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Sample records for nonlinear fractional differential

  1. Solutions to Class of Linear and Nonlinear Fractional Differential Equations

    NASA Astrophysics Data System (ADS)

    Abdel-Salam, Emad A.-B.; Hassan, Gamal F.

    2016-02-01

    In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional KdV equation, the space-time fractional RLW equation, the space-time fractional Boussinesq equation, and the (3+1)-space-time fractional ZK equation. The solutions are expressed in terms of fractional hyperbolic and fractional trigonometric functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The analytical solution of homogenous linear FDEs with constant coefficients are obtained by using the series and the Mittag–Leffler function methods. The obtained results recover the well-know solutions when α = 1.

  2. Solutions to Class of Linear and Nonlinear Fractional Differential Equations

    NASA Astrophysics Data System (ADS)

    Emad A-B., Abdel-Salam; Gamal, F. Hassan

    2016-02-01

    In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional KdV equation, the space-time fractional RLW equation, the space-time fractional Boussinesq equation, and the (3+1)-space-time fractional ZK equation. The solutions are expressed in terms of fractional hyperbolic and fractional trigonometric functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The analytical solution of homogenous linear FDEs with constant coefficients are obtained by using the series and the Mittag-Leffler function methods. The obtained results recover the well-know solutions when α = 1.

  3. Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations

    PubMed Central

    Baranwal, Vipul K.; Pandey, Ram K.

    2014-01-01

    We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ0, γ1, γ2,… and auxiliary functions H0(x), H1(x), H2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

  4. Approximate solutions for non-linear iterative fractional differential equations

    NASA Astrophysics Data System (ADS)

    Damag, Faten H.; Kiliçman, Adem; Ibrahim, Rabha W.

    2016-06-01

    This paper establishes approximate solution for non-linear iterative fractional differential equations: d/γv (s ) d sγ =ℵ (s ,v ,v (v )), where γ ∈ (0, 1], s ∈ I := [0, 1]. Our method is based on some convergence tools for analytic solution in a connected region. We show that the suggested solution is unique and convergent by some well known geometric functions.

  5. A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

    PubMed Central

    Güner, Özkan; Cevikel, Adem C.

    2014-01-01

    We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

  6. New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

    NASA Astrophysics Data System (ADS)

    Yao, Ruo-Xia; Wang, Wei; Chen, Ting-Hua

    2014-11-01

    Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.

  7. A class of nonlinear differential equations with fractional integrable impulses

    NASA Astrophysics Data System (ADS)

    Wang, JinRong; Zhang, Yuruo

    2014-09-01

    In this paper, we introduce a new class of impulsive differential equations, which is more suitable to characterize memory processes of the drugs in the bloodstream and the consequent absorption for the body. This fact offers many difficulties in applying the usual methods to analysis and novel techniques in Bielecki's normed Banach spaces and thus makes the study of existence and uniqueness theorems interesting. Meanwhile, new concepts of Bielecki-Ulam's type stability are introduced and generalized Ulam-Hyers-Rassias stability results on a compact interval are established. This is another novelty of this paper. Finally, an interesting example is given to illustrate our theory results.

  8. Finite difference methods with non-uniform meshes for nonlinear fractional differential equations

    NASA Astrophysics Data System (ADS)

    Li, Changpin; Yi, Qian; Chen, An

    2016-07-01

    In this article, finite difference methods with non-uniform meshes for solving nonlinear fractional differential equations are presented, where the non-equidistant stepsize is non-decreasing. The rectangle formula and trapezoid formula are proposed based on the non-uniform meshes. Combining the above two methods, we then establish the predictor-corrector scheme. The error and stability analysis are carefully investigated. At last, numerical examples are carried out to verify the theoretical analysis. Besides, the comparisons between non-uniform and uniform meshes are given, where the non-uniform meshes show the better performance when dealing with the less smooth problems.

  9. Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations

    NASA Astrophysics Data System (ADS)

    Lin, Yezhi; Liu, Yinping; Li, Zhibin

    2013-01-01

    The Adomian decomposition method (ADM) is one of the most effective methods to construct analytic approximate solutions for nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, Rach (2008) [22], the Adomian decomposition method and the Padé approximants technique, a new algorithm is proposed to construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore, a MAPLE software package is developed to implement this new algorithm, which is user-friendly and efficient. One only needs to input the system equation, initial or boundary conditions and several necessary parameters, then our package will automatically deliver the analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for non-smooth initial value problems. Our package provides a helpful and easy-to-use tool in science and engineering simulations. Program summaryProgram title: ADMP Catalogue identifier: AENE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12011 No. of bytes in distributed program, including test data, etc.: 575551 Distribution format: tar.gz Programming language: MAPLE R15. Computer: PCs. Operating system: Windows XP/7. RAM: 2 Gbytes Classification: 4.3. Nature of problem: Constructing analytic approximate solutions of nonlinear fractional differential equations with initial or boundary conditions. Non-smooth initial value problems can be solved by this program. Solution method: Based on the new definition of the Adomian polynomials [1], the Adomian decomposition method and the Pad

  10. Legendre wavelet operational matrix of fractional derivative through wavelet-polynomial transformation and its applications on non-linear system of fractional order differential equations

    NASA Astrophysics Data System (ADS)

    Isah, Abdulnasir; Chang, Phang

    2016-06-01

    In this article we propose the wavelet operational method based on shifted Legendre polynomial to obtain the numerical solutions of non-linear systems of fractional order differential equations (NSFDEs). The operational matrix of fractional derivative derived through wavelet-polynomial transformation are used together with the collocation method to turn the NSFDEs to a system of non-linear algebraic equations. Illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.

  11. Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

    NASA Astrophysics Data System (ADS)

    Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

    2015-07-01

    Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

  12. Nonlinear differential equations

    SciTech Connect

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  13. A Novel Effective Approach for Solving Fractional Nonlinear PDEs

    PubMed Central

    Aminikhah, Hossein; Malekzadeh, Nasrin; Rezazadeh, Hadi

    2014-01-01

    The present work introduces an effective modification of homotopy perturbation method for the solution of nonlinear time-fractional biological population model and a system of three nonlinear time-fractional partial differential equations. In this approach, the solution is considered a series expansion that converges to the nonlinear problem. The new approximate analytical procedure depends only on two iteratives. The analytical approximations to the solution are reliable and confirm the ability of the new homotopy perturbation method as an easy device for computing the solution of nonlinear equations.

  14. Solving Nonlinear Coupled Differential Equations

    NASA Technical Reports Server (NTRS)

    Mitchell, L.; David, J.

    1986-01-01

    Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

  15. Nonlinear Filtering with Fractional Brownian Motion

    SciTech Connect

    Amirdjanova, A.

    2002-12-19

    Our objective is to study a nonlinear filtering problem for the observation process perturbed by a Fractional Brownian Motion (FBM) with Hurst index 1/2 fractional' Zakai equation for the unnormalized optimal filter is derived.

  16. On the singular perturbations for fractional differential equation.

    PubMed

    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. PMID:24683357

  17. Analytical Solution of the Space-Time Fractional Nonlinear Schrödinger Equation

    NASA Astrophysics Data System (ADS)

    Abdel-Salam, Emad A.-B.; Yousif, Eltayeb A.; El-Aasser, Mostafa A.

    2016-02-01

    The space-time fractional nonlinear Schrödinger equation is solved by mean of on the fractional Riccati expansion method. These solutions include generalized trigonometric and hyperbolic functions which could be useful for further understanding of mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time.

  18. Lie group analysis method for two classes of fractional partial differential equations

    NASA Astrophysics Data System (ADS)

    Chen, Cheng; Jiang, Yao-Lin

    2015-09-01

    In this paper we deal with two classes of fractional partial differential equation: n order linear fractional partial differential equation and nonlinear fractional reaction diffusion convection equation, by using the Lie group analysis method. The infinitesimal generators general formula of n order linear fractional partial differential equation is obtained. For nonlinear fractional reaction diffusion convection equation, the properties of their infinitesimal generators are considered. The four special cases are exhaustively investigated respectively. At the same time some examples of the corresponding case are also given. So it is very convenient to solve the infinitesimal generator of some fractional partial differential equation.

  19. Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

    PubMed

    Deng, Mao-Lin; Zhu, Wei-Qiu

    2016-08-01

    In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems. PMID:27586630

  20. An Efficient Algorithm for Some Highly Nonlinear Fractional PDEs in Mathematical Physics

    PubMed Central

    Ahmad, Jamshad; Mohyud-Din, Syed Tauseef

    2014-01-01

    In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs and hence can be extended to other complex problems of diversified nonlinear nature. PMID:25525804

  1. Solving Space-Time Fractional Differential Equations by Using Modified Simple Equation Method

    NASA Astrophysics Data System (ADS)

    Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet

    2016-05-01

    In this article, we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method. The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.

  2. Differential operator multiplication method for fractional differential equations

    NASA Astrophysics Data System (ADS)

    Tang, Shaoqiang; Ying, Yuping; Lian, Yanping; Lin, Stephen; Yang, Yibo; Wagner, Gregory J.; Liu, Wing Kam

    2016-08-01

    Fractional derivatives play a very important role in modeling physical phenomena involving long-range correlation effects. However, they raise challenges of computational cost and memory storage requirements when solved using current well developed numerical methods. In this paper, the differential operator multiplication method is proposed to address the issues by considering a reaction-advection-diffusion equation with a fractional derivative in time. The linear fractional differential equation is transformed into an integer order differential equation by the proposed method, which can fundamentally fix the aforementioned issues for select fractional differential equations. In such a transform, special attention should be paid to the initial conditions for the resulting differential equation of higher integer order. Through numerical experiments, we verify the proposed method for both fractional ordinary differential equations and partial differential equations.

  3. A Study of Impulsive Multiterm Fractional Differential Equations with Single and Multiple Base Points and Applications

    PubMed Central

    Liu, Yuji; Ahmad, Bashir

    2014-01-01

    We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractional-order logistic models. PMID:24578623

  4. Face recognition with histograms of fractional differential gradients

    NASA Astrophysics Data System (ADS)

    Yu, Lei; Ma, Yan; Cao, Qi

    2014-05-01

    It has proved that fractional differentiation can enhance the edge information and nonlinearly preserve textural detailed information in an image. This paper investigates its ability for face recognition and presents a local descriptor called histograms of fractional differential gradients (HFDG) to extract facial visual features. HFDG encodes a face image into gradient patterns using multiorientation fractional differential masks, from which histograms of gradient directions are computed as the face representation. Experimental results on Yale, face recognition technology (FERET), Carnegie Mellon University pose, illumination, and expression (CMU PIE), and A. Martinez and R. Benavente (AR) databases validate the feasibility of the proposed method and show that HFDG outperforms local binary patterns (LBP), histograms of oriented gradients (HOG), enhanced local directional patterns (ELDP), and Gabor feature-based methods.

  5. Exact solutions for the fractional differential equations by using the first integral method

    NASA Astrophysics Data System (ADS)

    Aminikhah, Hossein; Sheikhani, A. Refahi; Rezazadeh, Hadi

    2015-03-01

    In this paper, we apply the first integral method to study the solutions of the nonlinear fractional modified Benjamin-Bona-Mahony equation, the nonlinear fractional modified Zakharov-Kuznetsov equation and the nonlinear fractional Whitham-Broer-Kaup-Like systems. This method is based on the ring theory of commutative algebra. The results obtained by the proposed method show that the approach is effective and general. This approach can also be applied to other nonlinear fractional differential equations, which are arising in the theory of solitons and other areas.

  6. Spurious Solutions Of Nonlinear Differential Equations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

    1992-01-01

    Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

  7. A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems

    NASA Astrophysics Data System (ADS)

    Ali, Hegagi M.; Pereira, Fernando Lobo; Gama, Sílvio M. A.

    2016-09-01

    In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo sense. We use a new approach to prove necessary conditions of optimality in the form of Pontryagin maximum principle for fractional nonlinear optimal control problems. Moreover, a new method based on a generalization of the Mittag-Leffler function is used to solving this class of fractional optimal control problems. A simple example is provided to illustrate the effectiveness of our main result.

  8. Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

    NASA Astrophysics Data System (ADS)

    Ansari, R.; Faraji Oskouie, M.; Gholami, R.

    2016-01-01

    In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

  9. Algorithms For Integrating Nonlinear Differential Equations

    NASA Technical Reports Server (NTRS)

    Freed, A. D.; Walker, K. P.

    1994-01-01

    Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

  10. Couple of the variational iteration method and fractional-order Legendre functions method for fractional differential equations.

    PubMed

    Yin, Fukang; Song, Junqiang; Leng, Hongze; Lu, Fengshun

    2014-01-01

    We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid "noise terms" is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303

  11. A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

    NASA Technical Reports Server (NTRS)

    Diethelm, Kai; Ford, Neville J.; Freed, Alan D.; Gray, Hugh R. (Technical Monitor)

    2002-01-01

    We discuss an Adams-type predictor-corrector method for the numerical solution of fractional differential equations. The method may be used both for linear and for nonlinear problems, and it may be extended to multi-term equations (involving more than one differential operator) too.

  12. New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

    PubMed Central

    2015-01-01

    In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

  13. Numerical study of fractional nonlinear Schrödinger equations

    PubMed Central

    Klein, Christian; Sparber, Christof; Markowich, Peter

    2014-01-01

    Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation. PMID:25484604

  14. Numerical study of fractional nonlinear Schrödinger equations.

    PubMed

    Klein, Christian; Sparber, Christof; Markowich, Peter

    2014-12-01

    Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation. PMID:25484604

  15. Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian

    PubMed Central

    2014-01-01

    We consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem. PMID:24723837

  16. Fuzzy fractional order sliding mode controller for nonlinear systems

    NASA Astrophysics Data System (ADS)

    Delavari, H.; Ghaderi, R.; Ranjbar, A.; Momani, S.

    2010-04-01

    In this paper, an intelligent robust fractional surface sliding mode control for a nonlinear system is studied. At first a sliding PD surface is designed and then, a fractional form of these networks PDα, is proposed. Fast reaching velocity into the switching hyperplane in the hitting phase and little chattering phenomena in the sliding phase is desired. To reduce the chattering phenomenon in sliding mode control (SMC), a fuzzy logic controller is used to replace the discontinuity in the signum function at the reaching phase in the sliding mode control. For the problem of determining and optimizing the parameters of fuzzy sliding mode controller (FSMC), genetic algorithm (GA) is used. Finally, the performance and the significance of the controlled system two case studies (robot manipulator and coupled tanks) are investigated under variation in system parameters and also in presence of an external disturbance. The simulation results signify performance of genetic-based fuzzy fractional sliding mode controller.

  17. Toward the existence and uniqueness of solutions for fractional integro-differential equations under uncertainty

    NASA Astrophysics Data System (ADS)

    Ahmadian, A.; Ismail, F.; Senu, N.; Salahshour, S.; Suleiman, M.

    2016-06-01

    The main contribution of the current paper is to obtain new results on the existence and uniqueness of the solution of fractional integro-differential equations under uncertainty with nonlocal conditions. For this purpose, we have used two basic tools, the contraction mapping principle and Krasnoselskii's fixed-point theorem. Indeed, we have considered the original problem involving fuzzy Caputo differentiability, together with fuzzy nonlinear condition.

  18. Long-Term Dynamics of Autonomous Fractional Differential Equations

    NASA Astrophysics Data System (ADS)

    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.

  19. Existence of a coupled system of fractional differential equations

    SciTech Connect

    Ibrahim, Rabha W.; Siri, Zailan

    2015-10-22

    We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.

  20. The fractional and nonlinear magneto-flexible rod

    NASA Astrophysics Data System (ADS)

    David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.

    2012-08-01

    This paper deals with a system involving a flexible rod subjected to magnetic forces that can bend it while simultaneously subjected to external excitations produces complex and nonlinear dynamic behavior, which may present different types of solutions for its different movement-related responses. This fact motivated us to analyze such a mechanical system based on modeling and numerical simulation involving both, integer order calculus (IOC) and fractional order calculus (FOC) approaches. The time responses, pseudo phase portraits and Fourier spectra have been presented. The results obtained can be used as a source for conduct experiments in order to obtain more realistic and more accurate results about fractional-order models when compared to the integer-order models.

  1. On fractional differential inclusions with the Jumarie derivative

    SciTech Connect

    Kamocki, Rafał; Obczyński, Cezary

    2014-02-15

    In the paper, fractional differential inclusions with the Jumarie derivative are studied. We discuss the existence and uniqueness of a solution to such problems. Our study relies on standard variational methods.

  2. In-fiber all-optical fractional differentiator.

    PubMed

    Cuadrado-Laborde, C; Andrés, M V

    2009-03-15

    We demonstrate that an asymmetrical pi phase-shifted fiber Bragg grating operated in reflection can provide the required spectral response for implementing an all-optical fractional differentiator. There are different (but equivalent) ways to design it, e.g., by using different gratings lengths and keeping the same index modulation depth at both sides of the pi phase shift, or vice versa. Analytical expressions were found relating the fractional differentiator order with the grating parameters. The device shows a good accuracy calculating the fractional time derivatives of the complex field of an arbitrary input optical waveform. The introduced concept is supported by numerical simulations. PMID:19282948

  3. Matrix approach to discrete fractional calculus II: Partial fractional differential equations

    NASA Astrophysics Data System (ADS)

    Podlubny, Igor; Chechkin, Aleksei; Skovranek, Tomas; Chen, YangQuan; Vinagre Jara, Blas M.

    2009-05-01

    A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny's matrix approach [I. Podlubny, Matrix approach to discrete fractional calculus, Fractional Calculus and Applied Analysis 3 (4) (2000) 359-386]. Four examples of numerical solution of fractional diffusion equation with various combinations of time-/space-fractional derivatives (integer/integer, fractional/integer, integer/fractional, and fractional/fractional) with respect to time and to the spatial variable are provided in order to illustrate how simple and general is the suggested approach. The fifth example illustrates that the method can be equally simply used for fractional differential equations with delays. A set of MATLAB routines for the implementation of the method as well as sample code used to solve the examples have been developed.

  4. Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

    NASA Astrophysics Data System (ADS)

    Moroney, Timothy; Yang, Qianqian

    2013-08-01

    We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space-fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Grünwald finite difference formulas to approximate the two-sided (i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobian-free Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space-fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

  5. Oscillation theorems for second order nonlinear forced differential equations.

    PubMed

    Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md

    2014-01-01

    In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature. PMID:25077054

  6. Nonlinear ordinary differential equations: A discussion on symmetries and singularities

    NASA Astrophysics Data System (ADS)

    Paliathanasis, Andronikos; Leach, P. G. L.

    2016-06-01

    Two essential methods, the symmetry analysis and the singularity analysis, for the study of the integrability of nonlinear ordinary differential equations is the purpose of this work. The main similarities and the differences of these two different methods are discussed.

  7. Entropy and convexity for nonlinear partial differential equations

    PubMed Central

    Ball, John M.; Chen, Gui-Qiang G.

    2013-01-01

    Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue. PMID:24249768

  8. On Lipschitz continuity of nonlinear differential operators

    NASA Technical Reports Server (NTRS)

    Keeling, Stephen L.

    1987-01-01

    In connection with approximations for nonlinear evolution equations, it is standard to assume that nonlinear terms are at least locally Lipschitz continuous. However, it is shown here that f = f(X,del sub u(X)) is Lipschitz continuous from the subspace W sup 1, infinity is a subset of L sub 2 into W sup 1,2, and maps W sup 2, infinity into W sup 1, infinity, if and only if f is affine with W sup 1, infinity coefficients. In fact, a local version of this claim is proved.

  9. Fractional domain varying-order differential denoising method

    NASA Astrophysics Data System (ADS)

    Zhang, Yan-Shan; Zhang, Feng; Li, Bing-Zhao; Tao, Ran

    2014-10-01

    Removal of noise is an important step in the image restoration process, and it remains a challenging problem in image processing. Denoising is a process used to remove the noise from the corrupted image, while retaining the edges and other detailed features as much as possible. Recently, denoising in the fractional domain is a hot research topic. The fractional-order anisotropic diffusion method can bring a less blocky effect and preserve edges in image denoising, a method that has received much interest in the literature. Based on this method, we propose a new method for image denoising, in which fractional-varying-order differential, rather than constant-order differential, is used. The theoretical analysis and experimental results show that compared with the state-of-the-art fractional-order anisotropic diffusion method, the proposed fractional-varying-order differential denoising model can preserve structure and texture well, while quickly removing noise, and yields good visual effects and better peak signal-to-noise ratio.

  10. Differential correction schemes in nonlinear regression

    NASA Technical Reports Server (NTRS)

    Decell, H. P., Jr.; Speed, F. M.

    1972-01-01

    Classical iterative methods in nonlinear regression are reviewed and improved upon. This is accomplished by discussion of the geometrical and theoretical motivation for introducing modifications using generalized matrix inversion. Examples having inherent pitfalls are presented and compared in terms of results obtained using classical and modified techniques. The modification is shown to be useful alone or in conjunction with other modifications appearing in the literature.

  11. Algebraic calculation of stroboscopic maps of ordinary, nonlinear differential equations

    SciTech Connect

    Wackerbauer, R. ); Huebler, A. . Center for Complex Systems Research); Mayer-Kress, G. California Univ., Santa Cruz, CA . Dept. of Mathematics)

    1991-07-25

    The relation between the parameters of a differential equation and corresponding discrete maps are becoming increasingly important in the study of nonlinear dynamical systems. Maps are well adopted for numerical computation and several universal properties of them are known. Therefore some perturbation methods have been proposed to deduce them for physical systems, which can be modeled by an ordinary differential equation (ODE) with a small nonlinearity. A new iterative, rigorous algebraic method for the calculation of the coefficients of a Taylor expansion of a stroboscopic map from ODE's with not necessarily small nonlinearities is presented. It is shown analytically that most of the coefficients are small for a small integration time and grow slowly in the course of time if the flow vector field of the ODE is polynomial and if the ODE has fixed point in the origin. Approximations of different orders respectively of the rest term are investigated for several nonlinear systems. 31 refs., 16 figs.

  12. Stochastic differential equations for non-linear hydrodynamics

    NASA Astrophysics Data System (ADS)

    Español, Pep

    1998-02-01

    We formulate the stochastic differential equations for non-linear hydrodynamic fluctuations. The equations incorporate the random forces through a random stres tensor and random heat flux as in the Landau and Lifshitz theory. However, the equations are non-linear and the random forces are non-Gaussian. We provide explicit expressions for these random quantities in terms of the well-defined increments of the Wienner process.

  13. A Solution to the Fundamental Linear Fractional Order Differential Equation

    NASA Technical Reports Server (NTRS)

    Hartley, Tom T.; Lorenzo, Carl F.

    1998-01-01

    This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

  14. Analysis of non-linearity in differential wavefront sensing technique.

    PubMed

    Duan, Hui-Zong; Liang, Yu-Rong; Yeh, Hsien-Chi

    2016-03-01

    An analytical model of a differential wavefront sensing (DWS) technique based on Gaussian Beam propagation has been derived. Compared with the result of the interference signals detected by quadrant photodiode, which is calculated by using the numerical method, the analytical model has been verified. Both the analytical model and numerical simulation show milli-radians level non-linearity effect of DWS detection. In addition, the beam clipping has strong influence on the non-linearity of DWS. The larger the beam clipping is, the smaller the non-linearity is. However, the beam walking effect hardly has influence on DWS. Thus, it can be ignored in laser interferometer. PMID:26974079

  15. Cosmic ray anisotropy in fractional differential models of anomalous diffusion

    SciTech Connect

    Uchaikin, V. V.

    2013-06-15

    The problem of galactic cosmic ray anisotropy is considered in two versions of the fractional differential model for anomalous diffusion. The simplest problem of cosmic ray propagation from a point instantaneous source in an unbounded medium is used as an example to show that the transition from the standard diffusion model to the Lagutin-Uchaikin fractional differential model (with characteristic exponent {alpha} = 3/5 and a finite velocity of free particle motion), which gives rise to a knee in the energy spectrum at 10{sup 6} GeV, increases the anisotropy coefficient only by 20%, while the anisotropy coefficient in the Lagutin-Tyumentsev model (with exponents {alpha} = 0.3 and {beta} = 0.8, a long stay of particles in traps, and an infinite velocity of their jumps) is close to one. This is because the parameters of the Lagutin-Tyumentsev model have been chosen improperly.

  16. Differential eigenvalue problems in which the parameter appears nonlinearly

    NASA Technical Reports Server (NTRS)

    Bridges, T. J.; Morris, P. J.

    1984-01-01

    Several methods are examined for determining the eigenvalues of a system of equations in which the parameter appears nonlinearly. The equations are the result of the discretization of differential eigenvalue problems using a finite Chebyshev series. Two global methods are considered which determine the spectrum of eigenvalues without an initial estimate. A local iteration scheme with cubic convergence is presented. Calculations are performed for a model second order differential problem and the Orr-Sommerfeld problem for plane Poiseuille flow.

  17. Differential geometry techniques for sets of nonlinear partial differential equations

    NASA Technical Reports Server (NTRS)

    Estabrook, Frank B.

    1990-01-01

    An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

  18. Bounded and periodic solutions of nonlinear functional differential equations

    SciTech Connect

    Slyusarchuk, Vasilii E

    2012-05-31

    Conditions for the existence of bounded and periodic solutions of the nonlinear functional differential equation d{sup m}x(t)/dt{sup m} + (Fx)(t) = h(t), t element of R, are presented, involving local linear approximations to the operator F. Bibliography: 23 titles.

  19. Extended Trial Equation Method for Nonlinear Partial Differential Equations

    NASA Astrophysics Data System (ADS)

    Gepreel, Khaled A.; Nofal, Taher A.

    2015-04-01

    The main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber-Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.

  20. An Effective Schema for Solving Some Nonlinear Partial Differential Equation Arising In Nonlinear Physics

    NASA Astrophysics Data System (ADS)

    Baskonus, Haci Mehmet; Bulut, Hasan

    2015-10-01

    In this paper, a new computational algorithm called the "Improved Bernoulli sub-equation function method" has been proposed. This algorithm is based on the Bernoulli Sub-ODE method. Firstly, the nonlinear evaluation equations used for representing various physical phenomena are converted into ordinary differential equations by using various wave transformations. In this way, nonlinearity is preserved and represent nonlinear physical problems. The nonlinearity of physical problems together with the derivations is seen as the secret key to solve the general structure of problems. The proposed analytical schema, which is newly submitted to the literature, has been expressed comprehensively in this paper. The analytical solutions, application results, and comparisons are presented by plotting the two and three dimensional surfaces of analytical solutions obtained by using the methods proposed for some important nonlinear physical problems. Finally, a conclusion has been presented by mentioning the important discoveries in this study.

  1. On the convergence of a new reliable algorithm for solving multi-order fractional differential equations

    NASA Astrophysics Data System (ADS)

    Hesameddini, Esmail; Rahimi, Azam; Asadollahifard, Elham

    2016-05-01

    In this paper, we will introduce the reconstruction of variational iteration method (RVIM) to solve multi-order fractional differential equations (M-FDEs), which include linear and nonlinear ones. We will easily obtain approximate analytical solutions of M-FDEs by means of the RVIM based on the properties of fractional calculus. Moreover, the convergence of proposed method will be shown. Our scheme has been constructed for the fully general set of M-FDEs without any special assumptions, and is easy to implement numerically. Therefore, our method is more practical and helpful for solving a broad class of M-FDEs. Numerical results are carried out to confirm the accuracy and efficiency of proposed method. Several numerical examples are presented in the format of table and graphs to make comparison with the results that previously obtained by some other well known methods.

  2. Reproducibility of Differential Proteomic Technologies in CPTAC Fractionated Xenografts

    PubMed Central

    2015-01-01

    The NCI Clinical Proteomic Tumor Analysis Consortium (CPTAC) employed a pair of reference xenograft proteomes for initial platform validation and ongoing quality control of its data collection for The Cancer Genome Atlas (TCGA) tumors. These two xenografts, representing basal and luminal-B human breast cancer, were fractionated and analyzed on six mass spectrometers in a total of 46 replicates divided between iTRAQ and label-free technologies, spanning a total of 1095 LC–MS/MS experiments. These data represent a unique opportunity to evaluate the stability of proteomic differentiation by mass spectrometry over many months of time for individual instruments or across instruments running dissimilar workflows. We evaluated iTRAQ reporter ions, label-free spectral counts, and label-free extracted ion chromatograms as strategies for data interpretation (source code is available from http://homepages.uc.edu/~wang2x7/Research.htm). From these assessments, we found that differential genes from a single replicate were confirmed by other replicates on the same instrument from 61 to 93% of the time. When comparing across different instruments and quantitative technologies, using multiple replicates, differential genes were reproduced by other data sets from 67 to 99% of the time. Projecting gene differences to biological pathways and networks increased the degree of similarity. These overlaps send an encouraging message about the maturity of technologies for proteomic differentiation. PMID:26653538

  3. Paradox of enrichment: A fractional differential approach with memory

    NASA Astrophysics Data System (ADS)

    Rana, Sourav; Bhattacharya, Sabyasachi; Pal, Joydeep; N'Guérékata, Gaston M.; Chattopadhyay, Joydev

    2013-09-01

    The paradox of enrichment (PoE) proposed by Rosenzweig [M. Rosenzweig, The paradox of enrichment, Science 171 (1971) 385-387] is still a fundamental problem in ecology. Most of the solutions have been proposed at an individual species level of organization and solutions at community level are lacking. Knowledge of how learning and memory modify behavioral responses to species is a key factor in making a crucial link between species and community levels. PoE resolution via these two organizational levels can be interpreted as a microscopic- and macroscopic-level solution. Fractional derivatives provide an excellent tool for describing this memory and the hereditary properties of various materials and processes. The derivatives can be physically interpreted via two time scales that are considered simultaneously: the ideal, equably flowing homogeneous local time, and the cosmic (inhomogeneous) non-local time. Several mechanisms and theories have been proposed to resolve the PoE problem, but a universally accepted theory is still lacking because most studies have focused on local effects and ignored non-local effects, which capture memory. Here we formulate the fractional counterpart of the Rosenzweig model and analyze the stability behavior of a system. We conclude that there is a threshold for the memory effect parameter beyond which the Rosenzweig model is stable and may be used as a potential agent to resolve PoE from a new perspective via fractional differential equations.

  4. Transformation matrices between non-linear and linear differential equations

    NASA Technical Reports Server (NTRS)

    Sartain, R. L.

    1983-01-01

    In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

  5. Observation and sliding mode observer for nonlinear fractional-order system with unknown input.

    PubMed

    Djeghali, Nadia; Djennoune, Said; Bettayeb, Maamar; Ghanes, Malek; Barbot, Jean-Pierre

    2016-07-01

    The main purpose of this paper is twofold. First, the observability and the left invertibility properties and the observable canonical form for nonlinear fractional-order systems are introduced. By using a transformation, we show that these properties can be deduced from an equivalent nonlinear integer-order system. Second, a step by step sliding mode observer for fault detection and estimation in nonlinear fractional-order systems is proposed. Starting with a chained fractional-order integrators form, a step by step first-order sliding mode observer is designed. The finite time convergence of the observer is established by using Lyapunov stability theory. A numerical example is given to illustrate the performance of the proposed approach. PMID:26961320

  6. Nonlinear Delayed Differential Dynamics for Encryption Using Chaos

    NASA Astrophysics Data System (ADS)

    Larger, Laurent; Goedgebuer, Jean-Pierre; Lee, Min Won

    2003-08-01

    Nonlinear time-delayed differential dynamics are knowing an increasing interest, especially in the area of encryption using chaos. Such dynamics are also met in many other fields, such as mechanics, biology, medicine and optics. In the frame of high dimensional chaotic encryption systems, we have explored several nonlinear oscillators in optics and electronics ruled by nonlinear delayed (or difference) differential equations. After a presentation of the general architecture of such systems, we describe four different experimental set-ups, which are operating respectively with the wavelength of a tunable laser diode, the optical intensity at the output of an integrated electro-optic Mach-Zehnder, the optical path-difference in a coherence modulation scheme, and the electronic frequency at the output of a voltage-controlled oscillator. Numerical bifurcation diagrams are compared with experimental ones, and various dynamical properties are discussed, such as entropy, Lyapunov dimension, time behavior statistics, and spectral properties. Recent developments are also discussed in the view of improving the performances of chaos generators in encryption systems.

  7. PVODE and KINSOL: parallel software for differential and nonlinear systems

    SciTech Connect

    Hindmarsh, A.C.; Taylor, A.G.

    1998-02-01

    In this project, parallel general-purpose software for two classes of mathematical problems has been developed. PVODE is a portable solver for ordinary differential equation systems, based on robustmathematical algorithms, and targeted at large systems on parallel machines. It is the parallel extension of the earlier sequential solver CVODE. A related solver called KINSOL has been developed for systems of nonlinear algebraic equations. KINSOL was first developed as a sequential solver, on a design that permitted extending it to a parallel version with fairly minimal additions. Both PVODE and KINSOL are being used within a parallel version of the tokamak edge plasma model UEDGE. KINSOL is also being applied in the ParFlow groundwater flow model to solve a nonlinear pressure equation.

  8. Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation

    NASA Astrophysics Data System (ADS)

    Wen, Shao-Fang; Shen, Yong-Jun; Wang, Xiao-Na; Yang, Shao-Pu; Xing, Hai-Jun

    2016-08-01

    In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system.

  9. Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation.

    PubMed

    Wen, Shao-Fang; Shen, Yong-Jun; Wang, Xiao-Na; Yang, Shao-Pu; Xing, Hai-Jun

    2016-08-01

    In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system. PMID:27586626

  10. Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics

    NASA Astrophysics Data System (ADS)

    Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan

    2016-05-01

    This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.

