters

    Directory of Open Access Journals (Sweden)

    Todd J. Freeborn

    2013-01-01

    Full Text Available We propose the use of a fractional order capacitor and fractional order inductor with orders 0≤α,  β≤1, respectively, in a fractional RLβCα series circuit to realize fractional-step lowpass, highpass, bandpass, and bandreject filters. MATLAB simulations of lowpass and highpass responses having orders of (α+β=1.1, 1.5, and 1.9 and bandpass and bandreject responses having orders of 1.5 and 1.9 are given as examples. PSPICE simulations of 1.1, 1.5, and 1.9 order lowpass and 1.0 and 1.4 order bandreject filters using approximated fractional order capacitors and fractional order inductors verify the implementations.

  12. Proposal for a Five-Step Method to Elicit Expert Judgment

    Directory of Open Access Journals (Sweden)

    Duco Veen

    2017-12-01

    Full Text Available Elicitation is a commonly used tool to extract viable information from experts. The information that is held by the expert is extracted and a probabilistic representation of this knowledge is constructed. A promising avenue in psychological research is to incorporated experts’ prior knowledge in the statistical analysis. Systematic reviews on elicitation literature however suggest that it might be inappropriate to directly obtain distributional representations from experts. The literature qualifies experts’ performance on estimating elements of a distribution as unsatisfactory, thus reliably specifying the essential elements of the parameters of interest in one elicitation step seems implausible. Providing feedback within the elicitation process can enhance the quality of the elicitation and interactive software can be used to facilitate the feedback. Therefore, we propose to decompose the elicitation procedure into smaller steps with adjustable outcomes. We represent the tacit knowledge of experts as a location parameter and their uncertainty concerning this knowledge by a scale and shape parameter. Using a feedback procedure, experts can accept the representation of their beliefs or adjust their input. We propose a Five-Step Method which consists of (1 Eliciting the location parameter using the trial roulette method. (2 Provide feedback on the location parameter and ask for confirmation or adjustment. (3 Elicit the scale and shape parameter. (4 Provide feedback on the scale and shape parameter and ask for confirmation or adjustment. (5 Use the elicited and calibrated probability distribution in a statistical analysis and update it with data or to compute a prior-data conflict within a Bayesian framework. User feasibility and internal validity for the Five-Step Method are investigated using three elicitation studies.

  13. A two-step method for developing a control rod program for boiling water reactors

    International Nuclear Information System (INIS)

    Taner, M.S.; Levine, S.H.; Hsiao, M.Y.

    1992-01-01

    This paper reports on a two-step method that is established for the generation of a long-term control rod program for boiling water reactors (BWRs). The new method assumes a time-variant target power distribution in core depletion. In the new method, the BWR control rod programming is divided into two steps. In step 1, a sequence of optimal, exposure-dependent Haling power distribution profiles is generated, utilizing the spectral shift concept. In step 2, a set of exposure-dependent control rod patterns is developed by using the Haling profiles generated at step 1 as a target. The new method is implemented in a computer program named OCTOPUS. The optimization procedure of OCTOPUS is based on the method of approximation programming, in which the SIMULATE-E code is used to determine the nucleonics characteristics of the reactor core state. In a test in cycle length over a time-invariant, target Haling power distribution case because of a moderate application of spectral shift. No thermal limits of the core were violated. The gain in cycle length could be increased further by broadening the extent of the spetral shift

  14. Validation of a One-Step Method for Extracting Fatty Acids from Salmon, Chicken and Beef Samples.

    Science.gov (United States)

    Zhang, Zhichao; Richardson, Christine E; Hennebelle, Marie; Taha, Ameer Y

    2017-10-01

    Fatty acid extraction methods are time-consuming and expensive because they involve multiple steps and copious amounts of extraction solvents. In an effort to streamline the fatty acid extraction process, this study compared the standard Folch lipid extraction method to a one-step method involving a column that selectively elutes the lipid phase. The methods were tested on raw beef, salmon, and chicken. Compared to the standard Folch method, the one-step extraction process generally yielded statistically insignificant differences in chicken and salmon fatty acid concentrations, percent composition and weight percent. Initial testing showed that beef stearic, oleic and total fatty acid concentrations were significantly lower by 9-11% with the one-step method as compared to the Folch method, but retesting on a different batch of samples showed a significant 4-8% increase in several omega-3 and omega-6 fatty acid concentrations with the one-step method relative to the Folch. Overall, the findings reflect the utility of a one-step extraction method for routine and rapid monitoring of fatty acids in chicken and salmon. Inconsistencies in beef concentrations, although minor (within 11%), may be due to matrix effects. A one-step fatty acid extraction method has broad applications for rapidly and routinely monitoring fatty acids in the food supply and formulating controlled dietary interventions. © 2017 Institute of Food Technologists®.

  15. Stability analysis and time-step limits for a Monte Carlo Compton-scattering method

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.

    2010-01-01

    A Monte Carlo method for simulating Compton scattering in high energy density applications has been presented that models the photon-electron collision kinematics exactly [E. Canfield, W.M. Howard, E.P. Liang, Inverse Comptonization by one-dimensional relativistic electrons, Astrophys. J. 323 (1987) 565]. However, implementing this technique typically requires an explicit evaluation of the material temperature, which can lead to unstable and oscillatory solutions. In this paper, we perform a stability analysis of this Monte Carlo method and develop two time-step limits that avoid undesirable behavior. The first time-step limit prevents instabilities, while the second, more restrictive time-step limit avoids both instabilities and nonphysical oscillations. With a set of numerical examples, we demonstrate the efficacy of these time-step limits.

  16. Method of making stepped photographic density standards of radiographic photographs

    International Nuclear Information System (INIS)

    Borovin, I.V.; Kondina, M.A.

    1987-01-01

    In industrial radiography practice the need often arises for a prompt evaluation of the photographic density of an x-ray film. A method of making stepped photographic density standards for industrial radiography by contact printing from a negative is described. The method is intended for industrial radiation flaw detection laboratories not having specialized sensitometric equipment

  17. Synthesis and characterization of copper nanofluid by a novel one-step method

    International Nuclear Information System (INIS)

    Kumar, S. Ananda; Meenakshi, K. Shree; Narashimhan, B.R.V.; Srikanth, S.; Arthanareeswaran, G.

    2009-01-01

    This paper presents a novel one-step method for the preparation of stable, non-agglomerated copper nanofluids by reducing copper sulphate pentahydrate with sodium hypophosphite as reducing agent in ethylene glycol as base fluid by means of conventional heating. This is an in situ, one-step method which gives high yield of product with less time consumption. The characterization of the nanofluid is done by particle size analyzer, X-ray diffraction topography, UV-vis analysis and Fourier transform infrared spectroscopy (FT-IR) followed by the study of thermal conductivity of nanofluid by the transient hot wire method

  18. A NEW FRACTIONAL MODEL OF SINGLE DEGREE OF FREEDOM SYSTEM, BY USING GENERALIZED DIFFERENTIAL TRANSFORM METHOD

    Directory of Open Access Journals (Sweden)

    HASHEM SABERI NAJAFI

    2016-07-01

    Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.

  19. Fractional laser therapy – the next step in alleviating the symptoms of skin aging (own observations

    Directory of Open Access Journals (Sweden)

    Adam Halbina

    2014-05-01

    Full Text Available Skin aging is a natural process of the skin, which accelerates in menopause and is additionally intensified by accumulating effects of repeated exposure to solar UV radiation and other external factors. Anti-aging skin treatment and constant improvement of its methods have become an important area of current research. The need to apply effective skin anti-aging methods that minimize traumatization resulted in the development of fractional laser technology delivering a laser beam to microscopic column skin zones in order to achieve skin photo-remodeling.

  20. Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials”

    Directory of Open Access Journals (Sweden)

    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.

  1. Accurate step-FMCW ultrasound ranging and comparison with pulse-echo signaling methods

    Science.gov (United States)

    Natarajan, Shyam; Singh, Rahul S.; Lee, Michael; Cox, Brian P.; Culjat, Martin O.; Grundfest, Warren S.; Lee, Hua

    2010-03-01

    This paper presents a method setup for high-frequency ultrasound ranging based on stepped frequency-modulated continuous waves (FMCW), potentially capable of producing a higher signal-to-noise ratio (SNR) compared to traditional pulse-echo signaling. In current ultrasound systems, the use of higher frequencies (10-20 MHz) to enhance resolution lowers signal quality due to frequency-dependent attenuation. The proposed ultrasound signaling format, step-FMCW, is well-known in the radar community, and features lower peak power, wider dynamic range, lower noise figure and simpler electronics in comparison to pulse-echo systems. In pulse-echo ultrasound ranging, distances are calculated using the transmit times between a pulse and its subsequent echoes. In step-FMCW ultrasonic ranging, the phase and magnitude differences at stepped frequencies are used to sample the frequency domain. Thus, by taking the inverse Fourier transform, a comprehensive range profile is recovered that has increased immunity to noise over conventional ranging methods. Step-FMCW and pulse-echo waveforms were created using custom-built hardware consisting of an arbitrary waveform generator and dual-channel super heterodyne receiver, providing high SNR and in turn, accuracy in detection.

  2. Series expansion in fractional calculus and fractional differential equations

    OpenAIRE

    Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

    2009-01-01

    Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functio...

  3. A two-step method for rapid characterization of electroosmotic flows in capillary electrophoresis.

    Science.gov (United States)

    Zhang, Wenjing; He, Muyi; Yuan, Tao; Xu, Wei

    2017-12-01

    The measurement of electroosmotic flow (EOF) is important in a capillary electrophoresis (CE) experiment in terms of performance optimization and stability improvement. Although several methods exist, there are demanding needs to accurately characterize ultra-low electroosmotic flow rates (EOF rates), such as in coated capillaries used in protein separations. In this work, a new method, called the two-step method, was developed to accurately and rapidly measure EOF rates in a capillary, especially for measuring the ultra-low EOF rates in coated capillaries. In this two-step method, the EOF rates were calculated by measuring the migration time difference of a neutral marker in two consecutive experiments, in which a pressure driven was introduced to accelerate the migration and the DC voltage was reversed to switch the EOF direction. Uncoated capillaries were first characterized by both this two-step method and a conventional method to confirm the validity of this new method. Then this new method was applied in the study of coated capillaries. Results show that this new method is not only fast in speed, but also better in accuracy. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  4. Labile rhizosphere soil solution fraction for prediction of bioavailability of heavy metals and rare earth elements to plants.

    Science.gov (United States)

    Shan, Xiao-Quan; Wang, Zhongwen; Wang, Weisheng; Zhang, Shuzhen; Wen, Bei

    2003-02-01

    A labile rhizosphere soil solution fraction has been recommended to predict the bioavailability of heavy metals and rare earth elements to plants. This method used moist rhizosphere soil in combination with a mixture of 0.01 mol L(-1) of low-molecular-weight organic acids (LMWOAs) as extractant. The extracted soil solutions were fractionated into two colloidal fractions of soil solution fraction, F(lrss). For the soil solutions extracted with a mixture of LMWOAs the concentrations of heavy metals and rare earth elements in F(2) and F(3) were quite similar. However, the mean concentrations of Cr, Ni, Zn, Cu, Pb, Cd, La, Ce, Pr, and Nd in F(lrss) accounted for 79.9%, 91.3%, 90.8%, 60.1%, 77.5%, 75.3%, 81.2%, 77.2%, 80.3%, and 79.5%, respectively, of their concentrations in F(2). In contrast, there were no differences in the extractable metal concentrations between the three fractions while the first step of the method recommended by the European Community of Reference (BCR), where 0.1 mol L(-1) acetic acid was used as an extractant. The single correlation analysis was made between metal concentrations in the different fractions of soil solutions and their concentrations in wheat. If the first step of BCR method was used there was no good correlation between heavy metals in soil pools and that in wheat shoots and roots. When LMWAOs were used a good correlation was obtained between the concentrations of heavy metals in soil pools and that in wheat roots, which followed a general order of r(1 kD, LMWOAs) >r(0.2 microm, LMWOAs) approximately r(0.45 microm, LMWOAs). In the case of rare earth elements the good correlation was obtained for both the wheat roots and shoots. Generally, the correlation coefficients obtained by LMWAOs were better than that obtained by the first step of BCR method. Therefore, LMWAOs and F(lrss) were strongly recommended to predict the bioavailability of metals in soil pools to plants.

  5. The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

    Directory of Open Access Journals (Sweden)

    Hasan Bulut

    2013-01-01

    Full Text Available We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM to some interesting nonhomogeneous fractional ordinary differential equations (FODEs. Finally, we use the solutions to form two-dimensional (2D graphs, by using the symbolic algebra package Mathematica Program 7.

  6. Hydrogen production via catalytic steam reforming of fast pyrolysis oil fractions

    International Nuclear Information System (INIS)

    Wang, D.; Czernik, S.; Montane, D.; Mann, M.; Chornet, E.

    1997-01-01

    Hydrogen is the prototype of the environmentally cleanest fuel of interest for power generation using fuel cells, and as a co-adjuvant or autonomous transportation fuel in internal combustion engines. The conversion of biomass to hydrogen can be carried out through two distinct thermochemical strategies: (a) gasification followed by shift conversion; (b) catalytic steam reforming and shift conversion of specific fractions derived from fast pyrolysis and aqueous/steam processes of biomass. This paper shows that fast pyrolysis of biomass results in a bio-oil that can be adequately fractionated into valuable co-products leaving as by-product an aqueous fraction containing soluble organics (a mixture of alcohols, aldehydes and acids). This fraction can be converted to hydrogen by catalytic steam reforming followed by a shift conversion step. The methods used, the yields obtained and their economic significance will be discussed. (author)

  7. Reduced differential transform method for partial differential equations within local fractional derivative operators

    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.

  8. A simple graphical method for deriving kinetics of repair from fractionated and protracted irradiations

    International Nuclear Information System (INIS)

    Scalliet, P.; Schueren, E. van der; Erfmann, R.K.L.; Landuyt, W.

    1988-01-01

    The authors present a method for the derivation of the time constant of repair from fractionated and protracted irradiations, using formulae based on those derived by Dale (1985) and Liversage (1969) establishing the correlation between the biological effects of low dose rate and acute fractionated irradiation. (UK)

  9. 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)

  10. Experimental facility and void fraction calibration methods for impedance probes

    International Nuclear Information System (INIS)

    Oliveira, Fernando L. de; Rocha, Marcelo S.

    2013-01-01

    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)

  11. One step linear reconstruction method for continuous wave diffuse optical tomography

    Science.gov (United States)

    Ukhrowiyah, N.; Yasin, M.

    2017-09-01

    The method one step linear reconstruction method for continuous wave diffuse optical tomography is proposed and demonstrated for polyvinyl chloride based material and breast phantom. Approximation which used in this method is selecting regulation coefficient and evaluating the difference between two states that corresponding to the data acquired without and with a change in optical properties. This method is used to recovery of optical parameters from measured boundary data of light propagation in the object. The research is demonstrated by simulation and experimental data. Numerical object is used to produce simulation data. Chloride based material and breast phantom sample is used to produce experimental data. Comparisons of results between experiment and simulation data are conducted to validate the proposed method. The results of the reconstruction image which is produced by the one step linear reconstruction method show that the image reconstruction almost same as the original object. This approach provides a means of imaging that is sensitive to changes in optical properties, which may be particularly useful for functional imaging used continuous wave diffuse optical tomography of early diagnosis of breast cancer.

  12. Methods for growth of relatively large step-free SiC crystal surfaces

    Science.gov (United States)

    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.

  13. Dynamics of fractional vortices in long Josephson junctions

    International Nuclear Information System (INIS)

    Gaber, Tobias

    2007-01-01

    In this thesis static and dynamic properties of fractional vortices in long Josephson junctions are investigated. Fractional vortices are circulating supercurrents similar to the well-known Josephson fluxons. Yet, they show the distinguishing property of carrying only a fraction of the magnetic flux quantum. Fractional vortices are interesting non-linear objects. They spontaneously appear and are pinned at the phase discontinuity points of so called 0-κ junctions but can be bend or flipped by external forces like bias currents or magnetic fields. 0-κ junctions and fractional vortices are generalizations of the well-known 0-π junctions and semifluxons, where not only phase jumps of pi but arbitrary values denoted by kappa are considered. By using so-called artificial 0-κ junctions that are based on standard Nb-AlO x -Nb technology the classical dynamics of fractional vortices has been investigated experimentally for the very first time. Here, half-integer zero field steps could be observed. These voltage steps on the junction's current-voltage characteristics correspond to the periodic flipping/hopping of fractional vortices. In addition, the oscillatory eigenmodes of fractional vortices were investigated. In contrast to fluxons fractional vortices have an oscillatory eigenmode with a frequency within the plasma gap. Using resonance spectroscopy the dependence of the eigenmode frequency on the flux carried by the vortex and an applied bias current was determined. (orig.)

  14. The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

    Science.gov (United States)

    Khader, M M

    2013-10-01

    In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

  15. Preconditioned iterative methods for space-time fractional advection-diffusion equations

    Science.gov (United States)

    Zhao, Zhi; Jin, Xiao-Qing; Lin, Matthew M.

    2016-08-01

    In this paper, we propose practical numerical methods for solving a class of initial-boundary value problems of space-time fractional advection-diffusion equations. First, we propose an implicit method based on two-sided Grünwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual (preconditioned GMRES) method and preconditioned conjugate gradient normal residual (preconditioned CGNR) method with easily constructed preconditioners. Importantly, because resulting systems are Toeplitz-like, fast Fourier transform can be applied to significantly reduce the computational cost. We perform numerical experiments to demonstrate the efficiency of our preconditioners, even in cases with variable coefficients.

  16. A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations

    Directory of Open Access Journals (Sweden)

    Inci Cilingir Sungu

    2015-01-01

    Full Text Available A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.

  17. Aerial robot intelligent control method based on back-stepping

    Science.gov (United States)

    Zhou, Jian; Xue, Qian

    2018-05-01

    The aerial robot is characterized as strong nonlinearity, high coupling and parameter uncertainty, a self-adaptive back-stepping control method based on neural network is proposed in this paper. The uncertain part of the aerial robot model is compensated online by the neural network of Cerebellum Model Articulation Controller and robust control items are designed to overcome the uncertainty error of the system during online learning. At the same time, particle swarm algorithm is used to optimize and fix parameters so as to improve the dynamic performance, and control law is obtained by the recursion of back-stepping regression. Simulation results show that the designed control law has desired attitude tracking performance and good robustness in case of uncertainties and large errors in the model parameters.

  18. Extension of the root-locus method to a certain class of fractional-order systems.

    Science.gov (United States)

    Merrikh-Bayat, Farshad; Afshar, Mahdi; Karimi-Ghartemani, Masoud

    2009-01-01

    In this paper, the well-known root-locus method is developed for the special subset of linear time-invariant systems commonly known as fractional-order systems. Transfer functions of these systems are rational functions with polynomials of rational powers of the Laplace variable s. Such systems are defined on a Riemann surface because of their multi-valued nature. A set of rules for plotting the root loci on the first Riemann sheet is presented. The important features of the classical root-locus method such as asymptotes, roots condition on the real axis and breakaway points are extended to the fractional case. It is also shown that the proposed method can assess the closed-loop stability of fractional-order systems in the presence of a varying gain in the loop. Moreover, the effect of perturbation on the root loci is discussed. Three illustrative examples are presented to confirm the effectiveness of the proposed algorithm.

  19. Exact solutions to the time-fractional differential equations via local fractional derivatives

    Science.gov (United States)

    Guner, Ozkan; Bekir, Ahmet

    2018-01-01

    This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

  20. Comparison of fractionation methods for nitrogen and starch in maize and grass silages

    NARCIS (Netherlands)

    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

  1. Method of bringing nuclear power plant to fractional electrical load conditions

    International Nuclear Information System (INIS)

    Iljunin, V.G.; Kuznetsoy, I.A.; Murogov, V.M.; Shmelev, A.N.

    1978-01-01

    A method is described of bringing a nuclear power plant to fractional electric load conditions, which power plant comprises at least two nuclear reactors, at least one nuclear reactor being a breeder and both reactors transferring heat to the turbine working substance, consisting in that the consumption of the turbine working substance is reduced in accordance with a predetermined fractional load. At the same time, the amount of heat being transferred from the nuclear reactors to the turbine working substance is reduced, for which purpose the reactors are included in autonomous cooling circuits to successively transfer heat to the turbine working substance. The breeding reactor is included in the cooling circuit with a lower coolant temperature, the temperature of the coolant at the inlet and outlet of the breeder being reduced to a level ensuring the operation of the nuclear power plant in predetermined fractional load conditions, due to which the power of the breeder is increased, and afterheat is removed

  2. Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G-expansion method

    Directory of Open Access Journals (Sweden)

    Tarikul Islam

    2018-03-01

    Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

  3. Method of increasing anhydrosugars, pyroligneous fractions and esterified bio-oil

    Science.gov (United States)

    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.

  4. Modified enthalpy method for the simulation of melting and ...

    Indian Academy of Sciences (India)

    These include the implicit time stepping method of Voller & Cross. (1981), explicit enthalpy method of Tacke (1985), centroidal temperature correction method ... In variable viscosity method, viscosity is written as a function of liquid fraction.

  5. Laplace transform overcoming principle drawbacks in application of the variational iteration method to fractional heat equations

    Directory of Open Access Journals (Sweden)

    Wu Guo-Cheng

    2012-01-01

    Full Text Available This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the successive iterations.

  6. On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators

    Directory of Open Access Journals (Sweden)

    Hossein Jafari

    2016-04-01

    Full Text Available In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.

  7. Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation

    KAUST Repository

    Jin, Bangti; Lazarov, Raytcho; Pasciak, Joseph; Zhou, Zhi

    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.

  8. Development of a new rapid HPLC method for the fractionation of histones

    International Nuclear Information System (INIS)

    Gurley, L.R.; Valdez, J.G.; Prentice, D.A.; Spall, W.D.

    1983-01-01

    To study histone functions, it is necessary to fractionate the histones into their five classes (H1, H2A, H2B, H3 and H4) and then to subfractionate these classes into variants having slightly different primary structures and into different phosphorylated and acetylated forms. With the advent of high-performance liquid chromatography (HPLC), it was hoped that laborious and time-consuming conventional methods could be replaced by a simple, rapid, high-resolving HPLC method for fractionating histones. However, problems of irreversible adsorption of the histones to HPLC column packings discouraged this development. Our laboratory has now determined that the strong adsorption of histones to HPLC columns results from two different forces: (1) polar interactions between the histones and the silanol groups of silica-based HPLC column packing, and (2) hydrophobic interactions between the histones and the bound organic phase of the column packings. By minimizing these forces, we have succeeded in developing an HPLC method suitable for histone studies

  9. Apparatus and method for rapid separation and detection of hydrocarbon fractions in a fluid stream

    Science.gov (United States)

    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.

  10. On the fractional systems fault detection: a comparison between fractional and rational residual sensitivity

    International Nuclear Information System (INIS)

    Aoun, M.; Aribi, A.; Najar, S.; Abdelkrim, M.N.

    2011-01-01

    This paper shows the interest of extending the dynamic parity space fault detection method for fractional systems. Accordingly, a comparison between fractional and rational residual generators using the later method is presented. An analysis of fractional and rational residuals sensitivity shows the merits of the fractional residual generators. A numerical example illustrating the advantage of using fractional residual generators for fractional systems diagnosis is given.

  11. SPAR-H Step-by-Step Guidance

    Energy Technology Data Exchange (ETDEWEB)

    April M. Whaley; Dana L. Kelly; Ronald L. Boring; William J. Galyean

    2012-06-01

    Step-by-step guidance was developed recently at Idaho National Laboratory for the US Nuclear Regulatory Commission on the use of the Standardized Plant Analysis Risk-Human Reliability Analysis (SPAR-H) method for quantifying Human Failure Events (HFEs). This work was done to address SPAR-H user needs, specifically requests for additional guidance on the proper application of various aspects of the methodology. This paper overviews the steps of the SPAR-H analysis process and highlights some of the most important insights gained during the development of the step-by-step directions. This supplemental guidance for analysts is applicable when plant-specific information is available, and goes beyond the general guidance provided in existing SPAR-H documentation. The steps highlighted in this paper are: Step-1, Categorizing the HFE as Diagnosis and/or Action; Step-2, Rate the Performance Shaping Factors; Step-3, Calculate PSF-Modified HEP; Step-4, Accounting for Dependence, and; Step-5, Minimum Value Cutoff.

  12. Dietary fibre fractions in cereal foods measured by a new integrated AOAC method.

    Science.gov (United States)

    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.

  13. Two-step method for creating a gastric tube during laparoscopic-thoracoscopic Ivor-Lewis esophagectomy.

    Science.gov (United States)

    Liu, Yu; Li, Ji-Jia; Zu, Peng; Liu, Hong-Xu; Yu, Zhan-Wu; Ren, Yi

    2017-12-07

    To introduce a two-step method for creating a gastric tube during laparoscopic-thoracoscopic Ivor-Lewis esophagectomy and assess its clinical application. One hundred and twenty-two patients with middle or lower esophageal cancer who underwent laparoscopic-thoracoscopic Ivor-Lewis esophagectomy at Liaoning Cancer Hospital and Institute from March 2014 to March 2016 were included in this study, and divided into two groups based on the procedure used for creating a gastric tube. One group used a two-step method for creating a gastric tube, and the other group used the conventional method. The two groups were compared regarding the operating time, surgical complications, and number of stapler cartridges used. The mean operating time was significantly shorter in the two-step method group than in the conventional method group [238 (179-293) min vs 272 (189-347) min, P creating a gastric tube during laparoscopic-thoracoscopic Ivor-Lewis esophagectomy has the advantages of simple operation, minimal damage to the tubular stomach, and reduced use of stapler cartridges.