  11. New Improved Fractional Order Differentiator Models Based on Optimized Digital Differentiators

    PubMed Central

    Gupta, Maneesha

    2014-01-01

    Different evolutionary algorithms (EAs), namely, particle swarm optimization (PSO), genetic algorithm (GA), and PSO-GA hybrid optimization, have been used to optimize digital differential operators so that these can be better fitted to exemplify their new improved fractional order differentiator counterparts. First, the paper aims to provide efficient 2nd and 3rd order operators in connection with process of minimization of error fitness function by registering mean, median, and standard deviation values in different random iterations to ascertain the best results among them, using all the abovementioned EAs. Later, these optimized operators are discretized for half differentiator models for utilizing their restored qualities inhibited from their optimization. Simulation results present the comparisons of the proposed half differentiators with the existing and amongst different models based on 2nd and 3rd order optimized operators. Proposed half differentiators have been observed to approximate the ideal half differentiator and also outperform the existing ones reasonably well in complete range of Nyquist frequency. PMID:24688426

  12. Synthesis of robust nonlinear autopilots using differential game theory

    NASA Technical Reports Server (NTRS)

    Menon, P. K. A.

    1991-01-01

    A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.

  13. Stochastic Computational Approach for Complex Nonlinear Ordinary Differential Equations

    NASA Astrophysics Data System (ADS)

    Junaid, Ali Khan; Muhammad, Asif Zahoor Raja; Ijaz Mansoor, Qureshi

    2011-02-01

    We present an evolutionary computational approach for the solution of nonlinear ordinary differential equations (NLODEs). The mathematical modeling is performed by a feed-forward artificial neural network that defines an unsupervised error. The training of these networks is achieved by a hybrid intelligent algorithm, a combination of global search with genetic algorithm and local search by pattern search technique. The applicability of this approach ranges from single order NLODEs, to systems of coupled differential equations. We illustrate the method by solving a variety of model problems and present comparisons with solutions obtained by exact methods and classical numerical methods. The solution is provided on a continuous finite time interval unlike the other numerical techniques with comparable accuracy. With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed.

  14. Nonlinear Dependence in the Discovery of Differentially Expressed Genes

    PubMed Central

    Deller, J. R.; Radha, Hayder; McCormick, J. Justin; Wang, Huiyan

    2012-01-01

    Microarray data are used to determine which genes are active in response to a changing cell environment. Genes are “discovered” when they are significantly differentially expressed in the microarray data collected under the differing conditions. In one prevalent approach, all genes are assumed to satisfy a null hypothesis, ℍ0, of no difference in expression. A false discovery (type 1 error) occurs when ℍ0 is incorrectly rejected. The quality of a detection algorithm is assessed by estimating its number of false discoveries, 𝔉. Work involving the second-moment modeling of the z-value histogram (representing gene expression differentials) has shown significantly deleterious effects of intergene expression correlation on the estimate of 𝔉. This paper suggests that nonlinear dependencies could likewise be important. With an applied emphasis, this paper extends the “moment framework” by including third-moment skewness corrections in an estimator of 𝔉. This estimator combines observed correlation (corrected for sampling fluctuations) with the information from easily identifiable null cases. Nonlinear-dependence modeling reduces the estimation error relative to that of linear estimation. Third-moment calculations involve empirical densities of 3 × 3 covariance matrices estimated using very few samples. The principle of entropy maximization is employed to connect estimated moments to 𝔉 inference. Model results are tested with BRCA and HIV data sets and with carefully constructed simulations. PMID:25937940

  15. Nonlinear fractional order proportion-integral-derivative active disturbance rejection control method design for hypersonic vehicle attitude control

    NASA Astrophysics Data System (ADS)

    Song, Jia; Wang, Lun; Cai, Guobiao; Qi, Xiaoqiang

    2015-06-01

    Near space hypersonic vehicle model is nonlinear, multivariable and couples in the reentry process, which are challenging for the controller design. In this paper, a nonlinear fractional order proportion integral derivative (NFOPIλDμ) active disturbance rejection control (ADRC) strategy based on a natural selection particle swarm (NSPSO) algorithm is proposed for the hypersonic vehicle flight control. The NFOPIλDμ ADRC method consists of a tracking-differentiator (TD), an NFOPIλDμ controller and an extended state observer (ESO). The NFOPIλDμ controller designed by combining an FOPIλDμ method and a nonlinear states error feedback control law (NLSEF) is to overcome concussion caused by the NLSEF and conversely compensate the insufficiency for relatively simple and rough signal processing caused by the FOPIλDμ method. The TD is applied to coordinate the contradiction between rapidity and overshoot. By attributing all uncertain factors to unknown disturbances, the ESO can achieve dynamic feedback compensation for these disturbances and thus reduce their effects. Simulation results show that the NFOPIλDμ ADRC method can make the hypersonic vehicle six-degree-of-freedom nonlinear model track desired nominal signals accurately and fast, has good stability, dynamic properties and strong robustness against external environmental disturbances.

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

    NASA Astrophysics Data System (ADS)

    Feng, Qing-Hua

    2013-05-01

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

  17. Constructing conservation laws for fractional-order integro-differential equations

    NASA Astrophysics Data System (ADS)

    Lukashchuk, S. Yu.

    2015-08-01

    In a class of functions depending on linear integro-differential fractional-order variables, we prove an analogue of the fundamental operator identity relating the infinitesimal operator of a point transformation group, the Euler-Lagrange differential operator, and Noether operators. Using this identity, we prove fractional-differential analogues of the Noether theorem and its generalizations applicable to equations with fractional-order integrals and derivatives of various types that are Euler-Lagrange equations. In explicit form, we give fractional-differential generalizations of Noether operators that gives an efficient way to construct conservation laws, which we illustrate with three examples.

  18. Exponential rational function method for space-time fractional differential equations

    NASA Astrophysics Data System (ADS)

    Aksoy, Esin; Kaplan, Melike; Bekir, Ahmet

    2016-04-01

    In this paper, exponential rational function method is applied to obtain analytical solutions of the space-time fractional Fokas equation, the space-time fractional Zakharov Kuznetsov Benjamin Bona Mahony, and the space-time fractional coupled Burgers' equations. As a result, some exact solutions for them are successfully established. These solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. The exact solutions obtained by the proposed method indicate that the approach is easy to implement and effective.

  19. Numerical solution of fractional differential equations using cubic B-spline wavelet collocation method

    NASA Astrophysics Data System (ADS)

    Li, Xinxiu

    2012-10-01

    Physical processes with memory and hereditary properties can be best described by fractional differential equations due to the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional differential equations using cubic B-spline wavelet. Analytical expressions of fractional derivatives in Caputo sense for cubic B-spline functions are presented. The main characteristic of the approach is that it converts such problems into a system of algebraic equations which is suitable for computer programming. It not only simplifies the problem but also speeds up the computation. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation.

  20. Nonlinear fractional Schrödinger equation on a half-line

    NASA Astrophysics Data System (ADS)

    Kaikina, Elena I.

    2015-09-01

    We study the initial-boundary value (IBV) problem for the nonlinear fractional Schrödinger equation {u t + i u x x + i |u|2 u + i|∂x|1/2 u = 0 , t > 0 , x > 0 u ( x , 0 ) = u 0 ( x ) , x > 0 , u ( 0 , t ) = h ( t ) , t > 0 , where |∂ x|1/2 u = /1 √{ 2 π } ∫ 0 ∞ /sign ( x - y ) √{|x-y|} u y ( y ) d y . We prove the global in time existence of solutions of IBV problem for nonlinear fractional Schrödinger equation with inhomogeneous Dirichlet boundary conditions. Also, we are interested in the study of the asymptotic behavior of solutions.

  1. The method of patches for solving stiff nonlinear differential equations

    NASA Astrophysics Data System (ADS)

    Brydon, David Van George, Jr.

    1998-12-01

    This dissertation describes a new method for solving very stiff sets of ordinary differential equations. The basic idea is to replace the original nonlinear equations with a set of equally stiff equations that are piecewise linear, and therefore can be solved exactly. We demonstrate the value of the method on small systems of equations for which some other methods are inefficient or produce spurious solutions, estimate error bounds, and discuss extensions of the method to larger systems of equations and to partial differential equations. Putzer's method is developed in a novel way for efficient and accurate solution of dx/dt = Ax+b. The physical problem of interest is spatial pattern formation in open reaction-diffusion chemical systems, as studied in the experiments of Kyoung Lee, Harry Swinney, et al. I develop a new experiment model that agrees reasonably well with experimental results. I solve the model, applying the new method to the two-variable Gaspar- Showalter chemical kinetics in two space dimensions. Because of time and computer limitations, only preliminary pattern-formation results are achieved and reported.

  2. A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators

    PubMed Central

    Jin, Boyuan; Yuan, Jinhui; Wang, Kuiru; Sang, Xinzhu; Yan, Binbin; Wu, Qiang; Li, Feng; Zhou, Xian; Zhou, Guiyao; Yu, Chongxiu; Lu, Chao; Yaw Tam, Hwa; Wai, P. K. A.

    2015-01-01

    Microring-based photonic fractional differentiators play an important role in the on-chip all-optical signal processing. Unfortunately, the previous works do not consider the time-reversal and the time delay characteristics of the microring-based fractional differentiator. They also do not include the effect of input pulse width on the output. In particular, it cannot explain why the microring-based differentiator with the differentiation order n > 1 has larger output deviation than that with n < 1, and why the microring-based differentiator cannot reproduce the three-peak output waveform of an ideal differentiator with n > 1. In this paper, a comprehensive theoretical model is proposed. The critically-coupled microring resonator is modeled as an ideal first-order differentiator, while the under-coupled and over-coupled resonators are modeled as the time-reversed ideal fractional differentiators. Traditionally, the over-coupled microring resonators are used to form the differentiators with 1 < n < 2. However, we demonstrate that smaller fitting error can be obtained if the over-coupled microring resonator is fitted by an ideal differentiator with n < 1. The time delay of the differentiator is also considered. Finally, the influences of some key factors on the output waveform and deviation are discussed. The proposed theoretical model is beneficial for the design and application of the microring-based fractional differentiators. PMID:26381934

  3. Comments on "Fuzzy fractional order sliding mode controller for nonlinear systems" [Commun Nonlinear Sci Numer Simulat 15 (2010) 963-978

    NASA Astrophysics Data System (ADS)

    Aghababa, Mohammad Pourmahmood

    2012-03-01

    The aim of this note is to point out some comments to the article [Delavari H, Ghaderi R, Ranjbar A, Momani S. Fuzzy fractional order sliding mode controller for nonlinear systems, Commun Nonlinear Sci Numer Simulat 15 (2010) 963-978].

  4. Solving Fractional Partial Differential Equations with Variable Coefficients by the Reconstruction of Variational Iteration Method

    NASA Astrophysics Data System (ADS)

    Hesameddini, Esmail; Rahimi, Azam

    2015-05-01

    In this article, we propose a new approach for solving fractional partial differential equations with variable coefficients, which is very effective and can also be applied to other types of differential equations. The main advantage of the method lies in its flexibility for obtaining the approximate solutions of time fractional and space fractional equations. The fractional derivatives are described based on the Caputo sense. Our method contains an iterative formula that can provide rapidly convergent successive approximations of the exact solution if such a closed form solution exists. Several examples are given, and the numerical results are shown to demonstrate the efficiency of the newly proposed method.

  5. A Variable Order Fractional Differential-Based Texture Enhancement Algorithm with Application in Medical Imaging.

    PubMed

    Yu, Qiang; Vegh, Viktor; Liu, Fawang; Turner, Ian

    2015-01-01

    Texture enhancement is one of the most important techniques in digital image processing and plays an essential role in medical imaging since textures discriminate information. Most image texture enhancement techniques use classical integral order differential mask operators or fractional differential mask operators using fixed fractional order. These masks can produce excessive enhancement of low spatial frequency content, insufficient enhancement of large spatial frequency content, and retention of high spatial frequency noise. To improve upon existing approaches of texture enhancement, we derive an improved Variable Order Fractional Centered Difference (VOFCD) scheme which dynamically adjusts the fractional differential order instead of fixing it. The new VOFCD technique is based on the second order Riesz fractional differential operator using a Lagrange 3-point interpolation formula, for both grey scale and colour image enhancement. We then use this method to enhance photographs and a set of medical images related to patients with stroke and Parkinson's disease. The experiments show that our improved fractional differential mask has a higher signal to noise ratio value than the other fractional differential mask operators. Based on the corresponding quantitative analysis we conclude that the new method offers a superior texture enhancement over existing methods. PMID:26186221

  6. A Variable Order Fractional Differential-Based Texture Enhancement Algorithm with Application in Medical Imaging

    PubMed Central

    Yu, Qiang; Vegh, Viktor

    2015-01-01

    Texture enhancement is one of the most important techniques in digital image processing and plays an essential role in medical imaging since textures discriminate information. Most image texture enhancement techniques use classical integral order differential mask operators or fractional differential mask operators using fixed fractional order. These masks can produce excessive enhancement of low spatial frequency content, insufficient enhancement of large spatial frequency content, and retention of high spatial frequency noise. To improve upon existing approaches of texture enhancement, we derive an improved Variable Order Fractional Centered Difference (VOFCD) scheme which dynamically adjusts the fractional differential order instead of fixing it. The new VOFCD technique is based on the second order Riesz fractional differential operator using a Lagrange 3-point interpolation formula, for both grey scale and colour image enhancement. We then use this method to enhance photographs and a set of medical images related to patients with stroke and Parkinson’s disease. The experiments show that our improved fractional differential mask has a higher signal to noise ratio value than the other fractional differential mask operators. Based on the corresponding quantitative analysis we conclude that the new method offers a superior texture enhancement over existing methods. PMID:26186221

  7. A hybrid algorithm for Caputo fractional differential equations

    NASA Astrophysics Data System (ADS)

    Salgado, G. H. O.; Aguirre, L. A.

    2016-04-01

    This paper is concerned with the numerical solution of fractional initial value problems (FIVP) in sense of Caputo's definition for dynamical systems. Unlike for integer-order derivatives that have a single definition, there is more than one definition of non integer-order derivatives and the solution of an FIVP is definition-dependent. In this paper, the chief differences of the main definitions of fractional derivatives are revisited and a numerical algorithm to solve an FIVP for Caputo derivative is proposed. The main advantages of the algorithm are twofold: it can be initialized with integer-order derivatives, and it is faster than the corresponding standard algorithm. The performance of the proposed algorithm is illustrated with examples which suggest that it requires about half the computation time to achieve the same accuracy than the standard algorithm.

  8. Nonlinear acoustic pulse propagation in dispersive sediments using fractional loss operators.

    PubMed

    Maestas, Joseph T; Collis, Jon M

    2016-03-01

    The nonlinear progressive wave equation (NPE) is a time-domain formulation of the Euler fluid equations designed to model low-angle wave propagation using a wave-following computational domain. The wave-following frame of reference permits the simulation of long-range propagation and is useful in modeling blast wave effects in the ocean waveguide. Existing models do not take into account frequency-dependent sediment attenuation, a feature necessary for accurately describing sound propagation over, into, and out of the ocean sediment. Sediment attenuation is addressed in this work by applying lossy operators to the governing equation that are based on a fractional Laplacian. These operators accurately describe frequency-dependent attenuation and dispersion in typical ocean sediments. However, dispersion within the sediment is found to be a secondary process to absorption and effectively negligible for ranges of interest. The resulting fractional NPE is benchmarked against a Fourier-transformed parabolic equation solution for a linear case, and against the analytical Mendousse solution to Burgers' equation for the nonlinear case. The fractional NPE is then used to investigate the effects of attenuation on shock wave propagation. PMID:27036279

  9. A note on the generation of phase plane plots on a digital computer. [for solution of nonlinear differential equations

    NASA Technical Reports Server (NTRS)

    Simon, M. K.

    1980-01-01

    A technique is presented for generating phase plane plots on a digital computer which circumvents the difficulties associated with more traditional methods of numerical solving nonlinear differential equations. In particular, the nonlinear differential equation of operation is formulated.

  10. Boundedness of the solutions for certain classes of fractional differential equations with application to adaptive systems.

    PubMed

    Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A

    2016-01-01

    This paper presents the analysis of three classes of fractional differential equations appearing in the field of fractional adaptive systems, for the case when the fractional order is in the interval α∈(0,1] and the Caputo definition for fractional derivatives is used. The boundedness of the solutions is proved for all three cases, and the convergence to zero of the mean value of one of the variables is also proved. Applications of the obtained results to fractional adaptive schemes in the context of identification and control problems are presented at the end of the paper, including numerical simulations which support the analytical results. PMID:26632495

  11. Understanding of Phase Noise Squeezing Under Fractional Synchronization of a Nonlinear Spin Transfer Vortex Oscillator.

    PubMed

    Lebrun, R; Jenkins, A; Dussaux, A; Locatelli, N; Tsunegi, S; Grimaldi, E; Kubota, H; Bortolotti, P; Yakushiji, K; Grollier, J; Fukushima, A; Yuasa, S; Cros, V

    2015-07-01

    We investigate experimentally the synchronization of vortex based spin transfer nano-oscillators to an external rf current whose frequency is at multiple integers, as well as at an integer fraction, of the oscillator frequency. Through a theoretical study of the locking mechanism, we highlight the crucial role of both the symmetries of the spin torques and the nonlinear properties of the oscillator in understanding the phase locking mechanism. In the locking regime, we report a phase noise reduction down to -90  dBc/Hz at 1 kHz offset frequency. Our demonstration that the phase noise of these nanoscale nonlinear oscillators can be tuned and eventually lessened, represents a key achievement for targeted radio frequency applications using spin torque devices. PMID:26182117

  12. Instantaneous frequency measurement by in-fiber 0.5th order fractional differentiation

    NASA Astrophysics Data System (ADS)

    Poveda-Wong, L.; Carrascosa, A.; Cuadrado-Laborde, C.; Cruz, J. L.; Díez, A.; Andrés, M. V.

    2016-07-01

    We experimentally demonstrate the possibility to retrieve the instantaneous frequency profile of a given temporal light pulse by in-fiber fractional order differentiation of 0.5th-order. The signal's temporal instantaneous frequency profile is obtained by simple dividing two temporal intensity profiles, namely the intensities of the input and output pulses of a spectrally-shifted fractional order differentiation. The results are supported by the experimental measurement of the instantaneous frequency profile of a mode-locked laser.

  13. Fractionation of gold in a differentiated tholeiitic dolerite

    USGS Publications Warehouse

    Rowe, J.J.

    1969-01-01

    Gold content was determined, by neutron-activation analysis, in samples from a drill core through the Great Lake sheet, Tasmania, a differentiated tholeiitic dolerite. The gold content of parts of the core seems to be related to the mafic index. The variation of gold content with depth and mafic index is similar to that of copper, indicating that gold and copper may have been concomitantly crystallized from the magma. ?? 1969.

  14. Regarding on the prototype solutions for the nonlinear fractional-order biological population model

    NASA Astrophysics Data System (ADS)

    Baskonus, Haci Mehmet; Bulut, Hasan

    2016-06-01

    In this study, we have submitted to literature a method newly extended which is called as Improved Bernoulli sub-equation function method based on the Bernoulli Sub-ODE method. The proposed analytical scheme has been expressed with steps. We have obtained some new analytical solutions to the nonlinear fractional-order biological population model by using this technique. Two and three dimensional surfaces of analytical solutions have been drawn by wolfram Mathematica 9. Finally, a conclusion has been submitted by mentioning important acquisitions founded in this study.

  15. On the blow-up solutions for the nonlinear fractional Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Zhu, Shihui

    2016-07-01

    This paper is dedicated to the blow-up solutions for the nonlinear fractional Schrödinger equation arising from pseudorelativistic Boson stars. First, we compute the best constant of a gG-N inequality by the profile decomposition theory and variational arguments. Then, we find the sharp threshold mass of the existence of finite-time blow-up solutions. Finally, we study the dynamical properties of finite-time blow-up solutions around the sharp threshold mass by giving a refined compactness lemma.

  16. Finite element method combined with second-order time discrete scheme for nonlinear fractional Cable equation

    NASA Astrophysics Data System (ADS)

    Wang, Yajun; Liu, Yang; Li, Hong; Wang, Jinfeng

    2016-03-01

    In this article, a Galerkin finite element method combined with second-order time discrete scheme for finding the numerical solution of nonlinear time fractional Cable equation is studied and discussed. At time t_{k-α/2} , a second-order two step scheme with α -parameter is proposed to approximate the first-order derivative, and a weighted discrete scheme covering second-order approximation is used to approximate the Riemann-Liouville fractional derivative, where the approximate order is higher than the obtained results by the L1-approximation with order (2-α in the existing references. For the spatial direction, Galerkin finite element approximation is presented. The stability of scheme and the rate of convergence in L^2 -norm with O(Δ t^2+(1+Δ t^{-α})h^{m+1}) are derived in detail. Moreover, some numerical tests are shown to support our theoretical results.

  17. Pinning synchronization of fractional-order complex networks with Lipschitz-type nonlinear dynamics.

    PubMed

    Wang, Junwei; Ma, Qinghua; Chen, Aimin; Liang, Zhipeng

    2015-07-01

    This paper deals with pinning synchronization problem of fractional-order complex networks with Lipschitz-type nonlinear nodes and directed communication topology. We first reformulate the problem as a global asymptotic stability problem by describing network evolution in terms of error dynamics. Then, a novel frequency domain approach is developed by using Laplace transform, algebraic graph theory and generalized Gronwall inequality. We show that pinning synchronization can be ensured if the extended network topology contains a spanning tree and the coupling strength is large enough. Furthermore, we provide an easily testable criterion for global pinning synchronization depending on fractional-order, network topology, oscillator dynamics and state feedback. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis. PMID:25721408

  18. Identification of Input Nonlinear Control Autoregressive Systems Using Fractional Signal Processing Approach

    PubMed Central

    Chaudhary, Naveed Ishtiaq; Raja, Muhammad Asif Zahoor; Khan, Junaid Ali; Aslam, Muhammad Saeed

    2013-01-01

    A novel algorithm is developed based on fractional signal processing approach for parameter estimation of input nonlinear control autoregressive (INCAR) models. The design scheme consists of parameterization of INCAR systems to obtain linear-in-parameter models and to use fractional least mean square algorithm (FLMS) for adaptation of unknown parameter vectors. The performance analyses of the proposed scheme are carried out with third-order Volterra least mean square (VLMS) and kernel least mean square (KLMS) algorithms based on convergence to the true values of INCAR systems. It is found that the proposed FLMS algorithm provides most accurate and convergent results than those of VLMS and KLMS under different scenarios and by taking the low-to-high signal-to-noise ratio. PMID:23853538

  19. Numerical solution of distributed order fractional differential equations by hybrid functions

    NASA Astrophysics Data System (ADS)

    Mashayekhi, S.; Razzaghi, M.

    2016-06-01

    In this paper, a new numerical method for solving the distributed fractional differential equations is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is introduced. This operator is then utilized to reduce the solution of the distributed fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

  20. The numerical dynamic for highly nonlinear partial differential equations

    NASA Technical Reports Server (NTRS)

    Lafon, A.; Yee, H. C.

    1992-01-01

    Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

  1. Iron isotope fractionation during magmatic differentiation in Kilauea Iki lava lake

    USGS Publications Warehouse

    Teng, F.-Z.; Dauphas, N.; Helz, R.T.

    2008-01-01

    Magmatic differentiation helps produce the chemical and petrographic diversity of terrestrial rocks. The extent to which magmatic differentiation fractionates nonradiogenic isotopes is uncertain for some elements. We report analyses of iron isotopes in basalts from Kilauea Iki lava lake, Hawaii. The iron isotopic compositions (56Fe/54Fe) of late-stage melt veins are 0.2 per mil (???) greater than values for olivine cumulates. Olivine phenocrysts are up to 1.2??? lighter than those of whole rocks. These results demonstrate that iron isotopes fractionate during magmatic differentiation at both whole-rock and crystal scales. This characteristic of iron relative to the characteristics of magnesium and lithium, for which no fractionation has been found, may be related to its complex redox chemistry in magmatic systems and makes iron a potential tool for studying planetary differentiation.

  2. The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model.

    PubMed

    Mendoza, Carlos I; Santamaría-Holek, I

    2009-01-28

    We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction, which allows constructing a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions. PMID:19191410

  3. A matrix approach for partial differential equations with Riesz space fractional derivatives

    NASA Astrophysics Data System (ADS)

    Popolizio, M.

    2013-09-01

    Fractional partial differential equations are emerging in many scientific fields and their numerical solution is becoming a fundamental topic. In this paper we consider the Riesz fractional derivative operator and its discretization by fractional centered differences. The resulting matrix is studied, with an interesting result on a connection between the decay behavior of its entries and the short memory principle from fractional calculus. The Shift-and-Invert method is then applied to approximate the solution of the partial differential equation as the action of the matrix exponential on a suitable vector which mimics the given initial conditions. The numerical results confirm the good approximation quality and encourage the use of the proposed approach.

  4. Evaluation of fractional photothermolysis effect in a mouse model using nonlinear optical microscopy

    NASA Astrophysics Data System (ADS)

    Guo, Han Wen; Tseng, Te-Yu; Dong, Chen-Yuan; Tsai, Tsung-Hua

    2014-07-01

    Fractional photothermolysis (FP) induces discrete columns of photothermal damage in skin dermis, thereby promoting collagen regeneration. This technique has been widely used for treating wrinkles, sun damage, and scar. In this study, we evaluate the potential of multiphoton microscopy as a noninvasive imaging modality for the monitoring of skin rejuvenation following FP treatment. The dorsal skin of a nude mouse underwent FP treatment in order to induce microthermal zones (MTZs). We evaluated the effect of FP on skin remodeling at 7 and 14 days after treatment. Corresponding histology was performed for comparison. After 14 days of FP treatment at 10 mJ, the second harmonic generation signal recovered faster than the skin treated with 30 mJ, indicating a more rapid regeneration of dermal collagen at 10 mJ. Our results indicate that nonlinear optical microscopy is effective in detecting the damaged areas of MTZ and monitoring collagen regeneration following FP treatment.

  5. Solving nonlinear differential equation governing on the rigid beams on viscoelastic foundation by AGM

    NASA Astrophysics Data System (ADS)

    Akbari, M. R.; Ganji, D. D.; Rostami, A. K.; Nimafar, M.

    2015-03-01

    In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji's method (AGM). AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method (Runk45) and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration ( A), the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure. Therefore, AGM can be considered as a significant progress in nonlinear sciences.

  6. Existence results for a system of coupled hybrid fractional differential equations.

    PubMed

    Ahmad, Bashir; Ntouyas, Sotiris K; Alsaedi, Ahmed

    2014-01-01

    This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations with Dirichlet boundary conditions. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example. PMID:25215320

  7. Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

    PubMed

    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. PMID:23547228

  8. Thermal rectification and negative differential thermal conductance in harmonic chains with nonlinear system-bath coupling

    NASA Astrophysics Data System (ADS)

    Ming, Yi; Li, Hui-Min; Ding, Ze-Jun

    2016-03-01

    Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011), 10.1038/nnano.2011.71]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.

  9. Differential rotation of the unstable nonlinear r -modes

    NASA Astrophysics Data System (ADS)

    Friedman, John L.; Lindblom, Lee; Lockitch, Keith H.

    2016-01-01

    At second order in perturbation theory, the r -modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation reaction, the differential rotation is constant in time and has been computed by Sá. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance ϖ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the r -mode instability removes this gauge freedom; the exponentially growing differential rotation of the unstable second-order r -mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for slowly rotating models with polytropic equations of state.

  10. An improved non-classical method for the solution of fractional differential equations

    NASA Astrophysics Data System (ADS)

    Birk, Carolin; Song, Chongmin

    2010-10-01

    A procedure to construct temporally local schemes for the computation of fractional derivatives is proposed. The frequency-domain counterpart (i ω) α of the fractional differential operator of order α is expressed as an improper integral of a rational function in i ω. After applying a quadrature rule, the improper integral is approximated by a series of partial fractions. Each term of the partial fractions corresponds to an exponential kernel in the time domain. The convolution integral in a fractional derivative can be evaluated recursively leading to a local scheme. As the arguments of the exponential functions are always real and negative, the scheme is stable. The present procedure provides a convenient way to evaluate the quality of a given algorithm by examining its accuracy in fitting the function (i ω) α . It is revealed that the non-classical solution methods for fractional differential equations proposed by Yuan and Agrawal (ASME J Vib Acoust 124:321-324, 2002) and by Diethelm (Numer Algorithms 47:361-390, 2008) can also be interpreted as applying specific quadrature rules to evaluate the improper integral numerically. Over a wider range of frequencies, Diethelm’s algorithm provides a more accurate fitting than the YA algorithm. Therefore, it leads to better performance. Further exploiting this advantage of the proposed derivation, a novel quadrature rule leading to an even better performance than Diethelm’s algorithm is proposed. Significant gains in accuracy are achieved at the extreme ends of the frequency range. This results in significant improvements in accuracy for late time responses. Several numerical examples, including fractional differential equations of degree α = 0.3 and α = 1.5, demonstrate the accuracy and efficiency of the proposed method.

  11. Novel controller design for plants with relay nonlinearity to reduce amplitude of sustained oscillations: Illustration with a fractional controller.

    PubMed

    Kesarkar, Ameya Anil; Selvaganesan, N; Priyadarshan, H

    2015-07-01

    This paper proposes a novel constrained optimization problem to design a controller for plants containing relay nonlinearity to reduce the amplitude of sustained oscillations. The controller is additionally constrained to satisfy desirable loop specifications. The proposed formulation is validated by designing a fractional PI controller for a plant with relay. PMID:25636380

  12. Numerical solution of control problems governed by nonlinear differential equations

    SciTech Connect

    Heinkenschloss, M.

    1994-12-31

    In this presentation the author investigates an iterative method for the solution of optimal control problems. These problems are formulated as constrained optimization problems with constraints arising from the state equation and in the form of bound constraints on the control. The method for the solution of these problems uses the special structure of the problem arising from the bound constraint and the state equation. It is derived from SQP methods and projected Newton methods and combines the advantages of both methods. The bound constraint is satisfied by all iterates using a projection, the nonlinear state equation is satisfied in the limit. Only a linearized state equation has to be solved in every iteration. The solution of the linearized problems are done using multilevel methods and GMRES.

  13. A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations

    PubMed Central

    Li, Hong; Gao, Wei; He, Siriguleng; Fang, Zhichao

    2014-01-01

    A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L2(Ω)2) space replacing the complex H(div; Ω) space. Some a priori error estimates in L2-norm for the scalar unknown u and in (L2)2-norm for its gradient σ. Moreover, we also discuss a priori error estimates in H1-norm for the scalar unknown u. PMID:24737957

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

    NASA Astrophysics Data System (ADS)

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

    2013-10-01

    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.

  15. Mellin transform approach for the solution of coupled systems of fractional differential equations

    NASA Astrophysics Data System (ADS)

    Butera, Salvatore; Di Paola, Mario

    2015-01-01

    In this paper, the solution of a multi-order, multi-degree-of-freedom fractional differential equation is addressed by using the Mellin integral transform. By taking advantage of a technique that relates the transformed function, in points of the complex plane differing in the value of their real part, the solution is found in the Mellin domain by solving a linear set of algebraic equations. The approximate solution of the differential (or integral) equation is restored, in the time domain, by using the inverse Mellin transform in its discretized form.

  16. Applying Linear and Non-Linear Methods for Parallel Prediction of Volume of Distribution and Fraction of Unbound Drug

    PubMed Central

    del Amo, Eva M.; Ghemtio, Leo; Xhaard, Henri; Yliperttula, Marjo; Urtti, Arto; Kidron, Heidi

    2013-01-01

    Volume of distribution and fraction unbound are two key parameters in pharmacokinetics. The fraction unbound describes the portion of free drug in plasma that may extravasate, while volume of distribution describes the tissue access and binding of a drug. Reliable in silico predictions of these pharmacokinetic parameters would benefit the early stages of drug discovery, as experimental measuring is not feasible for screening purposes. We have applied linear and nonlinear multivariate approaches to predict these parameters: linear partial least square regression and non-linear recursive partitioning classification. The volume of distribution and fraction of unbound drug in plasma are predicted in parallel within the model, since the two are expected to be affected by similar physicochemical drug properties. Predictive models for both parameters were built and the performance of the linear models compared to models included in the commercial software Volsurf+. Our models performed better in predicting the unbound fraction (Q2 0.54 for test set compared to 0.38 with Volsurf+ model), but prediction accuracy of the volume of distribution was comparable to the Volsurf+ model (Q2 of 0.70 for test set compared to 0.71 with Volsurf+ model). The nonlinear classification models were able to identify compounds with a high or low volume of distribution (sensitivity 0.81 and 0.71, respectively, for test set), while classification of fraction unbound was less successful. The interrelationship between the volume of distribution and fraction unbound is investigated and described in terms of physicochemical descriptors. Lipophilicity and solubility descriptors were found to have a high influence on both volume of distribution and fraction unbound, but with an inverse relationship. PMID:24116008

  17. Principal patterns of fractional-order differential gradients for face recognition

    NASA Astrophysics Data System (ADS)

    Yu, Lei; Cao, Qi; Zhao, Anping

    2015-01-01

    We investigate the ability of fractional-order differentiation (FD) for facial texture representation and present a local descriptor, called the principal patterns of fractional-order differential gradients (PPFDGs), for face recognition. In PPFDG, multiple FD gradient patterns of a face image are obtained utilizing multiorientation FD masks. As a result, each pixel of the face image can be represented as a high-dimensional gradient vector. Then, by employing principal component analysis to the gradient vectors over the centered neighborhood of each pixel, we capture the principal gradient patterns and meanwhile compute the corresponding orientation patterns from which oriented gradient magnitudes are computed. Histogram features are finally extracted from these oriented gradient magnitude patterns as the face representation using local binary patterns. Experimental results on face recognition technology, A.M. Martinez and R. Benavente, Extended Yale B, and labeled faces in the wild face datasets validate the effectiveness of the proposed method.