  14. A Three Step Explicit Method for Direct Solution of Third Order ...

    African Journals Online (AJOL)

    This study produces a three step discrete Linear Multistep Method for Direct solution of third order initial value problems of ordinary differential equations of the form y'''= f(x,y,y',y''). Taylor series expansion technique was adopted in the development of the method. The differential system from the basis polynomial function to ...

  15. Numerical treatment for solving two-dimensional space-fractional advection-dispersion equation using meshless method

    Science.gov (United States)

    Cheng, Rongjun; Sun, Fengxin; Wei, Qi; Wang, Jufeng

    2018-02-01

    Space-fractional advection-dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann-Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

  16. Sumudu transform series expansion method for solving the local fractional Laplace equation in fractal thermal problems

    Directory of Open Access Journals (Sweden)

    Guo Zheng-Hong

    2016-01-01

    Full Text Available In this article, the Sumudu transform series expansion method is used to handle the local fractional Laplace equation arising in the steady fractal heat-transfer problem via local fractional calculus.

  17. Two-step calibration method for multi-algorithm score-based face recognition systems by minimizing discrimination loss

    NARCIS (Netherlands)

    Susyanto, N.; Veldhuis, R.N.J.; Spreeuwers, L.J.; Klaassen, C.A.J.; Fierrez, J.; Li, S.Z.; Ross, A.; Veldhuis, R.; Alonso-Fernandez, F.; Bigun, J.

    2016-01-01

    We propose a new method for combining multi-algorithm score-based face recognition systems, which we call the two-step calibration method. Typically, algorithms for face recognition systems produce dependent scores. The two-step method is based on parametric copulas to handle this dependence. Its

  18. Anaerobic degradation of the various fractions of slaughterhouse wastewater

    Energy Technology Data Exchange (ETDEWEB)

    Sayed, S.; Zanden, J. van der; Wijffels, R.; Lettinga, G.

    1988-01-01

    The main objectives of the present investigations were to determine the maximum extent of anaerobic biological degradation of the soluble, colloidal and Coarse Suspended Solids fractions of slaughterhouse wastewater, in order to elucidate the mechanisms involved in the removal of these organic pollutant fractions and to determine the rate-limiting steps in the degradation of each fraction of the wastewater, and to assess the effects of the fractions on the methanogenic activity of the sludge.

  19. A Hybrid Dry and Aqueous Fractionation Method to Obtain Protein-Rich Fractions from Quinoa (Chenopodium quinoa Willd)

    NARCIS (Netherlands)

    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

  20. Design of a Two-Step Calibration Method of Kinematic Parameters for Serial Robots

    Science.gov (United States)

    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.

  1. Fractional order differentiation by integration: An application to fractional linear systems

    KAUST Repository

    Liu, Dayan

    2013-02-04

    In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.

  2. The large discretization step method for time-dependent partial differential equations

    Science.gov (United States)

    Haras, Zigo; Taasan, Shlomo

    1995-01-01

    A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

  3. Comparison of Three Analytical Methods for Separation of Mineral and Chelated Fraction from an Adulterated Zn-EDTA Fertilizer

    International Nuclear Information System (INIS)

    Khan, M.S.; Qazi, M.A.; Khan, N.A.; Mian, S.M.; Ahmed, N.; Ahmed, N.

    2013-01-01

    Summary: Different analytical procedures are being employed in the world to quantify the chelated portion in a Zn-EDTA fertilizer. Agriculture Department, Government of the Punjab is following Shahid's analytical method in this regard. This method is based on Ion-chromatography (IC) that separates the mineral zinc (Zn) from an adulterated Zn-EDTA fertilizer sample i.e. mixture of mineral and chelated Zn fractions. To find out its effectiveness and suitability, this comparative study was carried out by analyzing adulterated, non-adulterated Zn-EDTA standard and Zn-EDTA samples taken from market in thrice following three methods namely Shahid's (IC) analytical method, Atomic Absorption Spectrophotometric (AAS) method based on the principle of precipitating the mineral Zn fraction at high pH value by using alkali solution of suitable concentration and analysis of filtrate containing only chelated fraction and Association of Official Analytical Chemists (AOAC) method FM-841 respectively. Adulterated Zn-EDTA samples were prepared by mixing of known quantity of mineral Zn with chelated Zn-EDTA standard. The results showed that Shahid's analytical method and AAS method, both successfully estimated the chelated fraction. The AOAC FM-841 method was insensitive to put a ceiling on the mineral fraction hence did not furnish the reliable results. The Shahid's analytical method was selected being equallyeffective to produce reliable results both for solid and liquid Zn-EDTA samples. The AAS method was comparable in only liquid samples. (author)

  4. New Monte Carlo-based method to evaluate fission fraction uncertainties for the reactor antineutrino experiment

    Energy Technology Data Exchange (ETDEWEB)

    Ma, X.B., E-mail: maxb@ncepu.edu.cn; Qiu, R.M.; Chen, Y.X.

    2017-02-15

    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 {sup 235}U and {sup 239}Pu, 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. - Highlights: • The covariance coefficients between isotopes vs reactor burnup may change its sign because of two opposite effects. • The relation between fission fraction uncertainty and atomic density are first studied. • A new MC-based method of evaluating the covariance coefficients between isotopes was proposed.

  5. Fractional Klein-Gordon equation composed of Jumarie fractional derivative and its interpretation by a smoothness parameter

    Science.gov (United States)

    Ghosh, Uttam; Banerjee, Joydip; Sarkar, Susmita; Das, Shantanu

    2018-06-01

    Klein-Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein-Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein-Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein-Gordon equation, we can overcome the problem. The fractional Klein-Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases.

  6. Ion-step method for surface potential sensing of silicon nanowires

    NARCIS (Netherlands)

    Chen, S.; van Nieuwkasteele, Jan William; van den Berg, 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.

  7. expansion method for solving nonlinear space–time fractional

    Indian Academy of Sciences (India)

    2016-07-06

    Jul 6, 2016 ... Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059, Bursa, Turkey. ∗ ... of fractional calculus dates back to three hundred years ago. ... tions by fractional complex transformation [12,13].

  8. The Effect of Cow Manure and Vermicompost Application on Fractionation and Availability of Zinc and Copper in wheat planting

    Directory of Open Access Journals (Sweden)

    Alireza Hosseinpur`

    2017-03-01

    Full Text Available Introduction: Application of organic fertilizers in agricultural soils with low organic matter content is one of the best ways of nutrientsaddition to these soils. Different organic fertilizers have different effects on nutrient availability in soil. Moreover study of the distribution of nutrients in the soil allows investigating their mobility and bioavailability. The nutrients availability and kinetics of nutrients desorption into the soil solution is often closely related to the distribution of nutrients to different fractions in the soil. It has been assumed that the factors influencing metal fractionation and availability in soil include rate of amendment application, amount of nutrients in amendment, root-induced pH changes, metal binding by root exudates, root-induced changes of microbial activities, and metal depletion because of plant uptake. Materials and Methods: In this study, availability and fractionation of Zinc (Zn and Copper (Cu were compared in one calcareous soil amended with 0, 0.5, and 1% (w/w of cow manure and vermicompost in a completely randomized design. Also, wheat was planted in treated and untreated soils in greenhouse condition.Available Zn and Cu were determined using different methods (DTPA-TEA, AB-DTPA, and Mehlich 3. For Zn and Cu fractionation, the soil samples were sequentially extracted using an operationally defined sequential fractionation procedure, based on that employed by Tessier et al. (1979 in which increasingly strong extractants were used to release Zn and Cu associated with different soil fractions. Five Zn and Cu -fractions were extracted in the following sequence: Step 1: exchangeable fraction (a 8 ml volume of 1.0 MNaOAc (pH= 8.2 for 120 min. at room temperature., Step 2: carbonate-associated fraction (a 8 ml volume of 1.0 MNaOAc adjusted to pH 5.0 with acetic acid for 6 h at room temperature, Step 3: iron-manganese oxides-associated fraction (20 ml of 0.04 M NH2OH.HCl in 25% (v/v HOAc for 6 h at

  9. Fractionation for Biodiesel Purification Using Supercritical Carbon Dioxide

    Directory of Open Access Journals (Sweden)

    Chao-Yi Wei

    2014-02-01

    Full Text Available In recent years, biodegradable and alternative biodiesel has attracted increased attention worldwide. Producing biodiesel from biomass involves critical separation and purification technology. Conventional technologies such as gravitational settling, decantation, filtration, water washing, acid washing, organic solvent washing and absorbent applications are inefficient, less cost effective and environmentally less friendly. In this study supercritical carbon dioxide (SC-CO2 with few steps and a low environmental impact, was used for biodiesel fractionation from impure fatty acid methyl ester (FAME solution mixes. The method is suitable for application in a variety of biodiesel production processes requiring subsequent stages of purification. The fractionation and purification was carried out using continuous SC-CO2 fractionation equipment, consisting of three columns filled with stainless steel fragments. A 41.85% FAME content solution mix was used as the raw material in this study. Variables were a temperature range of 40–70 °C, pressure range of 10–30 MPa, SC-CO2 flow rate range of 7–21 mL/min and a retention time range of 30–90 min. The Taguchi method was used to identify optimal operating conditions. The results show that a separated FAME content of 99.94% was verified by GC-FID under optimal fractionation conditions, which are a temperature of 40 °C of, a pressure level of 30MPa and a flow rate of 7 mL/min of SC-CO2 for a retention time of 90 min.

  10. Approximate analytical solution of diffusion equation with fractional time derivative using optimal homotopy analysis method

    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.

  11. SWeRF--A method for estimating the relevant fine particle fraction in bulk materials for classification and labelling purposes.

    Science.gov (United States)

    Pensis, Ingeborg; Luetzenkirchen, Frank; Friede, Bernd

    2014-05-01

    In accordance with the European regulation for classification, labelling and packaging of substances and mixtures (CLP) as well as the criteria as set out in the Globally Harmonized System (GHS), fine fraction of crystalline silica (CS) has been classified as a specific target organ toxicity, the specific organ in this case being the lung. Generic cut-off values for products containing a fine fraction of CS trigger the need for a method for the quantification of the fine fraction of CS in bulk materials. This article describes the so-called SWeRF method, the size-weighted relevant fine fraction. The SWeRF method combines the particle size distribution of a powder with probability factors from the EN 481 standard and allows the relevant fine fraction of a material to be calculated. The SWeRF method has been validated with a number of industrial minerals. This will enable manufacturers and blenders to apply the CLP and GHS criteria for the classification of mineral products containing RCS a fine fraction of CS.

  12. Simulating transient dynamics of the time-dependent time fractional Fokker–Planck systems

    Energy Technology Data Exchange (ETDEWEB)

    Kang, Yan-Mei, E-mail: ymkang@mail.xjtu.edu.cn

    2016-09-16

    For a physically realistic type of time-dependent time fractional Fokker–Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker–Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed. - Highlights: • An iteration method is proposed for the transient dynamics of time-dependent time fractional Fokker–Planck equations. • The method is based on Fourier Series solution and the multi-step transition probability formula. • With the time-modulated subdiffusion on finite interval as example, the polarized motion orientation is disclosed. • With the time-modulated subdiffusion within a confined potential as example, the death of dynamic response is observed.

  13. Simulating transient dynamics of the time-dependent time fractional Fokker–Planck systems

    International Nuclear Information System (INIS)

    Kang, Yan-Mei

    2016-01-01

    For a physically realistic type of time-dependent time fractional Fokker–Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker–Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed. - Highlights: • An iteration method is proposed for the transient dynamics of time-dependent time fractional Fokker–Planck equations. • The method is based on Fourier Series solution and the multi-step transition probability formula. • With the time-modulated subdiffusion on finite interval as example, the polarized motion orientation is disclosed. • With the time-modulated subdiffusion within a confined potential as example, the death of dynamic response is observed.

  14. A Dimensionality Reduction-Based Multi-Step Clustering Method for Robust Vessel Trajectory Analysis

    Directory of Open Access Journals (Sweden)

    Huanhuan Li

    2017-08-01

    Full Text Available The Shipboard Automatic Identification System (AIS is crucial for navigation safety and maritime surveillance, data mining and pattern analysis of AIS information have attracted considerable attention in terms of both basic research and practical applications. Clustering of spatio-temporal AIS trajectories can be used to identify abnormal patterns and mine customary route data for transportation safety. Thus, the capacities of navigation safety and maritime traffic monitoring could be enhanced correspondingly. However, trajectory clustering is often sensitive to undesirable outliers and is essentially more complex compared with traditional point clustering. To overcome this limitation, a multi-step trajectory clustering method is proposed in this paper for robust AIS trajectory clustering. In particular, the Dynamic Time Warping (DTW, a similarity measurement method, is introduced in the first step to measure the distances between different trajectories. The calculated distances, inversely proportional to the similarities, constitute a distance matrix in the second step. Furthermore, as a widely-used dimensional reduction method, Principal Component Analysis (PCA is exploited to decompose the obtained distance matrix. In particular, the top k principal components with above 95% accumulative contribution rate are extracted by PCA, and the number of the centers k is chosen. The k centers are found by the improved center automatically selection algorithm. In the last step, the improved center clustering algorithm with k clusters is implemented on the distance matrix to achieve the final AIS trajectory clustering results. In order to improve the accuracy of the proposed multi-step clustering algorithm, an automatic algorithm for choosing the k clusters is developed according to the similarity distance. Numerous experiments on realistic AIS trajectory datasets in the bridge area waterway and Mississippi River have been implemented to compare our

  15. A Dimensionality Reduction-Based Multi-Step Clustering Method for Robust Vessel Trajectory Analysis.

    Science.gov (United States)

    Li, Huanhuan; Liu, Jingxian; Liu, Ryan Wen; Xiong, Naixue; Wu, Kefeng; Kim, Tai-Hoon

    2017-08-04

    The Shipboard Automatic Identification System (AIS) is crucial for navigation safety and maritime surveillance, data mining and pattern analysis of AIS information have attracted considerable attention in terms of both basic research and practical applications. Clustering of spatio-temporal AIS trajectories can be used to identify abnormal patterns and mine customary route data for transportation safety. Thus, the capacities of navigation safety and maritime traffic monitoring could be enhanced correspondingly. However, trajectory clustering is often sensitive to undesirable outliers and is essentially more complex compared with traditional point clustering. To overcome this limitation, a multi-step trajectory clustering method is proposed in this paper for robust AIS trajectory clustering. In particular, the Dynamic Time Warping (DTW), a similarity measurement method, is introduced in the first step to measure the distances between different trajectories. The calculated distances, inversely proportional to the similarities, constitute a distance matrix in the second step. Furthermore, as a widely-used dimensional reduction method, Principal Component Analysis (PCA) is exploited to decompose the obtained distance matrix. In particular, the top k principal components with above 95% accumulative contribution rate are extracted by PCA, and the number of the centers k is chosen. The k centers are found by the improved center automatically selection algorithm. In the last step, the improved center clustering algorithm with k clusters is implemented on the distance matrix to achieve the final AIS trajectory clustering results. In order to improve the accuracy of the proposed multi-step clustering algorithm, an automatic algorithm for choosing the k clusters is developed according to the similarity distance. Numerous experiments on realistic AIS trajectory datasets in the bridge area waterway and Mississippi River have been implemented to compare our proposed method with

  16. Fractional order absolute vibration suppression (AVS) controllers

    Science.gov (United States)

    Halevi, Yoram

    2017-04-01

    Absolute vibration suppression (AVS) is a control method for flexible structures. The first step is an accurate, infinite dimension, transfer function (TF), from actuation to measurement. This leads to the collocated, rate feedback AVS controller that in some cases completely eliminates the vibration. In case of the 1D wave equation, the TF consists of pure time delays and low order rational terms, and the AVS controller is rational. In all other cases, the TF and consequently the controller are fractional order in both the delays and the "rational parts". The paper considers stability, performance and actual implementation in such cases.

  17. Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

    Energy Technology Data Exchange (ETDEWEB)

    Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.

    2014-10-15

    Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.

  18. Fractionation study in bioleached metallurgy wastes using six-step sequential extraction.

    Science.gov (United States)

    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.

  19. Evaluation of surviving fraction using nonclonogenic staining densitometry method

    International Nuclear Information System (INIS)

    Nishiguchi, Iku; Ogawa, Koichi; Ito, Hisao; Hashimoto, Shozo

    1994-01-01

    This study was performed to compare our nonclonogenic survival assay (densitometry assay, DM assay) with the widely used clonogenic assay. The established cell lines (HaLa, RMUG, IMR, GOTO) were grown in F 10 medium. The cells were spread in 24-well plates, irradiated with different doses, cultured for about one week and stained with crystal violet after the culture period. Taking the transparent images of the stained well on the light source with the CCD camera, the images were collected with the matrix size 64 x 64, and the integrated optical density of the entire surface of each well was determined by computer with our original program. As the number of cells in the well is reflected by its staining density, the surviving fraction was calculated as the fraction of growth in the irradiated wells relative to controls. The survival curves obtained by the densitometry method showed good correlations with those obtained by clonogenic assay. It is possible to predict intrinsic radiosensitivity with this assay, even if the cells do not form good colonies. However, this method is based on measurements in cultures which depend on the metabolism and growth kinetics of the irradiated cells. Cells should grow exponetially in the same manner in any well to obtain a result similar to that of clonogenic assay, although growth kinetics may be altered by irradiation. This, the endpoint must be strictly standardized. (author)

  20. Methods and Algorithms for Solving Inverse Problems for Fractional Advection-Dispersion Equations

    KAUST Repository

    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

  1. A single-step method for rapid extraction of total lipids from green microalgae.

    Directory of Open Access Journals (Sweden)

    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.

  2. a Two-Step Classification Approach to Distinguishing Similar Objects in Mobile LIDAR Point Clouds

    Science.gov (United States)

    He, H.; Khoshelham, K.; Fraser, C.

    2017-09-01

    Nowadays, lidar is widely used in cultural heritage documentation, urban modeling, and driverless car technology for its fast and accurate 3D scanning ability. However, full exploitation of the potential of point cloud data for efficient and automatic object recognition remains elusive. Recently, feature-based methods have become very popular in object recognition on account of their good performance in capturing object details. Compared with global features describing the whole shape of the object, local features recording the fractional details are more discriminative and are applicable for object classes with considerable similarity. In this paper, we propose a two-step classification approach based on point feature histograms and the bag-of-features method for automatic recognition of similar objects in mobile lidar point clouds. Lamp post, street light and traffic sign are grouped as one category in the first-step classification for their inter similarity compared with tree and vehicle. A finer classification of the lamp post, street light and traffic sign based on the result of the first-step classification is implemented in the second step. The proposed two-step classification approach is shown to yield a considerable improvement over the conventional one-step classification approach.

  3. A stabilized Runge–Kutta–Legendre method for explicit super-time-stepping of parabolic and mixed equations

    International Nuclear Information System (INIS)

    Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D.

    2014-01-01

    Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s 2 times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful

  4. Nutrient digestibility and evaluation of protein and carbohydrate fractionation of citrus by-products

    DEFF Research Database (Denmark)

    Lashkari, Saman; Taghizadeh, Akbar

    2013-01-01

    The protein and carbohydrate fractionation and nutrient digestibility of citrus by‐products were determined. Ruminal, intestinal and total tract CP disappearance values were measured by a modified three‐step (MTSP) method and in vitro CP disappearance method (IVCP). Test feeds were orange pulp (OP...... to the results, it could be concluded that citrus by‐products have high nutritive value and also, the in vitro techniques can be easily used to determine of the nutritive value of citrus by‐products....

  5. Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2014-01-01

    Full Text Available We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.

  6. Developing Methods for Fraction Cover Estimation Toward Global Mapping of Ecosystem Composition

    Science.gov (United States)

    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.

  7. Study of the properties of the anthracene fraction by the thermogravimetric method

    Energy Technology Data Exchange (ETDEWEB)

    Belkina, T.V.; Chernyak, P.E.; Ulanovskii, M.L.

    1980-01-01

    With the use of the TGA method, the effect of temperature, thermal exposure time, a179975d the medium on the relation of the rates and the intensity of the processes of distillation and synthesis during thermal treatment of the anthracene fraction were determined.

  8. Convergence and Stability of the Split-Step θ-Milstein Method for Stochastic Delay Hopfield Neural Networks

    Directory of Open Access Journals (Sweden)

    Qian Guo

    2013-01-01

    Full Text Available A new splitting method designed for the numerical solutions of stochastic delay Hopfield neural networks is introduced and analysed. Under Lipschitz and linear growth conditions, this split-step θ-Milstein method is proved to have a strong convergence of order 1 in mean-square sense, which is higher than that of existing split-step θ-method. Further, mean-square stability of the proposed method is investigated. Numerical experiments and comparisons with existing methods illustrate the computational efficiency of our method.

  9. Laplace transform series expansion method for solving the local fractional heat-transfer equation defined on Cantor sets

    Directory of Open Access Journals (Sweden)

    Sun Huan

    2016-01-01

    Full Text Available In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.

  10. One-step leapfrog ADI-FDTD method for simulating electromagnetic wave propagation in general dispersive media.

    Science.gov (United States)

    Wang, Xiang-Hua; Yin, Wen-Yan; Chen, Zhi Zhang David

    2013-09-09

    The one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is reformulated for simulating general electrically dispersive media. It models material dispersive properties with equivalent polarization currents. These currents are then solved with the auxiliary differential equation (ADE) and then incorporated into the one-step leapfrog ADI-FDTD method. The final equations are presented in the form similar to that of the conventional FDTD method but with second-order perturbation. The adapted method is then applied to characterize (a) electromagnetic wave propagation in a rectangular waveguide loaded with a magnetized plasma slab, (b) transmission coefficient of a plane wave normally incident on a monolayer graphene sheet biased by a magnetostatic field, and (c) surface plasmon polaritons (SPPs) propagation along a monolayer graphene sheet biased by an electrostatic field. The numerical results verify the stability, accuracy and computational efficiency of the proposed one-step leapfrog ADI-FDTD algorithm in comparison with analytical results and the results obtained with the other methods.

  11. Recursive regularization step for high-order lattice Boltzmann methods

    Science.gov (United States)

    Coreixas, Christophe; Wissocq, Gauthier; Puigt, Guillaume; Boussuge, Jean-François; Sagaut, Pierre

    2017-09-01

    A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from 104 to 106, and where a thorough analysis of the case at Re=3 ×104 is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.

  12. New solitary wave solutions of the time-fractional Cahn-Allen equation via the improved (G'/G)-expansion method

    Science.gov (United States)

    Batool, Fiza; Akram, Ghazala

    2018-05-01

    An improved (G'/G)-expansion method is proposed for extracting more general solitary wave solutions of the nonlinear fractional Cahn-Allen equation. The temporal fractional derivative is taken in the sense of Jumarie's fractional derivative. The results of this article are generalized and extended version of previously reported solutions.

  13. Single-Camera-Based Method for Step Length Symmetry Measurement in Unconstrained Elderly Home Monitoring.

    Science.gov (United States)

    Cai, Xi; Han, Guang; Song, Xin; Wang, Jinkuan

    2017-11-01

    single-camera-based gait monitoring is unobtrusive, inexpensive, and easy-to-use to monitor daily gait of seniors in their homes. However, most studies require subjects to walk perpendicularly to camera's optical axis or along some specified routes, which limits its application in elderly home monitoring. To build unconstrained monitoring environments, we propose a method to measure step length symmetry ratio (a useful gait parameter representing gait symmetry without significant relationship with age) from unconstrained straight walking using a single camera, without strict restrictions on walking directions or routes. according to projective geometry theory, we first develop a calculation formula of step length ratio for the case of unconstrained straight-line walking. Then, to adapt to general cases, we propose to modify noncollinear footprints, and accordingly provide general procedure for step length ratio extraction from unconstrained straight walking. Our method achieves a mean absolute percentage error (MAPE) of 1.9547% for 15 subjects' normal and abnormal side-view gaits, and also obtains satisfactory MAPEs for non-side-view gaits (2.4026% for 45°-view gaits and 3.9721% for 30°-view gaits). The performance is much better than a well-established monocular gait measurement system suitable only for side-view gaits with a MAPE of 3.5538%. Independently of walking directions, our method can accurately estimate step length ratios from unconstrained straight walking. This demonstrates our method is applicable for elders' daily gait monitoring to provide valuable information for elderly health care, such as abnormal gait recognition, fall risk assessment, etc. single-camera-based gait monitoring is unobtrusive, inexpensive, and easy-to-use to monitor daily gait of seniors in their homes. However, most studies require subjects to walk perpendicularly to camera's optical axis or along some specified routes, which limits its application in elderly home monitoring

  14. A simple two-step method to fabricate highly transparent ITO/polymer nanocomposite films

    International Nuclear Information System (INIS)

    Liu, Haitao; Zeng, Xiaofei; Kong, Xiangrong; Bian, Shuguang; Chen, Jianfeng

    2012-01-01

    Highlights: ► A simple two-step method without further surface modification step was employed. ► ITO nanoparticles were easily to be uniformly dispersed in polymer matrix. ► 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.

  15. Fractional quantum mechanics

    CERN Document Server

    Laskin, Nick

    2018-01-01

    Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique...

  16. A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

    Science.gov (United States)

    Bhrawy, A. H.; Zaky, M. A.

    2015-01-01

    In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

  17. An Improved Split-Step Wavelet Transform Method for Anomalous Radio Wave Propagation Modelling

    Directory of Open Access Journals (Sweden)

    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.