  18. The method of local linear approximation in the theory of nonlinear functional-differential equations

    SciTech Connect

    Slyusarchuk, Vasilii E

    2010-10-06

    Conditions for the existence of solutions to the nonlinear functional-differential equation (d{sup m}x(t))/dt{sup m} + (fx)(t)=h(t), t element of R in the space of functions bounded on the axes are obtained by using local linear approximation to the operator F. Bibliography: 21 items.

  19. Boundedness of solutions for non-linear quasi-periodic differential equations with Liouvillean frequency

    NASA Astrophysics Data System (ADS)

    Wang, Jing; You, Jiangong

    2016-07-01

    We study the boundedness of solutions for non-linear quasi-periodic differential equations with Liouvillean frequencies. We proved that if the forcing is quasi-periodic in time with two frequencies which is not super-Liouvillean, then all solutions of the equation are bounded. The proof is based on action-angle variables and modified KAM theory.

  20. An approximation theory for nonlinear partial differential equations with applications to identification and control

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Kunisch, K.

    1982-01-01

    Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

  1. Differential Polarization Nonlinear Optical Microscopy with Adaptive Optics Controlled Multiplexed Beams

    PubMed Central

    Samim, Masood; Sandkuijl, Daaf; Tretyakov, Ian; Cisek, Richard; Barzda, Virginijus

    2013-01-01

    Differential polarization nonlinear optical microscopy has the potential to become an indispensable tool for structural investigations of ordered biological assemblies and microcrystalline aggregates. Their microscopic organization can be probed through fast and sensitive measurements of nonlinear optical signal anisotropy, which can be achieved with microscopic spatial resolution by using time-multiplexed pulsed laser beams with perpendicular polarization orientations and photon-counting detection electronics for signal demultiplexing. In addition, deformable membrane mirrors can be used to correct for optical aberrations in the microscope and simultaneously optimize beam overlap using a genetic algorithm. The beam overlap can be achieved with better accuracy than diffraction limited point-spread function, which allows to perform polarization-resolved measurements on the pixel-by-pixel basis. We describe a newly developed differential polarization microscope and present applications of the differential microscopy technique for structural studies of collagen and cellulose. Both, second harmonic generation, and fluorescence-detected nonlinear absorption anisotropy are used in these investigations. It is shown that the orientation and structural properties of the fibers in biological tissue can be deduced and that the orientation of fluorescent molecules (Congo Red), which label the fibers, can be determined. Differential polarization microscopy sidesteps common issues such as photobleaching and sample movement. Due to tens of megahertz alternating polarization of excitation pulses fast data acquisition can be conveniently applied to measure changes in the nonlinear signal anisotropy in dynamically changing in vivo structures. PMID:24022688

  2. Adaptive neural network nonlinear control for BTT missile based on the differential geometry method

    NASA Astrophysics Data System (ADS)

    Wu, Hao; Wang, Yongji; Xu, Jiangsheng

    2007-11-01

    A new nonlinear control strategy incorporated the differential geometry method with adaptive neural networks is presented for the nonlinear coupling system of Bank-to-Turn missile in reentry phase. The basic control law is designed using the differential geometry feedback linearization method, and the online learning neural networks are used to compensate the system errors due to aerodynamic parameter errors and external disturbance in view of the arbitrary nonlinear mapping and rapid online learning ability for multi-layer neural networks. The online weights and thresholds tuning rules are deduced according to the tracking error performance functions by Levenberg-Marquardt algorithm, which will make the learning process faster and more stable. The six degree of freedom simulation results show that the attitude angles can track the desired trajectory precisely. It means that the proposed strategy effectively enhance the stability, the tracking performance and the robustness of the control system.

  3. Zinc isotope fractionation during magmatic differentiation and the isotopic composition of the bulk Earth

    NASA Astrophysics Data System (ADS)

    Chen, Heng; Savage, Paul S.; Teng, Fang-Zhen; Helz, Rosalind T.; Moynier, Frédéric

    2013-05-01

    The zinc stable isotope system has been successfully applied to many and varied fields in geochemistry, but to date it is still not completely clear how this isotope system is affected by igneous processes. In order to evaluate the potential application of Zn isotopes as a proxy for planetary differentiation and volatile history, it is important to constrain the magnitude of Zn isotopic fractionation induced by magmatic differentiation. In this study we present high-precision Zn isotope analyses of two sets of chemically diverse, cogenetic samples from Kilauea Iki lava lake, Hawaii, and Hekla volcano, Iceland, which both show clear evidence of having undergone variable and significant degrees of magmatic differentiation. The Kilauea Iki samples display small but resolvable variations in Zn isotope composition (0.26‰<δ66Zn<0.36‰; δ66Zn defined as the per mille deviation of a sample's 66Zn/64Zn compositional ratio from the JMC-Lyon standard), with the most differentiated lithologies exhibiting more positive δ66Zn values. This fractionation is likely a result of the crystallization of olivine and/or Fe-Ti oxides, which can both host Zn in their crystal structures. Samples from Hekla have a similar range of isotopic variation (0.22‰<δ66Zn<0.33‰), however, the degree of fractionation caused by magmatic differentiation is less significant (only 0.07‰) and no correlation between isotope composition and degree of differentiation is seen. We conclude that high temperature magmatic differentiation can cause Zn isotope fractionation that is resolvable at current levels of precision, but only in compositionally-evolved lithologies. With regards to primitive (ultramafic and basaltic) material, this signifies that the terrestrial mantle is essentially homogeneous with respect to Zn isotopes. Utilizing basaltic and ultramafic sample analyses, from different geologic settings, we estimate that the average Zn isotopic composition of Bulk Silicate Earth is δ66Zn=0.28

  4. Choas and instabilities in finite difference approximations to nonlinear differential equations

    SciTech Connect

    Cloutman, L. D., LLNL

    1998-07-01

    The numerical solution of time-dependent ordinary and partial differential equations by finite difference techniques is a common task in computational physics and engineering The rate equations for chemical kinetics in combustion modeling are an important example. They not only are nonlinear, but they tend to be stiff, which makes their solution a challenge for transient problems. We show that one must be very careful how such equations are solved In addition to the danger of large time-marching errors, there can be unphysical chaotic solutions that remain numerically stable for a range of time steps that depends on the particular finite difference method used We point out that the solutions of the finite difference equations converge to those of the differential equations only in the limit as the time step approaches zero for stable and consistent finite difference approximations The chaotic behavior observed for finite time steps in some nonlinear difference equations is unrelated to solutions of the differential equations, but is connected with the onset of numerical instabilities of the finite difference equations This behavior suggests that the use of the theory of chaos in nonlinear iterated maps may be useful in stability anlaysis of finite difference approximations to nonlinear differential equations, providing more stringent time step limits than the formal linear stability analysis that tests only for unbounded solutions This observation implies that apparently stable numerical solutions of nonlinear differential equations by finite difference techniques may in fact be contaminated (if not dominated) by nonphysical chaotic parasitic solutions that degrade the accuracy of the numerical solution We demonstrate this phenomenon with some solutions of the logistic equation and a simple two-dimensional computational fluid dynamics example

  5. Determining mixed linear-nonlinear coupled differential equations from multivariate discrete time series sequences

    NASA Astrophysics Data System (ADS)

    Irving, A. D.; Dewson, T.

    1997-02-01

    A new method is described for extracting mixed linear-nonlinear coupled differential equations from multivariate discrete time series data. It is assumed in the present work that the solution of the coupled ordinary differential equations can be represented as a multivariate Volterra functional expansion. A tractable hierarchy of moment equations is generated by operating on a suitably truncated Volterra functional expansion. The hierarchy facilitates the calculation of the coefficients of the coupled differential equations. In order to demonstrate the method's ability to accurately estimate the coefficients of the governing differential equations, it is applied to data derived from the numerical solution of the Lorenz equations with additive noise. The method is then used to construct a dynamic global mid- and high-magnetic latitude ionospheric model where nonlinear phenomena such as period doubling and quenching occur. It is shown that the estimated inhomogeneous coupled second-order differential equation model for the ionospheric foF2 peak plasma density can accurately forecast the future behaviour of a set of ionosonde stations which encompass the earth. Finally, the method is used to forecast the future behaviour of a portfolio of Japanese common stock prices. The hierarchy method can be used to characterise the observed behaviour of a wide class of coupled linear and mixed linear-nonlinear phenomena.

  6. Zinc isotope fractionation during magmatic differentiation and the isotopic composition of the bulk Earth

    USGS Publications Warehouse

    Chen, Heng; Savage, Paul S.; Teng, Fang-Zehn; Helz, Rosalind T.; Moynier, Frédéric

    2013-01-01

    he zinc stable isotope system has been successfully applied to many and varied fields in geochemistry, but to date it is still not completely clear how this isotope system is affected by igneous processes. In order to evaluate the potential application of Zn isotopes as a proxy for planetary differentiation and volatile history, it is important to constrain the magnitude of Zn isotopic fractionation induced by magmatic differentiation. In this study we present high-precision Zn isotope analyses of two sets of chemically diverse, cogenetic samples from Kilauea Iki lava lake, Hawaii, and Hekla volcano, Iceland, which both show clear evidence of having undergone variable and significant degrees of magmatic differentiation. The Kilauea Iki samples display small but resolvable variations in Zn isotope composition (0.26‰66Zn66Zn defined as the per mille deviation of a sample's 66Zn/64Zn compositional ratio from the JMC-Lyon standard), with the most differentiated lithologies exhibiting more positive δ66Zn values. This fractionation is likely a result of the crystallization of olivine and/or Fe–Ti oxides, which can both host Zn in their crystal structures. Samples from Hekla have a similar range of isotopic variation (0.22‰66Zn66Zn=0.28±0.05‰ (2s.d.).

  7. Traveling Wave Solutions for Nonlinear Differential-Difference Equations of Rational Types

    NASA Astrophysics Data System (ADS)

    İsmail, Aslan

    2016-01-01

    Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous. Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations, the majority of the results deal with polynomial types. Limited research has been reported regarding such equations of rational type. In this paper we present an adaptation of the (G‧/G)-expansion method to solve nonlinear rational differential-difference equations. The procedure is demonstrated using two distinct equations. Our approach allows one to construct three types of exact traveling wave solutions (hyperbolic, trigonometric, and rational) by means of the simplified form of the auxiliary equation method with reduced parameters. Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.

  8. Experimentally determined sulfur isotope fractionation between metal and silicate and implications for planetary differentiation

    NASA Astrophysics Data System (ADS)

    Labidi, J.; Shahar, A.; Le Losq, C.; Hillgren, V. J.; Mysen, B. O.; Farquhar, J.

    2016-02-01

    The Earth's mantle displays a subchondritic 34S/32S ratio. Sulfur is a moderately siderophile element (i.e. iron-loving), and its partitioning into the Earth's core may have left such a distinctive isotope composition on the terrestrial mantle. In order to constrain the sulfur isotope fractionation occurring during core-mantle differentiation, high-pressure and temperature experiments were conducted with synthetic mixtures of metal and silicate melts. With the purpose to identify the mechanism(s) responsible for the S isotope fractionations, we performed our experiments in different capsules - namely, graphite and boron nitride capsules - and thus at different fO2, with varying major element chemistry of the silicate and metal fractions. The S isotope fractionations Δ34Smetal-silicate of equilibrated metal alloys versus silicate melts is +0.2 ± 0.1‰ in a boron-free and aluminum-poor system quenched at 1-1.5 GPa and 1650 °C. The isotope fractionation increases linearly with increasing boron and aluminum content, up to +1.4 ± 0.2‰, and is observed to be independent of the silicon abundance as well as of the fO2 over ∼3.5 log units of variations explored here. The isotope fractionations are also independent of the graphite or nitride saturation of the metal. Only the melt structural changes associated with aluminum and boron concentration in silicate melts have been observed to affect the strength of sulfur bonding. These results establish that the structure of silicate melts has a direct influence on the S2- average bonding strengths. These results can be interpreted in the context of planetary differentiation. Indeed, the structural environments of silicate evolve strongly with pressure. For example, the aluminum, iron or silicon coordination numbers increase under the effect of pressure. Consequently, based on our observations, the sulfur-bonding environment is likely to be affected. In this scheme, we tentatively hypothesize that S isotope fractionations

  9. Global Identification and Differential Distribution Analysis of Glycans in Subcellular Fractions of Bladder Cells

    PubMed Central

    Yang, Ganglong; Huang, Luyu; Zhang, Jiaxu; Yu, Hanjie; Li, Zheng; Guan, Feng

    2016-01-01

    Compartmentalization of cellular components and their associated biological processes is crucial for cellular function. Protein glycosylation provides a basis for diversity of protein functions. Diversity of glycan composition in animal cells remains poorly understood. We used differential centrifugation techniques to isolate four subcellular protein fractions from homogenate of metastatic bladder YTS1 cells, low grade nonmuscle invasive bladder cancer KK47 cells and normal bladder epithelia HCV29 cells: microsomal (Mic), mitochondrial (Mito), nuclear (Nuc), and cytosolic (Cyto). An integrated strategy combining lectin microarray and mass spectrometry (MS) analysis was then applied to evaluate protein glycosylation of the four fractions. Lectin microarray analysis revealed significant differences among the four fractions in terms of glycan binding to the lectins LCA, AAL, MPL, WGA and PWM in YTS1 cell, STL, Jacalin, VVA, LCA and WGA in KK47, and ConA, GNA, VVA and ACA in HCV29 cell. Among a total of 40, 32 and 15 N-glycans in four fractions of three cells detected by MS analysis, high-mannose and fucosylated structures were predominant, 10 N-glycans in YTS1, 5 N-glycans in KK47 and 7 N-glycans in HCV29 were present in all four fractions; and 10 N-glycans in YTS1, 16 N-glycans in KK47, and 3 N-glycans in HCV29 were present in only one fraction. Glycans in the latter category are considered potential markers for the corresponding organelles. The integrated strategy described here allows detailed examination of glycomes subcellular fraction with high resolution and sensitivity, and will be useful for elucidation of the functional roles of glycans and corresponding glycosylated proteins in distinct organelles. PMID:27313494

  10. Global Identification and Differential Distribution Analysis of Glycans in Subcellular Fractions of Bladder Cells.

    PubMed

    Yang, Ganglong; Huang, Luyu; Zhang, Jiaxu; Yu, Hanjie; Li, Zheng; Guan, Feng

    2016-01-01

    Compartmentalization of cellular components and their associated biological processes is crucial for cellular function. Protein glycosylation provides a basis for diversity of protein functions. Diversity of glycan composition in animal cells remains poorly understood. We used differential centrifugation techniques to isolate four subcellular protein fractions from homogenate of metastatic bladder YTS1 cells, low grade nonmuscle invasive bladder cancer KK47 cells and normal bladder epithelia HCV29 cells: microsomal (Mic), mitochondrial (Mito), nuclear (Nuc), and cytosolic (Cyto). An integrated strategy combining lectin microarray and mass spectrometry (MS) analysis was then applied to evaluate protein glycosylation of the four fractions. Lectin microarray analysis revealed significant differences among the four fractions in terms of glycan binding to the lectins LCA, AAL, MPL, WGA and PWM in YTS1 cell, STL, Jacalin, VVA, LCA and WGA in KK47, and ConA, GNA, VVA and ACA in HCV29 cell. Among a total of 40, 32 and 15 N-glycans in four fractions of three cells detected by MS analysis, high-mannose and fucosylated structures were predominant, 10 N-glycans in YTS1, 5 N-glycans in KK47 and 7 N-glycans in HCV29 were present in all four fractions; and 10 N-glycans in YTS1, 16 N-glycans in KK47, and 3 N-glycans in HCV29 were present in only one fraction. Glycans in the latter category are considered potential markers for the corresponding organelles. The integrated strategy described here allows detailed examination of glycomes subcellular fraction with high resolution and sensitivity, and will be useful for elucidation of the functional roles of glycans and corresponding glycosylated proteins in distinct organelles. PMID:27313494

  11. Control of AUVs using differential flatness theory and the derivative-free nonlinear Kalman Filter

    NASA Astrophysics Data System (ADS)

    Rigatos, Gerasimos; Raffo, Guilerme

    2015-12-01

    The paper proposes nonlinear control and filtering for Autonomous Underwater Vessels (AUVs) based on differential flatness theory and on the use of the Derivative-free nonlinear Kalman Filter. First, it is shown that the 6-DOF dynamic model of the AUV is a differentially flat one. This enables its transformation into the linear canonical (Brunovsky) form and facilitates the design of a state feedback controller. A problem that has to be dealt with is the uncertainty about the parameters of the AUV's dynamic model, as well the external perturbations which affect its motion. To cope with this, it is proposed to use a disturbance observer which is based on the Derivative-free nonlinear Kalman Filter. The considered filtering method consists of the standard Kalman Filter recursion applied on the linearized model of the vessel and of an inverse transformation based on differential flatness theory, which enables to obtain estimates of the state variables of the initial nonlinear model of the vessel. The Kalman Filter-based disturbance observer performs simultaneous estimation of the non-measurable state variables of the AUV and of the perturbation terms that affect its dynamics. By estimating such disturbances, their compensation is also succeeded through suitable modification of the feedback control input. The efficiency of the proposed AUV control and estimation scheme is confirmed through simulation experiments.

  12. A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

    NASA Astrophysics Data System (ADS)

    Chen, Lin-Jie; Ma, Chang-Feng

    2010-01-01

    This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form ut + αuux + βunux + γuxx + δuxxx + ζuxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.

  13. A nonlinear time-lag differential equation model for predicting monthly precipitation

    NASA Astrophysics Data System (ADS)

    Peng, Yongqing; Yan, Shaojin; Wang, Tongmei

    1995-08-01

    This paper investigates the nonlinear prediction of monthly rainfall time series which consists of phase space continuation of one-dimensional sequence, followed by least-square determination of the coefficients for the terms of the time-lag differential equation model and then fitting of the prognostic expression is made to 1951 1980 monthly rainfall datasets from Changsha station. Results show that the model is likely to describe the nonlinearity of the annual cycle of precipitation on a monthly basis and to provide a basis for flood prevention and drought combating for the wet season.

  14. Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations

    NASA Astrophysics Data System (ADS)

    Aydogmus, F.

    2015-02-01

    The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the "Heisenberg dream." In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented.

  15. A method for exponential propagation of large systems of stiff nonlinear differential equations

    NASA Technical Reports Server (NTRS)

    Friesner, Richard A.; Tuckerman, Laurette S.; Dornblaser, Bright C.; Russo, Thomas V.

    1989-01-01

    A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

  16. An ansatz for solving nonlinear partial differential equations in mathematical physics.

    PubMed

    Akbar, M Ali; Ali, Norhashidah Hj Mohd

    2016-01-01

    In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems. PMID:26783508

  17. A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances.

    PubMed

    Pashaei, Shabnam; Badamchizadeh, Mohammadali

    2016-07-01

    This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers. PMID:27108564

  18. Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument

    PubMed Central

    2014-01-01

    We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use Green's function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results. PMID:24574895

  19. Periodic solutions for nonlinear integro-differential systems with piecewise constant argument.

    PubMed

    Chiu, Kuo-Shou

    2014-01-01

    We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use Green's function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results. PMID:24574895

  20. Symbolic computation of conservation laws of nonlinear partial differential equations in multi-dimensions

    NASA Astrophysics Data System (ADS)

    Hereman, Willy

    A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead, it is solely based on calculus, variational calculus, and linear algebra. Densities are constructed as linear combinations of scaling homogeneous terms with undetermined coefficients. The variational derivative (Euler operator) is used to compute the undetermined coefficients. The homotopy operator is used to compute the fluxes. The method is illustrated with nonlinear PDEs describing wave phenomena in fluid dynamics, plasma physics, and quantum physics. For PDEs with parameters, the method determines the conditions on the parameters so that a sequence of conserved densities might exist. The existence of a large number of conservation laws is a predictor of complete integrability. The method is algorithmic, applicable to a variety of PDEs, and can be implemented in computer algebra systems such as Mathematica, Maple, and REDUCE.

  1. Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

    NASA Astrophysics Data System (ADS)

    Akbari, M. R.; Ganji, D. D.; Majidian, A.; Ahmadi, A. R.

    2014-06-01

    In the present paper, three complicated nonlinear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method (AGM). Investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by numerical method (Runge-Kutte 4th). Based on the comparisons which have been made between the gained solutions by AGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. The results reveal that this method is not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear problems.

  2. Homotopy Perturbation Transform Method with He's Polynomial for Solution of Coupled Nonlinear Partial Differential Equations

    NASA Astrophysics Data System (ADS)

    Sharma, Dinkar; Singh, Prince; Chauhan, Shubha

    2016-01-01

    In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers' equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He's polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.

  3. Analytical solutions for non-linear differential equations with the help of a digital computer

    NASA Technical Reports Server (NTRS)

    Cromwell, P. C.

    1964-01-01

    A technique was developed with the help of a digital computer for analytic (algebraic) solutions of autonomous and nonautonomous equations. Two operational transform techniques have been programmed for the solution of these equations. Only relatively simple nonlinear differential equations have been considered. In the cases considered it has been possible to assimilate the secular terms into the solutions. For cases where f(t) is not a bounded function, a direct series solution is developed which can be shown to be an analytic function. All solutions have been checked against results obtained by numerical integration for given initial conditions and constants. It is evident that certain nonlinear differential equations can be solved with the help of a digital computer.

  4. Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action

    SciTech Connect

    Dvirny, A. I.; Slyn'ko, V. I. E-mail: vitstab@ukr.net

    2014-06-01

    Inverse theorems to Lyapunov's direct method are established for quasihomogeneous systems of differential equations with impulsive action. Conditions for the existence of Lyapunov functions satisfying typical bounds for quasihomogeneous functions are obtained. Using these results, we establish conditions for an equilibrium of a nonlinear system with impulsive action to be stable, using the properties of a quasihomogeneous approximation to the system. The results are illustrated by an example of a large-scale system with homogeneous subsystems. Bibliography: 30 titles. (paper)

  5. Study of coupled nonlinear partial differential equations for finding exact analytical solutions

    PubMed Central

    Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

    2015-01-01

    Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

  6. Absence of molybdenum isotope fractionation during magmatic differentiation at Hekla volcano, Iceland

    NASA Astrophysics Data System (ADS)

    Yang, Jie; Siebert, Christopher; Barling, Jane; Savage, Paul; Liang, Yu-Hsuan; Halliday, Alex N.

    2015-08-01

    This study investigates the behaviour of molybdenum (Mo) isotopes during magmatic differentiation. Molybdenum isotope compositions, as well as concentrations of rare earth elements and a selection of trace elements, have been determined for a well characterised sequence of lavas from Hekla volcano, Iceland, covering a compositional range from basalt to rhyolite (46-72 wt.% SiO2), and thought to have developed by differentiation and mixing of melts derived from a cogenetic source. All samples have identical Mo isotopic compositions with an average δ98Mo of -0.15 ± 0.05‰ (2 s.d.; n = 23). There is therefore no resolvable Mo isotope fractionation during magmatic differentiation at Hekla. This finding is supported by the fact that Mo remains highly incompatible in Hekla lavas, increasing from 1.3 to 4.6 μg/g from basalt to rhyolite, indicating that the crystallising phases are extracting only limited amounts of Mo from the magma and therefore that significant fractionation of Mo isotopes is unlikely. It has previously been proposed that cerium (Ce) and Mo have similar bulk distribution coefficients and are equally incompatible during mantle melting. While both Ce and Mo remain incompatible in Hekla lavas, the Ce/Mo ratio decreases from 50 to 36 during magmatic differentiation indicating that Mo is more incompatible than Ce. Comparison of Mo with other incompatible trace elements indicates that Mo is as incompatible as La and slightly less incompatible than K. Sulphur (S) decreases strongly from ∼200 to as low as ∼2 μg/g from basalt to andesite and more evolved compositions, yet this has no effect on the Mo isotopes. Therefore, Mo does not exhibit significant chalcophile behaviour in Hekla magmas. The Mo isotopic signature therefore may be used as an indicator of parent magma composition and a potential discriminant of assimilation processes.

  7. A non-linear preprocessing for opto-digital image encryption using multiple-parameter discrete fractional Fourier transform

    NASA Astrophysics Data System (ADS)

    Azoug, Seif Eddine; Bouguezel, Saad

    2016-01-01

    In this paper, a novel opto-digital image encryption technique is proposed by introducing a new non-linear preprocessing and using the multiple-parameter discrete fractional Fourier transform (MPDFrFT). The non-linear preprocessing is performed digitally on the input image in the spatial domain using a piecewise linear chaotic map (PLCM) coupled with the bitwise exclusive OR (XOR). The resulting image is multiplied by a random phase mask before applying the MPDFrFT to whiten the image. Then, a chaotic permutation is performed on the output of the MPDFrFT using another PLCM different from the one used in the spatial domain. Finally, another MPDFrFT is applied to obtain the encrypted image. The parameters of the PLCMs together with the multiple fractional orders of the MPDFrFTs constitute the secret key for the proposed cryptosystem. Computer simulation results and security analysis are presented to show the robustness of the proposed opto-digital image encryption technique and the great importance of the new non-linear preprocessing introduced to enhance the security of the cryptosystem and overcome the problem of linearity encountered in the existing permutation-based opto-digital image encryption schemes.

  8. Differential geometry measures of nonlinearity for the bearing-only tracking problem

    NASA Astrophysics Data System (ADS)

    Mallick, Mahendra; La Scala, Barbara F.; Arulampalam, M. S.

    2005-05-01

    The bearing-only tracking problem arises in many radar and sonar tracking applications. Since the bearing measurement model is a nonlinear function of the target state, the filtering problem is nonlinear in nature. A great deal of attention has been focused on this problem due to the difficulty posed by the so-called high degree of nonlinearity (DoN) in the problem. However, a quantitative measure of the DoN is not calculated in previous works. It has been observed that the extended Kalman filter (EKF) in which the state vector consists of the Cartesian components of position and velocity is unstable and diverges in some cases. The range parametrized EKF (RPEKF) and particle filter (PF) have been shown to produce improved estimates for the bearing-only tracking problem. In this paper, we calculate two measures of nonlinearity, (1) the parameter-effects curvature and (2) intrinsic curvature for the bearing-only tracking problem using the differential geometry measures of nonlinearity. We present numerical results using simulated data for the constant velocity motion of a target in 2D with bearing-only measurements where the sensor platform uses a higher order motion than the target to achieve observability. We analyze the DoN by varying the distance between the target and sensor.

  9. Differential branching fraction and angular analysis of Λ {/b 0} → Λμ + μ - decays

    NASA Astrophysics Data System (ADS)