  18. Fractional-order RC and RL circuits

    KAUST Repository

    Radwan, Ahmed Gomaa

    2012-05-30

    This paper is a step forward to generalize the fundamentals of the conventional RC and RL circuits in fractional-order sense. The effect of fractional orders is the key factor for extra freedom, more flexibility, and novelty. The conditions for RC and RL circuits to act as pure imaginary impedances are derived, which are unrealizable in the conventional case. In addition, the sensitivity analyses of the magnitude and phase response with respect to all parameters showing the locations of these critical values are discussed. A qualitative revision for the fractional RC and RL circuits in the frequency domain is provided. Numerical and PSpice simulations are included to validate this study. © Springer Science+Business Media, LLC 2012.

  19. Destruction of the fractional quantum Hall effect by disorder

    International Nuclear Information System (INIS)

    Laughlin, R.B.

    1985-07-01

    It is suggested that Hall steps in the fractional quantum Hall effect are physically similar to those in the ordinary quantum Hall effect. This proposition leads to a simple scaling diagram containing a new type of fixed point, which is identified with the destruction of the fractional states by disorder. 15 refs., 3 figs

  20. Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations

    Directory of Open Access Journals (Sweden)

    Haiyan Yuan

    2013-01-01

    Full Text Available This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of (k,l-algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a (k,l-algebraically stable two-step Runge-Kutta method with 0step Runge-Kutta method is algebraically stable and diagonally stable and its generalized stage order is p, then the method with compound quadrature formula is D-convergent of order at least min{p,ν}, where ν depends on the compound quadrature formula.

  1. Study on evaluation method for image quality of radiograph by step plate, (2)

    International Nuclear Information System (INIS)

    Terada, Yukihiro; Hirayama, Kazuo; Katoh, Mitsuaki.

    1992-01-01

    Recently, penetrameter sensitivity is used not only for the evaluation of radiographic image quality but also as a control method for examination conditions. However, it is necessary to take the parametric data for radiation quality in order to use it for the second purpose. The quantitative factor of radiation quality is determined by the absorption coefficient and the ratio of scattered radiation to transmitted radiation reaching the X-ray film. When the X-ray equipment changes in conducting the radiographic examination, these data must be measured in each case. This is a demerit in controlling examination conditions based on parametric data. As shown theoretically in the first report, the image quality value of a step plate which is defined by the density difference divided by film contrast and step plate thickness is useful to obtain the value of the radiation quality factor. This report deal with experimental investigation to measure it with the step plate. The result is showing that the value of the radiation quality factor calculated by the parametric data corresponded well with the image quality value measured by the step plate. Therefore, the convenient method to measure the value of the radiation quality factor has been established in order to control examination conditions in radiographic examination. (author)

  2. nduced hyperlipidemic rats. Methods: Column chromatographic fractionation of butanol fraction of total methanol extract of leaves of Bauhinia variegata (Linn. yields four sub-fractions (sub-fraction A-D. All sub-fractions tested for their anti-hyperlipidemic activity. Sub-fractions 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

    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.

  3. 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.

  4. A TWO-STEP CLASSIFICATION APPROACH TO DISTINGUISHING SIMILAR OBJECTS IN MOBILE LIDAR POINT CLOUDS

    Directory of Open Access Journals (Sweden)

    H. He

    2017-09-01

    Full Text Available Nowadays, lidar is widely used in cultural heritage documentation, urban modeling, and driverless car technology for its fast and accurate 3D scanning ability. However, full exploitation of the potential of point cloud data for efficient and automatic object recognition remains elusive. Recently, feature-based methods have become very popular in object recognition on account of their good performance in capturing object details. Compared with global features describing the whole shape of the object, local features recording the fractional details are more discriminative and are applicable for object classes with considerable similarity. In this paper, we propose a two-step classification approach based on point feature histograms and the bag-of-features method for automatic recognition of similar objects in mobile lidar point clouds. Lamp post, street light and traffic sign are grouped as one category in the first-step classification for their inter similarity compared with tree and vehicle. A finer classification of the lamp post, street light and traffic sign based on the result of the first-step classification is implemented in the second step. The proposed two-step classification approach is shown to yield a considerable improvement over the conventional one-step classification approach.

  5. A parallel algorithm for the two-dimensional time fractional diffusion equation with implicit difference method.

    Science.gov (United States)

    Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie

    2014-01-01

    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(M(x)M(y)N(2)). 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.

  6. SYSTEMATIZATION OF THE BASIC STEPS OF THE STEP-AEROBICS

    Directory of Open Access Journals (Sweden)

    Darinka Korovljev

    2011-03-01

    Full Text Available Following the development of the powerful sport industry, in front of us appeared a lot of new opportunities for creating of the new programmes of exercising with certain requisites. One of such programmes is certainly step-aerobics. Step-aerobics can be defined as a type of aerobics consisting of the basic aerobic steps (basic steps applied in exercising on stepper (step bench, with a possibility to regulate its height. Step-aerobics itself can be divided into several groups, depending on the following: type of music, working methods and adopted knowledge of the attendants. In this work, the systematization of the basic steps in step-aerobics was made on the basis of the following criteria: steps origin, number of leg motions in stepping and relating the body support at the end of the step. Systematization of the basic steps of the step-aerobics is quite significant for making a concrete review of the existing basic steps, thus making creation of the step-aerobics lesson easier

  7. On matrix fractional differential equations

    Directory of Open Access Journals (Sweden)

    Adem Kılıçman

    2017-01-01

    Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

  8. LiLEDDA: A Six-Step Forum-Based Netnographic Research Method for Nursing Science

    Directory of Open Access Journals (Sweden)

    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.

  9. Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations

    International Nuclear Information System (INIS)

    Lu, Bin

    2012-01-01

    In this Letter, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations. -- Highlights: ► Backlund transformation of fractional Riccati equation is presented. ► A new method for solving nonlinear fractional differential equations is proposed. ► Three important fractional differential equations are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained.

  10. Limitations of a convolution method for modeling geometric uncertainties in radiation therapy: the radiobiological dose-per-fraction effect

    International Nuclear Information System (INIS)

    Song, William; Battista, Jerry; Van Dyk, Jake

    2004-01-01

    The convolution method can be used to model the effect of random geometric uncertainties into planned dose distributions used in radiation treatment planning. This is effectively done by linearly adding infinitesimally small doses, each with a particular geometric offset, over an assumed infinite number of fractions. However, this process inherently ignores the radiobiological dose-per-fraction effect since only the summed physical dose distribution is generated. The resultant potential error on predicted radiobiological outcome [quantified in this work with tumor control probability (TCP), equivalent uniform dose (EUD), normal tissue complication probability (NTCP), and generalized equivalent uniform dose (gEUD)] has yet to be thoroughly quantified. In this work, the results of a Monte Carlo simulation of geometric displacements are compared to those of the convolution method for random geometric uncertainties of 0, 1, 2, 3, 4, and 5 mm (standard deviation). The α/β CTV ratios of 0.8, 1.5, 3, 5, and 10 Gy are used to represent the range of radiation responses for different tumors, whereas a single α/β OAR ratio of 3 Gy is used to represent all the organs at risk (OAR). The analysis is performed on a four-field prostate treatment plan of 18 MV x rays. The fraction numbers are varied from 1-50, with isoeffective adjustments of the corresponding dose-per-fractions to maintain a constant tumor control, using the linear-quadratic cell survival model. The average differences in TCP and EUD of the target, and in NTCP and gEUD of the OAR calculated from the convolution and Monte Carlo methods reduced asymptotically as the total fraction number increased, with the differences reaching negligible levels beyond the treatment fraction number of ≥20. The convolution method generally overestimates the radiobiological indices, as compared to the Monte Carlo method, for the target volume, and underestimates those for the OAR. These effects are interconnected and attributed

  11. Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

    International Nuclear Information System (INIS)

    Yang, Xiao-Jun; Srivastava, H.M.; He, Ji-Huan; Baleanu, Dumitru

    2013-01-01

    In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.

  12. An Effective Numerical Method and Its Utilization to Solution of Fractional Models Used in Bioengineering Applications

    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.

  13. Tempered fractional calculus

    Energy Technology Data Exchange (ETDEWEB)

    Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Chen, Jinghua, E-mail: cjhdzdz@163.com [School of Sciences, Jimei University, Xiamen, Fujian, 361021 (China)

    2015-07-15

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

  14. Tempered fractional calculus

    Science.gov (United States)

    Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

    2015-07-01

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

  15. Tempered fractional calculus

    International Nuclear Information System (INIS)

    Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

    2015-01-01

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series

  16. On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

    Science.gov (United States)

    Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei

    2018-06-01

    In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.

  17. An In-Pile Kinetic Method for Determining the Delayed Neutron Fraction βeff

    International Nuclear Information System (INIS)

    Gilad, E.; Rivin, O.; Ettedgui, H.; Yaar, I.; Geslot, B.; Pepino, A.; Di Salvo, J.; Gruel, A.; Blaise, P.

    2014-01-01

    Delayed neutrons are of fundamental importance in the field of nuclear reactor dynamics and control. Although only a small fraction of the neutrons emitted by fission are not prompt, the knowledge of the delayed neutrons parameters is essential for transient analysis, such as startup or shutdown of the reactor, as well as for accidents analysis and control system design [1]. One of the main delayed neutron parameters used in the point reactor model equations is the effective delayed neutron fraction, which incorporates both delayed neutron spectral properties and core geometrical configuration [1,2]. Additional delayed neutron parameters include the fraction of fission neutrons emitted in each delayed group, and the delayed neutron precursors decay constants . Experimental efforts aimed at determining the value ofβ, which provide experimental support for the evaluation of delayed neutron parameters, are extremely valuable. This is due to the fact that unlike other fields in reactor physics, e.g. criticality safety or shielding, the availability of experimental data and benchmark problems for validating delayed neutron parameters and its implementation in different models is highly limited. Furthermore, the existing experimental data exhibit significant discrepancies between the different sets of parameter, which lead to substantial disparity in the analysis of kinetic experiments and reactor dynamic behavior]. In this work, a method for determining the effective delayed neutron fraction using in-pile reactivity oscillation and Fourier analysis is presented. The method is based on measurements of the reactor's power response to small periodic in-pile reactivity perturbations and utilizes Fourier analysis for reconstruction of the reactor zero power transfer function. Knowledge of the reactor transfer function enables the estimation of theβ value using multi-parameter nonlinear fit. The method accounts for higher harmonics, which are excited by the trapezoidal

  18. Basic features of boron isotope separation by SILARC method in the two-step iterative static model

    Science.gov (United States)

    Lyakhov, K. A.; Lee, H. J.

    2013-05-01

    In this paper we develop a new static model for boron isotope separation by the laser assisted retardation of condensation method (SILARC) on the basis of model proposed by Jeff Eerkens. Our model is thought to be adequate to so-called two-step iterative scheme for isotope separation. This rather simple model helps to understand combined action on boron separation by SILARC method of all important parameters and relations between them. These parameters include carrier gas, molar fraction of BCl3 molecules in carrier gas, laser pulse intensity, gas pulse duration, gas pressure and temperature in reservoir and irradiation cells, optimal irradiation cell and skimmer chamber volumes, and optimal nozzle throughput. A method for finding optimal values of these parameters based on some objective function global minimum search was suggested. It turns out that minimum of this objective function is directly related to the minimum of total energy consumed, and total setup volume. Relations between nozzle throat area, IC volume, laser intensity, number of nozzles, number of vacuum pumps, and required isotope production rate were derived. Two types of industrial scale irradiation cells are compared. The first one has one large throughput slit nozzle, while the second one has numerous small nozzles arranged in parallel arrays for better overlap with laser beam. It is shown that the last one outperforms the former one significantly. It is argued that NO2 is the best carrier gas for boron isotope separation from the point of view of energy efficiency and Ar from the point of view of setup compactness.

  19. One-step method for the production of nanofluids

    Science.gov (United States)

    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.

  20. Rapid expansion method (REM) for time‐stepping in reverse time migration (RTM)

    KAUST Repository

    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.

  1. Fractional calculus in bioengineering, part 3.

    Science.gov (United States)

    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

  2. Novel two-step method to form silk fibroin fibrous hydrogel

    International Nuclear Information System (INIS)

    Ming, Jinfa; Li, Mengmeng; Han, Yuhui; Chen, Ying; Li, Han; Zuo, Baoqi; Pan, Fukui

    2016-01-01

    Hydrogels prepared by silk fibroin solution have been studied. However, mimicking the nanofibrous structures of extracellular matrix for fabricating biomaterials remains a challenge. Here, a novel two-step method was applied to prepare fibrous hydrogels using regenerated silk fibroin solution containing nanofibrils in a range of tens to hundreds of nanometers. When the gelation process of silk solution occurred, it showed a top-down type gel within 30 min. After gelation, silk fibroin fibrous hydrogels exhibited nanofiber network morphology with β-sheet structure. Moreover, the compressive stress and modulus of fibrous hydrogels were 31.9 ± 2.6 and 2.8 ± 0.8 kPa, respectively, which was formed using 2.0 wt.% concentration solutions. In addition, fibrous hydrogels supported BMSCs attachment and proliferation over 12 days. This study provides important insight in the in vitro processing of silk fibroin into useful new materials. - Highlights: • SF fibrous hydrogel was prepared by a novel two-step method. • SF solution containing nanofibrils in a range of tens to hundreds of nanometers was prepared. • Gelation process was top-down type gel with several minutes. • SF fibrous hydrogels exhibited nanofiber network morphology with β-sheet structure. • Fibrous hydrogels had higher compressive stresses superior to porous hydrogels.

  3. The Galerkin finite element method for a multi-term time-fractional diffusion equation

    KAUST Repository

    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.

  4. Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    R. Darzi

    2013-01-01

    Full Text Available We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D0+αut+ft,ut=0, 0fractional derivative, β is positive real number, βξα−1≥2Γα, and f is continuous on 0,1×0,∞. As an application, one example is given to illustrate the main result.

  5. Fractional-Order Control of Pneumatic Position Servosystems

    Directory of Open Access Journals (Sweden)

    Cao Junyi

    2011-01-01

    Full Text Available A fractional-order control strategy for pneumatic position servosystem is presented in this paper. The idea of the fractional calculus application to control theory was introduced in many works, and its advantages were proved. However, the realization of fractional-order controllers for pneumatic position servosystems has not been investigated. Based on the relationship between the pressure in cylinder and the rate of mass flow into the cylinder, the dynamic model of pneumatic position servo system is established. The fractional-order controller for pneumatic position servo and its implementation in industrial computer is designed. The experiments with fractional-order controller are carried out under various conditions, which include sine position signal with different frequency and amplitude, step position signal, and variety inertial load. The results show the effectiveness of the proposed scheme and verify their fine control performance for pneumatic position servo system.

  6. Evaluation of lung and chest wall mechanics during anaesthesia using the PEEP-step method.

    Science.gov (United States)

    Persson, P; Stenqvist, O; Lundin, S

    2018-04-01

    Postoperative pulmonary complications are common. Between patients there are differences in lung and chest wall mechanics. Individualised mechanical ventilation based on measurement of transpulmonary pressures would be a step forward. A previously described method evaluates lung and chest wall mechanics from a change of ΔPEEP and calculation of change in end-expiratory lung volume (ΔEELV). The aim of the present study was to validate this PEEP-step method (PSM) during general anaesthesia by comparing it with the conventional method using oesophageal pressure (PES) measurements. In 24 lung healthy subjects (BMI 18.5-32), three different sizes of PEEP steps were performed during general anaesthesia and ΔEELVs were calculated. Transpulmonary driving pressure (ΔPL) for a tidal volume equal to each ΔEELV was measured using PES measurements and compared to ΔPEEP with limits of agreement and intraclass correlation coefficients (ICC). ΔPL calculated with both methods was compared with a Bland-Altman plot. Mean differences between ΔPEEP and ΔPL were mechanical properties among the lung healthy patients stresses the need for individualised ventilator settings based on measurements of lung and chest wall mechanics. The agreement between ΔPLs measured by the two methods during general anaesthesia suggests the use of the non-invasive PSM in this patient population. NCT 02830516. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

  7. Rapid expansion method (REM) for time‐stepping in reverse time migration (RTM)

    KAUST Repository

    Pestana, Reynam C.; Stoffa, Paul L.

    2009-01-01

    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

  8. Coupling of Spinosad Fermentation and Separation Process via Two-Step Macroporous Resin Adsorption Method.

    Science.gov (United States)

    Zhao, Fanglong; Zhang, Chuanbo; Yin, Jing; Shen, Yueqi; Lu, Wenyu

    2015-08-01

    In this paper, a two-step resin adsorption technology was investigated for spinosad production and separation as follows: the first step resin addition into the fermentor at early cultivation period to decrease the timely product concentration in the broth; the second step of resin addition was used after fermentation to adsorb and extract the spinosad. Based on this, a two-step macroporous resin adsorption-membrane separation process for spinosad fermentation, separation, and purification was established. Spinosad concentration in 5-L fermentor increased by 14.45 % after adding 50 g/L macroporous at the beginning of fermentation. The established two-step macroporous resin adsorption-membrane separation process got the 95.43 % purity and 87 % yield for spinosad, which were both higher than that of the conventional crystallization of spinosad from aqueous phase that were 93.23 and 79.15 % separately. The two-step macroporous resin adsorption method has not only carried out the coupling of spinosad fermentation and separation but also increased spinosad productivity. In addition, the two-step macroporous resin adsorption-membrane separation process performs better in spinosad yield and purity.

  9. Investigating the Effectiveness of Teaching Methods Based on a Four-Step Constructivist Strategy

    Science.gov (United States)

    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.

  10. A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line

    Directory of Open Access Journals (Sweden)

    Ali H. Bhrawy

    2014-01-01

    Full Text Available The modified generalized Laguerre-Gauss collocation (MGLC method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.

  11. Hydrogen solubility measurements of analyzed tall oil fractions and a solubility model

    International Nuclear Information System (INIS)

    Uusi-Kyyny, Petri; Pakkanen, Minna; Linnekoski, Juha; Alopaeus, Ville

    2017-01-01

    Highlights: • Hydrogen solubility was measured in four tall oil fractions between 373 and 597 K. • Continuous flow synthetic isothermal and isobaric method was used. • A Henry’s law model was developed for the distilled tall oil fractions. • The complex composition of the samples was analyzed and is presented. - Abstract: Knowledge of hydrogen solubility in tall oil fractions is important for designing hydrotreatment processes of these complex nonedible biobased materials. Unfortunately measurements of hydrogen solubility into these fractions are missing in the literature. This work reports hydrogen solubility measured in four tall oil fractions between 373 and 597 K and at pressures from 5 to 10 MPa. Three of the fractions were distilled tall oil fractions their resin acids contents are respectively 2, 20 and 23 in mass-%. Additionally one fraction was a crude tall oil (CTO) sample containing sterols as the main neutral fraction. Measurements were performed using a continuous flow synthetic isothermal and isobaric method based on the visual observation of the bubble point. Composition of the flow was changed step-wise for the bubble point composition determination. We assume that the tall oil fractions did not react during measurements, based on the composition analysis performed before and after the measurements. Additionally the densities of the fractions were measured at atmospheric pressure from 293.15 to 323.15 K. A Henry’s law model was developed for the distilled tall oil fractions describing the solubility with an absolute average deviation of 2.1%. Inputs of the solubility model are temperature, total pressure and the density of the oil at 323.15 K. The solubility of hydrogen in the CTO sample can be described with the developed model with an absolute average deviation of 3.4%. The solubility of hydrogen increases both with increasing pressure and/or increasing temperature. The more dense fractions of the tall oil exhibit lower hydrogen

  12. Rapid Estimation Method for State of Charge of Lithium-Ion Battery Based on Fractional Continual Variable Order Model

    Directory of Open Access Journals (Sweden)

    Xin Lu

    2018-03-01

    Full Text Available In recent years, the fractional order model has been employed to state of charge (SOC estimation. The non integer differentiation order being expressed as a function of recursive factors defining the fractality of charge distribution on porous electrodes. The battery SOC affects the fractal dimension of charge distribution, therefore the order of the fractional order model varies with the SOC at the same condition. This paper proposes a new method to estimate the SOC. A fractional continuous variable order model is used to characterize the fractal morphology of charge distribution. The order identification results showed that there is a stable monotonic relationship between the fractional order and the SOC after the battery inner electrochemical reaction reaches balanced. This feature makes the proposed model particularly suitable for SOC estimation when the battery is in the resting state. Moreover, a fast iterative method based on the proposed model is introduced for SOC estimation. The experimental results showed that the proposed iterative method can quickly estimate the SOC by several iterations while maintaining high estimation accuracy.

  13. Generalized fractional Schroedinger equation with space-time fractional derivatives

    International Nuclear Information System (INIS)

    Wang Shaowei; Xu Mingyu

    2007-01-01

    In this paper the generalized fractional Schroedinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. The Green function for free particle is also presented in this paper. Finally, we discuss the relationship between the cases of the generalized fractional Schroedinger equation and the ones in standard quantum

  14. Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

    Science.gov (United States)

    Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

    2018-06-01

    The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

  15. Comparison on genomic predictions using GBLUP models and two single-step blending methods with different relationship matrices in the Nordic Holstein population

    DEFF Research Database (Denmark)

    Gao, Hongding; Christensen, Ole Fredslund; Madsen, Per

    2012-01-01

    Background A single-step blending approach allows genomic prediction using information of genotyped and non-genotyped animals simultaneously. However, the combined relationship matrix in a single-step method may need to be adjusted because marker-based and pedigree-based relationship matrices may...... not be on the same scale. The same may apply when a GBLUP model includes both genomic breeding values and residual polygenic effects. The objective of this study was to compare single-step blending methods and GBLUP methods with and without adjustment of the genomic relationship matrix for genomic prediction of 16......) a simple GBLUP method, 2) a GBLUP method with a polygenic effect, 3) an adjusted GBLUP method with a polygenic effect, 4) a single-step blending method, and 5) an adjusted single-step blending method. In the adjusted GBLUP and single-step methods, the genomic relationship matrix was adjusted...

  16. Design of distributed PID-type dynamic matrix controller for fractional-order systems

    Science.gov (United States)

    Wang, Dawei; Zhang, Ridong

    2018-01-01

    With the continuous requirements for product quality and safety operation in industrial production, it is difficult to describe the complex large-scale processes with integer-order differential equations. However, the fractional differential equations may precisely represent the intrinsic characteristics of such systems. In this paper, a distributed PID-type dynamic matrix control method based on fractional-order systems is proposed. First, the high-order approximate model of integer order is obtained by utilising the Oustaloup method. Then, the step response model vectors of the plant is obtained on the basis of the high-order model, and the online optimisation for multivariable processes is transformed into the optimisation of each small-scale subsystem that is regarded as a sub-plant controlled in the distributed framework. Furthermore, the PID operator is introduced into the performance index of each subsystem and the fractional-order PID-type dynamic matrix controller is designed based on Nash optimisation strategy. The information exchange among the subsystems is realised through the distributed control structure so as to complete the optimisation task of the whole large-scale system. Finally, the control performance of the designed controller in this paper is verified by an example.

  17. The Step Method - Battling Identity Theft Using E-Retailers' Websites

    Science.gov (United States)

    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.

  18. FRACTIONS: CONCEPTUAL AND DIDACTIC ASPECTS

    OpenAIRE

    Sead Rešić; Ismet Botonjić; Maid Omerović

    2016-01-01

    Fractions represent the manner of writing parts of whole numbers (integers). Rules for operations with fractions differ from rules for operations with integers. Students face difficulties in understanding fractions, especially operations with fractions. These difficulties are well known in didactics of Mathematics throughout the world and there is a lot of research regarding problems in learning about fractions. Methods for facilitating understanding fractions have been discovered...

  19. Development of a method to extract and purify target compounds from medicinal plants in a single step: online hyphenation of expanded bed adsorption chromatography and countercurrent chromatography.

    Science.gov (United States)

    Li, Yang; Wang, Nan; Zhang, Min; Ito, Yoichiro; Zhang, Hongyang; Wang, Yuerong; Guo, Xin; Hu, Ping

    2014-04-01

    Pure compounds extracted and purified from natural sources are crucial to lead discovery and drug screening. This study presents a novel two-dimensional hyphenation of expanded bed adsorption chromatography (EBAC) and high-speed countercurrent chromatography (HSCCC) for extraction and purification of target compounds from medicinal plants in a single step. The EBAC and HSCCC were hyphenated via a six-port injection valve as an interface. Fractionation of ingredients of Salvia miltiorrhiza and Rhizoma coptidis was performed on the hyphenated system to verify its efficacy. Two compounds were harvested from Salvia miltiorrhiza, one was 52.9 mg of salvianolic acid B with an over 95% purity and the other was 2.1 mg of rosmarinic acid with a 74% purity. Another two components were purified from Rhizoma coptidis, one was 4.6 mg of coptisine with a 98% purity and one was 4.1 mg of berberine with a 82% purity. The processing time was nearly 50% that of the multistep method. The results indicate that the present method is a rapid and green way to harvest targets from medicinal plants in a single step.

  20. Concentration of the genera Aspergillus, Eurotium and Penicillium in 63-μm house dust fraction as a method to predict hidden moisture damage in homes

    Directory of Open Access Journals (Sweden)

    Assadian Ojan

    2009-07-01

    Full Text Available Abstract Background Quantitative measurements of mould enrichment of indoor air or house dust might be suitable surrogates to evaluate present but hidden moisture damage. Our intent was to develop a house-dust monitoring method to detect hidden moisture damage excluding the influence of outdoor air, accumulated old dust, and dust swirled up from room surfaces. Methods Based on standardized measurement of mould spores in the 63-μm fraction of house dust yielded by carpets, the background concentrations were determined and compared to simultaneously obtained colony numbers and total spore numbers of the indoor air in 80 non-mouldy living areas during summer and winter periods. Additionally, sampling with a vacuum-cleaner or manual sieve was compared to sampling with a filter holder or sieving machine, and the evaluative power of an established two-step assessment model (lower and upper limits was compared to that of a one-step model (one limit in order to derive concentration limits for mould load in house dust. Results Comparison with existing evaluation procedures proved the developed method to be the most reliable means of evaluating hidden moisture damage, yielding the lowest false-positive results (specificity 98.7%. Background measurements and measurements in 14 mouldy rooms show that even by evaluating just the indicator genera in summer and winter, a relatively certain assessment of mould infestation is possible. Conclusion A one-step evaluation is finally possible for house dust. The house-dust evaluation method is based on analysis of the indicator genera Aspergillus, Eurotium and Penicillium spp., which depend on the total fungal count. Inclusion of further moisture indicators currently appears questionable, because of outdoor air influence and the paucity of measurements.

  1. Effects of projection and background correction method upon calculation of right ventricular ejection fraction using first-pass radionuclide angiography

    International Nuclear Information System (INIS)

    Caplin, J.L.; Flatman, W.D.; Dymond, D.S.

    1985-01-01

    There is no consensus as to the best projection or correction method for first-pass radionuclide studies of the right ventricle. We assessed the effects of two commonly used projections, 30 degrees right anterior oblique and anterior-posterior, on the calculation of right ventricular ejection fraction. In addition two background correction methods, planar background correction to account for scatter, and right atrial correction to account for right atrio-ventricular overlap were assessed. Two first-pass radionuclide angiograms were performed in 19 subjects, one in each projection, using gold-195m (half-life 30.5 seconds), and each study was analysed using the two methods of correction. Right ventricular ejection fraction was highest using the right anterior oblique projection with right atrial correction 35.6 +/- 12.5% (mean +/- SD), and lowest when using the anterior posterior projection with planar background correction 26.2 +/- 11% (p less than 0.001). The study design allowed assessment of the effects of correction method and projection independently. Correction method appeared to have relatively little effect on right ventricular ejection fraction. Using right atrial correction correlation coefficient (r) between projections was 0.92, and for planar background correction r = 0.76, both p less than 0.001. However, right ventricular ejection fraction was far more dependent upon projection. When the anterior-posterior projection was used calculated right ventricular ejection fraction was much more dependent on correction method (r = 0.65, p = not significant), than using the right anterior oblique projection (r = 0.85, p less than 0.001)

  2. An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

    Science.gov (United States)

    Macías-Díaz, J. E.

    2018-06-01

    In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.

  3. A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

    Directory of Open Access Journals (Sweden)

    Muhammed I. Syam

    2017-11-01

    Full Text Available This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional $2\\alpha $-order Sturm-Liouville problem where $\\frac{1}{2}< \\alpha \\leq 1$. In this paper, we implement the reproducing kernel method RKM to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at $x=1$. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.

  4. From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

    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.

  5. Application of radial basis functions and sinc method for solving the forced vibration of fractional viscoelastic beam

    Energy Technology Data Exchange (ETDEWEB)

    Permoon, M. R.; Haddadpour, H. [Sharif University of Tech, Tehran (Iran, Islamic Republic of); Rashidinia, J.; Parsa, A.; Salehi, R. [Iran University of Science and Technology, Tehran (Iran, Islamic Republic of)

    2016-07-15

    In this paper, the forced vibrations of the fractional viscoelastic beam with the Kelvin-Voigt fractional order constitutive relationship is studied. The equation of motion is derived from Newton's second law and the Galerkin method is used to discretize the equation of motion in to a set of linear ordinary differential equations. For solving the discretized equations, the radial basis functions and Sinc quadrature rule are used. In order to show the effectiveness and accuracy of this method, some test problem are considered, and it is shown that the obtained results are in very good agreement with exact solution. In the following, the proposed numerical solution is applied to exploring the effects of fractional parameters on the response of the beam and finally some conclusions are outlined.

  6. Void fraction correlations analysis and their influence on heat transfer of helical double-pipe vertical evaporator

    International Nuclear Information System (INIS)

    Parrales, Arianna; Colorado, Dario; Huicochea, Armando; Díaz, Juan; Alfredo Hernández, J.

    2014-01-01

    Highlights: • 50 void fraction correlations were evaluated on heat transfer in vertical evaporators. • Two-phase flow model based on control volume formulation was used. • The drift flux parameter is common in all correlations with satisfactory results. - Abstract: An analysis of 50 void fraction correlations available in the literature was performed to describe two-phase flow mechanism inside two helical double-pipe vertical evaporators. The evaporators considered water as working fluid connected in countercurrent so the change of phase was carried out into the internal tube. The discretized equations of continuity, momentum and energy in each flow were coupled using an implicit step by step method. The selection of the void fraction correlations for the mathematical model was based on inclusion of some theoretical limits. The results of this analysis were compared with the experimental data in steady state for two different evaporators, obtaining good agreement in the evaporation process for only 7 void fraction correlations. The Armand and Massena correlation had a mean percentage error (MPE) of 3.08%, followed by Rouhanni and Axelsson I adquired MPE=3.16%, Chisholm and Armand obtained MPE=3.18%, Steiner as well as Rouhanni and Axelsson II with MPE=3.19%, Bestion reached MPE=3.20% and Flanigan presented MPE=3.21%. Furthermore, the experimental and simulated heat flux were acceptable (R 2 =0.939). Finally, the results showed that the drift flux parameter was important to evaluate the void fraction

  7. Solid-phase extraction NMR studies of chromatographic fractions of saponins from Quillaja saponaria.

    Science.gov (United States)

    Nyberg, Nils T; Baumann, Herbert; Kenne, Lennart

    2003-01-15

    The saponin mixture QH-B from the tree Quillaja saponaria var. Molina was fractionated by RP-HPLC in several steps. The fractions were analyzed by solid-phase extraction NMR (SPE-NMR), a technique combining the workup by solid-phase extraction with on-line coupling to an NMR flow probe. Together with MALDI-TOF mass spectrometry and comparison with chemical shifts of similar saponins, the structures of both major and minor components in QH-B could be obtained. The procedure described is a simple method to determine the structure of components in a complex mixture. The two major fractions of the mixture were found to contain at least 28 saponins, differing in the carbohydrate substructures. Eight of these have not previously been determined. The 28 saponins formed 14 equilibrium pairs by the migration of an O-acyl group between two adjacent positions on a fucosyl residue.

  8. An In Silico Approach for Evaluating a Fraction-Based, Risk Assessment Method for Total Petroleum Hydrocarbon Mixtures

    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.

  9. A one-step separation of human serum high density lipoproteins 2 and 3 by rate-zonal density gradient ultracentrifugation in a swinging bucket rotor

    NARCIS (Netherlands)

    Groot, P.H.E.; Scheek, L.M.; Havekes, L.; Noort, W.L. van; Hooft, F.M. van 't

    1982-01-01

    A method was developed for the separation of the high density lipoprotein subclasses HDL2 and HDL3 from human serum. Six serum samples are fractionated in a single-step ultracentrifugal procedure using the Beckman (SW-40) swinging bucket rotor. The method is based on a difference in flotation rate

  10. Mathematical foundation of the optimization-based fluid animation method

    DEFF Research Database (Denmark)

    Erleben, Kenny; Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas

    2011-01-01

    We present the mathematical foundation of a fluid animation method for unstructured meshes. Key contributions not previously treated are the extension to include diffusion forces and higher order terms of non-linear force approximations. In our discretization we apply a fractional step method to ...

  11. Fraction Reduction in Membrane Systems

    Directory of Open Access Journals (Sweden)

    Ping Guo

    2014-01-01

    Full Text Available Fraction reduction is a basic computation for rational numbers. P system is a new computing model, while the current methods for fraction reductions are not available in these systems. In this paper, we propose a method of fraction reduction and discuss how to carry it out in cell-like P systems with the membrane structure and the rules with priority designed. During the application of fraction reduction rules, synchronization is guaranteed by arranging some special objects in these rules. Our work contributes to performing the rational computation in P systems since the rational operands can be given in the form of fraction.

  12. FRACTIONS: CONCEPTUAL AND DIDACTIC ASPECTS

    Directory of Open Access Journals (Sweden)

    Sead Rešić

    2016-09-01

    Full Text Available Fractions represent the manner of writing parts of whole numbers (integers. Rules for operations with fractions differ from rules for operations with integers. Students face difficulties in understanding fractions, especially operations with fractions. These difficulties are well known in didactics of Mathematics throughout the world and there is a lot of research regarding problems in learning about fractions. Methods for facilitating understanding fractions have been discovered, which are essentially related to visualizing operations with fractions.

  13. Development of interface between MCNP-FISPACT-MCNP (IPR-MFM) based on rigorous two step method

    International Nuclear Information System (INIS)

    Shaw, A.K.; Swami, H.L.; Danani, C.

    2015-01-01

    In this work we present the development of interface tool between MCNP-FISPACT-MCNP (MFM) based on Rigorous Two Step method for the shutdown dose rate (SDDR) calculation. The MFM links MCNP radiation transport and the FISPACT inventory code through a suitable coupling scheme. MFM coupling scheme has three steps. In first step it picks neutron spectrum and total flux from MCNP output file to use as input parameter for FISPACT. It prepares the FISPACT input files by using irradiation history, neutron flux and neutron spectrum and then execute the FISPACT input file in the second step. Third step of MFM coupling scheme extracts the decay gammas from the FISPACT output file and prepares MCNP input file for decay gamma transport followed by execution of MCNP input file and estimation of SDDR. Here detailing of MFM methodology and flow scheme has been described. The programming language PYTHON has been chosen for this development of the coupling scheme. A complete loop of MCNP-FISPACT-MCNP has been developed to handle the simplified geometrical problems. For validation of MFM interface a manual cross-check has been performed which shows good agreements. The MFM interface also has been validated with exiting MCNP-D1S method for a simple geometry with 14 MeV cylindrical neutron source. (author)

  14. Joint estimation of the fractional differentiation orders and the unknown input for linear fractional non-commensurate system

    KAUST Repository

    Belkhatir, Zehor

    2015-11-05

    This paper deals with the joint estimation of the unknown input and the fractional differentiation orders of a linear fractional order system. A two-stage algorithm combining the modulating functions with a first-order Newton method is applied to solve this estimation problem. First, the modulating functions approach is used to estimate the unknown input for a given fractional differentiation orders. Then, the method is combined with a first-order Newton technique to identify the fractional orders jointly with the input. To show the efficiency of the proposed method, numerical examples illustrating the estimation of the neural activity, considered as input of a fractional model of the neurovascular coupling, along with the fractional differentiation orders are presented in both noise-free and noisy cases.

  15. Early fractionation methods and the origins of the NSD concept

    International Nuclear Information System (INIS)

    Thames, H.D. Jr.

    1988-01-01

    The concept of the time factor in radiotherapy originated in the controversy surrounding single-dose and fractionated treatments during the first 20 years of this century. The success of Coutard's fractionated treatments of larynx tumors was an important factor in the abandonment of single-dose treatments. There was considerable research afterwards into the influence of dose rate and overall time of treatment on the responses of normal tissues. Recovery was modeled in terms of the Schwarzschild law of photochemistry, as exemplified by the analysis of Strandqvist in log dose-log time coordinates. Different conventions were followed in defining the time for a single-dose treatment. Subsequently the concept arose that the slopes of isoeffect lines relating dose and treatment time for normal tissues and tumors were different and moreover that the effects of fraction number and overall time could be separated; these developments constituted the foundation of the Ellis NSD model. It had an important influence on clinical practice and was reasonably successful in predicting isoeffective regimens for acute effects. It failed to predict severe late effects after large dose fractions. The dissociation between acute and late effects with altered fractionation led to recognition of the importance of the ratio α/β in characterizing the fractionation sensitivity of tissues. (orig.) With 125 refs

  16. Study of CdTe quantum dots grown using a two-step annealing method

    Science.gov (United States)

    Sharma, Kriti; Pandey, Praveen K.; Nagpal, Swati; Bhatnagar, P. K.; Mathur, P. C.

    2006-02-01

    High size dispersion, large average radius of quantum dot and low-volume ratio has been a major hurdle in the development of quantum dot based devices. In the present paper, we have grown CdTe quantum dots in a borosilicate glass matrix using a two-step annealing method. Results of optical characterization and the theoretical model of absorption spectra have shown that quantum dots grown using two-step annealing have lower average radius, lesser size dispersion, higher volume ratio and higher decrease in bulk free energy as compared to quantum dots grown conventionally.

  17. A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

    Science.gov (United States)

    Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

    2018-04-01

    In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

  18. SOLA-VOF, 2-D Transient Hydrodynamic Using Fractional Volume of Fluid Method

    International Nuclear Information System (INIS)

    Nichols, B.D.; Hirt, C.W.; Hotchkiss, R.S.

    1991-01-01

    1 - Description of problem or function: SOLA-VOF is a program for the solution of two-dimensional transient fluid flow with free boundaries, based on the concept of a fractional volume of fluid (VOF). Its basic mode of operation is for single fluid calculations having multiple free surfaces. However, SOLA-VOF can also be used for calculations involving two fluids separated by a sharp interface. In either case, the fluids may be treated as incompressible or as having limited compressibility. Surface tension forces with wall adhesion are permitted in both cases. Internal obstacles may be defined by blocking out any desired combination of cells in the mesh, which is composed of rectangular cells of variable size. 2 - Method of solution: The basis of the SOLA-VOF method is the fractional volume of fluid scheme for tracking free boundaries. In this technique, a function F(x,y,t) is defined whose value is unity at any point occupied by fluid and zero elsewhere. When averaged over the cells of a computational mesh, the average value of F in a cell is equal to the fractional volume of the cell occupied by fluid. In particular, a unit value of F corresponds to a cell full of fluid, whereas a zero value indicates that the cell contains no fluid. Cells with F values between zero and one contain a free surface. SOLA-VOF uses an Eulerian mesh of rectangular cells having variable sizes. The fluid equations solved are the finite difference approximations of the Navier-Stokes equations. 3 - Restrictions on the complexity of the problem: The setting of array dimensions is controlled through PARAMETER statements

  19. Control and Synchronization of the Fractional-Order Lorenz Chaotic System via Fractional-Order Derivative

    Directory of Open Access Journals (Sweden)

    Ping Zhou

    2012-01-01

    Full Text Available The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

  20. Approximate rational Jacobi elliptic function solutions of the fractional differential equations via the enhanced Adomian decomposition method

    International Nuclear Information System (INIS)

    Song Lina; Wang Weiguo

    2010-01-01

    In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.

  1. Elimination of Spurious Fractional Charges in Dissociating Molecules by Correcting the Shape of Approximate Kohn-Sham Potentials.

    Science.gov (United States)

    Komsa, Darya N; Staroverov, Viktor N

    2016-11-08

    Standard density-functional approximations often incorrectly predict that heteronuclear diatomic molecules dissociate into fractionally charged atoms. We demonstrate that these spurious charges can be eliminated by adapting the shape-correction method for Kohn-Sham potentials that was originally introduced to improve Rydberg excitation energies [ Phys. Rev. Lett. 2012 , 108 , 253005 ]. Specifically, we show that if a suitably determined fraction of electron charge is added to or removed from a frontier Kohn-Sham orbital level, the approximate Kohn-Sham potential of a stretched molecule self-corrects by developing a semblance of step structure; if this potential is used to obtain the electron density of the neutral molecule, charge delocalization is blocked and spurious fractional charges disappear beyond a certain internuclear distance.

  2. An evaluation of a single-step extraction chromatography separation method for Sm-Nd isotope analysis of micro-samples of silicate rocks by high-sensitivity thermal ionization mass spectrometry

    International Nuclear Information System (INIS)

    Li Chaofeng; Li Xianhua; Li Qiuli; Guo Jinghui; Li Xianghui; Liu Tao

    2011-01-01

    Graphical abstract: Distribution curve of all eluting fractions for a BCR-2 (1-2-3.5-7 mg) on LN column using HCl and HF as eluting reagent. Highlights: → This analytical protocol affords a simple and rapid analysis for Sm and Nd isotope in minor rock samples. → The single-step separation method exhibits satisfactory separation effect for complex silicate samples. → Corrected 143 Nd/ 144 Nd data show excellent accuracy even if the 140 Ce 16 O + / 144 Nd 16 O + ratio reached to 0.03. - Abstract: A single-step separation scheme is presented for Sm-Nd radiogenic isotope system on very small samples (1-3 mg) of silicate rock. This method is based on Eichrom LN Spec chromatographic material and affords a straightforward separation of Sm-Nd from complex matrix with good purity and satisfactory blank levels, suitable for thermal ionization mass spectrometry (TIMS). This technique, characterized by high efficiency (single-step Sm-Nd separation) and high sensitivity (TIMS on NdO + ion beam), is able to process rapidly (3-4 h), with low procedure blanks ( 143 Nd/ 144 Nd ratios and Sm-Nd concentrations are presented for eleven international silicate rock reference materials, spanning a wide range of Sm-Nd contents and bulk compositions. The analytical results show a good agreement with recommended values within ±0.004% for the 143 Nd/ 144 Nd isotopic ratio and ±2% for Sm-Nd quantification at the 95% confidence level. It is noted that the uncertainty of this method is about 3 times larger than typical precision achievable with two-stage full separation followed by state-of-the-art conventional TIMS using Nd + ion beams which require much larger amounts of Nd. Hence, our single-step separation followed by NdO + ion beam technique is preferred to the analysis for microsamples.

  3. Modelling and simulation of a dynamical system with the Atangana-Baleanu fractional derivative

    Science.gov (United States)

    Owolabi, Kolade M.

    2018-01-01

    In this paper, we model an ecological system consisting of a predator and two preys with the newly derived two-step fractional Adams-Bashforth method via the Atangana-Baleanu derivative in the Caputo sense. We analyze the dynamical system for correct choice of parameter values that are biologically meaningful. The local analysis of the main model is based on the application of qualitative theory for ordinary differential equations. By using the fixed point theorem idea, we establish the existence and uniqueness of the solutions. Convergence results of the new scheme are verified in both space and time. Dynamical wave phenomena of solutions are verified via some numerical results obtained for different values of the fractional index, which have some interesting ecological implications.

  4. Tests of equal effect per fraction in microcolony assays of survival after fractionated irradiations

    International Nuclear Information System (INIS)

    Taylor, J.M.G.

    1985-01-01

    H.D Thames, Jr. and H.R. Withers propose a test of an equal effect per fraction in microcolony assays after fractionated radiation, in which the total effect is measured by counting microcolonies derived from surviving cells in a tissue. The factors considered to influence the cytocidal effect per fraction are incomplete repair, repopulation, and synchrony. The statistics used in the method are criticized and conditions are given under which the test should not be used. An alternative method of testing for an equal effect per fraction is proposed. The pros and cons of each test are discussed and compared using some mouse jejunal crypt cell survival data

  5. Fraction Reduction through Continued Fractions

    Science.gov (United States)

    Carley, Holly

    2011-01-01

    This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

  6. Ultrastructure and electrophoretic protein pattern of a nuclear fraction enriched in interchromatin granule conglomerations

    Energy Technology Data Exchange (ETDEWEB)

    Krzyzowska-Gruca, S.; Zborek, A.; Gruca, S.

    1986-01-01

    Rats were injected with a cytostatic 1-nitro-9/3'-dimethylpropyloamine/acridine.2HCl to induce aggregation of interchromatin granules (IG). The conglomerations of IG were well preserved in isolated liver nuclei and in nuclear structures deprived of chromatin. This feature enabled obtaining a nuclear fraction enriched in IG. The method consisted in extraction of isolated nuclei with a non-ionic detergent and digestion with DNase I in a high ionic strength. Each step of isolation was ultrastructurally monitored using both the routine electron microscopy as well as a preferential staining of IG with bismuth. Presence of spots of tightly packed granules within IG conglomerations in the final fraction like in the nuclei in situ was a good ultrastructural marker of IG. The resulting fraction consisted predominantly of IG conglomerations. Their preferential staining with bismuth was well preserved. Minute amounts of fibrillar material originating from nuclear matrix and residual nuclei could be observed. Protein composition of the fraction enriched in IG was studied by SDS-polyacrylamide gel electrophoresis. After electrotransfer, nitrocellulose filters were fixed with glutaraldehyde and stained with bismuth method in order to identify IG proteins. The results of ultrastructural and cytochemical studies in comparison to electrophoretic protein pattern are discussed.

  7. A new modification in the exponential rational function method for nonlinear fractional differential equations

    Science.gov (United States)

    Ahmed, Naveed; Bibi, Sadaf; Khan, Umar; Mohyud-Din, Syed Tauseef

    2018-02-01

    We have modified the traditional exponential rational function method (ERFM) and have used it to find the exact solutions of two different fractional partial differential equations, one is the time fractional Boussinesq equation and the other is the (2+1)-dimensional time fractional Zoomeron equation. In both the cases it is observed that the modified scheme provides more types of solutions than the traditional one. Moreover, a comparison of the recent solutions is made with some already existing solutions. We can confidently conclude that the modified scheme works better and provides more types of solutions with almost similar computational cost. Our generalized solutions include periodic, soliton-like, singular soliton and kink solutions. A graphical simulation of all types of solutions is provided and the correctness of the solution is verified by direct substitution. The extended version of the solutions is expected to provide more flexibility to scientists working in the relevant field to test their simulation data.

  8. Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.

    Science.gov (United States)

    Pu, Yi-Fei; Yi, Zhang; Zhou, Ji-Liu

    2017-10-01

    This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron's fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.

  9. Analysis of TPH and Aliphatic and Aromatic Hydrocarbons Fractions in Environmental Interest Matrices

    International Nuclear Information System (INIS)

    Pindado, O.; Perez, R. M.; Garcia, S.

    2014-01-01

    Analytical methods to analyze TPH and several aliphatic and aromatic fractions present in soil and groundwater samples contaminated by hydrocarbons are showed. As a part of BIOXISOIL project, analyzing these parameters is fundamental and indispensable to know the initial contamination level, design an adequate method to decontaminate it and eventually assess decontamination accomplished. Analysis of both matrices involve different extraction stages such as microwave radiation, clean up steps based on solid phase extraction and finally a chromatograph analysis with flame ion detector. Analytical procedures have showed satisfactory analytical quality parameters and have been validated against several certified reference materials. (Author)

  10. 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.

  11. Parameter optimization in the regularized kernel minimum noise fraction transformation

    DEFF Research Database (Denmark)

    Nielsen, Allan Aasbjerg; Vestergaard, Jacob Schack

    2012-01-01

    Based on the original, linear minimum noise fraction (MNF) transformation and kernel principal component analysis, a kernel version of the MNF transformation was recently introduced. Inspired by we here give a simple method for finding optimal parameters in a regularized version of kernel MNF...... analysis. We consider the model signal-to-noise ratio (SNR) as a function of the kernel parameters and the regularization parameter. In 2-4 steps of increasingly refined grid searches we find the parameters that maximize the model SNR. An example based on data from the DLR 3K camera system is given....

  12. Step-Up DC-DC converters

    DEFF Research Database (Denmark)

    Forouzesh, Mojtaba; Siwakoti, Yam P.; Gorji, Saman A.

    2017-01-01

    on the general law and framework of the development of next-generation step-up dc-dc converters, this paper aims to comprehensively review and classify various step-up dc-dc converters based on their characteristics and voltage-boosting techniques. In addition, the advantages and disadvantages of these voltage......DC-DC converters with voltage boost capability are widely used in a large number of power conversion applications, from fraction-of-volt to tens of thousands of volts at power levels from milliwatts to megawatts. The literature has reported on various voltage-boosting techniques, in which......-boosting techniques and associated converters are discussed in detail. Finally, broad applications of dc-dc converters are presented and summarized with comparative study of different voltage-boosting techniques....

  13. Research on the range side lobe suppression method for modulated stepped frequency radar signals

    Science.gov (United States)

    Liu, Yinkai; Shan, Tao; Feng, Yuan

    2018-05-01

    The magnitude of time-domain range sidelobe of modulated stepped frequency radar affects the imaging quality of inverse synthetic aperture radar (ISAR). In this paper, the cause of high sidelobe in modulated stepped frequency radar imaging is analyzed first in real environment. Then, the chaos particle swarm optimization (CPSO) is used to select the amplitude and phase compensation factors according to the minimum sidelobe criterion. Finally, the compensated one-dimensional range images are obtained. Experimental results show that the amplitude-phase compensation method based on CPSO algorithm can effectively reduce the sidelobe peak value of one-dimensional range images, which outperforms the common sidelobe suppression methods and avoids the coverage of weak scattering points by strong scattering points due to the high sidelobes.

  14. A two-step method for fast and reliable EUV mask metrology

    Science.gov (United States)

    Helfenstein, Patrick; Mochi, Iacopo; Rajendran, Rajeev; Yoshitake, Shusuke; Ekinci, Yasin

    2017-03-01

    One of the major obstacles towards the implementation of extreme ultraviolet lithography for upcoming technology nodes in semiconductor industry remains the realization of a fast and reliable detection methods patterned mask defects. We are developing a reflective EUV mask-scanning lensless imaging tool (RESCAN), installed at the Swiss Light Source synchrotron at the Paul Scherrer Institut. Our system is based on a two-step defect inspection method. In the first step, a low-resolution defect map is generated by die to die comparison of the diffraction patterns from areas with programmed defects, to those from areas that are known to be defect-free on our test sample. In a later stage, a die to database comparison will be implemented in which the measured diffraction patterns will be compared to those calculated directly from the mask layout. This Scattering Scanning Contrast Microscopy technique operates purely in the Fourier domain without the need to obtain the aerial image and, given a sufficient signal to noise ratio, defects are found in a fast and reliable way, albeit with a location accuracy limited by the spot size of the incident illumination. Having thus identified rough locations for the defects, a fine scan is carried out in the vicinity of these locations. Since our source delivers coherent illumination, we can use an iterative phase-retrieval method to reconstruct the aerial image of the scanned area with - in principle - diffraction-limited resolution without the need of an objective lens. Here, we will focus on the aerial image reconstruction technique and give a few examples to illustrate the capability of the method.