    Aaij, R.; Adeva, B.; Adinolfi, M.; Affolder, A.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Alvarez Cartelle, P.; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; An, L.; Anderlini, L.; Anderson, J.; Andreotti, M.; Andrews, J. E.; Appleby, R. B.; Aquines Gutierrez, O.; Archilli, F.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Baalouch, M.; Bachmann, S.; Back, J. J.; Badalov, A.; Baesso, C.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Batozskaya, V.; Battista, V.; Bay, A.; Beaucourt, L.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Bel, L. J.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Benton, J.; Berezhnoy, A.; Bernet, R.; Bertolin, A.; Bettler, M.-O.; van Beuzekom, M.; Bien, A.; Bifani, S.; Bird, T.; Bizzeti, A.; Blake, T.; Blanc, F.; Blouw, J.; Blusk, S.; Bocci, V.; Bondar, A.; Bondar, N.; Bonivento, W.; Borghi, S.; Borsato, M.; Bowcock, T. J. V.; Bowen, E.; Bozzi, C.; Braun, S.; Brett, D.; Britsch, M.; Britton, T.; Brodzicka, J.; Brook, N. H.; Bursche, A.; Buytaert, J.; Cadeddu, S.; Calabrese, R.; Calvi, M.; Calvo Gomez, M.; Campana, P.; Campora Perez, D.; Capriotti, L.; Carbone, A.; Carboni, G.; Cardinale, R.; Cardini, A.; Carniti, P.; Carson, L.; Carvalho Akiba, K.; Casanova Mohr, R.; Casse, G.; Cassina, L.; Castillo Garcia, L.; Cattaneo, M.; Cauet, Ch.; Cavallero, G.; Cenci, R.; Charles, M.; Charpentier, Ph.; Chefdeville, M.; Chen, S.; Cheung, S.-F.; Chiapolini, N.; Chrzaszcz, M.; Cid Vidal, X.; Ciezarek, G.; Clarke, P. E. L.; Clemencic, M.; Cliff, H. V.; Closier, J.; Coco, V.; Cogan, J.; Cogneras, E.; Cogoni, V.; Cojocariu, L.; Collazuol, G.; Collins, P.; Comerma-Montells, A.; Contu, A.; Cook, A.; Coombes, M.; Coquereau, S.; Corti, G.; Corvo, M.; Counts, I.; Couturier, B.; Cowan, G. A.; Craik, D. C.; Crocombe, A. C.; Torres, M. Cruz; Cunliffe, S.; Currie, R.; D'Ambrosio, C.; Dalseno, J.; David, P. N. Y.; Davis, A.; De Bruyn, K.; De Capua, S.; De Cian, M.; De Miranda, J. M.; De Paula, L.; De Silva, W.; De Simone, P.; Dean, C.-T.; Decamp, D.; Deckenhoff, M.; Del Buono, L.; Déléage, N.; Derkach, D.; Deschamps, O.; Dettori, F.; Dey, B.; Di Canto, A.; Di Ruscio, F.; Dijkstra, H.; Donleavy, S.; Dordei, F.; Dorigo, M.; Dosil Suárez, A.; Dossett, D.; Dovbnya, A.; Dreimanis, K.; Dujany, G.; Dupertuis, F.; Durante, P.; Dzhelyadin, R.; Dziurda, A.; Dzyuba, A.; Easo, S.; Egede, U.; Egorychev, V.; Eidelman, S.; Eisenhardt, S.; Eitschberger, U.; Ekelhof, R.; Eklund, L.; El Rifai, I.; Elsasser, Ch.; Ely, S.; Esen, S.; Evans, H. M.; Evans, T.; Falabella, A.; Färber, C.; Farinelli, C.; Farley, N.; Farry, S.; Fay, R.; Ferguson, D.; Fernandez Albor, V.; Ferrari, F.; Ferreira Rodrigues, F.; Ferro-Luzzi, M.; Filippov, S.; Fiore, M.; Fiorini, M.; Firlej, M.; Fitzpatrick, C.; Fiutowski, T.; Fol, P.; Fontana, M.; Fontanelli, F.; Forty, R.; Francisco, O.; Frank, M.; Frei, C.; Frosini, M.; Fu, J.; Furfaro, E.; Gallas Torreira, A.; Galli, D.; Gallorini, S.; Gambetta, S.; Gandelman, M.; Gandini, P.; Gao, Y.; García Pardiñas, J.; Garofoli, J.; Garra Tico, J.; Garrido, L.; Gascon, D.; Gaspar, C.; Gastaldi, U.; Gauld, R.; Gavardi, L.; Gazzoni, G.; Geraci, A.; Gerick, D.; Gersabeck, E.; Gersabeck, M.; Gershon, T.; Ghez, Ph.; Gianelle, A.; Gianì, S.; Gibson, V.; Giubega, L.; Gligorov, V. V.; Göbel, C.; Golubkov, D.; Golutvin, A.; Gomes, A.; Gotti, C.; Grabalosa Gándara, M.; Graciani Diaz, R.; Granado Cardoso, L. A.; Graugés, E.; Graverini, E.; Graziani, G.; Grecu, A.; Greening, E.; Gregson, S.; Griffith, P.; Grillo, L.; Grünberg, O.; Gui, B.; Gushchin, E.; Guz, Yu.; Gys, T.; Hadjivasiliou, C.; Haefeli, G.; Haen, C.; Haines, S. C.; Hall, S.; Hamilton, B.; Hampson, T.; Han, X.; Hansmann-Menzemer, S.; Harnew, N.; Harnew, S. T.; Harrison, J.; He, J.; Head, T.; Heijne, V.; Hennessy, K.; Henrard, P.; Henry, L.; Hernando Morata, J. A.; van Herwijnen, E.; Heß, M.; Hicheur, A.; Hill, D.; Hoballah, M.; Hombach, C.; Hulsbergen, W.; Humair, T.; Hussain, N.; Hutchcroft, D.; Hynds, D.; Idzik, M.; Ilten, P.; Jacobsson, R.; Jaeger, A.; Jalocha, J.; Jans, E.; Jawahery, A.; Jing, F.; John, M.; Johnson, D.; Jones, C. R.; Joram, C.; Jost, B.; Jurik, N.; Kandybei, S.; Kanso, W.; Karacson, M.; Karbach, T. M.; Karodia, S.; Kelsey, M.; Kenyon, I. R.; Kenzie, M.; Ketel, T.; Khanji, B.; Khurewathanakul, C.; Klaver, S.; Klimaszewski, K.; Kochebina, O.; Kolpin, M.; Komarov, I.; Koopman, R. F.; Koppenburg, P.; Korolev, M.; Kravchuk, L.; Kreplin, K.; Kreps, M.; Krocker, G.; Krokovny, P.; Kruse, F.; Kucewicz, W.; Kucharczyk, M.; Kudryavtsev, V.; Kurek, K.; Kvaratskheliya, T.; La Thi, V. N.; Lacarrere, D.; Lafferty, G.; Lai, A.; Lambert, D.; Lambert, R. W.; Lanfranchi, G.; Langenbruch, C.; Langhans, B.; Latham, T.; Lazzeroni, C.; Le Gac, R.; van Leerdam, J.; Lees, J.-P.; Lefèvre, R.; Leflat, A.; Lefrançois, J.; Leroy, O.; Lesiak, T.; Leverington, B.; Li, Y.; Likhomanenko, T.; Liles, M.; Lindner, R.; Linn, C.; Lionetto, F.; Liu, B.; Lohn, S.; Longstaff, I.; Lopes, J. H.; Lowdon, P.; Lucchesi, D.; Luo, H.; Lupato, A.; Luppi, E.; Lupton, O.; Machefert, F.; Maciuc, F.; Maev, O.; Malde, S.; Malinin, A.; Manca, G.; Mancinelli, G.; Manning, P.; Mapelli, A.; Maratas, J.; Marchand, J. F.; Marconi, U.; Marin Benito, C.; Marino, P.; Märki, R.; Marks, J.; Martellotti, G.; Martinelli, M.; Martinez Santos, D.; Martinez Vidal, F.; Martins Tostes, D.; Massafferri, A.; Matev, R.; Mathad, A.; Mathe, Z.; Matteuzzi, C.; Mauri, A.; Maurin, B.; Mazurov, A.; McCann, M.; McCarthy, J.; McNab, A.; McNulty, R.; Meadows, B.; Meier, F.; Meissner, M.; Merk, M.; Milanes, D. A.; Minard, M.-N.; Mitzel, D. S.; Molina Rodriguez, J.; Monteil, S.; Morandin, M.; Morawski, P.; Mordà, A.; Morello, M. J.; Moron, J.; Morris, A.-B.; Mountain, R.; Muheim, F.; Müller, K.; Mussini, M.; Muster, B.; Naik, P.; Nakada, T.; Nandakumar, R.; Nasteva, I.; Needham, M.; Neri, N.; Neubert, S.; Neufeld, N.; Neuner, M.; Nguyen, A. D.; Nguyen, T. D.; Nguyen-Mau, C.; Niess, V.; Niet, R.; Nikitin, N.; Nikodem, T.; Novoselov, A.; O'Hanlon, D. P.; Oblakowska-Mucha, A.; Obraztsov, V.; Ogilvy, S.; Okhrimenko, O.; Oldeman, R.; Onderwater, C. J. G.; Osorio Rodrigues, B.; Otalora Goicochea, J. M.; Otto, A.; Owen, P.; Oyanguren, A.; Palano, A.; Palombo, F.; Palutan, M.; Panman, J.; Papanestis, A.; Pappagallo, M.; Pappalardo, L. L.; Parkes, C.; Passaleva, G.; Patel, G. D.; Patel, M.; Patrignani, C.; Pearce, A.; Pellegrino, A.; Penso, G.; Pepe Altarelli, M.; Perazzini, S.; Perret, P.; Pescatore, L.; Petridis, K.; Petrolini, A.; Picatoste Olloqui, E.; Pietrzyk, B.; Pilař, T.; Pinci, D.; Pistone, A.; Playfer, S.; Plo Casasus, M.; Poikela, T.; Polci, F.; Poluektov, A.; Polyakov, I.; Polycarpo, E.; Popov, A.; Popov, D.; Popovici, B.; Potterat, C.; Price, E.; Price, J. D.; Prisciandaro, J.; Pritchard, A.; Prouve, C.; Pugatch, V.; Puig Navarro, A.; Punzi, G.; Qian, W.; Quagliani, R.; Rachwal, B.; Rademacker, J. H.; Rakotomiaramanana, B.; Rama, M.; Rangel, M. S.; Raniuk, I.; Rauschmayr, N.; Raven, G.; Redi, F.; Reichert, S.; Reid, M. M.; dos Reis, A. C.; Ricciardi, S.; Richards, S.; Rihl, M.; Rinnert, K.; Rives Molina, V.; Robbe, P.; Rodrigues, A. B.; Rodrigues, E.; Rodriguez Lopez, J. A.; Rodriguez Perez, P.; Roiser, S.; Romanovsky, V.; Romero Vidal, A.; Rotondo, M.; Rouvinet, J.; Ruf, T.; Ruiz, H.; Ruiz Valls, P.; Saborido Silva, J. J.; Sagidova, N.; Sail, P.; Saitta, B.; Salustino Guimaraes, V.; Sanchez Mayordomo, C.; Sanmartin Sedes, B.; Santacesaria, R.; Santamarina Rios, C.; Santovetti, E.; Sarti, A.; Satriano, C.; Satta, A.; Saunders, D. M.; Savrina, D.; Schiller, M.; Schindler, H.; Schlupp, M.; Schmelling, M.; Schmidt, B.; Schneider, O.; Schopper, A.; Schune, M.-H.; Schwemmer, R.; Sciascia, B.; Sciubba, A.; Semennikov, A.; Sepp, I.; Serra, N.; Serrano, J.; Sestini, L.; Seyfert, P.; Shapkin, M.; Shapoval, I.; Shcheglov, Y.; Shears, T.; Shekhtman, L.; Shevchenko, V.; Shires, A.; Silva Coutinho, R.; Simi, G.; Sirendi, M.; Skidmore, N.; Skillicorn, I.; Skwarnicki, T.; Smith, N. A.; Smith, E.; Smith, E.; Smith, J.; Smith, M.; Snoek, H.; Sokoloff, M. D.; Soler, F. J. P.; Soomro, F.; Souza, D.; Souza De Paula, B.; Spaan, B.; Spradlin, P.; Sridharan, S.; Stagni, F.; Stahl, M.; Stahl, S.; Steinkamp, O.; Stenyakin, O.; Sterpka, F.; Stevenson, S.; Stoica, S.; Stone, S.; Storaci, B.; Stracka, S.; Straticiuc, M.; Straumann, U.; Stroili, R.; Sun, L.; Sutcliffe, W.; Swientek, K.; Swientek, S.; Syropoulos, V.; Szczekowski, M.; Szczypka, P.; Szumlak, T.; T'Jampens, S.; Teklishyn, M.; Tellarini, G.; Teubert, F.; Thomas, C.; Thomas, E.; van Tilburg, J.; Tisserand, V.; Tobin, M.; Todd, J.; Tolk, S.; Tomassetti, L.; Tonelli, D.; Topp-Joergensen, S.; Torr, N.; Tournefier, E.; Tourneur, S.; Trabelsi, K.; Tran, M. T.; Tresch, M.; Trisovic, A.; Tsaregorodtsev, A.; Tsopelas, P.; Tuning, N.; Ukleja, A.; Ustyuzhanin, A.; Uwer, U.; Vacca, C.; Vagnoni, V.; Valenti, G.; Vallier, A.; Vazquez Gomez, R.; Vazquez Regueiro, P.; Vázquez Sierra, C.; Vecchi, S.; Velthuis, J. J.; Veltri, M.; Veneziano, G.; Vesterinen, M.; Viana Barbosa, J. V.; Viaud, B.; Vieira, D.; Vieites Diaz, M.; Vilasis-Cardona, X.; Vollhardt, A.; Volyanskyy, D.; Voong, D.; Vorobyev, A.; Vorobyev, V.; Voß, C.; de Vries, J. A.; Waldi, R.; Wallace, C.; Wallace, R.; Walsh, J.; Wandernoth, S.; Wang, J.; Ward, D. R.; Watson, N. K.; Websdale, D.; Weiden, A.; Whitehead, M.; Wiedner, D.; Wilkinson, G.; Wilkinson, M.; Williams, M.; Williams, M. P.; Williams, M.; Wilson, F. F.; Wimberley, J.; Wishahi, J.; Wislicki, W.; Witek, M.; Wormser, G.; Wotton, S. A.; Wright, S.; Wyllie, K.; Xie, Y.; Xu, Z.; Yang, Z.; Yuan, X.; Yushchenko, O.; Zangoli, M.; Zavertyaev, M.; Zhang, L.; Zhang, Y.; Zhelezov, A.; Zhokhov, A.; Zhong, L.

    2015-06-01

    The differential branching fraction of the rare decay Λ {/b 0} → Λμ + μ - is measured as a function of q 2, the square of the dimuon invariant mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of 3 .0 fb-1, collected by the LHCb experiment. Evidence of signal is observed in the q 2 region below the square of the J/ψ mass. Integrating over 15 < q 2 < 20 GeV2 /c 4 the differential branching fraction is measured as where the uncertainties are statistical, systematic and due to the normalisation mode, Λ {/b 0} → J/ ψΛ, respectively. In the q 2 intervals where the signal is observed, angular distributions are studied and the forward-backward asymmetries in the dimuon ( A {FB/ ℓ }) and hadron ( A {FB/ h }) systems are measured for the first time. In the range 15 < q 2 < 20 GeV2 /c 4 they are found to be [Figure not available: see fulltext.

  10. Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities

    NASA Astrophysics Data System (ADS)

    Sun, Yuan Gong; Wong, James S. W.

    2007-10-01

    We present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities: where , p(t) is positive and differentiable, [alpha]1>...>[alpha]m>1>[alpha]m+1>...>[alpha]n. No restriction is imposed on the forcing term e(t) to be the second derivative of an oscillatory function. When n=1, our results reduce to those of El-Sayed [M.A. El-Sayed, An oscillation criterion for a forced second order linear differential equation, Proc. Amer. Math. Soc. 118 (1993) 813-817], Wong [J.S.W. Wong, Oscillation criteria for a forced second linear differential equations, J. Math. Anal. Appl. 231 (1999) 235-240], Sun, Ou and Wong [Y.G. Sun, C.H. Ou, J.S.W. Wong, Interval oscillation theorems for a linear second order differential equation, Comput. Math. Appl. 48 (2004) 1693-1699] for the linear equation, Nazr [A.H. Nazr, Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential, Proc. Amer. Math. Soc. 126 (1998) 123-125] for the superlinear equation, and Sun and Wong [Y.G. Sun, J.S.W. Wong, Note on forced oscillation of nth-order sublinear differential equations, JE Math. Anal. Appl. 298 (2004) 114-119] for the sublinear equation.

  11. Symmetries and reductions of order for certain nonlinear third- and second-order differential equations with arbitrary nonlinearity

    NASA Astrophysics Data System (ADS)

    Tamizhmani, K. M.; Krishnakumar, K.; Leach, P. G. L.

    2015-11-01

    We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to change from a nonlinearity with an arbitrary exponent to a nonlinearity with a specific numerical exponent.

  12. The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications

    NASA Technical Reports Server (NTRS)

    Koshak, William; Solakiewicz, Richard

    2012-01-01

    The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error

  13. Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Walker, K. P.; Freed, A. D.

    1991-01-01

    New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.

  14. Optimal Energy Measurement in Nonlinear Systems: An Application of Differential Geometry

    NASA Technical Reports Server (NTRS)

    Fixsen, Dale J.; Moseley, S. H.; Gerrits, T.; Lita, A.; Nam, S. W.

    2014-01-01

    Design of TES microcalorimeters requires a tradeoff between resolution and dynamic range. Often, experimenters will require linearity for the highest energy signals, which requires additional heat capacity be added to the detector. This results in a reduction of low energy resolution in the detector. We derive and demonstrate an algorithm that allows operation far into the nonlinear regime with little loss in spectral resolution. We use a least squares optimal filter that varies with photon energy to accommodate the nonlinearity of the detector and the non-stationarity of the noise. The fitting process we use can be seen as an application of differential geometry. This recognition provides a set of well-developed tools to extend our work to more complex situations. The proper calibration of a nonlinear microcalorimeter requires a source with densely spaced narrow lines. A pulsed laser multi-photon source is used here, and is seen to be a powerful tool for allowing us to develop practical systems with significant detector nonlinearity. The combination of our analysis techniques and the multi-photon laser source create a powerful tool for increasing the performance of future TES microcalorimeters.

  15. Evidence for high-temperature fractionation of lithium isotopes during differentiation of the Moon

    NASA Astrophysics Data System (ADS)

    Day, James M. D.; Qiu, Lin; Ash, Richard D.; McDonough, William F.; Teng, Fang-Zhen; Rudnick, Roberta L.; Taylor, Lawrence A.

    2016-04-01

    Lithium isotope and abundance data are reported for Apollo 15 and 17 mare basalts and the LaPaz low-Ti mare basalt meteorites, along with lithium isotope data for carbonaceous, ordinary, and enstatite chondrites, and chondrules from the Allende CV3 meteorite. Apollo 15 low-Ti mare basalts have lower Li contents and lower δ7Li (3.8 ± 1.2‰; all uncertainties are 2 standard deviations) than Apollo 17 high-Ti mare basalts (δ7Li = 5.2 ± 1.2‰), with evolved LaPaz mare basalts having high Li contents, but similar low δ7Li (3.7 ± 0.5‰) to Apollo 15 mare basalts. In low-Ti mare basalt 15555, the highest concentrations of Li occur in late-stage tridymite (>20 ppm) and plagioclase (11 ± 3 ppm), with olivine (6.1 ± 3.8 ppm), pyroxene (4.2 ± 1.6 ppm), and ilmenite (0.8 ± 0.7 ppm) having lower Li concentrations. Values of δ7Li in low- and high-Ti mare basalt sources broadly correlate negatively with 18O/16O and positively with 56Fe/54Fe (low-Ti: δ7Li ≤4‰; δ56Fe ≤0.04‰; δ18O ≥5.7‰; high-Ti: δ7Li >6‰ δ56Fe >0.18‰ δ18O <5.4‰). Lithium does not appear to have acted as a volatile element during planetary formation, with subequal Li contents in mare basalts compared with terrestrial, martian, or vestan basaltic rocks. Observed Li isotopic fractionations in mare basalts can potentially be explained through large-degree, high-temperature igneous differentiation of their source regions. Progressive magma ocean crystallization led to enrichment in Li and δ7Li in late-stage liquids, probably as a consequence of preferential retention of 7Li and Li in the melt relative to crystallizing solids. Lithium isotopic fractionation has not been observed during extensive differentiation in terrestrial magmatic systems and may only be recognizable during extensive planetary magmatic differentiation under volatile-poor conditions, as expected for the lunar magma ocean. Our new analyses of chondrites show that they have δ7Li ranging between -2.5‰ and 4

  16. Evidence for high-temperature fractionation of lithium isotopes during differentiation of the Moon

    NASA Astrophysics Data System (ADS)

    Day, James M. D.; Qiu, Lin; Ash, Richard D.; McDonough, William F.; Teng, Fang-Zhen; Rudnick, Roberta L.; Taylor, Lawrence A.

    2016-06-01

    Lithium isotope and abundance data are reported for Apollo 15 and 17 mare basalts and the LaPaz low-Ti mare basalt meteorites, along with lithium isotope data for carbonaceous, ordinary, and enstatite chondrites, and chondrules from the Allende CV3 meteorite. Apollo 15 low-Ti mare basalts have lower Li contents and lower δ7Li (3.8 ± 1.2‰; all uncertainties are 2 standard deviations) than Apollo 17 high-Ti mare basalts (δ7Li = 5.2 ± 1.2‰), with evolved LaPaz mare basalts having high Li contents, but similar low δ7Li (3.7 ± 0.5‰) to Apollo 15 mare basalts. In low-Ti mare basalt 15555, the highest concentrations of Li occur in late-stage tridymite (>20 ppm) and plagioclase (11 ± 3 ppm), with olivine (6.1 ± 3.8 ppm), pyroxene (4.2 ± 1.6 ppm), and ilmenite (0.8 ± 0.7 ppm) having lower Li concentrations. Values of δ7Li in low- and high-Ti mare basalt sources broadly correlate negatively with 18O/16O and positively with 56Fe/54Fe (low-Ti: δ7Li ≤4‰; δ56Fe ≤0.04‰; δ18O ≥5.7‰; high-Ti: δ7Li >6‰ δ56Fe >0.18‰ δ18O <5.4‰). Lithium does not appear to have acted as a volatile element during planetary formation, with subequal Li contents in mare basalts compared with terrestrial, martian, or vestan basaltic rocks. Observed Li isotopic fractionations in mare basalts can potentially be explained through large-degree, high-temperature igneous differentiation of their source regions. Progressive magma ocean crystallization led to enrichment in Li and δ7Li in late-stage liquids, probably as a consequence of preferential retention of 7Li and Li in the melt relative to crystallizing solids. Lithium isotopic fractionation has not been observed during extensive differentiation in terrestrial magmatic systems and may only be recognizable during extensive planetary magmatic differentiation under volatile-poor conditions, as expected for the lunar magma ocean. Our new analyses of chondrites show that they have δ7Li ranging between -2.5‰ and 4

  17. Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations

    SciTech Connect

    Aydogmus, F.

    2015-02-15

    The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the “Heisenberg dream.” In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented.

  18. Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations

    DOE PAGESBeta

    Zhang, Yang; Chong, Edwin K. P.; Hannig, Jan; Estep, Donald

    2013-01-01

    We inmore » troduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N , the number of nodes in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.« less

  19. Pulmonary hypertension in patients with heart failure and preserved ejection fraction: differential diagnosis and management

    PubMed Central

    Charalampopoulos, Athanasios; Ramjug, Sheila; Condliffe, Robin; Elliot, Charlie A.; O’Toole, Laurence; Swift, Andrew; Kiely, David G

    2016-01-01

    Abstract The most common cause of pulmonary hypertension (PH) due to left heart disease (LHD) was previously rheumatic mitral valve disease. However, with the disappearance of rheumatic fever and an aging population, nonvalvular LHD is now the most common cause of group 2 PH in the developed world. In this review, we examine the challenge of investigating patients who have PH and heart failure with preserved ejection fraction (HF-pEF), where differentiating between pulmonary arterial hypertension (PAH) and PH-LHD can be difficult, and also discuss the entity of combined precapillary and postcapillary PH. Given the proven efficacy of targeted therapy for the treatment of PAH, there is increasing interest in whether these treatments may benefit selected patients with PH associated with HF-pEF, and we review current trial data. PMID:27162611

  20. Third brain ventricle deformation analysis using fractional differentiation and evolution strategy in brain cine-MRI

    NASA Astrophysics Data System (ADS)

    Nakib, Amir; Aiboud, Fazia; Hodel, Jerome; Siarry, Patrick; Decq, Philippe

    2010-03-01

    In this paper, we present an original method to evaluate the deformations in the third cerebral ventricle on a brain cine- MR imaging. First, a segmentation process, based on a fractional differentiation method, is directly applied on a 2D+t dataset to detect the contours of the region of interest (i.e. lamina terminalis). Then, the successive segmented contours are matched using a procedure of global alignment, followed by a morphing process, based on the Covariance Matrix Adaptation Evolution Strategy (CMAES). Finally, local measurements of deformations are derived from the previously determined matched contours. The validation step is realized by comparing our results with the measurements achieved on the same patients by an expert.

  1. Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory

    NASA Astrophysics Data System (ADS)

    Szabo, Richard J.; Valentino, Alessandro

    2010-03-01

    We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the low-energy effective field theory, and which provides new consistency conditions for fractional D-branes and Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings of D-branes which generalize previous examples. We propose a definition for groups of differential characters associated to equivariant K-theory. We derive a Dirac quantization rule for Ramond-Ramond fluxes, and study flat Ramond-Ramond potentials on orbifolds.

  2. Pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations

    NASA Astrophysics Data System (ADS)

    Al-Islam, Najja Shakir

    In this Dissertation, the existence of pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations is established. For that, (Al-Islam [4]) is first studied and then obtained under some suitable assumptions. That is, the existence of pseudo almost periodic solutions to a hyperbolic second-order partial differential equation with delay. The second-order partial differential equation (1) represents a mathematical model for the dynamics of gas absorption, given by uxt+a x,tux=Cx,t,u x,t , u0,t=4 t, 1 where a : [0, L] x RR , C : [0, L] x R x RR , and ϕ : RR are (jointly) continuous functions ( t being the greatest integer function) and L > 0. The results in this Dissertation generalize those of Poorkarimi and Wiener [22]. Secondly, a generalization of the above-mentioned system consisting of the non-linear hyperbolic second-order partial differential equation uxt+a x,tux+bx,t ut+cx,tu=f x,t,u, x∈ 0,L,t∈ R, 2 equipped with the boundary conditions ux,0 =40x, u0,t=u 0t, uxx,0=y 0x, x∈0,L, t∈R, 3 where a, b, c : [0, L ] x RR and f : [0, L] x R x RR are (jointly) continuous functions is studied. Under some suitable assumptions, the existence and uniqueness of pseudo almost periodic solutions to particular cases, as well as the general case of the second-order hyperbolic partial differential equation (2) are studied. The results of all studies contained within this text extend those obtained by Aziz and Meyers [6] in the periodic setting.

  3. Multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions

    NASA Astrophysics Data System (ADS)

    Quaas, Alexander; Xia, Aliang

    2016-06-01

    In this article, we prove the existence and multiplicity of positive solutions for the following fractional elliptic equation with sign-changing weight functions: (-Δ)^α u= a_λ(x)|u|^{q-2}u+b(x)|u|^{2^*_α-1}u &in Ω, u=0&in {R}^N{setminus} Ω, where {0 < α < 1}, {Ω} is a bounded domain with smooth boundary in {{R}^N} with {N > 2 α} and {2^*_{α}=2N/(N-2α)} is the fractional critical Sobolev exponent. Our multiplicity results are based on studying the decomposition of the Nehari manifold and the Lusternik-Schnirelmann category.

  4. Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem.

    PubMed

    Lawson, Daniel J; Holtrop, Grietje; Flint, Harry

    2011-07-01

    Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally. PMID:21681780

  5. On Existence of Periodic Solutions for Certain Nonlinear Higher Order Autonomous Ordinary Differential Equations

    SciTech Connect

    Bayat, M.; Khatami, Z.; Mehri, B.

    2008-09-17

    In this paper, we study the existence of periodic solutions for autonomous nonlinear ordinary differential equations of order n. Our method is based on the evaluation of Brouwer's degree theory and making use of the homotopy invariance property of the topological degree and also suitable norm inequalities. For this, we prove two lemmas about the second and third order ODE systems and then present two theorems about the sufficient conditions for the existence of periodic solutions for the even and odd n-order ODE respectively.

  6. A procedure on the first integrals of second-order nonlinear ordinary differential equations

    NASA Astrophysics Data System (ADS)

    Yasar, Emrullah; Yıldırım, Yakup

    2015-12-01

    In this article, we demonstrate the applicability of the integrating factor method to path equation describing minimum drag work, and a special Hamiltonian equation corresponding Riemann zeros for obtaining the first integrals. The effectiveness and powerfullness of this method is verified by applying it for two selected second-order nonlinear ordinary differential equations (NLODEs). As a result integrating factors and first integrals for them are succesfully established. The obtained results show that the integrating factor approach can also be applied to other NLODEs.

  7. Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

    NASA Technical Reports Server (NTRS)

    Jameson, A.

    1976-01-01

    A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

  8. A nonlinear singular eigenvalue problem for a linear system of ordinary differential equations with redundant conditions

    NASA Astrophysics Data System (ADS)

    Abramov, A. A.; Yukhno, L. F.

    2016-07-01

    A nonlinear eigenvalue problem for a linear system of ordinary differential equations is examined on a semi-infinite interval. The problem is supplemented by nonlocal conditions specified by a Stieltjes integral. At infinity, the solution must be bounded. In addition to these basic conditions, the solution must satisfy certain redundant conditions, which are also nonlocal. A numerically stable method for solving such a singular overdetermined eigenvalue problem is proposed and analyzed. The essence of the method is that this overdetermined problem is replaced by an auxiliary problem consistent with all the above conditions.

  9. MicroRNA signatures differentiate preserved from reduced ejection fraction heart failure

    PubMed Central

    Watson, Chris J; Gupta, Shashi K; O'Connell, Eoin; Thum, Sabrina; Glezeva, Nadezhda; Fendrich, Jasmin; Gallagher, Joe; Ledwidge, Mark; Grote-Levi, Lea; McDonald, Kenneth; Thum, Thomas

    2015-01-01

    Aims Differentiation of heart failure with reduced (HFrEF) or preserved (HFpEF) ejection fraction independent of echocardiography is challenging in the community. Diagnostic strategies based on monitoring circulating microRNA (miRNA) levels may prove to be of clinical value in the near future. The aim of this study was to identify a novel miRNA signature that could be a useful HF diagnostic tool and provide valuable clinical information on whether a patient has HFrEF or HFpEF. Methods and results MiRNA biomarker discovery was carried out on three patient cohorts, no heart failure (no-HF), HFrEF, and HFpEF, using Taqman miRNA arrays. The top five miRNA candidates were selected based on differential expression in HFpEF and HFrEF (miR-30c, −146a, −221, −328, and −375), and their expression levels were also different between HF and no-HF. These selected miRNAs were further verified and validated in an independent cohort consisting of 225 patients. The discriminative value of BNP as a HF diagnostic could be improved by use in combination with any of the miRNA candidates alone or in a panel. Combinations of two or more miRNA candidates with BNP had the ability to improve significantly predictive models to distinguish HFpEF from HFrEF compared with using BNP alone (area under the receiver operating characteristic curve >0.82). Conclusion This study has shown for the first time that various miRNA combinations are useful biomarkers for HF, and also in the differentiation of HFpEF from HFrEF. The utility of these biomarker combinations can be altered by inclusion of natriuretic peptide. MiRNA biomarkers may support diagnostic strategies in subpopulations of patients with HF. PMID:25739750

  10. Modeling the collagen fibril network of biological tissues as a nonlinearly elastic material using a continuous volume fraction distribution function

    PubMed Central

    Shirazi, Reza; Vena, Pasquale; Sah, Robert L.; Klisch, Stephen M.

    2012-01-01

    Despite distinct mechanical functions, biological soft tissues have a common microstructure in which a ground matrix is reinforced by a collagen fibril network. The microstructural properties of the collagen network contribute to continuum mechanical tissue properties that are strongly anisotropic with tensile-compressive asymmetry. In this study, a novel approach based on a continuous distribution of collagen fibril volume fractions is developed to model fibril reinforced soft tissues as a nonlinearly elastic and anisotropic material. Compared with other approaches that use a normalized number of fibrils for the definition of the distribution function, this representation is based on a distribution parameter (i.e. volume fraction) that is commonly measured experimentally while also incorporating pre-stress of the collagen fibril network in a tissue natural configuration. After motivating the form of the collagen strain energy function, examples are provided for two volume fraction distribution functions. Consequently, collagen second-Piola Kirchhoff stress and elasticity tensors are derived, first in general form and then specifically for a model that may be used for immature bovine articular cartilage. It is shown that the proposed strain energy is a convex function of the deformation gradient tensor and, thus, is suitable for the formation of a polyconvex tissue strain energy function. PMID:23390357

  11. A critical nonlinear fractional elliptic equation with saddle-like potential in ℝN

    NASA Astrophysics Data System (ADS)

    O. Alves, Claudianor; Miyagaki, Olimpio H.

    2016-08-01

    In this paper, we study the existence of positive solution for the following class of fractional elliptic equation ɛ 2 s ( - Δ ) s u + V ( z ) u = λ |" separators=" u | q - 2 u + |" separators=" u | 2s ∗ - 2 u in R N , where ɛ, λ > 0 are positive parameters, q ∈ ( 2 , 2s ∗ ) , 2s ∗ = /2 N N - 2 s , N > 2 s , s ∈ ( 0 , 1 ) , ( - Δ ) s u is the fractional Laplacian, and V is a saddle-like potential. The result is proved by using minimizing method constrained to the Nehari manifold. A special minimax level is obtained by using an argument made by Benci and Cerami.

  12. Diffusion in heterogeneous media: An iterative scheme for finding approximate solutions to fractional differential equations with time-dependent coefficients

    NASA Astrophysics Data System (ADS)

    Bologna, Mauro; Svenkeson, Adam; West, Bruce J.; Grigolini, Paolo

    2015-07-01

    Diffusion processes in heterogeneous media, and biological systems in particular, are riddled with the difficult theoretical issue of whether the true origin of anomalous behavior is renewal or memory, or a special combination of the two. Accounting for the possible mixture of renewal and memory sources of subdiffusion is challenging from a computational point of view as well. This problem is exacerbated by the limited number of techniques available for solving fractional diffusion equations with time-dependent coefficients. We propose an iterative scheme for solving fractional differential equations with time-dependent coefficients that is based on a parametric expansion in the fractional index. We demonstrate how this method can be used to predict the long-time behavior of nonautonomous fractional differential equations by studying the anomalous diffusion process arising from a mixture of renewal and memory sources.

  13. Dynamics behaviour of an elastic non-ideal (NIS) portal frame, including fractional nonlinearities

    NASA Astrophysics Data System (ADS)

    Balthazar, J. M.; Brasil, R. M. L. F.; Felix, J. L. P.; Tusset, A. M.; Picirillo, V.; Iluik, I.; Rocha, R. T.; Nabarrete, A.; Oliveira, C.

    2016-05-01

    This paper overviews recent developments on some problems related to elastic structures, such as portal frames, taking into account the full interactions of the vibrating systems, with an energy source of limited power supply (small motors, electro-mechanical shakers). We include a discussion on fractional (rational) damping and stiffness effects on the adopted modelling. This was a plenary lecture, delivered in the event titled: Mechanics of Slender Structures, organized in Northampton, England from 21-22, September 2015.

  14. Differential evolution algorithm for nonlinear inversion of high-frequency Rayleigh wave dispersion curves

    NASA Astrophysics Data System (ADS)

    Song, Xianhai; Li, Lei; Zhang, Xueqiang; Huang, Jianquan; Shi, Xinchun; Jin, Si; Bai, Yiming

    2014-10-01

    In recent years, Rayleigh waves are gaining popularity to obtain near-surface shear (S)-wave velocity profiles. However, inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this study, we proposed and tested a new Rayleigh wave dispersion curve inversion scheme based on differential evolution (DE) algorithm. DE is a novel stochastic search approach that possesses several attractive advantages: (1) Capable of handling non-differentiable, non-linear and multimodal objective functions because of its stochastic search strategy; (2) Parallelizability to cope with computation intensive objective functions without being time consuming by using a vector population where the stochastic perturbation of the population vectors can be done independently; (3) Ease of use, i.e. few control variables to steer the minimization/maximization by DE's self-organizing scheme; and (4) Good convergence properties. The proposed inverse procedure was applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for near-surface S-wave velocity profiles. To evaluate calculation efficiency and stability of DE, we firstly inverted four noise-free and four noisy synthetic data sets. Secondly, we investigated effects of the number of layers on DE algorithm and made an uncertainty appraisal analysis by DE algorithm. Thirdly, we made a comparative analysis with genetic algorithms (GA) by a synthetic data set to further investigate the performance of the proposed inverse procedure. Finally, we inverted a real-world example from a waste disposal site in NE Italy to examine the applicability of DE on Rayleigh wave dispersion curves. Furthermore, we compared the performance of the proposed approach to that of GA to further evaluate scores of the inverse procedure described here. Results from both synthetic and actual field data demonstrate that differential evolution algorithm applied

  15. Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement.

    PubMed

    Mazzocco, Michèle M M; Myers, Gwen F; Lewis, Katherine E; Hanich, Laurie B; Murphy, Melissa M

    2013-06-01

    Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions equivalent to one-half, fraction pairs with common denominators) differentiates those with mathematics learning disability (MLD) versus low achievement (LA) or typical achievement (TA) in mathematics and whether long-term learning trajectories of this knowledge also differentiate these groups. We confirmed that although fourth graders with TA (n=93) were more accurate in evaluating "one-half" fractions than in evaluating "non-half" fractions (until they reached ceiling performance levels on both types of fractions), children with MLD (n=11) did not show a one-half advantage until Grade 7 and did not reach ceiling performance even by Grade 8. Both the MLD and LA groups had early difficulties with fractions, but by Grade 5 the LA group approached performance levels of the TA group and deviated from the MLD group. All groups showed a visual model advantage over Arabic number representation of fractions, but this advantage was short-lived for the TA group (because ceiling level was achieved across formats), whereas it was slightly more persistent for the LA group and persisted through Grade 8 for children with MLD. Thus, difficulties with fractions persist through Grade 8 for many students, but the nature and trajectories of those difficulties vary across children with math difficulties (MLD or LA). PMID:23587941

  16. A preconditioned fast finite volume scheme for a fractional differential equation discretized on a locally refined composite mesh

    NASA Astrophysics Data System (ADS)

    Jia, Jinhong; Wang, Hong

    2015-10-01

    Numerical methods for fractional differential equations generate full stiffness matrices, which were traditionally solved via Gaussian type direct solvers that require O (N3) of computational work and O (N2) of memory to store where N is the number of spatial grid points in the discretization. We develop a preconditioned fast Krylov subspace iterative method for the efficient and faithful solution of finite volume schemes defined on a locally refined composite mesh for fractional differential equations to resolve boundary layers of the solutions. Numerical results are presented to show the utility of the method.

  17. Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

    NASA Technical Reports Server (NTRS)

    Gnoffo, Peter A.

    2015-01-01

    Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

  18. Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) vs. low mathematics achievement

    PubMed Central

    Mazzocco, Michèle M. M.; Myers, Gwen F.; Lewis, Katherine E.; Hanich, Laurie B.; Murphy, Melissa M.