  15. Adapting IMRT delivery fraction-by-fraction to cater for variable intrafraction motion

    International Nuclear Information System (INIS)

    Webb, S

    2008-01-01

    This paper presents a technique for coping with variable intrafraction organ motion when delivering intensity-modulated radiation therapy (IMRT). The strategy is an adaptive delivery in which the fluence delivered up to a particular fraction is subtracted from the required total-course planned fluence to create an adapted residual fluence for the next fraction. This requires that the fluence already delivered can be computed, knowing the intrafraction motion during each fraction. If the adaptation is unconstrained, as would be required for perfect delivery of the planned fluence, then the individual fractional fluences would become unphysical, with both negative components and spikes. Hence it is argued that constraints must be applied; first, positivity constraints and second, constraints to limit fluence spikes. Additionally, it is shown to be helpful to constrain other quantities which are explained. The power of the strategy is that it adapts to the (potentially variable) moving geometry during each fraction. It is not a perfect delivery but it is always better than making no adaptation. The fractionated nature of radiation therapy is thus exploited to advantage. The fluence adaptation method does not require re-planning at each fraction but this imposes limitations which are stated. The fuller theory of dose adaptation is also developed for intrafraction motion. The method is complementary to other adaptive strategies recently discussed with respect to interfraction motion

  16. Solving delay differential equations in S-ADAPT by method of steps.

    Science.gov (United States)

    Bauer, Robert J; Mo, Gary; Krzyzanski, Wojciech

    2013-09-01

    S-ADAPT is a version of the ADAPT program that contains additional simulation and optimization abilities such as parametric population analysis. S-ADAPT utilizes LSODA to solve ordinary differential equations (ODEs), an algorithm designed for large dimension non-stiff and stiff problems. However, S-ADAPT does not have a solver for delay differential equations (DDEs). Our objective was to implement in S-ADAPT a DDE solver using the methods of steps. The method of steps allows one to solve virtually any DDE system by transforming it to an ODE system. The solver was validated for scalar linear DDEs with one delay and bolus and infusion inputs for which explicit analytic solutions were derived. Solutions of nonlinear DDE problems coded in S-ADAPT were validated by comparing them with ones obtained by the MATLAB DDE solver dde23. The estimation of parameters was tested on the MATLB simulated population pharmacodynamics data. The comparison of S-ADAPT generated solutions for DDE problems with the explicit solutions as well as MATLAB produced solutions which agreed to at least 7 significant digits. The population parameter estimates from using importance sampling expectation-maximization in S-ADAPT agreed with ones used to generate the data. Published by Elsevier Ireland Ltd.

  17. The synchronization of three fractional differential systems

    International Nuclear Information System (INIS)

    Li Changpin; Yan Jianping

    2007-01-01

    In this paper, a new method is proposed and applied to the synchronization of fractional differential systems (or 'differential systems with fractional orders'), where both drive and response systems have the same dimensionality and are coupled by the driving signal. The present technique is based on the stability criterion of linear fractional systems. This method is implemented in (chaos) synchronization of the fractional Lorenz system, Chen system and Chua circuit. Numerical simulations show the present synchronization method works well

  18. Shortened screening method for phosphorus fractionation in sediments A complementary approach to the standards, measurements and testing harmonised protocol

    International Nuclear Information System (INIS)

    Pardo, Patricia; Rauret, Gemma; Lopez-Sanchez, Jose Fermin

    2004-01-01

    The SMT protocol, a sediment phosphorus fractionation method harmonised and validated in the frame of the standards, measurements and testing (SMT) programme (European Commission), establishes five fractions of phosphorus according to their extractability. The determination of phosphate extracted is carried out spectrophotometrically. This protocol has been applied to 11 sediments of different origin and characteristics and the phosphorus extracted in each fraction was determined not only by UV-Vis spectrophotometry, but also by inductively coupled plasma-atomic emission spectrometry. The use of these two determination techniques allowed the differentiation between phosphorus that was present in the extracts as soluble reactive phosphorus and as total phosphorus. From the comparison of data obtained with both determination techniques a shortened screening method, for a quick evaluation of the magnitude and importance of the fractions given by the SMT protocol, is proposed and validated using two certified reference materials

  19. A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

    Science.gov (United States)

    Tayebi, A.; Shekari, Y.; Heydari, M. H.

    2017-07-01

    Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

  20. Maxwell’s Equations on Cantor Sets: A Local Fractional Approach

    Directory of Open Access Journals (Sweden)

    Yang Zhao

    2013-01-01

    Full Text Available Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Local fractional differential forms of Maxwell’s equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained. Maxwell's equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell’s equations for the dynamics of cold dark matter.

  1. The Value of Step-by-Step Risk Assessment for Unmanned Aircraft

    DEFF Research Database (Denmark)

    La Cour-Harbo, Anders

    2018-01-01

    The new European legislation expected in 2018 or 2019 will introduce a step-by-step process for conducting risk assessments for unmanned aircraft flight operations. This is a relatively simple approach to a very complex challenge. This work compares this step-by-step process to high fidelity risk...... modeling, and shows that at least for a series of example flight missions there is reasonable agreement between the two very different methods....

  2. ANALISYS OF FRACTIONAL-N FREQUENCY SYNTHESIZERS

    Directory of Open Access Journals (Sweden)

    Boris I. Shakhtarin

    2018-01-01

    Full Text Available Modern information and control systems cannot be imagined without synchronization subsystems. These are the basic elements that provide tracking of the frequency and phase of reference and information signals, the evaluation of information parameters, and the synthesis of reference and clock signals. Frequency synthesizers (FS are widely used due to the high speed of frequency setting, a wide range of frequency grids and minimal phase noise in the operating frequency range. Since with the mass appearance of specialized microprocessors and with the improvement of automatic design systems, the feasibility and repeatability of products has become simpler, digital FS are increasingly being used. The most widely used are FS with a frequency divider on digital elements, which serves to convert the signal of a reference oscillator and a controlled generator. For FS using a divisor with an integer division factor in the feedback loop, there are a number of limitations, such as the lower frequency of the FS and the frequency step of the FS. To solve this problem, divisors with fractional-variable division factors in the feedback loop are used, which allow to obtain the required range and the grid frequency step of the FS. The methods of improving the quality of spectral and dynamic characteristics of digital synthesizers in a given band of frequency detuning are analyzed. The principles of the FS operation with a divisor with a fractionalvariable fission coefficient are described, and structural schemes are given. The results of imitation simulation in the Simulink system of the software package MATLAB of frequency synthesizers with a divisor with a fractional-variable fission factor implemented in various ways are presented, and a comparative analysis of the spectral characteristics of the obtained models is carried out. 

  3. Pyrosequencing™ : A one-step method for high resolution HLA typing

    Directory of Open Access Journals (Sweden)

    Marincola Francesco M

    2003-11-01

    Full Text Available Abstract While the use of high-resolution molecular typing in routine matching of human leukocyte antigens (HLA is expected to improve unrelated donor selection and transplant outcome, the genetic complexity of HLA still makes the current methodology limited and laborious. Pyrosequencing™ is a gel-free, sequencing-by-synthesis method. In a Pyrosequencing reaction, nucleotide incorporation proceeds sequentially along each DNA template at a given nucleotide dispensation order (NDO that is programmed into a pyrosequencer. Here we describe the design of a NDO that generates a pyrogram unique for any given allele or combination of alleles. We present examples of unique pyrograms generated from each of two heterozygous HLA templates, which would otherwise remain cis/trans ambiguous using standard sequencing based typing (SBT method. In addition, we display representative data that demonstrate long read and linear signal generation. These features are prerequisite of high-resolution typing and automated data analysis. In conclusion Pyrosequencing is a one-step method for high resolution DNA typing.

  4. Spectral finite element methods for solving fractional differential equations with applications in anomalous transport

    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)

  5. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

    KAUST Repository

    Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

    2017-01-01

    This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

  6. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

    KAUST Repository

    Belkhatir, Zehor

    2017-05-31

    This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

  7. Fractional Order Element Based Impedance Matching

    KAUST Repository

    Radwan, Ahmed Gomaa

    2014-06-24

    Disclosed are various embodiments of methods and systems related to fractional order element based impedance matching. In one embodiment, a method includes aligning a traditional Smith chart (|.alpha.|=1) with a fractional order Smith chart (|.alpha.|.noteq.1). A load impedance is located on the traditional Smith chart and projected onto the fractional order Smith chart. A fractional order matching element is determined by transitioning along a matching circle of the fractional order Smith chart based at least in part upon characteristic line impedance. In another embodiment, a system includes a fractional order impedance matching application executed in a computing device. The fractional order impedance matching application includes logic that obtains a first set of Smith chart coordinates at a first order, determines a second set of Smith chart coordinates at a second order, and determines a fractional order matching element from the second set of Smith chart coordinates.

  8. Neutral pumping rates for a next step tokamak ignition device

    International Nuclear Information System (INIS)

    Galambos, J.D.; Peng, Y.K.M.; Heifetz, D.

    1985-01-01

    Neutral pumping rates are calculated for pump-limiter and divertor options of a next step tokamak ignition device using a method that accounts for the coupled effects of neutral transport and plasma transport. For both pump limiters and divertors the plasma flow into the channel surrounding the neutralizer plate is greatly reduced by the neutral recycling. The fraction of this flow that is pumped can be large (>50%) but in general is dependent on the particular geometry and plasma conditions. It is estimated that pumping speeds greater than or approximately 10 5 L/s are adequate for the exhaust requirements in the pump-limiter and the divertor cases

  9. Optimization of One-Step In Situ Transesterification Method for Accurate Quantification of EPA in Nannochloropsis gaditana

    Directory of Open Access Journals (Sweden)

    Yuting Tang

    2016-11-01

    Full Text Available Microalgae are a valuable source of lipid feedstocks for biodiesel and valuable omega-3 fatty acids. Nannochloropsis gaditana has emerged as a promising producer of eicosapentaenoic acid (EPA due to its fast growth rate and high EPA content. In the present study, the fatty acid profile of Nannochloropsis gaditana was found to be naturally high in EPA and devoid of docosahexaenoic acid (DHA, thereby providing an opportunity to maximize the efficacy of EPA production. Using an optimized one-step in situ transesterification method (methanol:biomass = 90 mL/g; HCl 5% by vol.; 70 °C; 1.5 h, the maximum fatty acid methyl ester (FAME yield of Nannochloropsis gaditana cultivated under rich condition was quantified as 10.04% ± 0.08% by weight with EPA-yields as high as 4.02% ± 0.17% based on dry biomass. The total FAME and EPA yields were 1.58- and 1.23-fold higher separately than that obtained using conventional two-step method (solvent system: methanol and chloroform. This one-step in situ method provides a fast and simple method to measure fatty acid methyl ester (FAME yields and could serve as a promising method to generate eicosapentaenoic acid methyl ester from microalgae.

  10. Fractionation list: F0000000183 [jPOST repository metadata[Archive

    Lifescience Database Archive (English)

    Full Text Available 's protocol with slight modifications, i.e., purification by centrifugation at 700 g after the homogenizat...ion step was conducted twice to increase the purity of the fractions. For Cyp2b enz

  11. Fractionation list: F0000000184 [jPOST repository metadata[Archive

    Lifescience Database Archive (English)

    Full Text Available s protocol with slight modifications, i.e., purification by centrifugation at 700 g after the homogenizati...on step was conducted twice to increase the purity of the fractions. For Cyp2b enzy

  12. Density fractions versus size separates: does physical fractionation isolate functional soil compartments?

    Directory of Open Access Journals (Sweden)

    C. Moni

    2012-12-01

    Full Text Available Physical fractionation is a widely used methodology to study soil organic matter (SOM dynamics, but concerns have been raised that the available fractionation methods do not well describe functional SOM pools. In this study we explore whether physical fractionation techniques isolate soil compartments in a meaningful and functionally relevant way for the investigation of litter-derived nitrogen dynamics at the decadal timescale. We do so by performing aggregate density fractionation (ADF and particle size-density fractionation (PSDF on mineral soil samples from two European beech forests a decade after application of 15N labelled litter.

    Both density and size-based fractionation methods suggested that litter-derived nitrogen became increasingly associated with the mineral phase as decomposition progressed, within aggregates and onto mineral surfaces. However, scientists investigating specific aspects of litter-derived nitrogen dynamics are pointed towards ADF when adsorption and aggregation processes are of interest, whereas PSDF is the superior tool to research the fate of particulate organic matter (POM.

    Some methodological caveats were observed mainly for the PSDF procedure, the most important one being that fine fractions isolated after sonication can not be linked to any defined decomposition pathway or protective mechanism. This also implies that historical assumptions about the "adsorbed" state of carbon associated with fine fractions need to be re-evaluated. Finally, this work demonstrates that establishing a comprehensive picture of whole soil OM dynamics requires a combination of both methodologies and we offer a suggestion for an efficient combination of the density and size-based approaches.

  13. Imaginary Time Step Method to Solve the Dirac Equation with Nonlocal Potential

    International Nuclear Information System (INIS)

    Zhang Ying; Liang Haozhao; Meng Jie

    2009-01-01

    The imaginary time step (ITS) method is applied to solve the Dirac equation with nonlocal potentials in coordinate space. Taking the nucleus 12 C as an example, even with nonlocal potentials, the direct ITS evolution for the Dirac equation still meets the disaster of the Dirac sea. However, following the recipe in our former investigation, the disaster can be avoided by the ITS evolution for the corresponding Schroedinger-like equation without localization, which gives the convergent results exactly the same with those obtained iteratively by the shooting method with localized effective potentials.

  14. Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Xu, Kaixuan, E-mail: kaixuanxubjtu@yeah.net; Wang, Jun

    2017-02-26

    In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

  15. Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

    International Nuclear Information System (INIS)

    Xu, Kaixuan; Wang, Jun

    2017-01-01

    In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

  16. Accelerated solvent extraction method with one-step clean-up for hydrocarbons in soil

    International Nuclear Information System (INIS)

    Nurul Huda Mamat Ghani; Norashikin Sain; Rozita Osman; Zuraidah Abdullah Munir

    2007-01-01

    The application of accelerated solvent extraction (ASE) using hexane combined with neutral silica gel and sulfuric acid/ silica gel (SA/ SG) to remove impurities prior to analysis by gas chromatograph with flame ionization detector (GC-FID) was studied. The efficiency of extraction was evaluated based on the three hydrocarbons; dodecane, tetradecane and pentadecane spiked to soil sample. The effect of ASE operating conditions (extraction temperature, extraction pressure, static time) was evaluated and the optimized condition obtained from the study was extraction temperature of 160 degree Celsius, extraction pressure of 2000 psi with 5 minutes static extraction time. The developed ASE with one-step clean-up method was applied in the extraction of hydrocarbons from spiked soil and the amount extracted was comparable to ASE extraction without clean-up step with the advantage of obtaining cleaner extract with reduced interferences. Therefore in the developed method, extraction and clean-up for hydrocarbons in soil can be achieved rapidly and efficiently with reduced solvent usage. (author)

  17. Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

    Science.gov (United States)

    Chen, Z.; Shu, C.; Tan, D.

    2018-05-01

    An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

  18. Fractional Dynamics and Control

    CERN Document Server

    Machado, José; Luo, Albert

    2012-01-01

    Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science. Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation  Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics  Develops new methods for control and synchronization of...

  19. A three operator split-step method covering a larger set of non-linear partial differential equations

    Science.gov (United States)

    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.

  20. Extension of the method of moments for population balances involving fractional moments and application to a typical agglomeration problem.

    Science.gov (United States)

    Alexiadis, Alessio; Vanni, Marco; Gardin, Pascal

    2004-08-01

    The method of moment (MOM) is a powerful tool for solving population balance. Nevertheless it cannot be used in every circumstance. Sometimes, in fact, it is not possible to write the governing equations in closed form. Higher moments, for instance, could appear in the evolution of the lower ones. This obstacle has often been resolved by prescribing some functional form for the particle size distribution. Another example is the occurrence of fractional moment, usually connected with the presence of fractal aggregates. For this case we propose a procedure that does not need any assumption on the form of the distribution but it is based on the "moments generating function" (that is the Laplace transform of the distribution). An important result of probability theory is that the kth derivative of the moments generating function represents the kth moment of the original distribution. This result concerns integer moments but, taking in account the Weyl fractional derivative, could be extended to fractional orders. Approximating fractional derivative makes it possible to express the fractional moments in terms of the integer ones and so to use regularly the method of moments.

  1. Long-Term Dynamics of Autonomous Fractional Differential Equations

    Science.gov (United States)

    Liu, Tao; Xu, Wei; Xu, Yong; Han, Qun

    This paper aims to investigate long-term dynamic behaviors of autonomous fractional differential equations with effective numerical method. The long-term dynamic behaviors predict where systems are heading after long-term evolution. We make some modification and transplant cell mapping methods to autonomous fractional differential equations. The mapping time duration of cell mapping is enlarged to deal with the long memory effect. Three illustrative examples, i.e. fractional Lotka-Volterra equation, fractional van der Pol oscillator and fractional Duffing equation, are studied with our revised generalized cell mapping method. We obtain long-term dynamics, such as attractors, basins of attraction, and saddles. Compared with some existing stability and numerical results, the validity of our method is verified. Furthermore, we find that the fractional order has its effect on the long-term dynamics of autonomous fractional differential equations.

  2. Dynamics of fractional vortices in long Josephson junctions; Dynamik fraktionaler Flusswirbel in langen Josephsonkontakten

    Energy Technology Data Exchange (ETDEWEB)

    Gaber, Tobias

    2007-07-01

    In this thesis static and dynamic properties of fractional vortices in long Josephson junctions are investigated. Fractional vortices are circulating supercurrents similar to the well-known Josephson fluxons. Yet, they show the distinguishing property of carrying only a fraction of the magnetic flux quantum. Fractional vortices are interesting non-linear objects. They spontaneously appear and are pinned at the phase discontinuity points of so called 0-{kappa} junctions but can be bend or flipped by external forces like bias currents or magnetic fields. 0-{kappa} junctions and fractional vortices are generalizations of the well-known 0-{pi} junctions and semifluxons, where not only phase jumps of pi but arbitrary values denoted by kappa are considered. By using so-called artificial 0-{kappa} junctions that are based on standard Nb-AlO{sub x}-Nb technology the classical dynamics of fractional vortices has been investigated experimentally for the very first time. Here, half-integer zero field steps could be observed. These voltage steps on the junction's current-voltage characteristics correspond to the periodic flipping/hopping of fractional vortices. In addition, the oscillatory eigenmodes of fractional vortices were investigated. In contrast to fluxons fractional vortices have an oscillatory eigenmode with a frequency within the plasma gap. Using resonance spectroscopy the dependence of the eigenmode frequency on the flux carried by the vortex and an applied bias current was determined. (orig.)

  3. Ultracentrifugation for ultrafine nanodiamond fractionation

    Science.gov (United States)

    Koniakhin, S. V.; Besedina, N. A.; Kirilenko, D. A.; Shvidchenko, A. V.; Eidelman, E. D.

    2018-01-01

    In this paper we propose a method for ultrafine fractionation of nanodiamonds using the differential centrifugation in the fields up to 215000g. The developed protocols yield 4-6 nm fraction giving main contribution to the light scattering intensity. The desired 4-6 nm fraction can be obtained from various types of initial nanodiamonds: three types of detonation nanodiamonds differing in purifying methods, laser synthesis nanodiamonds and nanodiamonds made by milling. The characterization of the obtained hydrosols was conducted with Dynamic Light Scattering, Zeta potential measurements, powder XRD and TEM. According to powder XRD and TEM data ultracentrifugation also leads to a further fractionation of the primary diamond nanocrystallites in the hydrosols from 4 to 2 nm.

  4. A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

    Science.gov (United States)

    Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

    2017-09-01

    Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

  5. Methods for optimizing over the efficient and weakly efficient sets of an affine fractional vector optimization program

    DEFF Research Database (Denmark)

    Le, T.H.A.; Pham, D. T.; Canh, Nam Nguyen

    2010-01-01

    Both the efficient and weakly efficient sets of an affine fractional vector optimization problem, in general, are neither convex nor given explicitly. Optimization problems over one of these sets are thus nonconvex. We propose two methods for optimizing a real-valued function over the efficient...... and weakly efficient sets of an affine fractional vector optimization problem. The first method is a local one. By using a regularization function, we reformulate the problem into a standard smooth mathematical programming problem that allows applying available methods for smooth programming. In case...... the objective function is linear, we have investigated a global algorithm based upon a branch-and-bound procedure. The algorithm uses Lagrangian bound coupling with a simplicial bisection in the criteria space. Preliminary computational results show that the global algorithm is promising....

  6. DETERMINATION OF DIETARY FIBRE – THE INFLUENCE OF MILLING FRACTION AND MIXING PROCESS

    Directory of Open Access Journals (Sweden)

    Blaž FERJANČIČ

    2018-04-01

    Full Text Available Dietary fibre is an important constituent of a healthy diet, composed of non-digestible carbohydrates and lignin. Over the last decades dietary fibre has gained importance for human nutrition, due to its beneficial effects on health. In addition to classical enzyme-gravimetric methods, new methods for the determination of total, insoluble and soluble dietary fibres in foods have recently been developed, but have not yet been fully implemented for use. For the purpose of creating food composition databases and for food labelling, the classical AOAC 985.29 and 991.43 methods are still widely used. The methods are enzyme-gravimetric and therefore sensitive to enzyme kinetics. The aim of the study was to investigate the effect of milling fraction and mixing of the sample on dietary fibre content determined with the AOAC method 991.43. The results showed that milling fraction significantly influences the content of dietary fibre, especially in unprocessed or slightly processed cereals, the mixing acts synergistically with milling. According to the results it is proposed to mill the sample between 200 and 500 μm. For accurate determination of dietary fibre content, it is necessary to prepare the sample correctly, since the AOAC 991.43 method is, despite its robustness, sensitive during the sample preparation step.

  7. Fractional Order Element Based Impedance Matching

    KAUST Repository

    Radwan, Ahmed Gomaa; Salama, Khaled N.; Shamim, Atif

    2014-01-01

    Disclosed are various embodiments of methods and systems related to fractional order element based impedance matching. In one embodiment, a method includes aligning a traditional Smith chart (|.alpha.|=1) with a fractional order Smith chart (|.alpha

  8. Calibration of shahid's analytical method for adulterated Zn-edta fertilizers by ion chromatography and atomic absorption spectroscopy

    International Nuclear Information System (INIS)

    Khan, M.S.A.; Akram, M.; Qazi, M.A.

    2010-01-01

    Chelated zinc fertilizers are usually recommended in calcareous alkaline soils to provide Zn nutrition in order to prevent possible Zn precipitation. In Punjab (Pakistan), Zn EDTA products are being manufactured, and marketed to meet the zinc requirement of various crops grown in Zn deficient soils. Under fertilizer control order, 1973 (amended), their quality has to be monitored by the Agriculture Department, Government of the Punjab. None of the traditional method was found suitable which can separate the mineral fraction from that of chelated adulterated fertilizer except for those methods based on ion chromatography. Calibration of ion chromatography method was carried out by determining the mineral Zn fraction leading to estimate remaining Zn EDTA fraction in fertilizer samples of adulterated nature i.e. mixture of chelated and mineral fraction. In order to achieve the objective atomic absorption spectroscopy was coupled with ion chromatography. The method offers a specific, reliable technique for determination of chelated zinc in fertilizers. In the first step chelation was broken down with concentrated sulphuric acid treatment and total zinc contents were determined by atomic absorption spectroscopy. In second step, non-chelated (mineral) portion of zinc was determined by ion chromatography using cation column and conductivity detector. Chelated zinc was calculated by subtracting non-chelated (mineral) fraction from total zinc contents. (author)

  9. A numerical technique for solving fractional optimal control problems and fractional Riccati differential equations

    Directory of Open Access Journals (Sweden)

    F. Ghomanjani

    2016-10-01

    Full Text Available In the present paper, we apply the Bezier curves method for solving fractional optimal control problems (OCPs and fractional Riccati differential equations. The main advantage of this method is that it can reduce the error of the approximate solutions. Hence, the solutions obtained using the Bezier curve method give good approximations. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.

  10. Fractional smith chart theory

    KAUST Repository

    Shamim, Atif

    2011-03-01

    For the first time, a generalized Smith chart is introduced here to represent fractional order circuit elements. It is shown that the standard Smith chart is a special case of the generalized fractional order Smith chart. With illustrations drawn for both the conventional integer based lumped elements and the fractional elements, a graphical technique supported by the analytical method is presented to plot impedances on the fractional Smith chart. The concept is then applied towards impedance matching networks, where the fractional approach proves to be much more versatile and results in a single element matching network for a complex load as compared to the two elements in the conventional approach. © 2010 IEEE.

  11. Acomparative Study Comparing Low-dose Step-up Versus Step-down in Polycystic Ovary Syndrome Resistant to Clomiphene

    Directory of Open Access Journals (Sweden)

    S Peivandi

    2010-03-01

    Full Text Available Introduction: Polycystic ovary syndrome(PCOS is one of the most common cause of infertility in women. clomiphene is the first line of treatment. however 20% of patients are resistant to clomiphene. because of follicular hypersensitivity to gonadotropins in pcod, multiple follicular growth and development occurs which is cause of OHSS and multiple pregnancy. Our aim of this random and clinical study was comparation between step-down and low dose step-up methods for induction ovulation in clomiphene resistant. Methods: 60 cases were included 30 women in low-dose step-up group and 30 women in step-down group. In low-dose step-up HMG 75u/d and in step-down HMG 225u/d was started on 3th days of cycle, monitoring with vaginal sonography was done on 8th days of cycle. When follicle with>14 mm in diameter was seen HMG dose was continued in low-dose step-up and was decreased in step-down group. When follicle reached to 18mm in diameter, amp HCG 10000 unit was injected and IUI was performed 36 hours later. Results: Number of HMG ampules, number of follicles> 14mm on the day of HCG injection and level of serum estradiol was greater in low dose step up protocol than step down protocol(p<0/0001. Ovulation rate and pregnancy rate was greater in lowdose step up group than step down group with significant difference (p<0/0001. Conclusion: Our study showed that low-dose step-up regimen with HMG is effective for stimulating ovulation and clinical pregnancy but in view of monofollicular growth, the step down method was more effective and safe. In our study multifolliular growth in step-up method was higher than step-down method. We can predict possibility of Ovarian Hyperstimulation Syndrome syndrome in highly sensitive PCOS patients.

  12. Influence of the drying method in chitosans purification step

    International Nuclear Information System (INIS)

    Fonseca, Ana C.M.; Batista, Jorge G.S.; Bettega, Antonio; Lima, Nelson B. de

    2015-01-01

    Currently, the study of extracellular biopolymers properties has received prominence for being easy extraction and purification. Chitosan has been an attractive proposition for applications in various fields such as engineering, biotechnology, medicine and pharmacology. For such applications, it is necessary purification of chitosan to obtain a product more concentrated and free of undesirable impurities. However, at this stage of the process of obtaining the biopolymer may occur morphological and physicochemical changes. This study evaluated the influence of the drying process after purification of a commercial chitosan sample and the importance of this step and its cost/benefit in applications requiring a high degree of purity. The method of drying influenced in the organoleptic properties and in the main characteristics of material. Analysis of the crystal structure by X-ray diffraction showed that the degree of crystallinity, X (%), in the purified chitosan samples was lower when compared with the unpurified sample. The degree of acetylation, DA (%), was analyzed by spectroscopy infrared with no significant changes on the three drying methods assessed, unlike the viscosimetric molecular weight, M_v, determined by capillary viscometry. (author)

  13. Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

    Science.gov (United States)

    Owolabi, Kolade M.

    2018-03-01

    In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

  14. The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.

    Science.gov (United States)

    Thamareerat, N; Luadsong, A; Aschariyaphotha, N

    2016-01-01

    In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.

  15. Incompressible spectral-element method: Derivation of equations

    Science.gov (United States)

    Deanna, Russell G.

    1993-01-01

    A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

  16. Influence of application methods of one-step self-etching adhesives on microtensile bond strength

    OpenAIRE

    Chul-Kyu Choi,; Sung-Ae Son; Jin-Hee Ha; Bock Hur; Hyeon-Cheol Kim; Yong-Hun Kwon; Jeong-Kil Park

    2011-01-01

    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) T...

  17. On matrix fractional differential equations

    OpenAIRE

    Adem Kılıçman; Wasan Ajeel Ahmood

    2017-01-01

    The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objec...

  18. An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

    Science.gov (United States)

    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.

  19. On the singular perturbations for fractional differential equation.

    Science.gov (United States)

    Atangana, Abdon

    2014-01-01

    The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  20. Matrix formulation of fractional supersymmetry and q-deformation

    Energy Technology Data Exchange (ETDEWEB)

    Benkaddour, I.

    2006-02-24

    Supersymmetry, which is the only non-trivial Z{sub 2} extension of the Poincare algebra, can be generalized to fractional supersymmetry, when the space time is smaller than 3. Since symmetries play an important role in physics; the principal task of quantum groups consist in extanding these standard symmetries to the deformed ones, which might be used in physics as well. This two aspects will be the main focus of this thesis. In this work, we discuss the matrix formulation of fractional supersymmetry, the q-deformation of KdV hierarchy systems and noncommutative geometry. In the first part fractional supersymmetry generated by more than one charge operator and those which can be described as a matrix model are studied. Using parafermionic field-theoretical methods, the fundamentals of two-dimensional fractional supersymmetry Q{sup k}=P are set up. Known difficulties induced by methods based on the U{sub q}(sl(2)) quantum group representations and noncommutative geometry are avoided in the parafermionic approach. Moreover, we find that fractional supersymmetric algebras are naturally realized as matrix models. The k=3 case is studied in detail. In the second part we will study the q-deformed algebra and the q-analogues of the generalised KdV hierarchy. We construct in this part the algebra of q-deformed pseudo-differential operators, shown to be an essential step toward setting up a q-deformed integrability program. In fact, using the results of this q-deformed algebra, we derive the q-analogues of the generalised KdV hierarchy. We focus in particular on the first leading orders of this q-deformed hierarchy, namely the q-KdV and q-Boussinesq integrable systems. We also present the q-generalisation of the conformal transformations of the currents u{sub n}, n{>=}2, and discuss the primary condition of the fields w{sub n}, n{>=}2, by using the Volterra gauge group transformations for the q-covariant Lax operators. In the last part we will discuss quantum groups and

  1. New Exact Solutions of Time Fractional Gardner Equation by Using New Version of F -Expansion Method

    International Nuclear Information System (INIS)

    Pandir, Yusuf; Duzgun, Hasan Huseyin

    2017-01-01

    In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are situated in the solution function. As a result, various exact analytical solutions consisting of single and combined Jacobi elliptic functions solutions are obtained. (paper)

  2. An optimized regulating method for composting phosphorus fractions transformation based on biochar addition and phosphate-solubilizing bacteria inoculation.

    Science.gov (United States)

    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. Copyright © 2016 Elsevier Ltd. All rights reserved.

  3. Mathematical basis for the measurement of absolute and fractional cardiac output with diffusible tracers by compartmental analysis methods

    International Nuclear Information System (INIS)

    Charkes, N.D.

    1984-01-01

    Using compartmental analysis methods, a mathematical basis is given for the measurement of absolute and fractional cardiac output with diffusible tracers. Cardiac output is shown to be the product of the blood volume and the sum of the rate constants of tracer egress from blood, modified by a factor reflecting transcapillary diffusibility, the transfer fraction. The return of tracer to the blood and distant (intracellular) events are shown to play no role in the solution. Fractional cardiac output is the ratio of the rate constant of tracer egress from blood to an organ, divided by the sum of the egress constants from blood. Predominantly extracellular ions such as sodium or bromide are best suited for this technique, although theoretically any diffusible tracer whose compartmental model can be solved may be used. It is shown that fractional cardiac output is independent of the transfer fraction, and therefore can be measured accurately by tracers which are not freely diffusible

  4. Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

    Energy Technology Data Exchange (ETDEWEB)

    Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J [Intelligent System Research Group, Faculty of Electrical and Computer Engineering, Babol, Noushirvani University of Technology, PO Box 47135-484, Babol (Iran, Islamic Republic of); Ranjbar, A [Golestan University, Gorgan (Iran, Islamic Republic of); Momani, S [Department of Mathematics, 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 enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

  5. Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

    International Nuclear Information System (INIS)

    Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J; Ranjbar, A; Momani, S

    2009-01-01

    The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

  6. Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

    Science.gov (United States)

    Zolfaghari, M.; Ghaderi, R.; Sheikhol Eslami, A.; Ranjbar, A.; Hosseinnia, S. H.; Momani, S.; Sadati, J.

    2009-10-01

    The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

  7. Analysis of errors in the measurement of unattached fractions of radon and thoron progeny in a Canadian uranium mine using wire screen methods

    International Nuclear Information System (INIS)

    Khan, A.; Phillips, C.R.

    1987-01-01

    The unattached fraction of radon/thoron progeny in uranium mines is generally small and therefore difficult to measure accurately. The simple wire screen method provides a direct estimate of the unattached fraction from the screen count, or an indirect estimate from the difference between the reference and back-up filter counts. Wire screen method results are often difficult to analyse, especially when the unattached activity is small. Experimental data obtained in Canadian uranium mines are presented here, together with a detailed error analysis. The method consisting of counting the wire screen and the back-up filter is found to be the most precise method for unattached fraction determination. (author)

  8. Radiation grafting of pH-sensitive acrylic acid and 4-vinyl pyridine onto nylon-6 using one- and two-step methods

    International Nuclear Information System (INIS)

    Ortega, Alejandra; Alarcón, Darío; Muñoz-Muñoz, Franklin; Garzón-Fontecha, Angélica; Burillo, Guillermina

    2015-01-01

    Acrylic acid (AAc) and 4-vinyl pyridine (4VP) were γ-ray grafted onto nylon-6 (Ny 6 ) films via pre-irradiation oxidative method. These monomers were grafted using a one-step method to render Ny 6 -g–(AAc/4VP). A two-step or sequential method was used to render (Ny 6 -g–AAc)-g–4VP. Random copolymer branches were obtained when the grafting was carried out via one-step method using the two monomers together. The two-step method was applied to graft chains of 4VP on both Ny 6 substrate and previously grafted AAc chains (Ny 6 -g–AAc). The two types of binary copolymers synthesized were characterized to determine the amount of grafted polymers, the thermal behavior (DSC and TGA), the surface composition (XPS), and the pH responsiveness. In the two-step process, it is possible to achieve a higher graft yield, better control of the amount of each monomer, good reversibility in the swelling/deswelling process and shorter time to achieve equilibrium swelling. - Highlights: • A new binary graft of 4VP and AAc onto Ny 6 films was synthesized by γ-radiation. • The binary grafted material has potential application for heavy ion retention. • The two-step method shows better conditions in swelling and reversibility properties. • Surface distribution of monomers was evaluate by XPS characterization

  9. Canine distemper virus detection by different methods of One-Step RT-qPCR

    Directory of Open Access Journals (Sweden)

    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.

  10. Three-step interferometric method with blind phase shifts by use of interframe correlation between interferograms

    Science.gov (United States)

    Muravsky, Leonid I.; Kmet', Arkady B.; Stasyshyn, Ihor V.; Voronyak, Taras I.; Bobitski, Yaroslav V.

    2018-06-01

    A new three-step interferometric method with blind phase shifts to retrieve phase maps (PMs) of smooth and low-roughness engineering surfaces is proposed. Evaluating of two unknown phase shifts is fulfilled by using the interframe correlation between interferograms. The method consists of two stages. The first stage provides recording of three interferograms of a test object and their processing including calculation of unknown phase shifts, and retrieval of a coarse PM. The second stage implements firstly separation of high-frequency and low-frequency PMs and secondly producing of a fine PM consisting of areal surface roughness and waviness PMs. Extraction of the areal surface roughness and waviness PMs is fulfilled by using a linear low-pass filter. The computer simulation and experiments fulfilled to retrieve a gauge block surface area and its areal surface roughness and waviness have confirmed the reliability of the proposed three-step method.

  11. Effect of One-Step and Multi-Steps Polishing System on Enamel Roughness

    Directory of Open Access Journals (Sweden)

    Cynthia Sumali

    2013-07-01

    Full Text Available Normal 0 false false false MicrosoftInternetExplorer4 The final procedures of orthodontic treatment are bracket debonding and cleaning the remaining adhesive. Multi-step polishing system is the most common method used. The disadvantage of that system is long working time, because of the stages that should be done. Therefore, dental material manufacturer make an improvement to the system, to reduce several stages into one stage only. This new system is known as one-step polishing system. Objective: To compare the effect of one-step and multi-step polishing system on enamel roughness after orthodontic bracket debonding. Methods: Randomized control trial was conducted included twenty-eight maxillary premolar randomized into two polishing system; one-step OptraPol (Ivoclar, Vivadent and multi-step AstroPol (Ivoclar, Vivadent. After bracket debonding, the remaining adhesive on each group was cleaned by subjective polishing system for ninety seconds using low speed handpiece. The enamel roughness was subjected to profilometer, registering two roughness parameters (Ra, Rz. Independent t-test was used to analyze the mean score of enamel roughness in each group. Results: There was no significant difference of enamel roughness between one-step and multi-step polishing system (p>0.005. Conclusion: One-step polishing system can produce a similar enamel roughness to multi-step polishing system after bracket debonding and adhesive cleaning.DOI: 10.14693/jdi.v19i3.136

  12. Transformation method for the MIRD absorbed fractions as applied to various physiques

    International Nuclear Information System (INIS)

    Yamaguchi, Hiroshi

    1978-01-01

    This study concerns with the transformation method of the MIRD absorbed fraction (AF) to the AF corresponding to an individual having the dimensions different from those of the MIRD standard man. The absorbed dose of a target organ T from a source organs S, received by the administration of a radiopharmaceutical agent is expressed with the equilibrium absorbed dose constant, the cumulative activity in the S, and the specific absorbed fraction (SAF). It is dealt only with how the MIRD SAF data can be modified for estimating individual SAF values. The SAF for individuals is given for penetrating and non-penetrating radiations. In case of the penetrating radiation, the SAF is given from the corresponding MIRD SAF by using a transformation coefficient for the MIRD SAF, when the MIRD standard man is transfigured to a corresponding phantom of an individual by the scale factors selected separately for the head section, trunk section and leg section of the MIRD standard man. The obtained results were compared with the ORNL results, and showed good agreement. (Kato, T.)

  13. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

    KAUST Repository

    N U+02BC Doye, Ibrahima

    2018-02-13

    In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

  14. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

    KAUST Repository

    N U+02BC Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem

    2018-01-01

    In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

  15. Overview of multifluid-flow-calculation methods

    International Nuclear Information System (INIS)

    Stewart, H.B.

    1981-01-01

    Two categories of numerical methods which may be useful in multiphase flow research are discussed. The first category includes methods which are specifically intended for accurate computation of discontinuities, such as the method of characteristics, particle-in-cell method, flux-corrected transport, and random choice methods. Methods in this category could be applied to research on rocket exhaust plumes and interior ballistics. The second category includes methods for smooth, subsonic flows, such as fractional step methods, semi-implicit method, and methods which treat convection implicitly. The subsonic flow methods could be of interest for ice flows

  16. Assessment of New Calculation Method for Toxicological Sums-of-Fractions for Hanford Tank Farm Wastes

    International Nuclear Information System (INIS)

    Mahoney, Lenna A.

    2006-01-01

    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.

  17. 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.

  18. Maximum photovoltaic power tracking for the PV array using the fractional-order incremental conductance method

    International Nuclear Information System (INIS)

    Lin, Chia-Hung; Huang, Cong-Hui; Du, Yi-Chun; Chen, Jian-Liung

    2011-01-01

    Highlights: → The FOICM can shorten the tracking time less than traditional methods. → The proposed method can work under lower solar radiation including thin and heavy clouds. → The FOICM algorithm can achieve MPPT for radiation and temperature changes. → It is easy to implement in a single-chip microcontroller or embedded system. -- Abstract: This paper proposes maximum photovoltaic power tracking (MPPT) for the photovoltaic (PV) array using the fractional-order incremental conductance method (FOICM). Since the PV array has low conversion efficiency, and the output power of PV array depends on the operation environments, such as various solar radiation, environment temperature, and weather conditions. Maximum charging power can be increased to a battery using a MPPT algorithm. The energy conversion of the absorbed solar light and cell temperature is directly transferred to the semiconductor, but electricity conduction has anomalous diffusion phenomena in inhomogeneous material. FOICM can provide a dynamic mathematical model to describe non-linear characteristics. The fractional-order incremental change as dynamic variable is used to adjust the PV array voltage toward the maximum power point. For a small-scale PV conversion system, the proposed method is validated by simulation with different operation environments. Compared with traditional methods, experimental results demonstrate the short tracking time and the practicality in MPPT of PV array.

  19. Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

    Science.gov (United States)

    Mohebbi, Akbar

    2018-02-01

    In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones.

  20. State-Space Modelling of Loudspeakers using Fractional Derivatives

    DEFF Research Database (Denmark)

    King, Alexander Weider; Agerkvist, Finn T.

    2015-01-01

    This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractio......This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data...

  1. The estimation possibility of cleaning from radionuclides for the coast parts of drainage system by the soil fractionating method

    International Nuclear Information System (INIS)

    Karlin, Y.V.; Chuikov, V.Y.; Belianina, N.G.; Barinov, A.S.

    1996-01-01

    In this paper is considered the possibility of the cleaning from the radionuclides for the coast parts of the drainage system at the Moscow SIA open-quotes Radonclose quotes by the soil fractionating treatment. It is showed that this method cannot to be used for the cleaning of the soils near water flowing (a river, a spring or a open drainage system) because the most part of the soil size-fractions is the fine fractions and the main contaminant radionuclide ( 137 Cs) is distributed among the different soil components homogeneously

  2. Sharp Penalty Term and Time Step Bounds for the Interior Penalty Discontinuous Galerkin Method for Linear Hyperbolic Problems

    NARCIS (Netherlands)

    Geevers, Sjoerd; van der Vegt, J.J.W.

    2017-01-01

    We present sharp and sucient bounds for the interior penalty term and time step size to ensure stability of the symmetric interior penalty discontinuous Galerkin (SIPDG) method combined with an explicit time-stepping scheme. These conditions hold for generic meshes, including unstructured

  3. On the Singular Perturbations for Fractional Differential Equation

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2014-01-01

    Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  4. Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

    KAUST Repository

    Jin, B.; Lazarov, R.; Pasciak, J.; Zhou, Z.

    2014-01-01

    © 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.

  5. Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

    KAUST Repository

    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.

  6. Abundant closed form solutions of the conformable time fractional Sawada-Kotera-Ito equation using (G‧ / G) -expansion method

    Science.gov (United States)

    Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.

    2018-06-01

    In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.

  7. A Novel Motion Compensation Method for Random Stepped Frequency Radar with M-sequence

    Science.gov (United States)

    Liao, Zhikun; Hu, Jiemin; Lu, Dawei; Zhang, Jun

    2018-01-01

    The random stepped frequency radar is a new kind of synthetic wideband radar. In the research, it has been found that it possesses a thumbtack-like ambiguity function which is considered to be the ideal one. This also means that only a precise motion compensation could result in the correct high resolution range profile. In this paper, we will introduce the random stepped frequency radar coded by M-sequence firstly and briefly analyse the effect of relative motion between target and radar on the distance imaging, which is called defocusing problem. Then, a novel motion compensation method, named complementary code cancellation, will be put forward to solve this problem. Finally, the simulated experiments will demonstrate its validity and the computational analysis will show up its efficiency.

  8. Large-area gold nanohole arrays fabricated by one-step method for surface plasmon resonance biochemical sensing.

    Science.gov (United States)

    Qi, Huijie; Niu, Lihong; Zhang, Jie; Chen, Jian; Wang, Shujie; Yang, Jingjing; Guo, Siyi; Lawson, Tom; Shi, Bingyang; Song, Chunpeng

    2018-04-01

    Surface plasmon resonance (SPR) nanosensors based on metallic nanohole arrays have been widely reported to detect binding interactions in biological specimens. A simple and effective method for constructing nanoscale arrays is essential for the development of SPR nanosensors. In this work, we report a one-step method to fabricate nanohole arrays by thermal nanoimprinting in the matrix of IPS (Intermediate Polymer Stamp). No additional etching process or supporting substrate is required. The preparation process is simple, time-saving and compatible for roll-to-roll process, potentially allowing mass production. Moreover, the nanohole arrays were integrated into detection platform as SPR sensors to investigate different types of biological binding interactions. The results demonstrate that our one-step method can be used to efficiently fabricate large-area and uniform nanohole arrays for biochemical sensing.

  9. Fractional exclusion statistics: the method for describing interacting particle systems as ideal gases

    International Nuclear Information System (INIS)

    Anghel, Dragoş-Victor

    2012-01-01

    I show that if the total energy of a system of interacting particles may be written as a sum of quasiparticle energies, then the system of quasiparticles can be viewed, in general, as an ideal gas with fractional exclusion statistics (FES). The general method for calculating the FES parameters is also provided. The interacting particle system cannot be described as an ideal gas of Bose and Fermi quasiparticles except in trivial situations.

  10. The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation

    OpenAIRE

    Jin, Bangti; Lazarov, Raytcho; Liu, Yikan; Zhou, Zhi

    2014-01-01

    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...

  11. Fractional distillation of oil

    Energy Technology Data Exchange (ETDEWEB)

    Jones, L D

    1931-10-31

    A method of dividing oil into lubricating oil fractions without substantial cracking by introducing the oil in a heated state into a fractionating column from which oil fractions having different boiling points are withdrawn at different levels, while reflux liquid is supplied to the top of the column, and additional heat is introduced into the column by contacting with the oil therein a heated fluid of higher monlecular weight than water and less susceptible to thermal decomposition than is the highest boiling oil fraction resulting from the distillation, or of which any products produced by thermal decomposition will not occur in the highest boiling distillate withdrawn from the column.

  12. On the limitations of fixed-step-size adaptive methods with response confidence.

    Science.gov (United States)

    Hsu, Yung-Fong; Chin, Ching-Lan

    2014-05-01

    The family of (non-parametric, fixed-step-size) adaptive methods, also known as 'up-down' or 'staircase' methods, has been used extensively in psychophysical studies for threshold estimation. Extensions of adaptive methods to non-binary responses have also been proposed. An example is the three-category weighted up-down (WUD) method (Kaernbach, 2001) and its four-category extension (Klein, 2001). Such an extension, however, is somewhat restricted, and in this paper we discuss its limitations. To facilitate the discussion, we characterize the extension of WUD by an algorithm that incorporates response confidence into a family of adaptive methods. This algorithm can also be applied to two other adaptive methods, namely Derman's up-down method and the biased-coin design, which are suitable for estimating any threshold quantiles. We then discuss via simulations of the above three methods the limitations of the algorithm. To illustrate, we conduct a small scale of experiment using the extended WUD under different response confidence formats to evaluate the consistency of threshold estimation. © 2013 The British Psychological Society.

  13. Some comparison of two fractional oscillators

    International Nuclear Information System (INIS)

    Kang Yonggang; Zhang Xiu'e

    2010-01-01

    The other form of fractional oscillator equation comparing to the widely discussed one is ushered in. The properties of vibration of two fractional oscillators are discussed under the influence of different initial conditions. The interpretation of the characteristics of the fractional oscillators using different method is illustrated. Based on two fractional oscillator equations, two linked bodies and the continuous system are studied.

  14. A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line

    Directory of Open Access Journals (Sweden)

    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.

  15. Disequilibrium dihedral angles in layered intrusions: the microstructural record of fractionation

    Science.gov (United States)

    Holness, Marian; Namur, Olivier; Cawthorn, Grant

    2013-04-01

    The dihedral angle formed at junctions between two plagioclase grains and a grain of augite is only rarely in textural equilibrium in gabbros from km-scale crustal layered intrusions. The median of a population of these disequilibrium angles, Θcpp, varies systematically within individual layered intrusions, remaining constant over large stretches of stratigraphy with significant increases or decreases associated with the addition or reduction respectively of the number of phases on the liquidus of the bulk magma. The step-wise changes in Θcpp are present in Upper Zone of the Bushveld Complex, the Megacyclic Unit I of the Sept Iles Intrusion, and the Layered Series of the Skaergaard Intrusion. The plagioclase-bearing cumulates of Rum have a bimodal distribution of Θcpp, dependent on whether the cumulus assemblage includes clinopyroxene. The presence of the step-wise changes is independent of the order of arrival of cumulus phases and of the composition of either the cumulus phases or the interstitial liquid inferred to be present in the crystal mush. Step-wise changes in the rate of change in enthalpy with temperature (ΔH) of the cooling and crystallizing magma correspond to the observed variation of Θcpp, with increases of both ΔH and Θcpp associated with the addition of another liquidus phase, and decreases of both associated with the removal of a liquidus phase. The replacement of one phase by another (e.g. olivine ⇔ orthpyroxene) has little effect on ΔH and no discernible effect on Θcpp. An increase of ΔH is manifest by an increase in the fraction of the total enthalpy budget that is the latent heat of crystallization (the fractional latent heat). It also results in an increase in the amount crystallized in each incremental temperature drop (the crystal productivity). An increased fractional latent heat and crystal productivity result in an increased rate of plagioclase growth compared to that of augite during the final stages of solidification

  16. The Fractionation and Enrichment of La Content by Precipitation

    International Nuclear Information System (INIS)

    Suyanti; Purwani, MV

    2007-01-01

    The fractionation and enrichment of La content by precipitation have been done. The feed was La hydroxide by product of monazite sand. La hydroxide was diluted in HNO 3 and was precipitated with ammonia. For to obtain La, diluent was precipitated at pH 8 and the filtrate was precipitated with oxalic acid. The precipitant of La concentrated was more rich than the feed. This process was done continue and fractionally. The best yield of enrichment of La was obtained at dilution of 25 gram La Hydroxide in 20 ml HNO 3 . The efficient degree of fractionation was XV. The average weight of La concentrate was obtained at every fraction was 1 gram. The total sum weight from fraction I until fraction XV 13.5 grams. The average of La content was 48%, average fractionation efficiency of La for every step of fractionation was 48 %. Total efficiency all process was 100%. The average ratio of La/Nd was 2 and the ratio of La/Ce almost infinite. Before processed La/Ce was 7.86, and after process increase to 26.92 - to approach ∞. Before processed ratio of La/Nd was 2.79, after processed increased to 4.4 - to approach ∞. (author)

  17. Two-step purification of scutellarin from Erigeron breviscapus (vant.) Hand. Mazz. by high-speed counter-current chromatography.