    2014-01-01

    Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions equivalent to “one-half,” and fraction pairs with common denominators) differentiates those with mathematical learning disability (MLD) versus low achievement (LA) or typical achievement (TA) in mathematics, and whether long term learning trajectories of this knowledge also differentiate these groups. We confirmed that although 4th graders with LA (n = 18) or TA (n = 93) are more accurate evaluating one-half vs. non-half fractions (until they reach ceiling performance levels on both types of fractions), children with MLD (n=11) do not show a one-half advantage until Grade 7 and do not reach ceiling performance even by Grade 8. Both the MLD and LA groups have early difficulties with fractions, but by Grade 5 the LA group approaches performance levels of the TA group and deviates from the MLD group. All groups showed a visual model advantage over Arabic number representation of fractions, but this advantage was short lived for the TA group (because ceiling level was achieved across formats), slightly more persistent for the LA group, and persisted through Grade 8 for children with MLD. Thus, difficulties with fractions persist through Grade 8 for many students, but the nature and trajectories of those difficulties varies across children with math difficulties (MLD or LA). PMID:23587941

  19. Sorption of selected organic compounds from water to a peat soil and its humic-acid and humin fractions: Potential sources of the sorption nonlinearity

    USGS Publications Warehouse

    Chiou, C.T.; Kile, D.E.; Rutherford, D.W.; Sheng, G.; Boyd, S.A.

    2000-01-01

    The sorption isotherms of ethylene dibromide (EDB), diuron (DUN), and 3,5-dichlorophenol (DCP) from water on the humic acid and humin fractions of a peat soil and on the humic-acid of a muck soil have been measured. The data were compared with those of the solutes with the whole peat from which the humic-acid (HA) and humin (HM) fractions were derived and on which the sorption of the solutes exhibited varying extents of nonlinear capacities at low relative concentrations (C(e)/S(w)). The HA fraction as prepared by the density-fractionated method is relatively pure and presumably free of high- surface-area carbonaceous material (HSACM) that is considered to be responsible for the observed nonlinear sorption for nonpolar solutes (e.g., EDB) on the peat; conversely, the base-insoluble HM fraction as prepared is presumed to be enriched with HSACM, as manifested by the greatly higher BET- (N2) surface area than that of the whole peat. The sorption of EDB on HA exhibits no visible nonlinear effect, whereas the sorption on HM shows an enhanced nonlinearity over that on the whole peat. The sorption of polar DUN and DCP on HA and HM display nonlinear effects comparable with those on the whole peat; the effects are much more significant than those with nonpolar EDB. These results conform to the hypothesis that adsorption onto a small amount of strongly adsorbing HSACM is largely responsible for the nonlinear sorption of nonpolar solutes on soils and that additional specific interactions with the active groups of soil organic matter are responsible for the generally higher nonlinear sorption of the polar solutes.

  20. Nonlinear evolution of r-modes: The role of differential rotation

    SciTech Connect

    Sa, Paulo M.; Tome, Brigitte

    2005-02-15

    Recent work has shown that differential rotation, producing large scale drifts of fluid elements along stellar latitudes, is an unavoidable feature of r-modes in the nonlinear theory. We investigate the role of this differential rotation in the evolution of the l=2 r-mode instability of a newly born, hot, rapidly-rotating neutron star. It is shown that the amplitude of the r-mode saturates a few hundred seconds after the mode instability sets in. The saturation amplitude depends on the amount of differential rotation at the time the instability becomes active and can take values much smaller than unity. It is also shown that, independently of the saturation amplitude of the mode, the star spins down to rotation rates that are comparable to the inferred initial rotation rates of the fastest pulsars associated with supernova remnants. Finally, it is shown that, when the drift of fluid elements at the time the instability sets in is significant, most of the initial angular momentum of the star is transferred to the r-mode and, consequently, almost none is carried away by gravitational-radiation.

  1. Non-Linear Wavelet Regression and Branch & Bound Optimization for the Full Identification of Bivariate Operator Fractional Brownian Motion

    NASA Astrophysics Data System (ADS)

    Frecon, Jordan; Didier, Gustavo; Pustelnik, Nelly; Abry, Patrice

    2016-08-01

    Self-similarity is widely considered the reference framework for modeling the scaling properties of real-world data. However, most theoretical studies and their practical use have remained univariate. Operator Fractional Brownian Motion (OfBm) was recently proposed as a multivariate model for self-similarity. Yet it has remained seldom used in applications because of serious issues that appear in the joint estimation of its numerous parameters. While the univariate fractional Brownian motion requires the estimation of two parameters only, its mere bivariate extension already involves 7 parameters which are very different in nature. The present contribution proposes a method for the full identification of bivariate OfBm (i.e., the joint estimation of all parameters) through an original formulation as a non-linear wavelet regression coupled with a custom-made Branch & Bound numerical scheme. The estimation performance (consistency and asymptotic normality) is mathematically established and numerically assessed by means of Monte Carlo experiments. The impact of the parameters defining OfBm on the estimation performance as well as the associated computational costs are also thoroughly investigated.

  2. A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

    PubMed

    Benhammouda, Brahim

    2016-01-01

    Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems. PMID:27330880

  3. THE LOSS OF ACCURACY OF STOCHASTIC COLLOCATION METHOD IN SOLVING NONLINEAR DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA

    SciTech Connect

    Webster, Clayton G; Tran, Hoang A; Trenchea, Catalin S

    2013-01-01

    n this paper we show how stochastic collocation method (SCM) could fail to con- verge for nonlinear differential equations with random coefficients. First, we consider Navier-Stokes equation with uncertain viscosity and derive error estimates for stochastic collocation discretization. Our analysis gives some indicators on how the nonlinearity negatively affects the accuracy of the method. The stochastic collocation method is then applied to noisy Lorenz system. Simulation re- sults demonstrate that the solution of a nonlinear equation could be highly irregular on the random data and in such cases, stochastic collocation method cannot capture the correct solution.

  4. Second-order non-iterative ADI solution of non-linear partial differential equations. [Alternating Direction Implicit scheme

    NASA Technical Reports Server (NTRS)

    Wolfshtein, M.; Hirsh, R. S.; Pitts, B. H.

    1975-01-01

    A new method for the solution of non-linear partial differential equations by an ADI procedure is described. Although the method is second order accurate in time, it does not require either iterations or predictor corrector methods to overcome the nonlinearity of the equations. Thus the computational effort required for the solution of the non-linear problem becomes similar to that required for the linear case. The method is applied to a two-dimensional 'extended Burgers equation'. Linear stability is studied, and some numerical solutions obtained. The improved accuracy obtained by the 2nd order truncation error is clearly manifested.

  5. Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation

    SciTech Connect

    Zhang, Yu-Juan; Zhao, Dun; Luo, Hong-Gang

    2014-11-15

    We consider a wide class of integrable nonautonomous nonlinear integro-differential Schrödinger equation which contains the models for the soliton management in Bose–Einstein condensates, nonlinear optics, and inhomogeneous Heisenberg spin chain. With the help of the nonisospectral AKNS hierarchy, we obtain the N-fold Darboux transformation and the N-fold soliton-like solutions for the equation. The soliton management, especially the synchronized dispersive and nonlinear management in optical fibers is discussed. It is found that in the situation without external potential, the synchronized dispersive and nonlinear management can keep the integrability of the nonlinear Schrödinger equation; this suggests that in optical fibers, the synchronized dispersive and nonlinear management can control and maintain the propagation of a multi-soliton. - Highlights: • We consider a unified model for soliton management by an integrable integro-differential Schrödinger equation. • Using Lax pair, the N-fold Darboux transformation for the equation is presented. • The multi-soliton management is considered. • The synchronized dispersive and nonlinear management is suggested.

  6. Applying Differential Transforms and ADER to Multi-Dimensional Atmospheric Transport and Non-Linear Dynamics

    NASA Astrophysics Data System (ADS)

    Norman, M. R.

    2013-12-01

    Differential Transforms (DTs), a core component of so-called "automatic" or "algorithmic" differentiation, offer significant flexibility and efficiency to any numerical method. The i-th and j-th DT, U(i,j), of a function, u(x,y), is simply U(i,j)=1/(i!j!)*∂(i+j)u/∂xi∂yj. Being a term in the Taylor series of u(x,y) makes the reverse transform trivial. This relation also computes initial DTs from known spatial derivatives. What is novel about DTs is how they simplify a complex PDE system, transforming most arithmetic, trigonometric, and other operators into simple recurrence relations in derivative space. This allows one to simply and quickly compute analytical derivatives of highly complex and non-linear functions. Consider a pseudo-conservation law system, u(x)t+f(u,x)x=s(u,x), for instance. The fluxes and source terms could be (and often are) highly complex, non-linear functions of the state vector and independent variables. Regardless of the spatial discretization (variational / finite-element, weak / finite-volume, or strong / finite-difference), one nearly always must resort to tensored quadrature to evaluate face fluxes and body source terms, and this treatment is expensive. However, if one uses DTs to analytically compute spatial derivatives of the flux and source terms, given spatial derivatives of u, then the fluxes and source terms are directly expanded as polynomials, allowing for significantly cheaper, quadrature-free integration, sampling, and differentiation with a single dot product. Besides being simpler, this also allows flexibility for Galerkin methods in particular to analytically and cheaply compute body integrals, which are often approximated inexactly with quadrature. Computing Nth-order DTs in D dimensions is of O(D2*N) complexity, and whether for transport or non-linear compressible Euler equations, they are cheaper to compute and integrate analytically than quadrature. Further, because time-dependent PDE systems relate spatial

  7. Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations

    NASA Astrophysics Data System (ADS)

    Baldwin, D.; Göktaş, Ü.; Hereman, W.

    2004-10-01

    A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the equations might admit polynomial solutions in tanh. Examples illustrate the key steps of the algorithm. Through discussion and example, parallels are drawn to the tanh-method for partial differential equations. The new algorithm is implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute traveling wave solutions of nonlinear polynomial differential-difference equations. Use of the package, implementation issues, scope, and limitations of the software are addressed. Program summaryTitle of program: DDESpecialSolutions.m Catalogue identifier:ADUJ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUJ Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: Created using a PC, but can be run on UNIX and Apple machines Operating systems under which the program has been tested: Windows 2000 and Windows XP Programming language used: Mathematica, version 3.0 or higher Memory required to execute with typical data: 9 MB Number of processors used: 1 Has the code been vectorised or parallelized?: No Number of lines in distributed program, including test data, etc.: 3221 Number of bytes in distributed program, including test data, etc.: 23 745 Nature of physical problem: The program computes exact solutions to differential-difference equations in terms of the tanh function. Such solutions describe particle vibrations in lattices, currents in electrical networks, pulses in biological chains, etc. Method of solution: After the differential-difference equation is put in a traveling frame of reference, the coefficients of a candidate polynomial solution in tanh are solved for. The resulting traveling wave solutions are tested by

  8. Global Stability Analysis of Some Nonlinear Delay Differential Equations in Population Dynamics

    NASA Astrophysics Data System (ADS)

    Huang, Gang; Liu, Anping; Foryś, Urszula

    2016-02-01

    By using the direct Lyapunov method and constructing appropriate Lyapunov functionals, we investigate the global stability for the following scalar delay differential equation with nonlinear term y'(t)=f(1-y(t), y(t-τ ))-cy(t), where c is a positive constant and f: {R}^2 → R is of class C^1 and satisfies some additional requirements. This equation is a generalization of the SIS model proposed by Cooke (Rocky Mt J Math 7: 253-263, 1979). Criterions of global stability for the trivial and the positive equilibria of this delay equation are given. A special case of the function f depending only on the variable y(t-τ ) is also considered. Both general and special cases of this equation are often used in biomathematical modelling.

  9. Parachute dynamics and stability analysis. [using nonlinear differential equations of motion

    NASA Technical Reports Server (NTRS)

    Ibrahim, S. K.; Engdahl, R. A.

    1974-01-01

    The nonlinear differential equations of motion for a general parachute-riser-payload system are developed. The resulting math model is then applied for analyzing the descent dynamics and stability characteristics of both the drogue stabilization phase and the main descent phase of the space shuttle solid rocket booster (SRB) recovery system. The formulation of the problem is characterized by a minimum number of simplifying assumptions and full application of state-of-the-art parachute technology. The parachute suspension lines and the parachute risers can be modeled as elastic elements, and the whole system may be subjected to specified wind and gust profiles in order to assess their effects on the stability of the recovery system.

  10. Control of quadrotors using differential flatness theory and the derivative-free nonlinear Kalman filter

    NASA Astrophysics Data System (ADS)

    Rigatos, Gerasimos; Siano, Pierluigi

    2013-10-01

    Using differential flatness theory it is shown that the model of a quadropter can be transformed to linear canonical form. For the linearized equivalent of the quadropter it is shown that a state feedback controller can be designed. Since certain elements of the state vector of the linearized system can not be measured directly, it is proposed to estimate them with the use of a novel filtering method, the so-called Derivative-free nonlinear Kalman Filter. Moreover, by redesigning the Kalman Filter as a disturbance observer, it is is shown that one can estimate simultaneously external disturbances terms that affect the quadropter or disturbance terms which are associated with parametric uncertainty. The efficiency of the proposed control scheme is checked through simulation experiments.

  11. A pertinent approach to solve nonlinear fuzzy integro-differential equations.

    PubMed

    Narayanamoorthy, S; Sathiyapriya, S P

    2016-01-01

    Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach. PMID:27119053

  12. Nonlinear zero-sum differential game analysis by singular perturbation methods

    NASA Technical Reports Server (NTRS)

    Sinar, J.; Farber, N.

    1982-01-01

    A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

  13. Mass dependent fractionation of stable chromium isotopes in mare basalts: Implications for the formation and the differentiation of the Moon

    NASA Astrophysics Data System (ADS)

    Bonnand, Pierre; Parkinson, Ian J.; Anand, Mahesh

    2016-02-01

    We present the first stable chromium isotopic data from mare basalts in order to investigate the similarity between the Moon and the Earth's mantle. A double spike technique coupled with MC-ICP-MS measurements was used to analyse 19 mare basalts, comprising high-Ti, low-Ti and KREEP-rich varieties. Chromium isotope ratios (δ53Cr) for mare basalts are positively correlated with indices of magmatic differentiation such as Mg# and Cr concentration which suggests that Cr isotopes were fractionated during magmatic differentiation. Modelling of the results provides evidence that spinel and pyroxene are the main phases controlling the Cr isotopic composition during fractional crystallisation. The most evolved samples have the lightest isotopic compositions, complemented by cumulates that are isotopically heavy. Two hypotheses are proposed to explain this fractionation: (i) equilibrium fractionation where heavy isotopes are preferentially incorporated into the spinel lattice and (ii) a difference in isotopic composition between Cr2+ and Cr3+ in the melt. However, both processes require magmatic temperatures below 1200 °C for appreciable Cr3+ to be present at the low oxygen fugacities found in the Moon (IW -1 to -2 log units). There is no isotopic difference between the most primitive high-Ti, low-Ti and KREEP basalts, which suggest that the sources of these basalts were homogeneous in terms of stable Cr isotopes. The least differentiated sample in our sample set is the low-Ti basalt 12016, characterised by a Cr isotopic composition of -0.222 ± 0.025‰, which is within error of the current BSE value (-0.124 ± 0.101‰). The similarity between the mantles of the Moon and Earth is consistent with a terrestrial origin for a major fraction of the lunar Cr. This similarity also suggests that Cr isotopes were not fractionated by core formation on the Moon.

  14. Scrutiny of non-linear differential equations Euler-Bernoulli beam with large rotational deviation by AGM

    NASA Astrophysics Data System (ADS)

    Akbari, M. R.; Nimafar, M.; Ganji, D. D.; Akbarzade, M. M.

    2014-12-01

    The kinematic assumptions upon which the Euler-Bernoulli beam theory is founded allow it to be extended to more advanced analysis. Simple superposition allows for three-dimensional transverse loading. Using alternative constitutive equations can allow for viscoelastic or plastic beam deformation. Euler-Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams and geometrically nonlinear beam deflection. In this study, solving the nonlinear differential equation governing the calculation of the large rotation deviation of the beam (or column) has been discussed. Previously to calculate the rotational deviation of the beam, the assumption is made that the angular deviation of the beam is small. By considering the small slope in the linearization of the governing differential equation, the solving is easy. The result of this simplification in some cases will lead to an excessive error. In this paper nonlinear differential equations governing on this system are solved analytically by Akbari-Ganji's method (AGM). Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration solving. The solution of the problem can be obtained very simply and easily. Furthermore, to enhance the accuracy of the results, the Taylor expansion is not needed in most cases via AGM manner. Also, comparisons are made between AGM and numerical method (Runge-Kutta 4th). The results reveal that this method is very effective and simple, and can be applied for other nonlinear problems.

  15. Non-linear Bio-geophysical and Remote Sensing Relations Revealed in Neural Network Training for Fractional Snow Cover Estimation

    NASA Astrophysics Data System (ADS)

    Czyzowska-Wisniewski, E. H.; Van Leeuwen, W. J. D.; Marsh, S. E.; Hirschboeck, K. K.; Wisniewski, W. T.

    2014-12-01

    Accurate estimation of Fractional Snow Cover (FSC) in complex alpine-forested terrain is now possible with appropriate remote sensing data and analysis techniques. This research examines what minimum combination of input variables are required to obtain state-of-the-art FSC estimates for heterogeneous alpine-forested terrains. Currently, one of the most accurate FSC estimators for alpine regions is based on training an Artificial Neural Network (ANN) that can deconvolve the relationships between numerous compounded and possibly non-linear bio-geophysical relations encountered in rugged terrain. Under the assumption that the ANN optimally extracts available information from its input data, we can exploit the ANN as a tool to assess the contributions toward FSC estimation of each of the data sources, and combinations thereof. By assessing the quality of the modeled FSC estimates versus ground equivalent data, suitable combinations of input variables can be identified. High spatial resolution imagery from IKONOS are used to estimate snow cover for ANN training and validation, and also for error assessment of the ANN FSC results. Input variables are initially chosen representing information already incorporated into leading snow cover estimators. Additional variables such as topographic slope, aspect, and shadow distribution are evaluated to observe the ANN as it accounts for illumination incidence and directional reflectance of surfaces affecting the viewed radiance in complex terrain. Snow usually covers vegetation and underlying geology partially, therefore the ANN also has to resolve spectral mixtures of unobscured surfaces surrounded by snow. Multispectral imagery if therefore acquired in the fall prior to the first snow of the season and are included in the ANN analyses for assessing the baseline reflectance values of the environment that later become modified by the snow. The best ANN FSC model performance was achieved when all 15 pre-selected inputs were used

  16. A general fractional differential equation associated with an integral operator with the H-function in the kernel

    NASA Astrophysics Data System (ADS)

    Srivastava, H. M.; Harjule, P.; Jain, R.

    2015-01-01

    In this paper, we introduce and investigate a fractional integral operator which contains Fox's H-function in its kernel. We find solutions to some fractional differential equations by using this operator. The results derived in this paper generalize the results obtained in earlier works by Kilbas et al. [7] and Srivastava and Tomovski [23]. A number of corollaries and consequences of the main results are also considered. Using some of these corollaries, graphical illustrations are presented and it is found that the graphs given here are quite comparable to the physical phenomena of decay processes.

  17. Singularities and symmetries of nonlinear ordinary and partial differential equations. Technical report, May 15, 1993--May 14, 1994

    SciTech Connect

    Not Available

    1994-10-01

    In this project we have studied singularities as both fundamental mathematical objects in their own right determining, for example, integrable and nonintegrable properties of nonlinear differential equations; and the determining mechanism of crucial physical processes such as self-focusing singularities and current sheet formation. This approach defines broad based, interdisciplinary research program relevant to the DOE/AMS mission.

  18. Investigation of magnesium isotope fractionation during granite differentiation: Implication for Mg isotopic composition of the continental crust

    NASA Astrophysics Data System (ADS)

    Liu, Sheng-Ao; Teng, Fang-Zhen; He, Yongsheng; Ke, Shan; Li, Shuguang

    2010-09-01

    High-precision Mg isotopic analysis was performed on a suite of well-characterized I-type granitoids and associated hornblende and biotite minerals from the Dabie Orogen in central China, to address the behavior of Mg isotopes during granite differentiation. Although these granitoids formed through different degrees of partial melting and fractional crystallization, with large variations in elemental and mineral compositions, their δ26Mg values vary from -0.26 to -0.14 and are indistinguishable within our analytical precision (± 0.07‰; 2 SD). Coexisting hornblendes and biotites in these granitoids display similar Mg isotopic composition, with δ26Mg ranging from -0.31 to -0.14 in hornblendes and -0.23 to -0.12 in biotites. The inter-mineral fractionation factors (Δ 26Mg Hbl-Bt = δ26Mg Hbl - δ26Mg Bt) vary from -0.10 to -0.02, with an average = -0.06 ± 0.08 (2 SD). The limited inter-mineral fractionation agrees with the theoretic prediction that Mg cations in both hornblende and biotite are octahedrally coordinated with oxygen, which restricts the magnitude of equilibrium isotope fractionation. Overall, data from both bulk granitoids and associated mineral separates suggest that Mg isotope fractionation during I-type granite differentiation is limited. Collectively, granitoids studied here have Mg isotopic composition similar to that of terrestrial basalts and peridotites ( δ26Mg = -0.21 ± 0.07 vs. -0.25 ± 0.07; 2 SD), confirming that magmatic processes do not significantly fractionate Mg isotopes. The continental crust in the Dabie Orogen, as sampled by these I-type granitoids, has a mantle-like Mg isotopic composition. Given that significant Mg isotope fractionation occurs during chemical weathering processes, Mg isotopes may potentially be used for tracing granite genesis, in particular, if sedimentary materials are involved in granite sources.

  19. Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

    NASA Astrophysics Data System (ADS)

    Kiryakova, Virginia S.

    2012-11-01

    The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order

  20. A 2-to-2.4-GHz differentially-tuned fractional-N frequency synthesizer for DVB tuner applications

    NASA Astrophysics Data System (ADS)

    Lingbu, Meng; Lei, Lu; Wei, Zhao; Zhangwen, Tang

    2010-07-01

    This paper describes the design of a fractional-N frequency synthesizer for digital video broadcasting-terrestrial (DVB-T) receivers. Transfer functions in differentially-tuned PLL are derived and loop parameters are designed. In addition, a fully-differential charge pump is presented. An 8/9 high speed prescaler is analyzed and the design considerations for the CML logic are also presented. Test results show that the RMS phase error is less than 0.7° in integer-N mode and less than 1° in fractional-N mode. The implemented frequency synthesizer draws 10 mA from a 1.8-V supply while occupying a die area of about 1-mm2 in a 0.18-μm CMOS process.

  1. Angular analysis and differential branching fraction of the decay B {/s 0} → ϕμ + μ -

    NASA Astrophysics Data System (ADS)

    Aaij, R.; Adeva, B.; Adinolfi, M.; Affolder, A.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Alvarez Cartelle, P.; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; An, L.; Anderlini, L.; Anderson, J.; Andreassi, G.; Andreotti, M.; Andrews, J. E.; Appleby, R. B.; Aquines Gutierrez, O.; Archilli, F.; d'Argent, P.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Baalouch, M.; Bachmann, S.; Back, J. J.; Badalov, A.; Baesso, C.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Batozskaya, V.; Battista, V.; Bay, A.; Beaucourt, L.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Bel, L. J.; Bellee, V.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Benton, J.; Berezhnoy, A.; Bernet, R.; Bertolin, A.; Bettler, M.-O.; van Beuzekom, M.; Bien, A.; Bifani, S.; Bird, T.; Birnkraut, A.; Bizzeti, A.; Blake, T.; Blanc, F.; Blouw, J.; Blusk, S.; Bocci, V.; Bondar, A.; Bondar, N.; Bonivento, W.; Borghi, S.; Borsato, M.; Bowcock, T. J. V.; Bowen, E.; Bozzi, C.; Braun, S.; Brett, D.; Britsch, M.; Britton, T.; Brodzicka, J.; Brook, N. H.; Bursche, A.; Buytaert, J.; Cadeddu, S.; Calabrese, R.; Calvi, M.; Calvo Gomez, M.; Campana, P.; Campora Perez, D.; Capriotti, L.; Carbone, A.; Carboni, G.; Cardinale, R.; Cardini, A.; Carniti, P.; Carson, L.; Carvalho Akiba, K.; Casse, G.; Cassina, L.; Castillo Garcia, L.; Cattaneo, M.; Cauet, Ch.; Cavallero, G.; Cenci, R.; Charles, M.; Charpentier, Ph.; Chefdeville, M.; Chen, S.; Cheung, S.-F.; Chiapolini, N.; Chrzaszcz, M.; Cid Vidal, X.; Ciezarek, G.; Clarke, P. E. L.; Clemencic, M.; Cliff, H. V.; Closier, J.; Coco, V.; Cogan, J.; Cogneras, E.; Cogoni, V.; Cojocariu, L.; Collazuol, G.; Collins, P.; Comerma-Montells, A.; Contu, A.; Cook, A.; Coombes, M.; Coquereau, S.; Corti, G.; Corvo, M.; Couturier, B.; Cowan, G. A.; Craik, D. C.; Crocombe, A.; Cruz Torres, M.; Cunliffe, S.; Currie, R.; D'Ambrosio, C.; Dall'Occo, E.; Dalseno, J.; David, P. N. Y.; Davis, A.; De Bruyn, K.; De Capua, S.; De Cian, M.; De Miranda, J. M.; De Paula, L.; De Simone, P.; Dean, C.-T.; Decamp, D.; Deckenhoff, M.; Del Buono, L.; Déléage, N.; Demmer, M.; Derkach, D.; Deschamps, O.; Dettori, F.; Dey, B.; Di Canto, A.; Di Ruscio, F.; Dijkstra, H.; Donleavy, S.; Dordei, F.; Dorigo, M.; Dosil Suárez, A.; Dossett, D.; Dovbnya, A.; Dreimanis, K.; Dufour, L.; Dujany, G.; Dupertuis, F.; Durante, P.; Dzhelyadin, R.; Dziurda, A.; Dzyuba, A.; Easo, S.; Egede, U.; Egorychev, V.; Eidelman, S.; Eisenhardt, S.; Eitschberger, U.; Ekelhof, R.; Eklund, L.; El Rifai, I.; Elsasser, Ch.; Ely, S.; Esen, S.; Evans, H. M.; Evans, T.; Falabella, A.; Färber, C.; Farinelli, C.; Farley, N.; Farry, S.; Fay, R.; Ferguson, D.; Fernandez Albor, V.; Ferrari, F.; Ferreira Rodrigues, F.; Ferro-Luzzi, M.; Filippov, S.; Fiore, M.; Fiorini, M.; Firlej, M.; Fitzpatrick, C.; Fiutowski, T.; Fohl, K.; Fol, P.; Fontana, M.; Fontanelli, F.; Forty, R.; Francisco, O.; Frank, M.; Frei, C.; Frosini, M.; Fu, J.; Furfaro, E.; Gallas Torreira, A.; Galli, D.; Gallorini, S.; Gambetta, S.; Gandelman, M.; Gandini, P.; Gao, Y.; García Pardiñas, J.; Garra Tico, J.; Garrido, L.; Gascon, D.; Gaspar, C.; Gauld, R.; Gavardi, L.; Gazzoni, G.; Geraci, A.; Gerick, D.; Gersabeck, E.; Gersabeck, M.; Gershon, T.; Ghez, Ph.; Gianelle, A.; Gianì, S.; Gibson, V.; Girard, O. G.; Giubega, L.; Gligorov, V. V.; Göbel, C.; Golubkov, D.; Golutvin, A.; Gomes, A.; Gotti, C.; Grabalosa Gándara, M.; Graciani Diaz, R.; Granado Cardoso, L. A.; Graugés, E.; Graverini, E.; Graziani, G.; Grecu, A.; Greening, E.; Gregson, S.; Griffith, P.; Grillo, L.; Grünberg, O.; Gui, B.; Gushchin, E.; Guz, Yu.; Gys, T.; Hadavizadeh, T.; Hadjivasiliou, C.; Haefeli, G.; Haen, C.; Haines, S. C.; Hall, S.; Hamilton, B.; Han, X.; Hansmann-Menzemer, S.; Harnew, N.; Harnew, S. T.; Harrison, J.; He, J.; Head, T.; Heijne, V.; Hennessy, K.; Henrard, P.; Henry, L.; Hernando Morata, J. A.; van Herwijnen, E.; Heß, M.; Hicheur, A.; Hill, D.; Hoballah, M.; Hombach, C.; Hulsbergen, W.; Humair, T.; Hussain, N.; Hutchcroft, D.; Hynds, D.; Idzik, M.; Ilten, P.; Jacobsson, R.; Jaeger, A.; Jalocha, J.; Jans, E.; Jawahery, A.; Jing, F.; John, M.; Johnson, D.; Jones, C. R.; Joram, C.; Jost, B.; Jurik, N.; Kandybei, S.; Kanso, W.; Karacson, M.; Karbach, T. M.; Karodia, S.; Kelsey, M.; Kenyon, I. R.; Kenzie, M.; Ketel, T.; Khanji, B.; Khurewathanakul, C.; Klaver, S.; Klimaszewski, K.; Kochebina, O.; Kolpin, M.; Komarov, I.; Koopman, R. F.; Koppenburg, P.; Kozeiha, M.; Kravchuk, L.; Kreplin, K.; Kreps, M.; Krocker, G.; Krokovny, P.; Kruse, F.; Kucewicz, W.; Kucharczyk, M.; Kudryavtsev, V.; Kuonen, A. K.; Kurek, K.; Kvaratskheliya, T.; Lacarrere, D.; Lafferty, G.; Lai, A.; Lambert, D.; Lanfranchi, G.; Langenbruch, C.; Langhans, B.; Latham, T.; Lazzeroni, C.; Le Gac, R.; van Leerdam, J.; Lees, J.-P.; Lefèvre, R.; Leflat, A.; Lefrançois, J.; Leroy, O.; Lesiak, T.; Leverington, B.; Li, Y.; Likhomanenko, T.; Liles, M.; Lindner, R.; Linn, C.; Lionetto, F.; Liu, B.; Liu, X.; Loh, D.; Lohn, S.; Longstaff, I.; Lopes, J. H.; Lucchesi, D.; Lucio Martinez, M.; Luo, H.; Lupato, A.; Luppi, E.; Lupton, O.; Lusardi, N.; Machefert, F.; Maciuc, F.; Maev, O.; Maguire, K.; Malde, S.; Malinin, A.; Manca, G.; Mancinelli, G.; Manning, P.; Mapelli, A.; Maratas, J.; Marchand, J. F.; Marconi, U.; Marin Benito, C.; Marino, P.; Märki, R.; Marks, J.; Martellotti, G.; Martin, M.; Martinelli, M.; Martinez Santos, D.; Martinez Vidal, F.; Martins Tostes, D.; Massafferri, A.; Matev, R.; Mathad, A.; Mathe, Z.; Matteuzzi, C.; Matthieu, K.; Mauri, A.; Maurin, B.; Mazurov, A.; McCann, M.; McCarthy, J.; McNab, A.; McNulty, R.; Meadows, B.; Meier, F.; Meissner, M.; Melnychuk, D.; Merk, M.; Milanes, D. A.; Minard, M.-N.; Mitzel, D. S.; Molina Rodriguez, J.; Monroy, I. A.; Monteil, S.; Morandin, M.; Morawski, P.; Mordà, A.; Morello, M. J.; Moron, J.; Morris, A. B.; Mountain, R.; Muheim, F.; Müller, J.; Müller, K.; Müller, V.; Mussini, M.; Muster, B.; Naik, P.; Nakada, T.; Nandakumar, R.; Nandi, A.; Nasteva, I.; Needham, M.; Neri, N.; Neubert, S.; Neufeld, N.; Neuner, M.; Nguyen, A. D.; Nguyen, T. D.; Nguyen-Mau, C.; Niess, V.; Niet, R.; Nikitin, N.; Nikodem, T.; Ninci, D.; Novoselov, A.; O'Hanlon, D. P.; Oblakowska-Mucha, A.; Obraztsov, V.; Ogilvy, S.; Okhrimenko, O.; Oldeman, R.; Onderwater, C. J. G.; Osorio Rodrigues, B.; Otalora Goicochea, J. M.; Otto, A.; Owen, P.; Oyanguren, A.; Palano, A.; Palombo, F.; Palutan, M.; Panman, J.; Papanestis, A.; Pappagallo, M.; Pappalardo, L. L.; Pappenheimer, C.; Parkes, C.; Passaleva, G.; Patel, G. D.; Patel, M.; Patrignani, C.; Pearce, A.; Pellegrino, A.; Penso, G.; Pepe Altarelli, M.; Perazzini, S.; Perret, P.; Pescatore, L.; Petridis, K.; Petrolini, A.; Petruzzo, M.; Picatoste Olloqui, E.; Pietrzyk, B.; Pilař, T.; Pinci, D.; Pistone, A.; Piucci, A.; Playfer, S.; Plo Casasus, M.; Poikela, T.; Polci, F.; Poluektov, A.; Polyakov, I.; Polycarpo, E.; Popov, A.; Popov, D.; Popovici, B.; Potterat, C.; Price, E.; Price, J. D.; Prisciandaro, J.; Pritchard, A.; Prouve, C.; Pugatch, V.; Puig Navarro, A.; Punzi, G.; Qian, W.; Quagliani, R.; Rachwal, B.; Rademacker, J. H.; Rama, M.; Rangel, M. S.; Raniuk, I.; Rauschmayr, N.; Raven, G.; Redi, F.; Reichert, S.; Reid, M. M.; dos Reis, A. C.; Ricciardi, S.; Richards, S.; Rihl, M.; Rinnert, K.; Rives Molina, V.; Robbe, P.; Rodrigues, A. B.; Rodrigues, E.; Rodriguez Lopez, J. A.; Rodriguez Perez, P.; Roiser, S.; Romanovsky, V.; Romero Vidal, A.; Ronayne, J. W.; Rotondo, M.; Rouvinet, J.; Ruf, T.; Ruiz, H.; Ruiz Valls, P.; Saborido Silva, J. J.; Sagidova, N.; Sail, P.; Saitta, B.; Salustino Guimaraes, V.; Sanchez Mayordomo, C.; Sanmartin Sedes, B.; Santacesaria, R.; Santamarina Rios, C.; Santimaria, M.; Santovetti, E.; Sarti, A.; Satriano, C.; Satta, A.; Saunders, D. M.; Savrina, D.; Schiller, M.; Schindler, H.; Schlupp, M.; Schmelling, M.; Schmelzer, T.; Schmidt, B.; Schneider, O.; Schopper, A.; Schubiger, M.; Schune, M.-H.; Schwemmer, R.; Sciascia, B.; Sciubba, A.; Semennikov, A.; Serra, N.; Serrano, J.; Sestini, L.; Seyfert, P.; Shapkin, M.; Shapoval, I.; Shcheglov, Y.; Shears, T.; Shekhtman, L.; Shevchenko, V.; Shires, A.; Siddi, B. G.; Silva Coutinho, R.; Simi, G.; Sirendi, M.; Skidmore, N.; Skillicorn, I.; Skwarnicki, T.; Smith, E.; Smith, E.; Smith, I. T.; Smith, J.; Smith, M.; Snoek, H.; Sokoloff, M. D.; Soler, F. J. P.; Soomro, F.; Souza, D.; Souza De Paula, B.; Spaan, B.; Spradlin, P.; Sridharan, S.; Stagni, F.; Stahl, M.; Stahl, S.; Steinkamp, O.; Stenyakin, O.; Sterpka, F.; Stevenson, S.; Stoica, S.; Stone, S.; Storaci, B.; Stracka, S.; Straticiuc, M.; Straumann, U.; Sun, L.; Sutcliffe, W.; Swientek, K.; Swientek, S.; Syropoulos, V.; Szczekowski, M.; Szczypka, P.; Szumlak, T.; T'Jampens, S.; Tayduganov, A.; Tekampe, T.; Teklishyn, M.; Tellarini, G.; Teubert, F.; Thomas, C.; Thomas, E.; van Tilburg, J.; Tisserand, V.; Tobin, M.; Todd, J.; Tolk, S.; Tomassetti, L.; Tonelli, D.; Topp-Joergensen, S.; Torr, N.; Tournefier, E.; Tourneur, S.; Trabelsi, K.; Tran, M. T.; Tresch, M.; Trisovic, A.; Tsaregorodtsev, A.; Tsopelas, P.; Tuning, N.; Ukleja, A.; Ustyuzhanin, A.; Uwer, U.; Vacca, C.; Vagnoni, V.; Valenti, G.; Vallier, A.; Vazquez Gomez, R.; Vazquez Regueiro, P.; Vázquez Sierra, C.; Vecchi, S.; Velthuis, J. J.; Veltri, M.; Veneziano, G.; Vesterinen, M.; Viaud, B.; Vieira, D.; Diaz, M. Vieites; Vilasis-Cardona, X.; Vollhardt, A.; Volyanskyy, D.; Voong, D.; Vorobyev, A.; Vorobyev, V.; Voß, C.; de Vries, J. A.; Waldi, R.; Wallace, C.; Wallace, R.; Walsh, J.; Wandernoth, S.; Wang, J.; Ward, D. R.; Watson, N. K.; Websdale, D.; Weiden, A.; Whitehead, M.; Wilkinson, G.; Wilkinson, M.; Williams, M.; Williams, M. P.; Williams, M.; Williams, T.; Wilson, F. F.; Wimberley, J.; Wishahi, J.; Wislicki, W.; Witek, M.; Wormser, G.; Wotton, S. A.; Wright, S.; Wyllie, K.; Xie, Y.; Xu, Z.; Yang, Z.; Yu, J.; Yuan, X.; Yushchenko, O.; Zangoli, M.; Zavertyaev, M.; Zhang, L.; Zhang, Y.; Zhelezov, A.; Zhokhov, A.; Zhong, L.; Zucchelli, S.