    Science.gov (United States)

    Gao, Min; Gu, Ming; Liu, Chun-Zhao

    2006-07-11

    Scutellarin, a flavone glycoside, popularly applied for the treatment of cardiopathy, has been purified in two-step purification by high-speed counter-current chromatography (HSCCC) from Erigeron breviscapus (vant.) Hand. Mazz. (Deng-zhan-hua in Chinese), a well-known traditional Chinese medicinal plant for heart disease. Two solvent systems, n-hexane-ethyl acetate-methanol-acetic acid-water (1:6:1.5:1:4, v/v/v/v/v) and ethyl acetate-n-butanol-acetonitrile-0.1% HCl (5:2:5:10, v/v/v/v) were used for the two-step purification. The purity of the collected fraction of scutellarin was 95.6%. This study supplies a new alternative method for purification of scutellarin.

  18. Semianalytic Solution of Space-Time Fractional Diffusion Equation

    Directory of Open Access Journals (Sweden)

    A. Elsaid

    2016-01-01

    Full Text Available We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM. Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.

  19. Robust Stabilization of Fractional-Order Systems with Interval Uncertainties via Fractional-Order Controllers

    Directory of Open Access Journals (Sweden)

    Mohammadtaghi Hamidi Beheshti

    2010-01-01

    Full Text Available We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.

  20. Robust Stabilization of Fractional-Order Systems with Interval Uncertainties via Fractional-Order Controllers

    Directory of Open Access Journals (Sweden)

    Sayyad Delshad Saleh

    2010-01-01

    Full Text Available Abstract We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.

  1. Future Directions in Fractional Calculus Research and Applications

    Science.gov (United States)

    2017-10-31

    00 Hong Wang: Fast Numerical Methods and Mathematical Analysis of Fractional Partial Dierential Equations [Abstract - Presentation] 5:00 Poster...Quantum Mechanics [Abstract] 3:00 Changpin Li: The Finite Dierence Method for Caputo-type Parabolic Equation with Fractional Laplacian [Abstract] 4...Session A Petrov-Galerkin Spectral Element Method for Fractional Elliptic Problems Density Bounds for some Degenerate Stable Driven SDEs. 11/8/2017 A

  2. 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.

  3. Accuracy of Single-Step versus 2-Step Double-Mix Impression Technique

    DEFF Research Database (Denmark)

    Franco, Eduardo Batista; da Cunha, Leonardo Fernandes; Herrera, Francyle Simões

    2011-01-01

    Objective. To investigate the accuracy of dies obtained from single-step and 2-step double-mix impressions. Material and Methods. Impressions (n = 10) of a stainless steel die simulating a complete crown preparation were performed using a polyether (Impregum Soft Heavy and Light body) and a vinyl...

  4. Numerical Analysis of an H1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

    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.

  5. Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

    Science.gov (United States)

    Dabiri, Arman; Butcher, Eric A.; Nazari, Morad

    2017-02-01

    Compliant impacts can be modeled using linear viscoelastic constitutive models. While such impact models for realistic viscoelastic materials using integer order derivatives of force and displacement usually require a large number of parameters, compliant impact models obtained using fractional calculus, however, can be advantageous since such models use fewer parameters and successfully capture the hereditary property. In this paper, we introduce the fractional Chebyshev collocation (FCC) method as an approximation tool for numerical simulation of several linear fractional viscoelastic compliant impact models in which the overall coefficient of restitution for the impact is studied as a function of the fractional model parameters for the first time. Other relevant impact characteristics such as hysteresis curves, impact force gradient, penetration and separation depths are also studied.

  6. A novel two-step optimization method for tandem and ovoid high-dose-rate brachytherapy treatment for locally advanced cervical cancer.

    Science.gov (United States)

    Sharma, Manju; Fields, Emma C; Todor, Dorin A

    2015-01-01

    To present a novel method allowing fast volumetric optimization of tandem and ovoid high-dose-rate treatments and to quantify its benefits. Twenty-seven CT-based treatment plans from 6 consecutive cervical cancer patients treated with four to five intracavitary tandem and ovoid insertions were used. Initial single-step optimized plans were manually optimized, approved, and delivered plans created with a goal to cover high-risk clinical target volume (HR-CTV) with D90 >90% and minimize rectum, bladder, and sigmoid D2cc. For the two-step optimized (TSO) plan, each single-step optimized plan was replanned adding a structure created from prescription isodose line to the existent physician delineated HR-CTV, rectum, bladder, and sigmoid. New, more rigorous dose-volume histogram constraints for the critical organs at risks (OARs) were used for the optimization. HR-CTV D90 and OAR D2ccs were evaluated in both plans. TSO plans had consistently smaller D2ccs for all three OARs while preserving HR-CTV D90. On plans with "excellent" CTV coverage, average D90 of 96% (91-102%), sigmoid, bladder, and rectum D2cc, respectively, reduced on average by 37% (16-73%), 28% (20-47%), and 27% (15-45%). Similar reductions were obtained on plans with "good" coverage, average D90 of 93% (90-99%). For plans with "inferior" coverage, average D90 of 81%, the coverage increased to 87% with concurrent D2cc reductions of 31%, 18%, and 11% for sigmoid, bladder, and rectum, respectively. The TSO can be added with minimal planning time increase but with the potential of dramatic and systematic reductions in OAR D2ccs and in some cases with concurrent increase in target dose coverage. These single-fraction modifications would be magnified over the course of four to five intracavitary insertions and may have real clinical implications in terms of decreasing both acute and late toxicities. Copyright © 2015 American Brachytherapy Society. Published by Elsevier Inc. All rights reserved.

  7. Advanced Semi-Implicit Method (ASIM) for hyperbolic two-fluid model

    International Nuclear Information System (INIS)

    Lee, Sung Jae; Chung, Moon Sun

    2003-01-01

    Introducing the interfacial pressure jump terms based on the surface tension into the momentum equations of two-phase two-fluid model, the system of governing equations is turned mathematically into the hyperbolic system. The eigenvalues of the equation system become always real representing the void wave and the pressure wave propagation speeds as shown in the previous manuscript. To solve the interfacial pressure jump terms with void fraction gradients implicitly, the conventional semi-implicit method should be modified as an intermediate iteration method for void fraction at fractional time step. This Advanced Semi-Implicit Method (ASIM) then becomes stable without conventional additive terms. As a consequence, including the interfacial pressure jump terms with the advanced semi-implicit method, the numerical solutions of typical two-phase problems can be more stable and sound than those calculated exclusively by using any other terms like virtual mass, or artificial viscosity

  8. A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

    Science.gov (United States)

    Macías-Díaz, J. E.

    2017-12-01

    In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

  9. Rapid one-step selection method for generating nucleic acid aptamers: development of a DNA aptamer against α-bungarotoxin.

    Directory of Open Access Journals (Sweden)

    Lasse H Lauridsen

    Full Text Available BACKGROUND: Nucleic acids based therapeutic approaches have gained significant interest in recent years towards the development of therapeutics against many diseases. Recently, research on aptamers led to the marketing of Macugen®, an inhibitor of vascular endothelial growth factor (VEGF for the treatment of age related macular degeneration (AMD. Aptamer technology may prove useful as a therapeutic alternative against an array of human maladies. Considering the increased interest in aptamer technology globally that rival antibody mediated therapeutic approaches, a simplified selection, possibly in one-step, technique is required for developing aptamers in limited time period. PRINCIPAL FINDINGS: Herein, we present a simple one-step selection of DNA aptamers against α-bungarotoxin. A toxin immobilized glass coverslip was subjected to nucleic acid pool binding and extensive washing followed by PCR enrichment of the selected aptamers. One round of selection successfully identified a DNA aptamer sequence with a binding affinity of 7.58 µM. CONCLUSION: We have demonstrated a one-step method for rapid production of nucleic acid aptamers. Although the reported binding affinity is in the low micromolar range, we believe that this could be further improved by using larger targets, increasing the stringency of selection and also by combining a capillary electrophoresis separation prior to the one-step selection. Furthermore, the method presented here is a user-friendly, cheap and an easy way of deriving an aptamer unlike the time consuming conventional SELEX-based approach. The most important application of this method is that chemically-modified nucleic acid libraries can also be used for aptamer selection as it requires only one enzymatic step. This method could equally be suitable for developing RNA aptamers.

  10. Validation of a computational method for assessing the impact of intra-fraction motion on helical tomotherapy plans

    Energy Technology Data Exchange (ETDEWEB)

    Ngwa, Wilfred; Meeks, Sanford L; Kupelian, Patrick A; Langen, Katja M [Department of Radiation Oncology, M D Anderson Cancer Center Orlando, 1400 South Orange Avenue, Orlando, FL 32806 (United States); Schnarr, Eric [TomoTherapy, Inc., 1240 Deming Way, Madison, WI 53717 (United States)], E-mail: wilfred.ngwa@orlandohealth.com

    2009-11-07

    In this work, a method for direct incorporation of patient motion into tomotherapy dose calculations is developed and validated. This computational method accounts for all treatment dynamics and can incorporate random as well as cyclical motion data. Hence, interplay effects between treatment dynamics and patient motion are taken into account during dose calculation. This allows for a realistic assessment of intra-fraction motion on the dose distribution. The specific approach entails modifying the position and velocity events in the tomotherapy delivery plan to accommodate any known motion. The computational method is verified through phantom and film measurements. Here, measured prostate motion and simulated respiratory motion tracks were incorporated in the dose calculation. The calculated motion-encoded dose profiles showed excellent agreement with the measurements. Gamma analysis using 3 mm and 3% tolerance criteria showed over 97% and 96% average of points passing for the prostate and breathing motion tracks, respectively. The profile and gamma analysis results validate the accuracy of this method for incorporating intra-fraction motion into the dose calculation engine for assessment of dosimetric effects on helical tomotherapy dose deliveries.

  11. Comparison of some peptidic and proteic ovine pineal fractions with a bovine pineal E5 fraction

    Energy Technology Data Exchange (ETDEWEB)

    Noteborn, H P; Ebels, I; Salemink, C A [State Univ. of Utrecht, Utrecht (Netherlands). Department of Organic Chemistry; Pevet, P [The Netherlands Institute for Brain Research, Amsterdam (Netherlands).; Reinharz, A C [Hopital Cantonal, Geneva (Switzerland). Department of Medicine, Division of Endocrinology; Neacsu, C [Institute of Cellular Biology and Pathology, Bucharest (Romania).

    1982-01-01

    Using rather simple and mild extraction and separation methods, three ovine pineal fractions (XM 300R - PP 7.2, PP 7.2' and PP 7.2S) were obtained, which contain peptidic/proteic substances and which show fluorescence characteristics of indoles. The ovine fractions were compared with the bovine pineal E5-fraction. The ovine fractions are chemically sensitive to normal laboratory light and stable in red light (..lambda.. > 600 nm). Immunologically, these fractions and the bovine E5 fraction are stable. From the results of radioimmunological experiments it was concluded that the bovine pineal E5 fraction as well as the ovine pineal fraction XM 300R - PP 7.2 and PP 7.2S may contain (a) peptide(s) ending by the same carboxy terminal tripeptide Pro-Arg-Gly(NH/sub 2/).

  12. Two-step reconstruction method using global optimization and conjugate gradient for ultrasound-guided diffuse optical tomography.

    Science.gov (United States)

    Tavakoli, Behnoosh; Zhu, Quing

    2013-01-01

    Ultrasound-guided diffuse optical tomography (DOT) is a promising method for characterizing malignant and benign lesions in the female breast. We introduce a new two-step algorithm for DOT inversion in which the optical parameters are estimated with the global optimization method, genetic algorithm. The estimation result is applied as an initial guess to the conjugate gradient (CG) optimization method to obtain the absorption and scattering distributions simultaneously. Simulations and phantom experiments have shown that the maximum absorption and reduced scattering coefficients are reconstructed with less than 10% and 25% errors, respectively. This is in contrast with the CG method alone, which generates about 20% error for the absorption coefficient and does not accurately recover the scattering distribution. A new measure of scattering contrast has been introduced to characterize benign and malignant breast lesions. The results of 16 clinical cases reconstructed with the two-step method demonstrates that, on average, the absorption coefficient and scattering contrast of malignant lesions are about 1.8 and 3.32 times higher than the benign cases, respectively.

  13. Method and apparatus for probing relative volume fractions

    Science.gov (United States)

    Jandrasits, Walter G.; Kikta, Thomas J.

    1998-01-01

    A relative volume fraction probe particularly for use in a multiphase fluid system includes two parallel conductive paths defining therebetween a sample zone within the system. A generating unit generates time varying electrical signals which are inserted into one of the two parallel conductive paths. A time domain reflectometer receives the time varying electrical signals returned by the second of the two parallel conductive paths and, responsive thereto, outputs a curve of impedance versus distance. An analysis unit then calculates the area under the curve, subtracts the calculated area from an area produced when the sample zone consists entirely of material of a first fluid phase, and divides this calculated difference by the difference between an area produced when the sample zone consists entirely of material of the first fluid phase and an area produced when the sample zone consists entirely of material of a second fluid phase. The result is the volume fraction.

  14. Ferroelectric Fractional-Order Capacitors

    KAUST Repository

    Agambayev, Agamyrat; Patole, Shashikant P.; Farhat, Mohamed; Elwakil, Ahmed; Bagci, Hakan; Salama, Khaled N.

    2017-01-01

    Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.

  15. Ferroelectric Fractional-Order Capacitors

    KAUST Repository

    Agambayev, Agamyrat

    2017-07-25

    Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.

  16. Element fractionation by sequential extraction in a soil with high carbonate content

    International Nuclear Information System (INIS)

    Sulkowski, Margareta; Hirner, Alfred V.

    2006-01-01

    The influence of carbonate and other buffering substances in soils on the results of a 3-step sequential extraction procedure (BCR) used for metal fractionation was investigated. Deviating from the original extraction scheme, where the extracts are analysed only for a limited number of metals, almost all elements in the soils were quantified by X-ray fluorescence spectroscopy, in the initial samples as well as in the residues of all extraction steps. Additionally, the mineral contents were determined by X-ray diffractometry. Using this methodology, it was possible to correlate changes in soil composition caused by the extraction procedure with the release of elements. Furthermore, the pH values of all extracts were monitored, and certain extraction steps were repeated until no significant pH-rise occurred. A soil with high dolomite content (27%) and a carbonate free soil were extracted. Applying the original BCR-sequence to the calcareous soil, carbonate was found in the residues of the first two steps and extract pH-values rose by around two units in the first and second step, caused mainly by carbonate dissolution. This led to wrong assignment of the carbonate elements Ca, Mg, Sr, Ba, and also to decreased desorption and increased re-adsorption of ions in those steps. After repetition of the acetic acid step until extract pH remained low, the carbonate was completely destroyed and the distributions of the elements Ca, Mg, Sr, Ba as well as those of Co, Ni, Cu, Zn and Pb were found to be quite different to those determined in the original extraction. Furthermore, it could be shown that the effectiveness of the reduction process in step two was reduced by increasing pH: Fe oxides were not significantly attacked by the repeated acetic acid treatments, but a 10-fold amount of Fe was mobilized by hydroxylamine hydrochloride after complete carbonate destruction. On the other hand, only small amounts of Fe were released anyway. Even repeated reduction steps did not

  17. Comparison between stochastic and machine learning methods for hydrological multi-step ahead forecasting: All forecasts are wrong!

    Science.gov (United States)

    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

  18. Test of equal effect per fraction and estimation of initial clonogen number in microcolony assays of survival after fractionated irradiation

    International Nuclear Information System (INIS)

    Thames, H.D.; Withers, H.R.

    1980-01-01

    In the use of multifraction microcolony assays to infer the low-dose response of in situ renewal systems such as intestinal crypts, the assumption of equal effect per dose fraction is required. Moreover, the construction of a cell-survival curve requires knowledge of the initial count of cells capable of repopulating each renewal structure. We describe a method of designing fractionation protocols which provides a regression estimate of the initial number of clonogens per renewal structure and a test of the hypothesis of equal effect per fraction. The essential factor in the experimental design is the use of common dose fractions (use of the same dose per fraction in series with different numbers of fractions). Applications of the method to data for which the assumption of equal effect per fraction holds (four-hour fractionation interval murine testis study) and does not hold (one-hour fractionation interval murine jejunal crypt study) are presented. (author)

  19. A method for removing sulfur bearing compounds from paraffinous hydrocarbons or a directly distilled benzine fraction

    Energy Technology Data Exchange (ETDEWEB)

    Konyukhova, T.P.; Bolotskaya, I.A.; Mikhaylova, L.A.; Sadykov, A.N.; Shitovkin, N.T.; Vlasov, V.V.

    1983-01-01

    In the known method for removing sulfurorganic compounds from paraffinous hydrocarbons or a directly distilled gasoline fraction through their adsorption using natural zeolite, in order to increase the degree of purification, clinoptilolite (Kp), which contains SiO2 and A12O3 in a molar ratio of 10.6 to 16.7 is used as the natural zeolite. The purification of the paraffinous hydrocarbons through clinoptilolite adsorption as compared with mordenite adsorption makes it possible to increase the degree of their purification of ethylmercaptane and dimethylsulfide. The effectiveness of clinoptilolite is also confirmed in removing mercaptanes and sulfides from directly distilled gasoline fractions.

  20. Mercury and trace element fractionation in Almaden soils by application of different sequential extraction procedures

    Energy Technology Data Exchange (ETDEWEB)

    Sanchez, D.M.; Quejido, A.J.; Fernandez, M.; Hernandez, C.; Schmid, T.; Millan, R.; Gonzalez, M.; Aldea, M.; Martin, R.; Morante, R. [CIEMAT, Madrid (Spain)

    2005-04-01

    A comparative evaluation of the mercury distribution in a soil sample from Almaden (Spain) has been performed by applying three different sequential extraction procedures, namely, modified BCR (three steps in sequence), Di Giulio-Ryan (four steps in sequence), and a specific SEP developed at CIEMAT (six steps in sequence). There were important differences in the mercury extraction results obtained by the three procedures according to the reagents applied and the sequence of their application. These findings highlight the difficulty of setting a universal SEP to obtain information on metal fractions of different mobility for any soil sample, as well as the requirement for knowledge about the mineralogical and chemical characteristics of the samples. The specific six-step CIEMAT sequential extraction procedure was applied to a soil profile (Ap, Ah, Bt1, and Bt2 horizons). The distribution of mercury and major, minor, and trace elements in the different fractions were determined. The results indicate that mercury is mainly released with 6 M HCl. The strong association of mercury with crystalline iron oxyhydroxides, present in all the horizons of the profile, and/or the solubility of some mercury compounds in such acid can explain this fact. Minor mercury is found in the fraction assigned to oxidizable matter and in the final insoluble residue (cinnabar). (orig.)

  1. Particle Simulation of Fractional Diffusion Equations

    KAUST Repository

    Allouch, Samer

    2017-07-12

    This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on direct differentiation of the particle representation, it follows the Riesz definition of the fractional derivative and results in a non-conservative scheme. The other three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, in the sense that the total particle strength is time invariant. The first PSE algorithm is based on using direct differentiation to estimate the fractional diffusion flux, and exploiting the resulting estimates in an integral representation of the divergence operator. Meanwhile, the second one relies on the regularized Riesz representation of the fractional diffusion term to derive a suitable interaction formula acting directly on the particle representation of the diffusing field. A third PSE construction is considered that exploits the Green\\'s function of the fractional diffusion equation. The performance of all four approaches is assessed for the case of a one-dimensional diffusion equation with constant diffusivity. This enables us to take advantage of known analytical solutions, and consequently conduct a detailed analysis of the performance of the methods. This includes a quantitative study of the various sources of error, namely filtering, quadrature, domain truncation, and time integration, as well as a space and time self-convergence analysis. These analyses are conducted for different values of the order of the fractional derivatives, and computational experiences are used to gain insight that can be used for generalization of the present constructions.

  2. Particle Simulation of Fractional Diffusion Equations

    KAUST Repository

    Allouch, Samer; Lucchesi, Marco; Maî tre, O. P. Le; Mustapha, K. A.; Knio, Omar

    2017-01-01

    This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on direct differentiation of the particle representation, it follows the Riesz definition of the fractional derivative and results in a non-conservative scheme. The other three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, in the sense that the total particle strength is time invariant. The first PSE algorithm is based on using direct differentiation to estimate the fractional diffusion flux, and exploiting the resulting estimates in an integral representation of the divergence operator. Meanwhile, the second one relies on the regularized Riesz representation of the fractional diffusion term to derive a suitable interaction formula acting directly on the particle representation of the diffusing field. A third PSE construction is considered that exploits the Green's function of the fractional diffusion equation. The performance of all four approaches is assessed for the case of a one-dimensional diffusion equation with constant diffusivity. This enables us to take advantage of known analytical solutions, and consequently conduct a detailed analysis of the performance of the methods. This includes a quantitative study of the various sources of error, namely filtering, quadrature, domain truncation, and time integration, as well as a space and time self-convergence analysis. These analyses are conducted for different values of the order of the fractional derivatives, and computational experiences are used to gain insight that can be used for generalization of the present constructions.

  3. Single-fraction vs. fractionated linac-based stereotactic radiosurgery for vestibular schwannoma: a single-institution study

    NARCIS (Netherlands)

    Meijer, O. W. M.; Vandertop, W. P.; Baayen, J. C.; Slotman, B. J.

    2003-01-01

    PURPOSE: In this single-institution trial, we investigated whether fractionated stereotactic radiation therapy is superior to single-fraction linac-based radiosurgery with respect to treatment-related toxicity and local control in patients with vestibular schwannoma. METHODS AND MATERIALS: All 129

  4. A fractional-N frequency synthesizer for wireless sensor network nodes

    International Nuclear Information System (INIS)

    Ma Xiao; Du Zhankun; Liu Chang; Liu Ke; Yan Yuepeng; Ye Tianchun

    2014-01-01

    This paper presents a fractional-N frequency synthesizer for wireless sensor network (WSN) nodes. The proposed frequency synthesizer adopts a phase locked loop (PLL) based structure, which employs an LC voltage-controlled oscillator (VCO) with small VCO gain (K VCO ) and frequency step (f step ) variations, a charge pump (CP) with current changing in proportion with the division ratio and a 20-bit ΔΣ modulator, etc. To realize constant K VCO and f step , a novel capacitor sub-bands grouping method is proposed. The VCO sub-groups' sizes are arranged according to the maximal allowed K VCO variation of the system. Besides, a current mode logic divide-by-2 circuit with inside-loop buffers ensures the synthesizer generates I/Q quadrature signals robustly. This synthesizer is implemented in a 0.13 μm CMOS process. Measurement results show that the frequency synthesizer has a frequency span from 2.07 to 3.11 GHz and the typical phase noise is −86.34 dBc/Hz at 100 kHz offset and −114.17 dBc/Hz at 1 MHz offset with a loop bandwidth of about 200 kHz, which meet the WSN nodes' requirements. (semiconductor integrated circuits)

  5. Bioavailability and mobility of organic contaminants in soil: new three-step ecotoxicological evaluation.

    Science.gov (United States)

    Prokop, Zbyněk; Nečasová, Anežka; Klánová, Jana; Čupr, Pavel

    2016-03-01

    A novel approach was developed for rapid assessment of bioavailability and potential mobility of contaminants in soil. The response of the same test organism to the organic extract, water extract and solid phase of soil was recorded and compared. This approach was designed to give an initial estimate of the total organic toxicity (response to organic extractable fraction), as well as the mobile (response to water extract) and bioavailable fraction (response to solid phase) of soil samples. Eighteen soil samples with different levels of pollution and content of organic carbon were selected to validate the novel three-step ecotoxicological evaluation approach. All samples were chemically analysed for priority contaminants, including aromatic hydrocarbons (PAHs), polychlorinated biphenyls (PCBs), hexachlorocyclohexane (HCH) and dichlordiphenyltrichloroethane (DDT). The ecotoxicological evaluation involved determination of toxicity of the organic, mobile and bioavailable fractions of soil to the test organism, bacterium Bacillus cereus. We found a good correlation between the chemical analysis and the toxicity of organic extract. The low toxicity of water extracts indicated low water solubility, and thus, low potential mobility of toxic contaminants present in the soil samples. The toxicity of the bioavailable fraction was significantly greater than the toxicity of water-soluble (mobile) fraction of the contaminants as deduced from comparing untreated samples and water extracts. The bioavailability of the contaminants decreased with increasing concentrations of organic carbon in evaluated soil samples. In conclusion, the three-step ecotoxicological evaluation utilised in this study can give a quick insight into soil contamination in context with bioavailability and mobility of the contaminants present. This information can be useful for hazard identification and risk assessment of soil-associated contaminants. Graphical Abstract New three-step ecotoxicological

  6. Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

    Science.gov (United States)

    Lorenzo, C F; Hartley, T T; Malti, R

    2013-05-13

    A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

  7. High-resolution wave-theory-based ultrasound reflection imaging using the split-step fourier and globally optimized fourier finite-difference methods

    Science.gov (United States)

    Huang, Lianjie

    2013-10-29

    Methods for enhancing ultrasonic reflection imaging are taught utilizing a split-step Fourier propagator in which the reconstruction is based on recursive inward continuation of ultrasonic wavefields in the frequency-space and frequency-wave number domains. The inward continuation within each extrapolation interval consists of two steps. In the first step, a phase-shift term is applied to the data in the frequency-wave number domain for propagation in a reference medium. The second step consists of applying another phase-shift term to data in the frequency-space domain to approximately compensate for ultrasonic scattering effects of heterogeneities within the tissue being imaged (e.g., breast tissue). Results from various data input to the method indicate significant improvements are provided in both image quality and resolution.