    2015-09-01

    An angular analysis and a measurement of the differential branching fraction of the decay B s 0 → ϕμ + μ - are presented, using data corresponding to an integrated luminosity of 3 .0 fb-1 of pp collisions recorded by the LHCb experiment at √{s}=7 and 8 TeV. Measurements are reported as a function of q 2, the square of the dimuon invariant mass and results of the angular analysis are found to be consistent with the Standard Model. In the range 1 < q 2 < 6 GeV2 /c 4, where precise theoretical calculations are available, the differential branching fraction is found to be more than 3 σ below the Standard Model predictions. [Figure not available: see fulltext.

  2. Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method

    NASA Astrophysics Data System (ADS)

    Akbari, M. R.; Ganji, D. D.; Ahmadi, A. R.; Kachapi, Sayyid H. Hashemi

    2014-03-01

    In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

  3. Investigation of magnesium isotope fractionation during basalt differentiation: Implications for a chondritic composition of the terrestrial mantle

    USGS Publications Warehouse

    Teng, F.-Z.; Wadhwa, M.; Helz, R.T.

    2007-01-01

    To investigate whether magnesium isotopes are fractionated during basalt differentiation, we have performed high-precision Mg isotopic analyses by multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS) on a set of well-characterized samples from Kilauea Iki lava lake, Hawaii, USA. Samples from the Kilauea Iki lava lake, produced by closed-system crystal-melt fractionation, range from olivine-rich cumulates to highly differentiated basalts with MgO content ranging from 2.37 to 26.87??wt.%. Our results demonstrate that although these basalts have diverse chemical compositions, mineralogies, crystallization temperatures and degrees of differentiation, their Mg isotopic compositions display no measurable variation within the limits of our external precision (average ??26Mg = - 0.36 ?? 0.10 and ??25Mg = - 0.20 ?? 0.07; uncertainties are 2SD). This indicates that Mg isotopic fractionation during crystal-melt fractionation at temperatures of ??? 1055????C is undetectable at the level of precision of the current investigation. Calculations based on our data suggest that at near-magmatic temperatures the maximum fractionation in the 26Mg/24Mg ratio between olivine and melt is 0.07???. Two additional oceanic basalts, two continental basalts (BCR-1 and BCR-2), and two primitive carbonaceous chondrites (Allende and Murchison) analyzed in this study have Mg isotopic compositions similar to the Kilauea Iki lava lake samples. In contrast to a recent report [U. Wiechert, A.N. Halliday, Non-chondritic magnesium and the origins of the inner terrestrial planets, Earth and Planetary Science Letters 256 (2007) 360-371], the results presented here suggest that the Bulk Silicate Earth has a chondritic Mg isotopic composition. ?? 2007.

  4. Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV Equation

    NASA Astrophysics Data System (ADS)

    İsmail, Aslan

    2014-05-01

    The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before.

  5. An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method.

    PubMed

    Xie, Lie-Jun; Zhou, Cai-Lian; Xu, Song

    2016-01-01

    In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian polynomials to handle the differential transforms of the nonlinearities arising in the given differential equation. The relation between the Adomian polynomials of those nonlinear functions and the coefficients of unknown truncated series solution is given by a simple formula, through which one can easily deduce the approximate solution which takes the form of a convergent series. An upper bound for the estimation of approximate error is presented. Several physical problems are discussed as illustrative examples to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods. PMID:27462514

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

    NASA Astrophysics Data System (ADS)

    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.

  7. An efficient algorithm for solving fractional differential equations with boundary conditions

    NASA Astrophysics Data System (ADS)

    Alkan, Sertan; Yildirim, Kenan; Secer, Aydin

    2016-01-01

    In this paper, a sinc-collocation method is described to determine the approximate solution of fractional order boundary value problem (FBVP). The results obtained are presented as two new theorems. The fractional derivatives are defined in the Caputo sense, which is often used in fractional calculus. In order to demonstrate the efficiency and capacity of the present method, it is applied to some FBVP with variable coefficients. Obtained results are compared to exact solutions as well as Cubic Spline solutions. The comparisons can be used to conclude that sinc-collocation method is powerful and promising method for determining the approximate solutions of FBVPs in different types of scenarios.

  8. Exact solution to fractional logistic equation

    NASA Astrophysics Data System (ADS)

    West, Bruce J.

    2015-07-01

    The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.

  9. Iron, zinc, magnesium and uranium isotopic fractionation during continental crust differentiation: The tale from migmatites, granitoids, and pegmatites

    NASA Astrophysics Data System (ADS)

    Telus, Myriam; Dauphas, Nicolas; Moynier, Frédéric; Tissot, François L. H.; Teng, Fang-Zhen; Nabelek, Peter I.; Craddock, Paul R.; Groat, Lee A.

    2012-11-01

    The causes of some stable isotopic variations in felsic rocks are not well understood. In particular, the origin of the heavy Fe isotopic compositions (i.e., high δ56Fe values, deviation in ‰ of the 56Fe/54Fe ratio relative to IRMM-014) of granites with SiO2 > 70 wt.% compared with less silicic rocks is still debated. It has been interpreted to reflect isotopic fractionation during late stage aqueous fluid exsolution, magma differentiation, partial melting, or Soret (thermal) diffusion. The present study addresses this issue by comparing the Fe isotopic compositions of a large range of differentiated crustal rocks (whole rocks of migmatites, granitoids, and pegmatites; mineral separates) with the isotopic compositions of Zn, Mg and U. The samples include granites, migmatites and pegmatites from the Black Hills, South Dakota (USA), as well as I-, S-, and A-type granitoids from Lachlan Fold Belt (Australia). The nature of the protolith (i.e., I- or S-type) does not influence the Fe isotopic composition of granitoids. Leucosomes (partial melts in migmatites) tend to have higher δ56Fe values than melanosomes (melt residues) indicating that partial melting of continental crust material can possibly fractionate Fe isotopes. No clear positive correlation is found between the isotopic compositions of Mg, U and Fe, which rules out the process of Soret diffusion in the systems studied here. Zinc isotopes were measured to trace fluid exsolution because Zn can easily be mobilized by aqueous fluids as chloride complexes. Pegmatites and some granitic rocks with high δ56Fe values also have high δ66Zn values. In addition, high-SiO2 granites show a large dispersion in the Zn/Fe ratio that cannot easily be explained by magma differentiation alone. These results suggest that fluid exsolution is responsible for some of the Fe isotopic fractionation documented in felsic rocks and in particular in pegmatites. However, some granites with high δ56Fe values have unfractionated δ66

  10. A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

    NASA Technical Reports Server (NTRS)

    Bartels, Robert E.

    2002-01-01

    A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

  11. Similarity solutions of nonlinear partial differential equations invariant to a family of affine groups

    SciTech Connect

    Dresner, L.

    1987-08-01

    Problems of technological interest can very often be described by partial differential equations (PDEs) with one dependent and two independent variables (call them c, z, and t, respectively). Many such PDEs are invariant to one-parameter families of one-parameter affine groups. Similarity solutions are solutions of the PDE that are invariant to one group of the family. The great utility of similarity solutions is that they may be calculated by solving an ODE rather than a PDE and are thus much more easily accessible than other solutions. The form of the principal ODE depends, of course, on the form of the PDE, but it can be proved quite generally that the principal ODE is itself invarient to the one-parameter affine group or associated group. because of the invariance of the principal ODE to the associated group, the dependence on the boundary and initial conditions of certain special values of the function y(x), e.g., y(O), y(infinity), y(O), ets., may be predicted a priori without solving the principal ODE. The nonlinear PDE of heat transport in superfluid He-II, is used as an illustration of these ideas in this review.

  12. Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Bogdan, V. M.; Bond, V. B.

    1980-01-01

    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

  13. Finger tapping movements of Parkinson's disease patients automatically rated using nonlinear delay differential equations

    NASA Astrophysics Data System (ADS)

    Lainscsek, C.; Rowat, P.; Schettino, L.; Lee, D.; Song, D.; Letellier, C.; Poizner, H.

    2012-03-01

    Parkinson's disease is a degenerative condition whose severity is assessed by clinical observations of motor behaviors. These are performed by a neurological specialist through subjective ratings of a variety of movements including 10-s bouts of repetitive finger-tapping movements. We present here an algorithmic rating of these movements which may be beneficial for uniformly assessing the progression of the disease. Finger-tapping movements were digitally recorded from Parkinson's patients and controls, obtaining one time series for every 10 s bout. A nonlinear delay differential equation, whose structure was selected using a genetic algorithm, was fitted to each time series and its coefficients were used as a six-dimensional numerical descriptor. The algorithm was applied to time-series from two different groups of Parkinson's patients and controls. The algorithmic scores compared favorably with the unified Parkinson's disease rating scale scores, at least when the latter adequately matched with ratings from the Hoehn and Yahr scale. Moreover, when the two sets of mean scores for all patients are compared, there is a strong (r = 0.785) and significant (p <0.0015) correlation between them.

  14. Sonicated Protein Fractions of Mycoplasma hyopneumoniae Induce Inflammatory Responses and Differential Gene Expression in a Murine Alveolar Macrophage Cell Line.

    PubMed

    Damte, Dereje; Lee, Seung-Jin; Birhanu, Biruk Tesfaye; Suh, Joo-Won; Park, Seung-Chun

    2015-12-28

    Mycoplasma hyopneumoniae is known to cause porcine enzootic pneumonia (EP), an important disease in swine production. The objective of this study was to examine the effects of sonicated protein fractions of M. hyopneumoniae on inflammatory response and gene expression in the murine alveolar macrophage MH-S cell line. The effects of sonicated protein fractions and intact M. hyopneumoniae on the gene expression of cytokines and iNOS were assessed using RT-PCR. The Annealing Control Primer (ACP)-based PCR method was used to screen differentially expressed genes. Increased transcription of interleukin (IL)-1β, IL-6, tumor necrosis factor (TNF)-α, COX-2, and iNOS mRNA was observed after exposure to the supernatant (SPT), precipitant (PPT), and intact M. hyopneumoniae protein. A time-dependent analysis of the mRNA expression revealed an upregulation after 4 h for IL-6 and iNOS and after 12 h for IL-1β and TNF-α, for both SPT and PPT; the fold change in COX-2 expression was less. A dose- and time-dependent correlation was observed in nitrite (NO) production for both protein fractions; however, there was no significant difference between the effects of the two protein fractions. In a differential gene analysis, PCR revealed differential expression for nine gene bands after 3 h of stimulation - only one gene was downregulated, while the remaining eight were upregulated. The results of this study provide insights that help improve our understanding of the mechanisms underlying the pathogenesis of and macrophage defenses against M. hyopneumoniae assault, and suggest targets for future studies on therapeutic interventions for M. hyopneumoniae infections. PMID:26370797

  15. Exact solutions of the time-fractional Fisher equation by using modified trial equation method

    NASA Astrophysics Data System (ADS)

    Tandogan, Yusuf Ali; Bildik, Necdet

    2016-06-01

    In this study, modified trial equation method has been proposed to obtain precise solutions of nonlinear fractional differential equation. Using the modified test equation method, we obtained some new exact solutions of the time fractional nonlinear Fisher equation. The obtained results are classified as a soliton solution, singular solutions, rational function solutions and periodic solutions.

  16. Variable-order fractional numerical differentiation for noisy signals by wavelet denoising

    NASA Astrophysics Data System (ADS)

    Chen, Yi-Ming; Wei, Yan-Qiao; Liu, Da-Yan; Boutat, Driss; Chen, Xiu-Kai

    2016-04-01

    In this paper, a numerical method is proposed to estimate the variable-order fractional derivatives of an unknown signal in noisy environment. Firstly, the wavelet denoising process is adopted to reduce the noise effect for the signal. Secondly, polynomials are constructed to fit the denoised signal in a set of overlapped subintervals of a considered interval. Thirdly, the variable-order fractional derivatives of these fitting polynomials are used as the estimations of the unknown ones, where the values obtained near the boundaries of each subinterval are ignored in the overlapped parts. Finally, numerical examples are presented to demonstrate the efficiency and robustness of the proposed method.

  17. Robust variable selection method for nonparametric differential equation models with application to nonlinear dynamic gene regulatory network analysis.

    PubMed

    Lu, Tao

    2016-01-01

    The gene regulation network (GRN) evaluates the interactions between genes and look for models to describe the gene expression behavior. These models have many applications; for instance, by characterizing the gene expression mechanisms that cause certain disorders, it would be possible to target those genes to block the progress of the disease. Many biological processes are driven by nonlinear dynamic GRN. In this article, we propose a nonparametric differential equation (ODE) to model the nonlinear dynamic GRN. Specially, we address following questions simultaneously: (i) extract information from noisy time course gene expression data; (ii) model the nonlinear ODE through a nonparametric smoothing function; (iii) identify the important regulatory gene(s) through a group smoothly clipped absolute deviation (SCAD) approach; (iv) test the robustness of the model against possible shortening of experimental duration. We illustrate the usefulness of the model and associated statistical methods through a simulation and a real application examples. PMID:26098537

  18. Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

    NASA Technical Reports Server (NTRS)

    Morozov, S. K.; Krasitskiy, O. P.

    1978-01-01

    A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

  19. A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games.

    PubMed

    He, Feng; Zhang, Wei; Zhang, Guoqiang

    2016-01-01

    A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful. PMID:27589229

  20. Phosphorus fractionation diagram as a quantitative indicator of crystallization differentiation of basaltic liquids

    USGS Publications Warehouse

    Anderson, A.T.; Greenland, L.P.

    1969-01-01

    Distribution factors of phosphorus (P in mineral/P in liquid) between phenocryst minerals and coexisting basaltic groundmass are: olivine (Fa20: 0.04 to 0.02; orthopyroxene (Fs20): 0.01; augite: 0.02 to 0.01; plagioclase: 0.02; ilmenite: 0.04. Because of the smallness of these distribution factors the ratio of phosphorus in the initial liquid to that in the residual liquid (phosphorus ratio) ideally equals the mass fraction of residual liquid minus 0.00 -0.04. The phosphorus ratio facilitates, therefore, quantitative comparison of the variation of major and minor elements with crystallization of basaltic liquids. A phosphorus fractionation diagram is a log-log graph of the wt. % of any chemical element or oxide vs. the phosphorus ratio. The slopes of variation curves on such a fractionation diagram approximately equal unity minus the crystal aggregate/liquid distribution factor. Knowledge of the individual mineral/liquid distribution factors makes it possible to estimate the relative proportions of crystallizing minerals from the slopes of curves on a phosphorus fractionation diagram prior to the crystallization of apatite or other phosphorus-rich mineral. This was done fairly successfully for the Alae Lava Lake, Hawaii. ?? 1969.

  1. Differential Response of Human Nasal and Bronchial Epithelial Cells upon Exposure to Size-fractionated Dairy Dust

    PubMed Central

    Hawley, Brie; Schaeffer, Joshua; Poole, Jill A.; Dooley, Gregory P.; Reynolds, Stephen; Volckens, John

    2015-01-01

    Exposure to organic dusts is associated with increased respiratory morbidity and mortality in agricultural workers. Organic dusts in dairy farm environments are complex, polydisperse mixtures of toxic and immunogenic compounds. Previous toxicological studies focused primarily on exposures to the respirable size fraction, however, organic dusts in dairy farm environments are known to contain larger particles. Given the size distribution of dusts from dairy farm environments, the nasal and bronchial epithelia represent targets of agricultural dust exposures. In this study, well-differentiated normal human bronchial epithelial cells and human nasal epithelial cells were exposed to two different size fractions (PM10 and PM>10) of dairy parlor dust using a novel aerosol-to-cell exposure system. Levels of pro-inflammatory transcripts (IL-8, IL-6, and TNF-α) were measured two hr after exposure. Lactate dehydrogenase (LDH) release was also measured as an indicator of cytotoxicity. Cell exposure to dust was measured in each size fraction as a function of mass, endotoxin, and muramic acid levels. To our knowledge, this is the first study to evaluate the effects of distinct size fractions of agricultural dust on human airway epithelial cells. Our results suggest that both PM10 and PM>10 size fractions elicit a pro-inflammatory response in airway epithelial cells and that the entire inhalable size fraction needs to be considered when assessing potential risks from exposure to agricultural dusts. Further, data suggest that human bronchial cells respond differently to these dusts than human nasal cells and, therefore, the two cell types need to be considered separately in airway cell models of agricultural dust toxicity. PMID:25965193

  2. Spatially dependent parameter estimation and nonlinear data assimilation by autosynchronization of a system of partial differential equations

    NASA Astrophysics Data System (ADS)

    Kramer, Sean; Bollt, Erik M.

    2013-09-01

    Given multiple images that describe chaotic reaction-diffusion dynamics, parameters of a partial differential equation (PDE) model are estimated using autosynchronization, where parameters are controlled by synchronization of the model to the observed data. A two-component system of predator-prey reaction-diffusion PDEs is used with spatially dependent parameters to benchmark the methods described. Applications to modeling the ecological habitat of marine plankton blooms by nonlinear data assimilation through remote sensing are discussed.

  3. Construction of the first-order stochastic nonlinear differential equations in the modeling of stimulated scattering of optical fields

    NASA Astrophysics Data System (ADS)

    Babin, Vasile D.; Grigore, Maria; Cojocaru, Laurentiu; Ersen, Simion; Moldovan, Adrian

    1998-07-01

    In this work we use a technique inspired by the inverse problem in the scattering theory, that is, the calculation of partial derivatives along the characteristic directions of the D'Alembert solution of the wave equation (Maxwell and Euler). In this way, we construct a system of stochastic non-linear differential equations. The analysis of this system, using algebraic invariants, gives more information in comparison with that given by Ghelfand-Levitan-Marcenko, in the inverse problem in the scattering theory.

  4. Nonlinear current-voltage characteristics and enhanced negative differential conductance in graphene field effect transistors

    NASA Astrophysics Data System (ADS)

    Wang, Lin; Chen, Xiaoshuang; Hu, Yibin; Yu, Anqi; Lu, Wei

    2014-10-01

    Recent observations of the negative differential conductance (NDC) phenomenon in graphene field-effect transistors (FET) open up new opportunities for their application in graphene-based fast switches, frequency multipliers and, most importantly, in high frequency oscillators up to the terahertz regime. Unlike conventional two-terminal NDC devices that rely on resonant tunneling and inter-valley transferring, in the present work, it has been shown that the universal NDC phenomenon of graphene-based FETs originates from their intrinsic nonlinear carrier transport under a strong electric field. The operation of graphene-NDC devices depends strongly on the interface between graphene and dielectric materials, the scattering-limited carrier mobility, and on the saturation velocity. To reveal such NDC behavior, the output characteristics of GFET are investigated rigorously, with both an analytical model and self-consistent transport equation, and with a multi-electrical parameter simulation. It is demonstrated that the contact-induced doping effect plays an important role in the operational efficiency of graphene-based NDC devices, rather than the ambipolar behavior associated with the competition between electron and hole conductances. In the absence of a NDC regime or beyond one, ambipolar transport starts at Vds > 2Vgs at the drain end, and as the dielectric layer begins to thin down, the kink-like saturation output characteristic is enhanced by the quantum capacitance contribution. These observations reveal the intrinsic mechanism of the NDC effect and open up new opportunities for the performance improvement of GFETs in future high-frequency applications, beyond the current paradigm based on two-terminal diodes.Recent observations of the negative differential conductance (NDC) phenomenon in graphene field-effect transistors (FET) open up new opportunities for their application in graphene-based fast switches, frequency multipliers and, most importantly, in high

  5. Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models

    PubMed Central

    Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

    2016-01-01

    Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization. PMID:27243005

  6. Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

    PubMed

    Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

    2016-01-01

    Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization. PMID:27243005

  7. Effect of a standardized liver and spleen fraction of peptides on the differentiation of human monocyte-derived macrophages.

    PubMed

    Spessotto, P; Bulla, R; Mittenzwei, H; Dri, P

    1994-06-01

    The effect of Factor AF2 (AF2), a standardized fraction of peptides with a molecular weight of < 10,000 Dalton obtained from livers and spleens of newborn lambs, on the differentiation of human monocyte-derived macrophages was studied, in view of the central role played by these cells in inflammation and tumor cytotoxicity. The results show that the drug 1. increases the cell density of cultures, 2. favours the morphologic differentiation of monocytes into macrophages, and 3. increases the macrophages phagocytic capacity. The first two effects are observed when monocytes are cultured in 1% serum but not in 10% serum while the enhancement of phagocytic activity is detected at both serum concentrations. PMID:8053979

  8. Differential branching fraction and angular analysis of the decay B0 → K*0 μ+ μ-.

    PubMed

    Aaij, R; Abellan Beteta, C; Adeva, B; Adinolfi, M; Adrover, C; Affolder, A; Ajaltouni, Z; Albrecht, J; Alessio, F; Alexander, M; Alkhazov, G; Alvarez Cartelle, P; Alves, A A; Amato, S; Amhis, Y; Anderson, J; Appleby, R B; Aquines Gutierrez, O; Archilli, F; Arrabito, L; Artamonov, A; Artuso, M; Aslanides, E; Auriemma, G; Bachmann, S; Back, J J; Bailey, D S; Balagura, V; Baldini, W; Barlow, R J; Barschel, C; Barsuk, S; Barter, W; Bates, A; Bauer, C; Bauer, Th; Bay, A; Bediaga, I; Belogurov, S; Belous, K; Belyaev, I; Ben-Haim, E; Benayoun, M; Bencivenni, G; Benson, S; Benton, J; Bernet, R; Bettler, M-O; van Beuzekom, M; Bien, A; Bifani, S; Bird, T; Bizzeti, A; Bjørnstad, P M; Blake, T; Blanc, F; Blanks, C; Blouw, J; Blusk, S; Bobrov, A; Bocci, V; Bondar, A; Bondar, N; Bonivento, W; Borghi, S; Borgia, A; Bowcock, T J V; Bozzi, C; Brambach, T; van den Brand, J; Bressieux, J; Brett, D; Britsch, M; Britton, T; Brook, N H; Brown, H; Büchler-Germann, A; Burducea, I; Bursche, A; Buytaert, J; Cadeddu, S; Callot, O; Calvi, M; Calvo Gomez, M; Camboni, A; Campana, P; Carbone, A; Carboni, G; Cardinale, R; Cardini, A; Carson, L; Carvalho Akiba, K; Casse, G; Cattaneo, M; Cauet, Ch; Charles, M; Charpentier, Ph; Chiapolini, N; Ciba, K; Cid Vidal, X; Ciezarek, G; Clarke, P E L; Clemencic, M; Cliff, H V; Closier, J; Coca, C; Coco, V; Cogan, J; Collins, P; Comerma-Montells, A; Constantin, F; Contu, A; Cook, A; Coombes, M; Corti, G; Cowan, G A; Currie, R; D'Ambrosio, C; David, P; David, P N Y; De Bonis, I; De Capua, S; De Cian, M; De Lorenzi, F; De Miranda, J M; De Paula, L; De Simone, P; Decamp, D; Deckenhoff, M; Degaudenzi, H; Del Buono, L; Deplano, C; Derkach, D; Deschamps, O; Dettori, F; Dickens, J; Dijkstra, H; Diniz Batista, P; Domingo Bonal, F; Donleavy, S; Dordei, F; Dosil Suárez, A; Dossett, D; Dovbnya, A; Dupertuis, F; Dzhelyadin, R; Dziurda, A; Easo, S; Egede, U; Egorychev, V; Eidelman, S; van Eijk, D; Eisele, F; Eisenhardt, S; Ekelhof, R; Eklund, L; Elsasser, Ch; Elsby, D; Esperante Pereira, D; Estève, L; Falabella, A; Fanchini, E; Färber, C; Fardell, G; Farinelli, C; Farry, S; Fave, V; Fernandez Albor, V; Ferro-Luzzi, M; Filippov, S; Fitzpatrick, C; Fontana, M; Fontanelli, F; Forty, R; Frank, M; Frei, C; Frosini, M; Furcas, S; Gallas Torreira, A; Galli, D; Gandelman, M; Gandini, P; Gao, Y; Garnier, J-C; Garofoli, J; Garra Tico, J; Garrido, L; Gascon, D; Gaspar, C; Gauvin, N; Gersabeck, M; Gershon, T; Ghez, Ph; Gibson, V; Gligorov, V V; Göbel, C; Golubkov, D; Golutvin, A; Gomes, A; Gordon, H; Grabalosa Gándara, M; Graciani Diaz, R; Granado Cardoso, L A; Graugés, E; Graziani, G; Grecu, A; Greening, E; Gregson, S; Gui, B; Gushchin, E; Guz, Yu; Gys, T; Haefeli, G; Haen, C; Haines, S C; Hampson, T; Hansmann-Menzemer, S; Harji, R; Harnew, N; Harrison, J; Harrison, P F; Hartmann, T; He, J; Heijne, V; Hennessy, K; Henrard, P; Hernando Morata, J A; van Herwijnen, E; Hicks, E; Holubyev, K; Hopchev, P; Hulsbergen, W; Hunt, P; Huse, T; Huston, R S; Hutchcroft, D; Hynds, D; Iakovenko, V; Ilten, P; Imong, J; Jacobsson, R; Jaeger, A; Jahjah Hussein, M; Jans, E; Jansen, F; Jaton, P; Jean-Marie, B; Jing, F; John, M; Johnson, D; Jones, C R; Jost, B; Kaballo, M; Kandybei, S; Karacson, M; Karbach, T M; Keaveney, J; Kenyon, I R; Kerzel, U; Ketel, T; Keune, A; Khanji, B; Kim, Y M; Knecht, M; Koppenburg, P; Kozlinskiy, A; Kravchuk, L; Kreplin, K; Kreps, M; Krocker, G; Krokovny, P; Kruse, F; Kruzelecki, K; Kucharczyk, M; Kvaratskheliya, T; La Thi, V N; Lacarrere, D; Lafferty, G; Lai, A; Lambert, D; Lambert, R W; Lanciotti, E; Lanfranchi, G; Langenbruch, C; Latham, T; Lazzeroni, C; Le Gac, R; van Leerdam, J; Lees, J-P; Lefèvre, R; Leflat, A; Lefrançois, J; Leroy, O; Lesiak, T; Li, L; Li Gioi, L; Lieng, M; Liles, M; Lindner, R; Linn, C; Liu, B; Liu, G; von Loeben, J; Lopes, J H; Lopez Asamar, E; Lopez-March, N; Lu, H; Luisier, J; Mac Raighne, A; Machefert, F; Machikhiliyan, I V; Maciuc, F; Maev, O; Magnin, J; Malde, S; Mamunur, R M D; Manca, G; Mancinelli, G; Mangiafave, N; Marconi, U; Märki, R; Marks, J; Martellotti, G; Martens, A; Martin, L; Martín Sánchez, A; Martinez Santos, D; Massafferri, A; Mathe, Z; Matteuzzi, C; Matveev, M; Maurice, E; Maynard, B; Mazurov, A; McGregor, G; McNulty, R; Meissner, M; Merk, M; Merkel, J; Messi, R; Miglioranzi, S; Milanes, D A; Minard, M-N; Molina Rodriguez, J; Monteil, S; Moran, D; Morawski, P; Mountain, R; Mous, I; Muheim, F; Müller, K; Muresan, R; Muryn, B; Muster, B; Musy, M; Mylroie-Smith, J; Naik, P; Nakada, T; Nandakumar, R; Nasteva, I; Nedos, M; Needham, M; Neufeld, N; Nguyen-Mau, C; Nicol, M; Niess, V; Nikitin, N; Nomerotski, A; Novoselov, A; Oblakowska-Mucha, A; Obraztsov, V; Oggero, S; Ogilvy, S; Okhrimenko, O; Oldeman, R; Orlandea, M; Otalora Goicochea, J M; Owen, P; Pal, K; Palacios, J; Palano, A; Palutan, M; Panman, J; Papanestis, A; Pappagallo, M; Parkes, C; Parkinson, C J; Passaleva, G; Patel, G D; Patel, M; Paterson, S K; Patrick, G N; Patrignani, C; Pavel-Nicorescu, C; Pazos Alvarez, A; Pellegrino, A; Penso, G; Pepe Altarelli, M; Perazzini, S; Perego, D L; Perez Trigo, E; Pérez-Calero Yzquierdo, A; Perret, P; Perrin-Terrin, M; Pessina, G; Petrella, A; Petrolini, A; Phan, A; Picatoste Olloqui, E; Pie Valls, B; Pietrzyk, B; Pilař, T; Pinci, D; Plackett, R; Playfer, S; Plo Casasus, M; Polok, G; Poluektov, A; Polycarpo, E; Popov, D; Popovici, B; Potterat, C; Powell, A; Prisciandaro, J; Pugatch, V; Puig Navarro, A; Qian, W; Rademacker, J H; Rakotomiaramanana, B; Rangel, M S; Raniuk, I; Raven, G; Redford, S; Reid, M M; dos Reis, A C; Ricciardi, S; Rinnert, K; Roa Romero, D A; Robbe, P; Rodrigues, E; Rodrigues, F; Rodriguez Perez, P; Rogers, G J; Roiser, S; Romanovsky, V; Rosello, M; Rouvinet, J; Ruf, T; Ruiz, H; Sabatino, G; Saborido Silva, J J; Sagidova, N; Sail, P; Saitta, B; Salzmann, C; Sannino, M; Santacesaria, R; Santamarina Rios, C; Santinelli, R; Santovetti, E; Sapunov, M; Sarti, A; Satriano, C; Satta, A; Savrie, M; Savrina, D; Schaack, P; Schiller, M; Schleich, S; Schlupp, M; Schmelling, M; Schmidt, B; Schneider, O; Schopper, A; Schune, M-H; Schwemmer, R; Sciascia, B; Sciubba, A; Seco, M; Semennikov, A; Senderowska, K; Sepp, I; Serra, N; Serrano, J; Seyfert, P; Shapkin, M; Shapoval, I; Shatalov, P; Shcheglov, Y; Shears, T; Shekhtman, L; Shevchenko, O; Shevchenko, V; Silva Coutinho, R; Shires, A; Skwarnicki, T; Smith, A C; Smith, N A; Smith, E; Sobczak, K; Soler, F J P; Solomin, A; Soomro, F; Souza De Paula, B; Spaan, B; Sparkes, A; Spradlin, P; Stagni, F; Stahl, S; Steinkamp, O; Stoica, S; Stone, S; Storaci, B; Straticiuc, M; Straumann, U; Subbiah, V K; Swientek, S; Szczekowski, M; Szczypka, P; Szumlak, T; T'Jampens, S; Teodorescu, E; Teubert, F; Thomas, C; Thomas, E; van Tilburg, J; Tisserand, V; Tobin, M; Topp-Joergensen, S; Torr, N; Tournefier, E; Tran, M T; Tsaregorodtsev, A; Tuning, N; Ubeda Garcia, M; Ukleja, A; Urquijo, P; Uwer, U; Vagnoni, V; Valenti, G; Vazquez Gomez, R; Vazquez Regueiro, P; Vecchi, S; Velthuis, J J; Veltri, M; Viaud, B; Videau, I; Vilasis-Cardona, X; Visniakov, J; Vollhardt, A; Volyanskyy, D; Voong, D; Vorobyev, A; Voss, H; Wandernoth, S; Wang, J; Ward, D R; Watson, N K; Webber, A D; Websdale, D; Whitehead, M; Wiedner, D; Wiggers, L; Wilkinson, G; Williams, M P; Williams, M; Wilson, F F; Wishahi, J; Witek, M; Witzeling, W; Wotton, S A; Wyllie, K; Xie, Y; Xing, F; Xing, Z; Yang, Z; Young, R; Yushchenko, O; Zavertyaev, M; Zhang, F; Zhang, L; Zhang, W C; Zhang, Y; Zhelezov, A; Zhong, L; Zverev, E; Zvyagin, A

    2012-05-01

    The angular distributions and the partial branching fraction of the decay B0 → K*0 μ+ μ- are studied by using an integrated luminosity of 0.37  fb(-1) of data collected with the LHCb detector. The forward-backward asymmetry of the muons, A(FB), the fraction of longitudinal polarization, F(L), and the partial branching fraction dB/dq2 are determined as a function of the dimuon invariant mass. The measurements are in good agreement with the standard model predictions and are the most precise to date. In the dimuon invariant mass squared range 1.00-6.00  GeV2/c4, the results are A(FB)=-0.06(-0.14)(+0.13)±0.04, F(L)=0.55±0.10±0.03, and dB/dq2=(0.42±0.06±0.03)×10(-7)  c4/GeV2. In each case, the first error is statistical and the second systematic. PMID:22681061

  9. A comparison/validation of a fractional derivative model with an empirical model of non-linear shock waves in swelling shales

    NASA Astrophysics Data System (ADS)

    Droghei, Riccardo; Salusti, Ettore

    2013-04-01

    Control of drilling parameters, as fluid pressure, mud weight, salt concentration is essential to avoid instabilities when drilling through shale sections. To investigate shale deformation, fundamental for deep oil drilling and hydraulic fracturing for gas extraction ("fracking"), a non-linear model of mechanic and chemo-poroelastic interactions among fluid, solute and the solid matrix is here discussed. The two equations of this model describe the isothermal evolution of fluid pressure and solute density in a fluid saturated porous rock. Their solutions are quick non-linear Burger's solitary waves, potentially destructive for deep operations. In such analysis the effect of diffusion, that can play a particular role in fracking, is investigated. Then, following Civan (1998), both diffusive and shock waves are applied to fine particles filtration due to such quick transients , their effect on the adjacent rocks and the resulting time-delayed evolution. Notice how time delays in simple porous media dynamics have recently been analyzed using a fractional derivative approach. To make a tentative comparison of these two deeply different methods,in our model we insert fractional time derivatives, i.e. a kind of time-average of the fluid-rocks interactions. Then the delaying effects of fine particles filtration is compared with fractional model time delays. All this can be seen as an empirical check of these fractional models.