  8. Application of the method of continued fractions for electron scattering by linear molecules

    International Nuclear Information System (INIS)

    Lee, M.-T.; Iga, I.; Fujimoto, M.M.; Lara, O.; Brasilia Univ., DF

    1995-01-01

    The method of continued fractions (MCF) of Horacek and Sasakawa is adapted for the first time to study low-energy electron scattering by linear molecules. Particularly, we have calculated the reactance K-matrices for an electron scattered by hydrogen molecule and hydrogen molecular ion as well as by a polar LiH molecule in the static-exchange level. For all the applications studied herein. the calculated physical quantities converge rapidly, even for a strongly polar molecule such as LiH, to the correct values and in most cases the convergence is monotonic. Our study suggests that the MCF could be an efficient method for studying electron-molecule scattering and also photoionization of molecules. (Author)

  9. Temperature dependence of carbon isotope fractionation in CAM plants

    International Nuclear Information System (INIS)

    Deleens, E.; Treichel, I.; O'Leary, M.H.

    1985-01-01

    The carbon isotope fractionation associated with nocturnal malic acid synthesis in Kalanchoë daigremontiana and Bryophyllum tubiflorum was calculated from the isotopic composition of carbon-4 of malic acid, after appropriate corrections. In the lowest temperature treatment (17 degrees C nights, 23 degrees C days), the isotope fractionation for both plants is -4 per thousand (that is, malate is enriched in (13)C relative to the atmosphere). For K. daigremontiana, the isotope fractionation decreases with increasing temperature, becoming approximately 0 per thousand at 27 degrees C/33 degrees C. Detailed analysis of temperature effects on the isotope fractionation indicates that stomatal aperture decreases with increasing temperature and carboxylation capacity increases. For B. tubiflorum, the temperature dependence of the isotope fractionation is smaller and is principally attributed to the normal temperature dependences of the rates of diffusion and carboxylation steps. The small change in the isotopic composition of remaining malic acid in both species which is observed during deacidification indicates that malate release, rather than decarboxylation, is rate limiting in the deacidification process

  10. Temperature dependence of carbon isotope fractionation in CAM plants

    Energy Technology Data Exchange (ETDEWEB)

    Deleens, E.; Treichel, I.; O' Leary, M.H.

    1985-09-01

    The carbon isotope fractionation associated with nocturnal malic acid synthesis in Kalanchoe daigremontiana and Bryophyllum tubiflorum was calculated from the isotopic composition of carbon-4 of malic acid, after appropriate corrections. In the lowest temperature treatment (17/sup 0/C nights, 23/sup 0/C days), the isotope fractionation for both plants is -4% per thousand (that is, malate is enriched in /sup 13/C relative to the atmosphere). For K. daigremontiana, the isotope fractionation decreases with increasing temperature, becoming approximately 0% per thousand at 27/sup 0/C/33/sup 0/C. Detailed analysis of temperature effects on the isotope fractionation indicates that stomatal aperture decreases with increasing temperature and carboxylation capacity increases. For B. tubiflorum, the temperature dependence of the isotope fractionation is smaller and is principally attributed to the normal temperature dependences of the rates of diffusion and carboxylation steps. The small change in the isotopic composition of remaining malic acid in both species which is observed during deacidification indicates that malate release, rather than decarboxylation, is rate limiting in the deacidification process. 28 references, 1 figure, 4 tables.

  11. The modified simple equation method for solving some fractional ...

    Indian Academy of Sciences (India)

    2016-06-21

    Jun 21, 2016 ... and AHMET BEKIR. Art-Science Faculty, Department of Mathematics-Computer, Eskisehir Osmangazi University, Eskisehir, Turkey ... chemistry, biology, engineering and in numerous other applications. ... fractional calculus.

  12. Single-step electrochemical method for producing very sharp Au scanning tunneling microscopy tips

    International Nuclear Information System (INIS)

    Gingery, David; Buehlmann, Philippe

    2007-01-01

    A single-step electrochemical method for making sharp gold scanning tunneling microscopy tips is described. 3.0M NaCl in 1% perchloric acid is compared to several previously reported etchants. The addition of perchloric acid to sodium chloride solutions drastically shortens etching times and is shown by transmission electron microscopy to produce very sharp tips with a mean radius of curvature of 15 nm

  13. In situ synthesis carbonated hydroxyapatite layers on enamel slices with acidic amino acids by a novel two-step method

    International Nuclear Information System (INIS)

    Wu, Xiaoguang; Zhao, Xu; Li, Yi; Yang, Tao; Yan, Xiujuan; Wang, Ke

    2015-01-01

    In situ fabrication of carbonated hydroxyapatite (CHA) remineralization layer on an enamel slice was completed in a novel, biomimetic two-step method. First, a CaCO 3 layer was synthesized on the surface of demineralized enamel using an acidic amino acid (aspartic acid or glutamate acid) as a soft template. Second, at the same concentration of the acidic amino acid, rod-like carbonated hydroxyapatite was produced with the CaCO 3 layer as a sacrificial template and a reactant. The morphology, crystallinity and other physicochemical properties of the crystals were characterized using field emission scanning electron microscopy (FESEM), Fourier transform infrared spectrometry (FTIR), X-ray diffraction (XRD) and energy-dispersive X-ray analysis (EDAX), respectively. Acidic amino acid could promote the uniform deposition of hydroxyapatite with rod-like crystals via absorption of phosphate and carbonate ions from the reaction solution. Moreover, compared with hydroxyapatite crystals coated on the enamel when synthesized by a one-step method, the CaCO 3 coating that was synthesized in the first step acted as an active bridge layer and sacrificial template. It played a vital role in orienting the artificial coating layer through the template effect. The results show that the rod-like carbonated hydroxyapatite crystals grow into bundles, which are similar in size and appearance to prisms in human enamel, when using the two-step method with either aspartic acid or acidic glutamate (20.00 mmol/L). - Graphical abstract: FESEM images of enamel slices etched for 60 s and repaired by the two-step method with Glu concentration of 20.00 mmol/L. (A) The boundary (dotted line) of the repaired areas (b) and unrepaired areas (a). (Some selected areas of etched enamel slices were coated with a nail polish before the reaction, which was removed by acetone after the reaction); (B) high magnification image of Ga, (C) high magnification image of Gb. In situ fabrication of carbonated

  14. In situ synthesis carbonated hydroxyapatite layers on enamel slices with acidic amino acids by a novel two-step method

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Xiaoguang [Department of Pediatric Dentistry, The Hospital of Stomatology, Jilin University, Changchun 130021 (China); Zhao, Xu [College of Chemistry, Jilin University, Changchun 130021 (China); Li, Yi, E-mail: lyi99@jlu.edu.cn [Department of Pediatric Dentistry, The Hospital of Stomatology, Jilin University, Changchun 130021 (China); Yang, Tao [Department of Stomatology, Children' s Hospital of Changchun, 130051 (China); Yan, Xiujuan; Wang, Ke [Department of Pediatric Dentistry, The Hospital of Stomatology, Jilin University, Changchun 130021 (China)

    2015-09-01

    In situ fabrication of carbonated hydroxyapatite (CHA) remineralization layer on an enamel slice was completed in a novel, biomimetic two-step method. First, a CaCO{sub 3} layer was synthesized on the surface of demineralized enamel using an acidic amino acid (aspartic acid or glutamate acid) as a soft template. Second, at the same concentration of the acidic amino acid, rod-like carbonated hydroxyapatite was produced with the CaCO{sub 3} layer as a sacrificial template and a reactant. The morphology, crystallinity and other physicochemical properties of the crystals were characterized using field emission scanning electron microscopy (FESEM), Fourier transform infrared spectrometry (FTIR), X-ray diffraction (XRD) and energy-dispersive X-ray analysis (EDAX), respectively. Acidic amino acid could promote the uniform deposition of hydroxyapatite with rod-like crystals via absorption of phosphate and carbonate ions from the reaction solution. Moreover, compared with hydroxyapatite crystals coated on the enamel when synthesized by a one-step method, the CaCO{sub 3} coating that was synthesized in the first step acted as an active bridge layer and sacrificial template. It played a vital role in orienting the artificial coating layer through the template effect. The results show that the rod-like carbonated hydroxyapatite crystals grow into bundles, which are similar in size and appearance to prisms in human enamel, when using the two-step method with either aspartic acid or acidic glutamate (20.00 mmol/L). - Graphical abstract: FESEM images of enamel slices etched for 60 s and repaired by the two-step method with Glu concentration of 20.00 mmol/L. (A) The boundary (dotted line) of the repaired areas (b) and unrepaired areas (a). (Some selected areas of etched enamel slices were coated with a nail polish before the reaction, which was removed by acetone after the reaction); (B) high magnification image of Ga, (C) high magnification image of Gb. In situ fabrication of

  15. Estimating population cause-specific mortality fractions from in-hospital mortality: validation of a new method.

    Directory of Open Access Journals (Sweden)

    Christopher J L Murray

    2007-11-01

    Full Text Available Cause-of-death data for many developing countries are not available. Information on deaths in hospital by cause is available in many low- and middle-income countries but is not a representative sample of deaths in the population. We propose a method to estimate population cause-specific mortality fractions (CSMFs using data already collected in many middle-income and some low-income developing nations, yet rarely used: in-hospital death records.For a given cause of death, a community's hospital deaths are equal to total community deaths multiplied by the proportion of deaths occurring in hospital. If we can estimate the proportion dying in hospital, we can estimate the proportion dying in the population using deaths in hospital. We propose to estimate the proportion of deaths for an age, sex, and cause group that die in hospital from the subset of the population where vital registration systems function or from another population. We evaluated our method using nearly complete vital registration (VR data from Mexico 1998-2005, which records whether a death occurred in a hospital. In this validation test, we used 45 disease categories. We validated our method in two ways: nationally and between communities. First, we investigated how the method's accuracy changes as we decrease the amount of Mexican VR used to estimate the proportion of each age, sex, and cause group dying in hospital. Decreasing VR data used for this first step from 100% to 9% produces only a 12% maximum relative error between estimated and true CSMFs. Even if Mexico collected full VR information only in its capital city with 9% of its population, our estimation method would produce an average relative error in CSMFs across the 45 causes of just over 10%. Second, we used VR data for the capital zone (Distrito Federal and Estado de Mexico and estimated CSMFs for the three lowest-development states. Our estimation method gave an average relative error of 20%, 23%, and 31% for

  16. Method and apparatus for processing oily wastewater

    International Nuclear Information System (INIS)

    Torline, W.N.; Williams, R.K.

    1993-01-01

    A method of treating oily wastewater is described comprising the steps of passing oily wastewater through a coalescer to coalesce dispersed oil droplets; separating a free oil fraction as a liquid stream having a lower specific gravity from a contaminated water stream having a higher specific gravity; filtering particulate material from said contaminated water stream; passing the filtered water stream under pressure across an ultrafiltration membrane to separate a retentate fraction enriched in residual emulsified oil from an aqueous permeate fraction; recycling said substantially only retentate fraction to said coalescer; filtering said aqueous permeate through an activated carbon filter to remove low molecular weight organic materials; subjecting the filtrate from said activated carbon filter to cation exchange to remove heavy metal ions; and periodically flushing said ultra filter with filtrate from said particulate filter to maintain the permeability of said ultrafiltration membrane

  17. Fractional Bateman—Feshbach Tikochinsky Oscillator

    Science.gov (United States)

    Dumitru, Baleanu; Jihad, H. Asad; Ivo, Petras

    2014-02-01

    In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function.

  18. Modified Legendre Wavelets Technique for Fractional Oscillation Equations

    Directory of Open Access Journals (Sweden)

    Syed Tauseef Mohyud-Din

    2015-10-01

    Full Text Available Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinear fractional order oscillation equation into a fractional order recurrence relation and then Legendre wavelets method is applied on the converted problem. In order to check the efficiency and accuracy of the suggested modification, we have considered three problems namely: fractional order force-free Duffing–van der Pol oscillator, forced Duffing–van der Pol oscillator and higher order fractional Duffing equations. The obtained results are compared with the results obtained via other techniques.

  19. Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

    Science.gov (United States)

    Priya, B. Ganesh; Muthukumar, P.

    2018-02-01

    This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

  20. Coronary plaque quantification and fractional flow reserve by coronary computed tomography angiography identify ischaemia-causing lesions

    DEFF Research Database (Denmark)

    Gaur, Sara; Øvrehus, Kristian Altern; Dey, Damini

    2016-01-01

    AIMS: Coronary plaque characteristics are associated with ischaemia. Differences in plaque volumes and composition may explain the discordance between coronary stenosis severity and ischaemia. We evaluated the association between coronary stenosis severity, plaque characteristics, coronary computed...... tomography angiography (CTA)-derived fractional flow reserve (FFRCT), and lesion-specific ischaemia identified by FFR in a substudy of the NXT trial (Analysis of Coronary Blood Flow Using CT Angiography: Next Steps). METHODS AND RESULTS: Coronary CTA stenosis, plaque volumes, FFRCT, and FFR were assessed...

  1. A vector/parallel method for a three-dimensional transport model coupled with bio-chemical terms

    NARCIS (Netherlands)

    B.P. Sommeijer (Ben); J. Kok (Jan)

    1995-01-01

    textabstractA so-called fractional step method is considered for the time integration of a three-dimensional transport-chemical model in shallow seas. In this method, the transport part and the chemical part are treated separately by appropriate integration techniques. This separation is motivated

  2. Influence of the void fraction in the linear reactivity model

    International Nuclear Information System (INIS)

    Castillo, J.A.; Ramirez, J.R.; Alonso, G.

    2003-01-01

    The linear reactivity model allows the multicycle analysis in pressurized water reactors in a simple and quick way. In the case of the Boiling water reactors the void fraction it varies axially from 0% of voids in the inferior part of the fuel assemblies until approximately 70% of voids to the exit of the same ones. Due to this it is very important the determination of the average void fraction during different stages of the reactor operation to predict the burnt one appropriately of the same ones to inclination of the pattern of linear reactivity. In this work a pursuit is made of the profile of power for different steps of burnt of a typical operation cycle of a Boiling water reactor. Starting from these profiles it builds an algorithm that allows to determine the voids profile and this way to obtain the average value of the same one. The results are compared against those reported by the CM-PRESTO code that uses another method to carry out this calculation. Finally, the range in which is the average value of the void fraction during a typical cycle is determined and an estimate of the impact that it would have the use of this value in the prediction of the reactivity produced by the fuel assemblies is made. (Author)

  3. On solutions of variable-order fractional differential equations

    Directory of Open Access Journals (Sweden)

    Ali Akgül

    2017-01-01

    solutions to fractional differential equations are compelling to get in real applications, due to the nonlocality and complexity of the fractional differential operators, especially for variable-order fractional differential equations. Therefore, it is significant to enhanced numerical methods for fractional differential equations. In this work, we consider variable-order fractional differential equations by reproducing kernel method. There has been much attention in the use of reproducing kernels for the solutions to many problems in the recent years. We give two examples to demonstrate how efficiently our theory can be implemented in practice.

  4. Two-Step Injection Method for Collecting Digital Evidence in Digital Forensics

    Directory of Open Access Journals (Sweden)

    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.

  5. Adaptive step-size algorithm for Fourier beam-propagation method with absorbing boundary layer of auto-determined width.

    Science.gov (United States)

    Learn, R; Feigenbaum, E

    2016-06-01

    Two algorithms that enhance the utility of the absorbing boundary layer are presented, mainly in the framework of the Fourier beam-propagation method. One is an automated boundary layer width selector that chooses a near-optimal boundary size based on the initial beam shape. The second algorithm adjusts the propagation step sizes based on the beam shape at the beginning of each step in order to reduce aliasing artifacts.

  6. A Tutorial Review on Fractal Spacetime and Fractional Calculus

    Science.gov (United States)

    He, Ji-Huan

    2014-11-01

    This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

  7. The use of linear fractional analogues of rheological models in the problem of approximating the experimental data on the stretch polyvinylchloride elastron

    Directory of Open Access Journals (Sweden)

    Luiza G. Ungarova

    2016-12-01

    Full Text Available We considere and analyze the uniaxial phenomenological models of viscoelastic deformation based on fractional analogues of Scott Blair, Voigt, Maxwell, Kelvin and Zener rheological models. Analytical solutions of the corresponding differential equations are obtained with fractional Riemann–Liouville operators under constant stress with further unloading, that are written by the generalized (two-parameter fractional exponential function and contains from two to four parameters depending on the type of model. A method for identifying the model parameters based on the background information for the experimental creep curves with constant stresses was developed. Nonlinear problem of parametric identification is solved by two-step iterative method. The first stage uses the characteristic data points diagrams and features in the behavior of the models under unrestricted growth of time and the initial approximation of parameters are determined. At the second stage, the refinement of these parameters by coordinate descent (the Hooke–Jeeves's method and minimizing the functional standard deviation for calculated and experimental values is made. Method of identification is realized for all the considered models on the basis of the known experimental data uniaxial viscoelastic deformation of Polyvinylchloride Elastron at a temperature of 20∘C and five the tensile stress levels. Table-valued parameters for all models are given. The errors analysis of constructed phenomenological models is made to experimental data over the entire ensemble of curves viscoelastic deformation. It was found that the approximation errors for the Scott Blair fractional model is 14.17 %, for the Voigt fractional model is 11.13 %, for the Maxvell fractional model is 13.02 %, for the Kelvin fractional model 10.56 %, for the Zener fractional model is 11.06 %. The graphs of the calculated and experimental dependences of viscoelastic deformation of Polyvinylchloride

  8. The method of quick satellite aiming with 3-Steps on the mobile satellite station

    Directory of Open Access Journals (Sweden)

    Sheng Liang

    2017-02-01

    Full Text Available The study analyses and concludes the technology of the satellite aiming during real-time broadcast of mobile video.We conclude a method of quick satellite aiming with 3-steps according to practical exercises and users' requirement to meet situation of facts and standardized operation,which can improve efficiency and quality of service.

  9. Understanding Magnitudes to Understand Fractions

    Science.gov (United States)

    Gabriel, Florence

    2016-01-01

    Fractions are known to be difficult to learn and difficult to teach, yet they are vital for students to have access to further mathematical concepts. This article uses evidence to support teachers employing teaching methods that focus on the conceptual understanding of the magnitude of fractions.

  10. Accessible solitons of fractional dimension

    Energy Technology Data Exchange (ETDEWEB)

    Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Belić, Milivoj [Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Zhang, Yiqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

    2016-05-15

    We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.

  11. Review and comparison of effective delayed neutron fraction calculation methods with Monte Carlo codes

    International Nuclear Information System (INIS)

    Bécares, V.; Pérez-Martín, S.; Vázquez-Antolín, M.; Villamarín, D.; Martín-Fuertes, F.; González-Romero, E.M.; Merino, I.

    2014-01-01

    Highlights: • Review of several Monte Carlo effective delayed neutron fraction calculation methods. • These methods have been implemented with the Monte Carlo code MCNPX. • They have been benchmarked against against some critical and subcritical systems. • Several nuclear data libraries have been used. - Abstract: The calculation of the effective delayed neutron fraction, β eff , with Monte Carlo codes is a complex task due to the requirement of properly considering the adjoint weighting of delayed neutrons. Nevertheless, several techniques have been proposed to circumvent this difficulty and obtain accurate Monte Carlo results for β eff without the need of explicitly determining the adjoint flux. In this paper, we make a review of some of these techniques; namely we have analyzed two variants of what we call the k-eigenvalue technique and other techniques based on different interpretations of the physical meaning of the adjoint weighting. To test the validity of all these techniques we have implemented them with the MCNPX code and we have benchmarked them against a range of critical and subcritical systems for which either experimental or deterministic values of β eff are available. Furthermore, several nuclear data libraries have been used in order to assess the impact of the uncertainty in nuclear data in the calculated value of β eff

  12. Study on calculation methods for the effective delayed neutron fraction

    International Nuclear Information System (INIS)

    Irwanto, Dwi; Obara, Toru; Chiba, Go; Nagaya, Yasunobu

    2011-03-01

    The effective delayed neutron fraction β eff is one of the important neutronic parameters from a view point of a reactor kinetics. Several Monte-Carlo-based methods to estimate β eff have been proposed to date. In order to quantify the accuracy of these methods, we study calculation methods for β eff by analyzing various fast neutron systems including the bare spherical systems (Godiva, Jezebel, Skidoo, Jezebel-240), the reflective spherical systems (Popsy, Topsy, Flattop-23), MASURCA-R2 and MASURCA-ZONA2, and FCA XIX-1, XIX-2 and XIX-3. These analyses are performed by using SLAROM-UF and CBG for the deterministic method and MVP-II for the Monte Carlo method. We calculate β eff with various definitions such as the fundamental value β 0 , the standard definition, Nauchi's definition and Meulekamp's definition, and compare these results with each other. Through the present study, we find the following: The largest difference among the standard definition of β eff , Nauchi's β eff and Meulekamp's β eff is approximately 10%. The fundamental value β 0 is quite larger than the others in several cases. For all the cases, Meulekamp's β eff is always higher than Nauchi's β eff . This is because Nauchi's β eff considers the average neutron multiplicity value per fission which is large in the high energy range (1MeV-10MeV), while the definition of Meulekamp's β eff does not include this parameter. Furthermore, we evaluate the multi-generation effect on β eff values and demonstrate that this effect should be considered to obtain the standard definition values of β eff . (author)

  13. A multiresidue method by high performance liquid chromatography-based fractionation and gas chromatographic determination of trace levels of pesticides in air and water.

    Science.gov (United States)

    Seiber, J N; Glotfelty, D E; Lucas, A D; McChesney, M M; Sagebiel, J C; Wehner, T A

    1990-01-01

    A multiresidue analytical method is described for pesticides, transformation products, and related toxicants based upon high performance liquid chromatographic (HPLC) fractionation of extracted residue on a Partisil silica gel normal phase column followed by selective-detector gas chromatographic (GC) determination of components in each fraction. The HPLC mobile phase gradient (hexane to methyl t-butyl ether) gave good chromatographic efficiency, resolution, reproducibility and recovery for 61 test compounds, and allowed for collection in four fractions spanning polarities from low polarity organochlorine compounds (fraction 1) to polar N-methylcarbamates and organophosphorus oxons (fraction 4). The multiresidue method was developed for use with air samples collected on XAD-4 and related trapping agents, and water samples extracted with methylene chloride. Detection limits estimated from spiking experiments were generally 0.3-1 ng/m3 for high-volume air samples, and 0.01-0.1 microgram/L for one-liter water samples. Applications were made to determination of pesticides in fogwater and air samples.

  14. Fractional Calculus and Shannon Wavelet

    Directory of Open Access Journals (Sweden)

    Carlo Cattani

    2012-01-01

    Full Text Available An explicit analytical formula for the any order fractional derivative of Shannon wavelet is given as wavelet series based on connection coefficients. So that for any 2(ℝ function, reconstructed by Shannon wavelets, we can easily define its fractional derivative. The approximation error is explicitly computed, and the wavelet series is compared with Grünwald fractional derivative by focusing on the many advantages of the wavelet method, in terms of rate of convergence.

  15. Investigation of biological material for metallic poisoning by the fractional method. Issledovaniya biologicheskogo materiala na metallicheskiya yady drobnym metodom

    Energy Technology Data Exchange (ETDEWEB)

    Krylova, A.N.

    1975-01-01

    A fractional method is developed for analysis of biological material for the presence of toxic quantities of Pb, Hg, Ba, Mn, Cr, Ag, Cu, Sb, Tl, As, Bi, Cd and Zn. The method satisfies the requirements of medical forensic toxicology. (Ref. Zh.)

  16. Characteristic analysis of laser isotope separation process by two-step photodissociation method

    International Nuclear Information System (INIS)

    Okamoto, Tsuyoshi; Suzuki, Atsuyuki; Kiyose, Ryohei

    1981-01-01

    A large number of laser isotope separation experiments have been performed actively in many countries. In this paper, the selective two-step photodissociation method is chosen and simultaneous nonlinear differential equations that express the separation process are solved directly by using computer. Predicted separation factors are investigated in relation to the incident pulse energy and the concentration of desired molecules. Furthermore, the concept of separative work is used to evaluate the results of separation for this method. It is shown from an example of numerical calculation that a very large separation factor can be obtained if the concentration of desired molecules is lowered and two laser pulses to be closely synchronized are not always required in operation for the photodissociation of molecules. (author)

  17. Methods and Algorithms for Solving Inverse Problems for Fractional Advection-Dispersion Equations

    KAUST Repository

    Aldoghaither, Abeer

    2015-01-01

    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

  18. Protein fraction heterogeneity in donkey’s milk analysed by proteomic methods

    Directory of Open Access Journals (Sweden)

    G. D'Urso

    2010-04-01

    Full Text Available Donkey’s milk is often well tolerate by patients affected by cow’s milk protein allergy, probably thanks to its protein composition. This empiric evidence, confirmed by some clinical trials, needs to be better investigated. A preliminary survey on the protein fraction of donkey’s milk was carried out: fifty-six individual milk samples have been collected and analysed by IEF and SDS-PAGE. Five different IEF patterns have been identified, showing a marked heterogeneity both in casein and whey protein fractions. A single IEF pattern showed an apparent reduced amount of casein fraction highlighted by SDS. Three of the five IEF patterns have been further investigated by Matrix-Assisted Laser Desorption Ionization-Time of Flight Mass Spectrometry (MALDI-TOF MS.

  19. 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...

  20. Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions

    Directory of Open Access Journals (Sweden)

    M.H.T. Alshbool

    2017-01-01

    Full Text Available An algorithm for approximating solutions to fractional differential equations (FDEs in a modified new Bernstein polynomial basis is introduced. Writing x→xα(0<α<1 in the operational matrices of Bernstein polynomials, the fractional Bernstein polynomials are obtained and then transformed into matrix form. Furthermore, using Caputo fractional derivative, the matrix form of the fractional derivative is constructed for the fractional Bernstein matrices. We convert each term of the problem to the matrix form by means of fractional Bernstein matrices. A basic matrix equation which corresponds to a system of fractional equations is utilized, and a new system of nonlinear algebraic equations is obtained. The method is given with some priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.