  10. Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation

    NASA Astrophysics Data System (ADS)

    Rui, Wenjuan; Zhang, Xiangzhi

    2016-05-01

    This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.

  11. New 3D parallel GILD electromagnetic modeling and nonlinear inversion using global magnetic integral and local differential equation

    SciTech Connect

    Xie, G.; Li, J.; Majer, E.; Zuo, D.

    1998-07-01

    This paper describes a new 3D parallel GILD electromagnetic (EM) modeling and nonlinear inversion algorithm. The algorithm consists of: (a) a new magnetic integral equation instead of the electric integral equation to solve the electromagnetic forward modeling and inverse problem; (b) a collocation finite element method for solving the magnetic integral and a Galerkin finite element method for the magnetic differential equations; (c) a nonlinear regularizing optimization method to make the inversion stable and of high resolution; and (d) a new parallel 3D modeling and inversion using a global integral and local differential domain decomposition technique (GILD). The new 3D nonlinear electromagnetic inversion has been tested with synthetic data and field data. The authors obtained very good imaging for the synthetic data and reasonable subsurface EM imaging for the field data. The parallel algorithm has high parallel efficiency over 90% and can be a parallel solver for elliptic, parabolic, and hyperbolic modeling and inversion. The parallel GILD algorithm can be extended to develop a high resolution and large scale seismic and hydrology modeling and inversion in the massively parallel computer.

  12. Rapid differentiation of Ralstonia solanacearum avirulent and virulent strains by cell fractioning of an isolate using high performance liquid chromatography.

    PubMed

    Zheng, Xuefang; Zhu, Yujing; Liu, Bo; Yu, Qian; Lin, Naiquan

    2016-01-01

    Ralstonia solanacearum is one of the most destructive plant bacterial pathogens worldwide. The population dynamics and genetic stability are important issues, especially when an avirulent strain is used for biocontrol. In this study, we developed a rapid method to differentiate the virulent and avirulent strains of R. solanacearum and to predict the biocontrol efficiency of an avirulent strain using high performance liquid chromatography (HPLC). Three chromatographic peaks P1, P2 and P3 were observed on the HPLC spectra among 68 avirulent and 28 virulent R. solanacearum strains. Based on the HPLC peaks, 96 strains total were assigned to three categories. For avirulent strains, the intense peak is P1, while for virulent strains, P3 is the majority. Based on the HLPC spectra of R. solanacearum strains, a chromatography titer index (CTI) was established as CTIi = Si/(S1+S2+S3) × 100% (i represents an individual HPLC peak; S1, S2 and S3 represent peak areas of P1, P2 and P3, respectively). The avirulent strains had high values of CTI1 ranging from 63.6 to 100.0%, while the virulent strains displayed high values of CTI3 ranging from 90.2 to 100.0%. Biological inoculation studies of 68 avirulent strains revealed that the biocontrol efficacy was the best when CTI1 = 100%. The purity and genetic stability of R. solanacearum strains were confirmed in the P1 fraction of avirulent strain FJAT-1957 and P3 fraction of virulent strain FJAT-1925 after 30 generations of consecutive subculture. These results confirmed that fractioning by HPLC and their deduced CTI can be used for rapid and efficient evaluation and prediction of an isolate of R. solanacearum. To the best of our knowledge, this is the first report that HPLC fractioning can be used for rapid differentiation of virulent and avirulent strains of R. solanacearum. PMID:26606869

  13. Fractional active disturbance rejection control.

    PubMed

    Li, Dazi; Ding, Pan; Gao, Zhiqiang

    2016-05-01

    A fractional active disturbance rejection control (FADRC) scheme is proposed to improve the performance of commensurate linear fractional order systems (FOS) and the robust analysis shows that the controller is also applicable to incommensurate linear FOS control. In FADRC, the traditional extended states observer (ESO) is generalized to a fractional order extended states observer (FESO) by using the fractional calculus, and the tracking differentiator plus nonlinear state error feedback are replaced by a fractional proportional-derivative controller. To simplify controller tuning, the linear bandwidth-parameterization method has been adopted. The impacts of the observer bandwidth ωo and controller bandwidth ωc on system performance are then analyzed. Finally, the FADRC stability and frequency-domain characteristics for linear single-input single-output FOS are analyzed. Simulation results by FADRC and ADRC on typical FOS are compared to demonstrate the superiority and effectiveness of the proposed scheme. PMID:26928516

  14. The study of nonlinear almost periodic differential equations without recourse to the H-classes of these equations

    SciTech Connect

    Slyusarchuk, V. E. E-mail: V.Ye.Slyusarchuk@NUWM.rv.ua

    2014-06-01

    The well-known theorems of Favard and Amerio on the existence of almost periodic solutions to linear and nonlinear almost periodic differential equations depend to a large extent on the H-classes and the requirement that the bounded solutions of these equations be separated. The present paper provides different conditions for the existence of almost periodic solutions. These conditions, which do not depend on the H-classes of the equations, are formulated in terms of a special functional on the set of bounded solutions of the equations under consideration. This functional is used, in particular, to test whether solutions are separated. Bibliography: 24 titles. (paper)

  15. On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

    NASA Technical Reports Server (NTRS)

    Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

    1994-01-01

    It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

  16. Differential adaptation of the linear and nonlinear components of the horizontal vestibuloocular reflex in squirrel monkeys

    NASA Technical Reports Server (NTRS)

    Clendaniel, Richard A.; Lasker, David M.; Minor, Lloyd B.; Shelhamer, M. J. (Principal Investigator)

    2002-01-01

    Previous work in squirrel monkeys has demonstrated the presence of linear and nonlinear components to the horizontal vestibuloocular reflex (VOR) evoked by high-acceleration rotations. The nonlinear component is seen as a rise in gain with increasing velocity of rotation at frequencies more than 2 Hz (a velocity-dependent gain enhancement). We have shown that there are greater changes in the nonlinear than linear component of the response after spectacle-induced adaptation. The present study was conducted to determine if the two components of the response share a common adaptive process. The gain of the VOR, in the dark, to sinusoidal stimuli at 4 Hz (peak velocities: 20-150 degrees /s) and 10 Hz (peak velocities: 20 and 100 degrees /s) was measured pre- and postadaptation. Adaptation was induced over 4 h with x0.45 minimizing spectacles. Sum-of-sines stimuli were used to induce adaptation, and the parameters of the stimuli were adjusted to invoke only the linear or both linear and nonlinear components of the response. Preadaptation, there was a velocity-dependent gain enhancement at 4 and 10 Hz. In postadaptation with the paradigms that only recruited the linear component, there was a decrease in gain and a persistent velocity-dependent gain enhancement (indicating adaptation of only the linear component). After adaptation with the paradigm designed to recruit both the linear and nonlinear components, there was a decrease in gain and no velocity-dependent gain enhancement (indicating adaptation of both components). There were comparable changes in the response to steps of acceleration. We interpret these results to indicate that separate processes drive the adaptation of the linear and nonlinear components of the response.

  17. Comparison of three methods for fractionation and enrichment of low molecular weight proteins for SELDI-TOF-MS differential analysis.

    PubMed

    De Bock, Muriel; de Seny, Dominique; Meuwis, Marie-Alice; Servais, Anne-Catherine; Minh, Tran Quang; Closset, Jean; Chapelle, Jean-Paul; Louis, Edouard; Malaise, Michel; Merville, Marie-Paule; Fillet, Marianne

    2010-06-30

    In most diseases, the clinical need for serum/plasma markers has never been so crucial, not only for diagnosis, but also for the selection of the most efficient therapies, as well as exclusion of ineffective or toxic treatment. Due to the high sample complexity, prefractionation is essential for exploring the deep proteome and finding specific markers. In this study, three different sample preparation methods (i.e., highly abundant protein precipitation, restricted access materials (RAM) combined with IMAC chromatography and peptide ligand affinity beads) were investigated in order to select the best fractionation step for further differential proteomic experiments focusing on the LMW proteome (MW inferior to 40,000 Da). Indeed, the aim was not to cover the entire plasma/serum proteome, but to enrich potentially interesting tissue leakage proteins. These three methods were evaluated on their reproducibility, on the SELDI-TOF-MS peptide/protein peaks generated after fractionation and on the information supplied. The studied methods appeared to give complementary information and presented good reproducibility (below 20%). Peptide ligand affinity beads were found to provide efficient depletion of HMW proteins and peak enrichment in protein/peptide profiles. PMID:20685463

  18. The absence of lithium isotope fractionation during basalt differentiation: New measurements by multicollector sector ICP-MS

    USGS Publications Warehouse

    Tomascak, P.B.; Tera, F.; Helz, R.T.; Walker, R.J.

    1999-01-01

    We report measurements of the isotopic composition of lithium in basalts using a multicollector magnetic sector plasma-source mass spectrometer (MC-ICP-MS). This is the first application of this analytical technique to Li isotope determination. External precision of multiple replicate and duplicate measurements for a variety of sample types averages ??1.1??? (2?? population). The method allows for the rapid (???8 min/sample) analysis of small samples (???40 ng Li) relative to commonly used thermal ionization methods. The technique has been applied to a suite of samples from Kilauea Iki lava lake, Hawaii. The samples range from olivine-rich cumulitic lava to SiO2 - and K2O-enriched differentiated liquids, and have ??7Li (per mil deviation of sample 7Li/6Li relative to the L-SVEC standard) of +3.0 to +4.8. The data indicate a lack of per mil-level Li isotope fractionation as a result of crystal-liquid fractionation at temperatures greater than 1050??C. This conclusion has been tacitly assumed but never demonstrated, and is important to the interpretation of Li isotope results from such geochemically complex environments as island arcs. Copyright ?? 1999 Elsevier Science Ltd.

  19. First measurement of the differential branching fraction and CP asymmetry of the B ± → π ± μ + μ - decay

    NASA Astrophysics Data System (ADS)

    Aaij, R.; Adeva, B.; Adinolfi, M.; Affolder, A.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Alvarez Cartelle, P.; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; An, L.; Anderlini, L.; Anderson, J.; Andreassi, G.; Andreotti, M.; Andrews, J. E.; Appleby, R. B.; Aquines Gutierrez, O.; Archilli, F.; d'Argent, P.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Baalouch, M.; Bachmann, S.; Back, J. J.; Badalov, A.; Baesso, C.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Batozskaya, V.; Battista, V.; Bay, A.; Beaucourt, L.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Bel, L. J.; Bellee, V.; Belloli, N.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Benton, J.; Berezhnoy, A.; Bernet, R.; Bertolin, A.; Bettler, M.-O.; van Beuzekom, M.; Bien, A.; Bifani, S.; Billoir, P.; Bird, T.; Birnkraut, A.; Bizzeti, A.; Blake, T.; Blanc, F.; Blouw, J.; Blusk, S.; Bocci, V.; Bondar, A.; Bondar, N.; Bonivento, W.; Borghi, S.; Borsato, M.; Bowcock, T. J. V.; Bowen, E.; Bozzi, C.; Braun, S.; Britsch, M.; Britton, T.; Brodzicka, J.; Brook, N. H.; Buchanan, E.; Bursche, A.; Buytaert, J.; Cadeddu, S.; Calabrese, R.; Calvi, M.; Calvo Gomez, M.; Campana, P.; Campora Perez, D.; Capriotti, L.; Carbone, A.; Carboni, G.; Cardinale, R.; Cardini, A.; Carniti, P.; Carson, L.; Carvalho Akiba, K.; Casse, G.; Cassina, L.; Castillo Garcia, L.; Cattaneo, M.; Cauet, Ch.; Cavallero, G.; Cenci, R.; Charles, M.; Charpentier, Ph.; Chefdeville, M.; Chen, S.; Cheung, S.-F.; Chiapolini, N.; Chrzaszcz, M.; Cid Vidal, X.; Ciezarek, G.; Clarke, P. E. L.; Clemencic, M.; Cliff, H. V.; Closier, J.; Coco, V.; Cogan, J.; Cogneras, E.; Cogoni, V.; Cojocariu, L.; Collazuol, G.; Collins, P.; Comerma-Montells, A.; Contu, A.; Cook, A.; Coombes, M.; Coquereau, S.; Corti, G.; Corvo, M.; Couturier, B.; Cowan, G. A.; Craik, D. C.; Crocombe, A.; Cruz Torres, M.; Cunliffe, S.; Currie, R.; D'Ambrosio, C.; Dall'Occo, E.; Dalseno, J.; David, P. N. Y.; Davis, A.; De Bruyn, K.; De Capua, S.; De Cian, M.; De Miranda, J. M.; De Paula, L.; De Simone, P.; Dean, C.-T.; Decamp, D.; Deckenhoff, M.; Del Buono, L.; Déléage, N.; Demmer, M.; Derkach, D.; Deschamps, O.; Dettori, F.; Dey, B.; Di Canto, A.; Di Ruscio, F.; Dijkstra, H.; Donleavy, S.; Dordei, F.; Dorigo, M.; Dosil Suárez, A.; Dossett, D.; Dovbnya, A.; Dreimanis, K.; Dufour, L.; Dujany, G.; Dupertuis, F.; Durante, P.; Dzhelyadin, R.; Dziurda, A.; Dzyuba, A.; Easo, S.; Egede, U.; Egorychev, V.; Eidelman, S.; Eisenhardt, S.; Eitschberger, U.; Ekelhof, R.; Eklund, L.; El Rifai, I.; Elsasser, Ch.; Ely, S.; Esen, S.; Evans, H. M.; Evans, T.; Falabella, A.; Färber, C.; Farley, N.; Farry, S.; Fay, R.; Ferguson, D.; Fernandez Albor, V.; Ferrari, F.; Ferreira Rodrigues, F.; Ferro-Luzzi, M.; Filippov, S.; Fiore, M.; Fiorini, M.; Firlej, M.; Fitzpatrick, C.; Fiutowski, T.; Fohl, K.; Fol, P.; Fontana, M.; Fontanelli, F.; Forty, R.; Francisco, O.; Frank, M.; Frei, C.; Frosini, M.; Fu, J.; Furfaro, E.; Gallas Torreira, A.; Galli, D.; Gallorini, S.; Gambetta, S.; Gandelman, M.; Gandini, P.; Gao, Y.; García Pardiñas, J.; Garra Tico, J.; Garrido, L.; Gascon, D.; Gaspar, C.; Gauld, R.; Gavardi, L.; Gazzoni, G.; Gerick, D.; Gersabeck, E.; Gersabeck, M.; Gershon, T.; Ghez, Ph.; Gianì, S.; Gibson, V.; Girard, O. G.; Giubega, L.; Gligorov, V. V.; Göbel, C.; Golubkov, D.; Golutvin, A.; Gomes, A.; Gotti, C.; Grabalosa Gándara, M.; Graciani Diaz, R.; Granado Cardoso, L. A.; Graugés, E.; Graverini, E.; Graziani, G.; Grecu, A.; Greening, E.; Gregson, S.; Griffith, P.; Grillo, L.; Grünberg, O.; Gui, B.; Gushchin, E.; Guz, Yu.; Gys, T.; Hadavizadeh, T.; Hadjivasiliou, C.; Haefeli, G.; Haen, C.; Haines, S. C.; Hall, S.; Hamilton, B.; Han, X.; Hansmann-Menzemer, S.; Harnew, N.; Harnew, S. T.; Harrison, J.; He, J.; Head, T.; Heijne, V.; Hennessy, K.; Henrard, P.; Henry, L.; van Herwijnen, E.; Heß, M.; Hicheur, A.; Hill, D.; Hoballah, M.; Hombach, C.; Hulsbergen, W.; Humair, T.; Hussain, N.; Hutchcroft, D.; Hynds, D.; Idzik, M.; Ilten, P.; Jacobsson, R.; Jaeger, A.; Jalocha, J.; Jans, E.; Jawahery, A.; Jing, F.; John, M.; Johnson, D.; Jones, C. R.; Joram, C.; Jost, B.; Jurik, N.; Kandybei, S.; Kanso, W.; Karacson, M.; Karbach, T. M.; Karodia, S.; Kecke, M.; Kelsey, M.; Kenyon, I. R.; Kenzie, M.; Ketel, T.; Khanji, B.; Khurewathanakul, C.; Klaver, S.; Klimaszewski, K.; Kochebina, O.; Kolpin, M.; Komarov, I.; Koopman, R. F.; Koppenburg, P.; Kozeiha, M.; Kravchuk, L.; Kreplin, K.; Kreps, M.; Krocker, G.; Krokovny, P.; Kruse, F.; Krzemien, W.; Kucewicz, W.; Kucharczyk, M.; Kudryavtsev, V.; Kuonen, A. K.; Kurek, K.; Kvaratskheliya, T.; Lacarrere, D.; Lafferty, G.; Lai, A.; Lambert, D.; Lanfranchi, G.; Langenbruch, C.; Langhans, B.; Latham, T.; Lazzeroni, C.; Le Gac, R.; van Leerdam, J.; Lees, J.-P.; Lefèvre, R.; Leflat, A.; Lefrançois, J.; Lemos Cid, E.; Leroy, O.; Lesiak, T.; Leverington, B.; Li, Y.; Likhomanenko, T.; Liles, M.; Lindner, R.; Linn, C.; Lionetto, F.; Liu, B.; Liu, X.; Loh, D.; Longstaff, I.; Lopes, J. H.; Lucchesi, D.; Lucio Martinez, M.; Luo, H.; Lupato, A.; Luppi, E.; Lupton, O.; Lusiani, A.; Machefert, F.; Maciuc, F.; Maev, O.; Maguire, K.; Malde, S.; Malinin, A.; Manca, G.; Mancinelli, G.; Manning, P.; Mapelli, A.; Maratas, J.; Marchand, J. F.; Marconi, U.; Marin Benito, C.; Marino, P.; Marks, J.; Martellotti, G.; Martin, M.; Martinelli, M.; Martinez Santos, D.; Martinez Vidal, F.; Martins Tostes, D.; Massafferri, A.; Matev, R.; Mathad, A.; Mathe, Z.; Matteuzzi, C.; Mauri, A.; Maurin, B.; Mazurov, A.; McCann, M.; McCarthy, J.; McNab, A.; McNulty, R.; Meadows, B.; Meier, F.; Meissner, M.; Melnychuk, D.; Merk, M.; Michielin, E.; Milanes, D. A.; Minard, M.-N.; Mitzel, D. S.; Molina Rodriguez, J.; Monroy, I. A.; Monteil, S.; Morandin, M.; Morawski, P.; Mordà, A.; Morello, M. J.; Moron, J.; Morris, A. B.; Mountain, R.; Muheim, F.; Müller, D.; Müller, J.; Müller, K.; Müller, V.; Mussini, M.; Muster, B.; Naik, P.; Nakada, T.; Nandakumar, R.; Nandi, A.; Nasteva, I.; Needham, M.; Neri, N.; Neubert, S.; Neufeld, N.; Neuner, M.; Nguyen, A. D.; Nguyen, T. D.; Nguyen-Mau, C.; Niess, V.; Niet, R.; Nikitin, N.; Nikodem, T.; Ninci, D.; Novoselov, A.; O'Hanlon, D. P.; Oblakowska-Mucha, A.; Obraztsov, V.; Ogilvy, S.; Okhrimenko, O.; Oldeman, R.; Onderwater, C. J. G.; Osorio Rodrigues, B.; Otalora Goicochea, J. M.; Otto, A.; Owen, P.; Oyanguren, A.; Palano, A.; Palombo, F.; Palutan, M.; Panman, J.; Papanestis, A.; Pappagallo, M.; Pappalardo, L. L.; Pappenheimer, C.; Parkes, C.; Passaleva, G.; Patel, G. D.; Patel, M.; Patrignani, C.; Pearce, A.; Pellegrino, A.; Penso, G.; Pepe Altarelli, M.; Perazzini, S.; Perret, P.; Pescatore, L.; Petridis, K.; Petrolini, A.; Petruzzo, M.; Picatoste Olloqui, E.; Pietrzyk, B.; Pilař, T.; Pinci, D.; Pistone, A.; Piucci, A.; Playfer, S.; Plo Casasus, M.; Poikela, T.; Polci, F.; Poluektov, A.; Polyakov, I.; Polycarpo, E.; Popov, A.; Popov, D.; Popovici, B.; Potterat, C.; Price, E.; Price, J. D.; Prisciandaro, J.; Pritchard, A.; Prouve, C.; Pugatch, V.; Puig Navarro, A.; Punzi, G.; Qian, W.; Quagliani, R.; Rachwal, B.; Rademacker, J. H.; Rama, M.; Rangel, M. S.; Raniuk, I.; Rauschmayr, N.; Raven, G.; Redi, F.; Reichert, S.; Reid, M. M.; dos Reis, A. C.; Ricciardi, S.; Richards, S.; Rihl, M.; Rinnert, K.; Rives Molina, V.; Robbe, P.; Rodrigues, A. B.; Rodrigues, E.; Rodriguez Lopez, J. A.; Rodriguez Perez, P.; Roiser, S.; Romanovsky, V.; Romero Vidal, A.; Ronayne, J. W.; Rotondo, M.; Rouvinet, J.; Ruf, T.; Ruiz Valls, P.; Saborido Silva, J. J.; Sagidova, N.; Sail, P.; Saitta, B.; Salustino Guimaraes, V.; Sanchez Mayordomo, C.; Sanmartin Sedes, B.; Santacesaria, R.; Santamarina Rios, C.; Santimaria, M.; Santovetti, E.; Sarti, A.; Satriano, C.; Satta, A.; Saunders, D. M.; Savrina, D.; Schiller, M.; Schindler, H.; Schlupp, M.; Schmelling, M.; Schmelzer, T.; Schmidt, B.; Schneider, O.; Schopper, A.; Schubiger, M.; Schune, M.-H.; Schwemmer, R.; Sciascia, B.; Sciubba, A.; Semennikov, A.; Serra, N.; Serrano, J.; Sestini, L.; Seyfert, P.; Shapkin, M.; Shapoval, I.; Shcheglov, Y.; Shears, T.; Shekhtman, L.; Shevchenko, V.; Shires, A.; Siddi, B. G.; Silva Coutinho, R.; Silva de Oliveira, L.; Simi, G.; Sirendi, M.; Skidmore, N.; Skillicorn, I.; Skwarnicki, T.; Smith, E.; Smith, E.; Smith, I. T.; Smith, J.; Smith, M.; Snoek, H.; Sokoloff, M. D.; Soler, F. J. P.; Soomro, F.; Souza, D.; Souza De Paula, B.; Spaan, B.; Spradlin, P.; Sridharan, S.; Stagni, F.; Stahl, M.; Stahl, S.; Stefkova, S.; Steinkamp, O.; Stenyakin, O.; Stevenson, S.; Stoica, S.; Stone, S.; Storaci, B.; Stracka, S.; Straticiuc, M.; Straumann, U.; Sun, L.; Sutcliffe, W.; Swientek, K.; Swientek, S.; Syropoulos, V.; Szczekowski, M.; Szczypka, P.; Szumlak, T.; T'Jampens, S.; Tayduganov, A.; Tekampe, T.; Teklishyn, M.; Tellarini, G.; Teubert, F.; Thomas, C.; Thomas, E.; van Tilburg, J.; Tisserand, V.; Tobin, M.; Todd, J.; Tolk, S.; Tomassetti, L.; Tonelli, D.; Topp-Joergensen, S.; Torr, N.; Tournefier, E.; Tourneur, S.; Trabelsi, K.; Tran, M. T.; Tresch, M.; Trisovic, A.; Tsaregorodtsev, A.; Tsopelas, P.; Tuning, N.; Ukleja, A.; Ustyuzhanin, A.; Uwer, U.; Vacca, C.; Vagnoni, V.; Valenti, G.; Vallier, A.; Vazquez Gomez, R.; Vazquez Regueiro, P.; Vázquez Sierra, C.; Vecchi, S.; Velthuis, J. J.; Veltri, M.; Veneziano, G.; Vesterinen, M.; Viaud, B.; Vieira, D.; Vieites Diaz, M.; Vilasis-Cardona, X.; Volkov, V.; Vollhardt, A.; Volyanskyy, D.; Voong, D.; Vorobyev, A.; Vorobyev, V.; Voß, C.; de Vries, J. A.; Waldi, R.; Wallace, C.; Wallace, R.; Walsh, J.; Wandernoth, S.; Wang, J.; Ward, D. R.; Watson, N. K.; Websdale, D.; Weiden, A.; Whitehead, M.; Wilkinson, G.; Wilkinson, M.; Williams, M.; Williams, M. P.; Williams, M.; Williams, T.; Wilson, F. F.; Wimberley, J.; Wishahi, J.; Wislicki, W.; Witek, M.; Wormser, G.; Wotton, S. A.; Wright, S.; Wyllie, K.; Xie, Y.; Xu, Z.; Yang, Z.; Yu, J.; Yuan, X.; Yushchenko, O.; Zangoli, M.; Zavertyaev, M.; Zhang, L.; Zhang, Y.; Zhelezov, A.; Zhokhov, A.; Zhong, L.; Zucchelli, S.

    2015-10-01

    The differential branching fraction with respect to the dimuon invariant mass squared, and the CP asymmetry of the B ± → π ± μ + μ - decay are measured for the first time. The CKM matrix elements | V td | and | V ts |, and the ratio | V td /V ts | are determined. The analysis is performed using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb-1, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The total branching fraction and CP asymmetry of B ± → π ± μ + μ - decays are measured to be B({B}^{±}to {π}^{± }{μ}+{μ}-)=(1.83± 0.24± 0.05)× {10-}^8and {A}_{CP}({B}^{±}to {π}^{± }{μ}+{μ}-)=-0.11± 0.12± 0.01, where the first uncertainties are statistical and the second are systematic. These are the most precise measurements of these observables to date, and they are compatible with the predictions of the Standard Model. [Figure not available: see fulltext.

  20. Non-Linear EMG Parameters for Differential and Early Diagnostics of Parkinson’s Disease

    PubMed Central

    Meigal, Alexander Y.; Rissanen, Saara M.; Tarvainen, Mika P.; Airaksinen, Olavi; Kankaanpää, Markku; Karjalainen, Pasi A.

    2013-01-01

    The pre-clinical diagnostics is essential for management of Parkinson’s disease (PD). Although PD has been studied intensively in the last decades, the pre-clinical indicators of that motor disorder have yet to be established. Several approaches were proposed but the definitive method is still lacking. Here we report on the non-linear characteristics of surface electromyogram (sEMG) and tremor acceleration as a possible diagnostic tool, and, in prospective, as a predictor for PD. Following this approach we calculated such non-linear parameters of sEMG and accelerometer signal as correlation dimension, entropy, and determinism. We found that the non-linear parameters allowed discriminating some 85% of healthy controls from PD patients. Thus, this approach offers considerable potential for developing sEMG-based method for pre-clinical diagnostics of PD. However, non-linear parameters proved to be more reliable for the shaking form of PD, while diagnostics of the rigid form of PD using EMG remains an open question. PMID:24062722

  1. Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

    NASA Technical Reports Server (NTRS)

    Gunderson, R. W.

    1975-01-01

    A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

  2. Review of the Software Package "Scientist": Mathematical Modeling/Differential and Nonlinear Equations.

    ERIC Educational Resources Information Center

    Scheidt, Douglas M.

    1995-01-01

    Reviews three functions of the "Scientist" software package useful for the social sciences: nonlinear curve fitting, parameter estimation, and data/regression plotting. Social scientists are likely to find limitations and unfamiliar procedures in "Scientist". Its value lies in its visual presentation of data and regression curves and the…

  3. A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects.

    PubMed

    Chow, Sy-Miin; Bendezú, Jason J; Cole, Pamela M; Ram, Nilam

    2016-01-01

    Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay & Silverman, 2005 ), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, & Peel, 2010 ), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 ). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children's self-regulation. PMID:27391255

  4. Interconnections between various analytic approaches applicable to third-order nonlinear differential equations

    PubMed Central

    Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

    2015-01-01

    We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ODEs. We establish an important interconnection between the extended Prelle–Singer procedure and λ-symmetries approach applicable to third-order ODEs to bring out the various linkages associated with these different techniques. By establishing this interconnection we demonstrate that given any one of the quantities as a starting point in the family consisting of Jacobi last multipliers, Darboux polynomials, Lie point symmetries, adjoint-symmetries, λ-symmetries, integrating factors and null forms one can derive the rest of the quantities in this family in a straightforward and unambiguous manner. We also illustrate our findings with three specific examples.

  5. Using the Homotopy Method to Find Periodic Solutions of Forced Nonlinear Differential Equations

    ERIC Educational Resources Information Center

    Fay, Temple H.; Lott, P. Aaron

    2002-01-01

    This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x[dots above] + kx[dot above] + g(x,t) = [epsilon](t) where k is a constant; g is continuous, continuously differentiable with respect to x , and is periodic of period P in the variable t; [epsilon](t) is continuous…

  6. The Paleocene Eocene carbon isotope excursion in higher plant organic matter: Differential fractionation of angiosperms and conifers in the Arctic

    NASA Astrophysics Data System (ADS)

    Schouten, Stefan; Woltering, Martijn; Rijpstra, W. Irene C.; Sluijs, Appy; Brinkhuis, Henk; Sinninghe Damsté, Jaap S.

    2007-06-01

    A study of upper Paleocene-lower Eocene (P-E) sediments deposited on the Lomonosov Ridge in the central Arctic Ocean reveals relatively high abundances of terrestrial biomarkers. These include dehydroabietane and simonellite derived from conifers (gymnosperms) and a tetra-aromatic triterpenoid derived from angiosperms. The relative percentage of the angiosperm biomarker of the summed angiosperm + conifer biomarkers was increased at the end of the Paleocene-Eocene thermal maximum (PETM), different when observed with pollen counts which showed a relative decrease in angiosperm pollen. Stable carbon isotopic analysis of these biomarkers shows that the negative carbon isotope excursion (CIE) during the PETM amounts to 3‰ for both conifer biomarkers, dehydroabietane and simonellite, comparable to the magnitude of the CIE inferred from marine carbonates, but significantly lower than the 4.5‰ of the terrestrial C 29n-alkane [M. Pagani, N. Pedentchouk, M. Huber, A. Sluijs, S. Schouten, H. Brinkhuis, J.S. Sinninghe Damsté, G.R. Dickens, and the IODP Expedition 302 Expedition Scientists (2006), Arctic's hydrology during global warming at the Paleocene-Eocene thermal maximum. Nature, 442, 671-675.], which is a compound sourced by both conifers and angiosperms. Conspicuously, the angiosperm-sourced aromatic triterpane shows a much larger CIE of 6‰ and suggests that angiosperms increased in their carbon isotopic fractionation during the PETM. Our results thus indicate that the 4.5‰ C 29n-alkane CIE reported previously represents the average CIE of conifers and angiosperms at this site and suggest that the large and variable CIE observed in terrestrial records may be partly explained by the variable contributions of conifers and angiosperms. The differential response in isotopic fractionation of angiosperms and conifers points to different physiological responses of these vegetation types to the rise in temperature, humidity, and greenhouse gases during the PETM.

  7. Label-free nonlinear optical microscopy detects early markers for osteogenic differentiation of human stem cells

    PubMed Central

    Hofemeier, Arne D.; Hachmeister, Henning; Pilger, Christian; Schürmann, Matthias; Greiner, Johannes F. W.; Nolte, Lena; Sudhoff, Holger; Kaltschmidt, Christian; Huser, Thomas; Kaltschmidt, Barbara

    2016-01-01

    Tissue engineering by stem cell differentiation is a novel treatment option for bone regeneration. Most approaches for the detection of osteogenic differentiation are invasive or destructive and not compatible with live cell analysis. Here, non-destructive and label-free approaches of Raman spectroscopy, coherent anti-Stokes Raman scattering (CARS) and second harmonic generation (SHG) microscopy were used to detect and image osteogenic differentiation of human neural crest-derived inferior turbinate stem cells (ITSCs). Combined CARS and SHG microscopy was able to detect markers of osteogenesis within 14 days after osteogenic induction. This process increased during continued differentiation. Furthermore, Raman spectroscopy showed significant increases of the PO43− symmetric stretch vibrations at 959 cm−1 assigned to calcium hydroxyapatite between days 14 and 21. Additionally, CARS microscopy was able to image calcium hydroxyapatite deposits within 14 days following osteogenic induction, which was confirmed by Alizarin Red-Staining and RT- PCR. Taken together, the multimodal label-free analysis methods Raman spectroscopy, CARS and SHG microscopy can monitor osteogenic differentiation of adult human stem cells into osteoblasts with high sensitivity and spatial resolution in three dimensions. Our findings suggest a great potential of these optical detection methods for clinical applications including in vivo observation of bone tissue–implant-interfaces or disease diagnosis. PMID:27225821

  8. Label-free nonlinear optical microscopy detects early markers for osteogenic differentiation of human stem cells

    NASA Astrophysics Data System (ADS)

    Hofemeier, Arne D.; Hachmeister, Henning; Pilger, Christian; Schürmann, Matthias; Greiner, Johannes F. W.; Nolte, Lena; Sudhoff, Holger; Kaltschmidt, Christian; Huser, Thomas; Kaltschmidt, Barbara

    2016-05-01

    Tissue engineering by stem cell differentiation is a novel treatment option for bone regeneration. Most approaches for the detection of osteogenic differentiation are invasive or destructive and not compatible with live cell analysis. Here, non-destructive and label-free approaches of Raman spectroscopy, coherent anti-Stokes Raman scattering (CARS) and second harmonic generation (SHG) microscopy were used to detect and image osteogenic differentiation of human neural crest-derived inferior turbinate stem cells (ITSCs). Combined CARS and SHG microscopy was able to detect markers of osteogenesis within 14 days after osteogenic induction. This process increased during continued differentiation. Furthermore, Raman spectroscopy showed significant increases of the PO43‑ symmetric stretch vibrations at 959 cm‑1 assigned to calcium hydroxyapatite between days 14 and 21. Additionally, CARS microscopy was able to image calcium hydroxyapatite deposits within 14 days following osteogenic induction, which was confirmed by Alizarin Red-Staining and RT- PCR. Taken together, the multimodal label-free analysis methods Raman spectroscopy, CARS and SHG microscopy can monitor osteogenic differentiation of adult human stem cells into osteoblasts with high sensitivity and spatial resolution in three dimensions. Our findings suggest a great potential of these optical detection methods for clinical applications including in vivo observation of bone tissue–implant-interfaces or disease diagnosis.

  9. Label-free nonlinear optical microscopy detects early markers for osteogenic differentiation of human stem cells.

    PubMed

    Hofemeier, Arne D; Hachmeister, Henning; Pilger, Christian; Schürmann, Matthias; Greiner, Johannes F W; Nolte, Lena; Sudhoff, Holger; Kaltschmidt, Christian; Huser, Thomas; Kaltschmidt, Barbara

    2016-01-01

    Tissue engineering by stem cell differentiation is a novel treatment option for bone regeneration. Most approaches for the detection of osteogenic differentiation are invasive or destructive and not compatible with live cell analysis. Here, non-destructive and label-free approaches of Raman spectroscopy, coherent anti-Stokes Raman scattering (CARS) and second harmonic generation (SHG) microscopy were used to detect and image osteogenic differentiation of human neural crest-derived inferior turbinate stem cells (ITSCs). Combined CARS and SHG microscopy was able to detect markers of osteogenesis within 14 days after osteogenic induction. This process increased during continued differentiation. Furthermore, Raman spectroscopy showed significant increases of the PO4(3-) symmetric stretch vibrations at 959 cm(-1) assigned to calcium hydroxyapatite between days 14 and 21. Additionally, CARS microscopy was able to image calcium hydroxyapatite deposits within 14 days following osteogenic induction, which was confirmed by Alizarin Red-Staining and RT- PCR. Taken together, the multimodal label-free analysis methods Raman spectroscopy, CARS and SHG microscopy can monitor osteogenic differentiation of adult human stem cells into osteoblasts with high sensitivity and spatial resolution in three dimensions. Our findings suggest a great potential of these optical detection methods for clinical applications including in vivo observation of bone tissue-implant-interfaces or disease diagnosis. PMID:27225821

  10. The importance of fractional crystallization and magma mixing in controlling chemical differentiation at Süphan stratovolcano, eastern Anatolia, Turkey

    NASA Astrophysics Data System (ADS)

    Özdemir, Yavuz; Blundy, Jon; Güleç, Nilgün

    2011-09-01

    Süphan is a 4,050 m high Pleistocene-age stratovolcano in eastern Anatolia, Turkey, with eruptive products consisting of transitional calc-alkaline to mildly alkaline basalts through trachyandesites and trachytes to rhyolites. We investigate the relative contributions of fractional crystallization and magma mixing to compositional diversity at Süphan using a combination of petrology, geothermometry, and melt inclusion analysis. Although major element chemistry shows near-continuous variation from basalt to rhyolite, mineral chemistry and textures indicate that magma mixing played an important role. Intermediate magmas show a wide range of pyroxene, olivine, and plagioclase compositions that are intermediate between those of basalts and rhyolites. Mineral thermometry of the same rocks yields a range of temperatures bracketed by rhyolite (~750°C) and basalt (~1,100°C). The linear chemical trends shown for most major and trace elements are attributed to mixing processes, rather than to liquid lines of descent from a basaltic parent. In contrast, glassy melt inclusions, hosted by a wide range of phenocryst types, display curved trends for most major elements, suggestive of fractional crystallization. Comparison of these trends to experimental data from basalts and trachyandesites of similar composition to those at Süphan indicates that melt inclusions approximate true liquid lines of descent from a common hydrous parent at pressures of ~500 MPa. Thus, the erupted magmas are cogenetic, but were generated at depths below the shallow, pre-eruptive magma storage region. We infer that chemical differentiation of a mantle-derived basalt occurred in the mid- to lower crust beneath Süphan. A variety of more and less evolved melts with ≥55 wt% SiO2 then ascended to shallow level where they interacted. The presence of glomerocrysts in many lavas suggests that cogenetic plutonic rocks were implicated in the interaction process. Blending of diverse, but cogenetic, minerals

  11. Some path-following techniques for solution of nonlinear equations and comparison with parametric differentiation

    NASA Technical Reports Server (NTRS)

    Barger, R. L.; Walters, R. W.

    1986-01-01

    Some path-following techniques are described and compared with other methods. Use of multipurpose techniques that can be used at more than one stage of the path-following computation results in a system that is relatively simple to understand, program, and use. Comparison of path-following methods with the method of parametric differentiation reveals definite advantages for the path-following methods. The fact that parametric differentiation has found a broader range of applications indicates that path-following methods have been underutilized.

  12. Modeling of long-range memory processes with inverse cubic distributions by the nonlinear stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Kaulakys, B.; Alaburda, M.; Ruseckas, J.

    2016-05-01

    A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.

  13. Unique signature of bivalent analyte surface plasmon resonance model: A model governed by non-linear differential equations

    NASA Astrophysics Data System (ADS)

    Tiwari, Purushottam; Wang, Xuewen; Darici, Yesim; He, Jin; Uren, Aykut

    Surface plasmon resonance (SPR) is a biophysical technique for the quantitative analysis of bimolecular interactions. Correct identification of the binding model is crucial for the interpretation of SPR data. Bivalent SPR model is governed by non-linear differential equations, which, in general, have no analytical solutions. Therefore, an analytical based approach cannot be employed in order to identify this particular model. There exists a unique signature in the bivalent analyte model, existence of an `optimal analyte concentration', which can distinguish this model from other biphasic models. The unambiguous identification and related analysis of the bivalent analyte model is demonstrated by using theoretical simulations and experimentally measured SPR sensorgrams. Experimental SPR sensorgrams were measured by using Biacore T200 instrument available in Biacore Molecular Interaction Shared Resource facility, supported by NIH Grant P30CA51008, at Georgetown University.

  14. Phase transitions driven by Lévy stable noise: Exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations

    NASA Astrophysics Data System (ADS)

    Ichiki, A.; Shiino, M.

    2009-08-01

    Phase transitions and effects of external noise on many-body systems are one of the main topics in physics. In mean-field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including nonequilibrium ones may appear. A Brownian motion is a special case of Lévy motion and the stochastic process based on the latter is an alternative choice for studying cooperative phenomena in various fields. Recently, fractional Fokker-Planck equations associated with Lévy noise have attracted much attention and behaviors of systems with double-well potential subjected to Lévy noise have been studied intensively. However, most of such studies have resorted to numerical computation. We construct an analytically solvable model to study the occurrence of phase transitions driven by Lévy stable noise.

  15. Superimposed linear psoriasis: differential therapeutic response of linear and nonlinear lesions.

    PubMed

    Seitz, C S; Garbaraviciene, J; Bröcker, E-B; Hamm, H

    2009-07-01

    Linear psoriasis is a very unusual clinical variation of psoriasis. Typical clinical features include early onset of erythematosquamous lesions along Blaschko's lines, ability to elicit psoriatic features, absence of pruritus and positive family history for psoriasis. Recently, the term 'superimposed linear psoriasis' was coined for cases with development of nonlinear psoriatic lesions at predilection sites in later life. We report a 19-year-old woman meeting all criteria for the diagnosis of superimposed linear psoriasis including typical histological features. Remarkably, treatment with topical steroids and dithranol cleared the psoriatic lesions on predilection sites whereas the linear lesions were resistant to topical therapy. Linear psoriatic lesions are believed to be caused by genetic alterations in early embryogenesis leading to loss of heterozygosity at a gene locus involved in the pathogenesis of psoriasis. Comparison of mosaic keratinocytes derived from linear lesions with wild-type keratinocytes from the same person may therefore allow identification of key regulatory genes. PMID:19094135

  16. The linkage of Zlib to Teapot for auto-differentiation map extraction and nonlinear analysis

    SciTech Connect

    Sun, N.; Yan, Y.T.; Pilat, F.; Bourianoff, G.

    1993-05-01

    The differential Lie algebraic numerical library, Zlib has been linked to Teapot, the accelerator simulator code. This makes possible the use of the operational correction features of Teapot to produce a corrected lattice, and then choose either map or thin element-by-element tracking for tracking studies. Thin-element tracking is more accurate but slower than map tracking; therefore, the option of choosing one or the other is very desirable.

  17. Negative differential resistance and characteristic nonlinear electromagnetic response of a Topological Insulator

    PubMed Central

    Lee, Ching Hua; Zhang, Xiao; Guan, Bochen

    2015-01-01

    Materials exhibiting negative differential resistance have important applications in technologies involving microwave generation, which range from motion sensing to radio astronomy. Despite their usefulness, there has been few physical mechanisms giving rise to materials with such properties, i.e. GaAs employed in the Gunn diode. In this work, we show that negative differential resistance also generically arise in Dirac ring systems, an example of which has been experimentally observed in the surface states of Topological Insulators. This novel realization of negative differential resistance is based on a completely different physical mechanism from that of the Gunn effect, relying on the characteristic non-monotonicity of the response curve that remains robust in the presence of nonzero temperature, chemical potential, mass gap and impurity scattering. As such, it opens up new possibilities for engineering applications, such as frequency upconversion devices which are highly sought for terahertz signal generation. Our results may be tested with thin films of Bi2Se3 Topological Insulators, and are expected to hold qualitatively even in the absence of a strictly linear Dirac dispersion, as will be the case in more generic samples of Bi2Se3 and other materials with topologically nontrivial Fermi sea regions. PMID:26657341

  18. Negative differential resistance and characteristic nonlinear electromagnetic response of a Topological Insulator

    NASA Astrophysics Data System (ADS)

    Lee, Ching Hua; Zhang, Xiao; Guan, Bochen

    2015-12-01

    Materials exhibiting negative differential resistance have important applications in technologies involving microwave generation, which range from motion sensing to radio astronomy. Despite their usefulness, there has been few physical mechanisms giving rise to materials with such properties, i.e. GaAs employed in the Gunn diode. In this work, we show that negative differential resistance also generically arise in Dirac ring systems, an example of which has been experimentally observed in the surface states of Topological Insulators. This novel realization of negative differential resistance is based on a completely different physical mechanism from that of the Gunn effect, relying on the characteristic non-monotonicity of the response curve that remains robust in the presence of nonzero temperature, chemical potential, mass gap and impurity scattering. As such, it opens up new possibilities for engineering applications, such as frequency upconversion devices which are highly sought for terahertz signal generation. Our results may be tested with thin films of Bi2Se3 Topological Insulators, and are expected to hold qualitatively even in the absence of a strictly linear Dirac dispersion, as will be the case in more generic samples of Bi2Se3 and other materials with topologically nontrivial Fermi sea regions.

  19. Negative differential resistance and characteristic nonlinear electromagnetic response of a Topological Insulator.

    PubMed

    Lee, Ching Hua; Zhang, Xiao; Guan, Bochen

    2015-01-01

    Materials exhibiting negative differential resistance have important applications in technologies involving microwave generation, which range from motion sensing to radio astronomy. Despite their usefulness, there has been few physical mechanisms giving rise to materials with such properties, i.e. GaAs employed in the Gunn diode. In this work, we show that negative differential resistance also generically arise in Dirac ring systems, an example of which has been experimentally observed in the surface states of Topological Insulators. This novel realization of negative differential resistance is based on a completely different physical mechanism from that of the Gunn effect, relying on the characteristic non-monotonicity of the response curve that remains robust in the presence of nonzero temperature, chemical potential, mass gap and impurity scattering. As such, it opens up new possibilities for engineering applications, such as frequency upconversion devices which are highly sought for terahertz signal generation. Our results may be tested with thin films of Bi2Se3 Topological Insulators, and are expected to hold qualitatively even in the absence of a strictly linear Dirac dispersion, as will be the case in more generic samples of Bi2Se3 and other materials with topologically nontrivial Fermi sea regions. PMID:26657341

  20. Limited Knowledge of Fraction Representations Differentiates Middle School Students with Mathematics Learning Disability (Dyscalculia) versus Low Mathematics Achievement

    ERIC Educational Resources Information Center

    Mazzocco, Michele M. M.; Myers, Gwen F.; Lewis, Katherine E.; Hanich, Laurie B.; Murphy, Melissa M.

    2013-01-01

    Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions…

  1. Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order

    NASA Astrophysics Data System (ADS)

    Johnston, S. J.; Jafari, H.; Moshokoa, S. P.; Ariyan, V. M.; Baleanu, D.

    2016-07-01

    The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.

  2. Stability of sequences generated by nonlinear differential systems. [for analysis of glider jet aircraft motion

    NASA Technical Reports Server (NTRS)

    Brown, R. L.

    1979-01-01

    A local stability analysis is presented for both the analytic and numerical solutions of the initial value problem for a system of ordinary differential equations. It is shown that, using a proper choice of Liapunov function, a connected region of stable initial values of both the analytic solution and the one-leg k-step numerical solution can be approximated. Attention is given to the example of the two-dimensional problem involving the stability of the longitudinal equations of motion of a gliding jet aircraft.

  3. The nonlinear differential equations governing a hierarchy of self-exciting coupled Faraday-disk homopolar dynamos

    NASA Astrophysics Data System (ADS)

    Hide, Raymond

    1997-02-01

    This paper discusses the derivation of the autonomous sets of dimensionless nonlinear ordinary differential equations (ODE's) that govern the behaviour of a hierarchy of related electro-mechanical self-exciting Faraday-disk homopolar dynamo systems driven by steady mechanical couples. Each system comprises N interacting units which could be arranged in a ring or lattice. Within each unit and connected in parallel or in series with the coil are electric motors driven into motion by the dynamo, all having linear characteristics, so that nonlinearity arises entirely through the coupling between components. By introducing simple extra terms into the equations it is possible to represent biasing effects arising from impressed electromotive forces due to thermoelectric or chemical processes and from the presence of ambient magnetic fields. Dissipation in the system is due not only to ohmic heating but also to mechanical friction in the disk and the motors, with the latter agency, no matter how weak, playing an unexpectedly crucial rôle in the production of régimes of chaotic behaviour. This has already been demonstrated in recent work on a case of a single unit incorporating just one series motor, which is governed by a novel autonomous set of nonlinear ODE's with three time-dependent variables and four control parameters. It will be of mathematical as well as geophysical and astrophysical interest to investigate systematically phase and amplitude locking and other types of behaviour in the more complicated cases that arise when N > 1, which can typically involve up to 6 N dependent variables and 19 N-5 control parameters. Even the simplest members of the hierarchy, with N as low as 1, 2 or 3, could prove useful as physically-realistic low-dimensional models in theoretical studies of fluctuating stellar and planetary magnetic fields. Geomagnetic polarity reversals could be affected by the presence of the Earth's solid metallic inner core, driven like an electric motor

  4. Nonzero bounded solutions of one class of nonlinear ordinary differential equations

    NASA Astrophysics Data System (ADS)

    Muhamadiev, Èrgashboy M.; Naimov, Alijon N.

    2011-09-01

    The paper is concerned with an ordinary differential equation of the form \\displaystyle -\\psi''(x)+\\biggl(1+\\frac c{x^2}\\biggr)\\psi(x)= \\frac1{x^\\alpha}\\vert\\psi(x)\\vert^{k-1}\\psi(x),\\qquad x>0,(1) where k and \\alpha are positive parameters, k>1, and c is a constant, subject to the boundary condition \\displaystyle \\psi(0)=0, \\qquad \\psi(+\\infty)=0.(2) A variational approach based on finding the eigenvalues of the gradient of the functional F_{k,\\alpha}(f)=\\displaystyle\\int_0^{+\\infty}\\vert f(s)\\vert^{k+1}s^{-\\alpha}\\,ds acting on the space of absolutely continuous functions H_0^1=\\{f:f,f'\\in L_2(0,+\\infty), f(0)=0\\} is used to show that if c>-1/4, k>1, 0<2\\alpha, then problem (1), (2) has a countable number of nonzero solutions, at least one of which is positive. For nonzero solutions, asymptotic formulae as x\\to0 and x\\to+\\infty are obtained. Bibliography: 7 titles.

  5. Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation

    NASA Astrophysics Data System (ADS)

    Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

    2016-04-01

    Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

  6. Nonzero bounded solutions of one class of nonlinear ordinary differential equations

    SciTech Connect

    Muhamadiev, Ergashboy M; Naimov, Alijon N

    2011-09-30

    The paper is concerned with an ordinary differential equation of the form -{psi}''(x)+(1+c/x{sup 2}){psi}(x)=1/x{sup {alpha}}|{psi}(x)|{sup k-1}{psi}(x), x>0; (1) where k and {alpha} are positive parameters, k>1, and c is a constant, subject to the boundary condition {psi}(0)=0, {psi}(+{infinity})=0; (2) A variational approach based on finding the eigenvalues of the gradient of the functional F{sub k,{alpha}}(f)={integral}{sub 0}{sup +}{infinity}|f(s)|{sup k+1}s{sup -}{alpha} ds acting on the space of absolutely continuous functions H{sub 0}{sup 1}={l_brace}f:f,f' element of L{sub 2}(0,+{infinity}), f(0)=0{r_brace} is used to show that if c>-1/4, k>1, 0<2{alpha}

  7. Differential Isotopic Fractionation during Cr(VI) Reduction by an Aquifer-Derived Bacterium under Aerobic versus Denitrifying Conditions

    PubMed Central

    Han, Ruyang; Qin, Liping; Brown, Shaun T.; Christensen, John N.

    2012-01-01

    We studied Cr isotopic fractionation during Cr(VI) reduction by Pseudomonas stutzeri strain RCH2. Despite the fact that strain RCH2 reduces Cr(VI) cometabolically under both aerobic and denitrifying conditions and at similar specific rates, fractionation was markedly different under these two conditions (ε was ∼2‰ aerobically and ∼0.4‰ under denitrifying conditions). PMID:22286991

  8. Differential Isotopic Fractionation during Cr(VI) Reduction by an Aquifer-Derived Bacterium under Aerobic versus Denitrifying Conditions

    SciTech Connect

    Han, R.; Qin, L.; Brown, S. T.; Christensen, J. N.; Beller, H. R.

    2012-01-27

    We studied Cr isotopic fractionation during Cr(VI) reduction by Pseudomonas stutzeri strain RCH2. Finally, despite the fact that strain RCH2 reduces Cr(VI) cometabolically under both aerobic and denitrifying conditions and at similar specific rates, fractionation was markedly different under these two conditions (ε was ~2‰ aerobically and ~0.4‰ under denitrifying conditions).

  9. Differentiation of roasted and soluble coffees through physical fractionation of selected essential and nonessential metals in their brews and exploratory data analysis.

    PubMed

    Pohl, Pawel; Szymczycha-Madeja, Anna; Stelmach, Ewelina; Welna, Maja

    2016-11-01

    An analytical scheme for physical fractionation of Al, Ba, Ca, Co, Fe, K, Mg, Mn, Na, Ni, Sr and Zn in ground roasted and soluble coffees brews was proposed. It was based on ultrafiltration through five ultrafiltration membranes having molecular weight cut-offs of 5, 10, 30, 50 and 100kDa. The highest ">100kDa" and the lowest "<5kDa" molecular weight fractions were established to differentiate the studied coffees brews the most. Al, Cu, Fe and Ni were mostly associated with the ">100kDa" fraction, while Co, K, Mg and Na - with the "<5kDa" fraction. For Ba, Ca, Mn, Sr and Zn, ">100kDa" and "<5kDa" fractions contributions were equally accounted. The physical fractionation pattern of selected metals was convenient for discovering important features of brews of both coffee types and differences between them by principal component analysis and then classifying them by linear discriminant analysis. PMID:27591664

  10. Adipose-Derived Stromal Vascular Fraction Differentially Expands Breast Progenitors in Tissue Adjacent to Tumors Compared to Healthy Breast Tissue

    PubMed Central

    Chatterjee, Sumanta; Laliberte, Mike; Blelloch, Sarah; Ratanshi, Imran; Safneck, Janice; Buchel, Ed

    2015-01-01

    Background: Autologous fat grafts supplemented with adipose-derived stromal vascular fraction are used in reconstructive and cosmetic breast procedures. Stromal vascular fraction contains adipose-derived stem cells that are thought to encourage wound healing, tissue regeneration, and graft retention. Although use of stromal vascular fraction has provided exciting perspectives for aesthetic procedures, no studies have yet been conducted to determine whether its cells contribute to breast tissue regeneration. The authors examined the effect of these cells on the expansion of human breast epithelial progenitors. Methods: From patients undergoing reconstructive breast surgery following mastectomies, abdominal fat, matching tissue adjacent to breast tumors, and the contralateral non–tumor-containing breast tissue were obtained. Ex vivo co-cultures using breast epithelial cells and the stromal vascular fraction cells were used to study the expansion potential of breast progenitors. Breast reduction samples were collected as a source of healthy breast cells. Results: The authors observed that progenitors present in healthy breast tissue or contralateral non–tumor-containing breast tissue showed significant and robust expansion in the presence of stromal vascular fraction (5.2- and 4.8-fold, respectively). Whereas the healthy progenitors expanded up to 3-fold without the stromal vascular fraction cells, the expansion of tissue adjacent to breast tumor progenitors required the presence of stromal vascular fraction cells, leading to a 7-fold expansion, which was significantly higher than the expansion of healthy progenitors with stromal vascular fraction. Conclusions: The use of stromal vascular fraction might be more beneficial to reconstructive operations following mastectomies compared with cosmetic corrections of the healthy breast. Future studies are required to examine the potential risk factors associated with its use. CLINICAL QUESTION/LEVEL OF EVIDENCE

  11. A New Inertial Aid Method for High Dynamic Compass Signal Tracking Based on a Nonlinear Tracking Differentiator

    PubMed Central

    Guo, Yao; Wu, Wenqi; Tang, Kanghua

    2012-01-01

    In Compass/INS integrated navigation systems, feedback inertial navigation solutions to baseband tracking loops may eliminate receiver dynamic effects, and effectively improve the tracking accuracy and sensitivity. In the conventional inertially-aided tracking loop, the satellite-receiver line-of-sight velocity is used directly to adjust local carrier frequency. However, if the inertial solution drifts, the phase tracking error will be enlarged. By using Kalman filter based carrier phase tracking loop, this paper introduces a new inertial aid method, in which the line-of-sight jerk obtained from inertial acceleration by a nonlinear tracking differentiator is used to adjust relevant parameters of the Kalman filter's process noise matrix. Validation is achieved through high dynamic Compass B3 signal with line-of-sight jerk of 10 g/s collected by a GNSS simulator. Experimental results indicate that the new inertial aid method proposed in this paper is free of the impact of the receiver dynamic and inertial errors. Therefore, when the integrated navigation system is starting or re-tracking after losing lock, the inertial error is absent from the navigation solution correction that induces large drift, and the new aid method proposed in this paper can track highly dynamic signals. PMID:22969365

  12. The Tocotrienol-Rich Fraction Is Superior to Tocopherol in Promoting Myogenic Differentiation in the Prevention of Replicative Senescence of Myoblasts.

    PubMed

    Khor, Shy Cian; Razak, Azraul Mumtazah; Wan Ngah, Wan Zurinah; Mohd Yusof, Yasmin Anum; Abdul Karim, Norwahidah; Makpol, Suzana

    2016-01-01

    Aging results in a loss of muscle mass and strength. Myoblasts play an important role in maintaining muscle mass through regenerative processes, which are impaired during aging. Vitamin E potentially ameliorates age-related phenotypes. Hence, this study aimed to determine the effects of the tocotrienol-rich fraction (TRF) and α-tocopherol (ATF) in protecting myoblasts from replicative senescence and promoting myogenic differentiation. Primary human myoblasts were cultured into young and senescent stages and were then treated with TRF or ATF for 24 h, followed by an analysis of cell proliferation, senescence biomarkers, cellular morphology and differentiation. Our data showed that replicative senescence impaired the normal regenerative processes of myoblasts, resulting in changes in cellular morphology, cell proliferation, senescence-associated β-galactosidase (SA-β-gal) expression, myogenic differentiation and myogenic regulatory factors (MRFs) expression. Treatment with both TRF and ATF was beneficial to senescent myoblasts in reclaiming the morphology of young cells, improved cell viability and decreased SA-β-gal expression. However, only TRF treatment increased BrdU incorporation in senescent myoblasts, as well as promoted myogenic differentiation through the modulation of MRFs at the mRNA and protein levels. MYOD1 and MYOG gene expression and myogenin protein expression were modulated in the early phases of myogenic differentiation. In conclusion, the tocotrienol-rich fraction is superior to α-tocopherol in ameliorating replicative senescence-related aberration and promoting differentiation via modulation of MRFs expression, indicating vitamin E potential in modulating replicative senescence of myoblasts. PMID:26885980

  13. The Tocotrienol-Rich Fraction Is Superior to Tocopherol in Promoting Myogenic Differentiation in the Prevention of Replicative Senescence of Myoblasts

    PubMed Central

    Khor, Shy Cian; Razak, Azraul Mumtazah; Wan Ngah, Wan Zurinah; Mohd Yusof, Yasmin Anum; Abdul Karim, Norwahidah; Makpol, Suzana

    2016-01-01

    Aging results in a loss of muscle mass and strength. Myoblasts play an important role in maintaining muscle mass through regenerative processes, which are impaired during aging. Vitamin E potentially ameliorates age-related phenotypes. Hence, this study aimed to determine the effects of the tocotrienol-rich fraction (TRF) and α-tocopherol (ATF) in protecting myoblasts from replicative senescence and promoting myogenic differentiation. Primary human myoblasts were cultured into young and senescent stages and were then treated with TRF or ATF for 24 h, followed by an analysis of cell proliferation, senescence biomarkers, cellular morphology and differentiation. Our data showed that replicative senescence impaired the normal regenerative processes of myoblasts, resulting in changes in cellular morphology, cell proliferation, senescence-associated β-galactosidase (SA-β-gal) expression, myogenic differentiation and myogenic regulatory factors (MRFs) expression. Treatment with both TRF and ATF was beneficial to senescent myoblasts in reclaiming the morphology of young cells, improved cell viability and decreased SA-β-gal expression. However, only TRF treatment increased BrdU incorporation in senescent myoblasts, as well as promoted myogenic differentiation through the modulation of MRFs at the mRNA and protein levels. MYOD1 and MYOG gene expression and myogenin protein expression were modulated in the early phases of myogenic differentiation. In conclusion, the tocotrienol-rich fraction is superior to α-tocopherol in ameliorating replicative senescence-related aberration and promoting differentiation via modulation of MRFs expression, indicating vitamin E potential in modulating replicative senescence of myoblasts. PMID:26885980

  14. Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm.

    PubMed

    Chow, Sy-Miin; Lu, Zhaohua; Sherwood, Andrew; Zhu, Hongtu

    2016-03-01

    The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation-maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed. PMID:25416456

  15. Relationship between fractional calculus and fractional Fourier transform

    NASA Astrophysics Data System (ADS)

    Zhang, Yanshan; Zhang, Feng; Lu, Mingfeng

    2015-09-01

    The fractional calculus (FC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus. The fractional Fourier transform (FRFT), which has been found having many applications in optics and other areas, is a generalization of the usual Fourier transform. The FC and the FRFT are two of the most interesting and useful fractional areas. In recent years, it appears many papers on the FC and FRFT, however, few of them discuss the connection of the two fractional areas. We study their relationship. The relational expression between them is deduced. The expectation of interdisciplinary cross fertilization is our motivation. For example, we can use the properties of the FC (non-locality, etc.) to solve the problem which is difficult to be solved by the FRFT in optical engineering; we can also through the physical meaning of the FRFT optical implementation to explain the physical meaning of the FC. The FC and FRFT approaches can be transposed each other in the two fractional areas. It makes that the success of the fractional methodology is unquestionable with a lot of applications, namely in nonlinear and complex system dynamics and image processing.

  16. Chaos in a Fractional Order Chua System

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.; Qammar, Helen Killory

    1996-01-01

    This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.

  17. On the Time Fractional Generalized Fisher Equation: Group Similarities and Analytical Solutions

    NASA Astrophysics Data System (ADS)

    M. S., Hashemi; Baleanu, D.

    2016-01-01

    In this letter, the Lie point symmetries of the time fractional Fisher (TFF) equation have been derived using a systematic investigation. Using the obtained Lie point symmetries, TFF equation has been transformed into a different nonlinear fractional ordinary differential equations with the Erdélyi-Kober fractional derivative which depends on the parameter α. After that some invariant solutions of underlying equation are reported.

  18. Improved generalized F-expansion method for the time fractional modified KdV(fmKdV) equation

    NASA Astrophysics Data System (ADS)

    Sonmezoglu, Abdullah

    2016-06-01

    In this article, an improved generalized F-expansion method is used for solving the time fractional modified KdV(fmKdV) equation. Using this approach new Jacobi elliptic function solutions are obtained. This method can be suitable for solving other nonlinear fractional differential equations.

  19. Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. Part 2; Global Asymptotic Behavior of Time Discretizations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sweby, P. K.

    1995-01-01

    The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

  20. Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. 2; Global Asymptotic Behavior of Time Discretizations; 2. Global Asymptotic Behavior of time Discretizations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sweby, P. K.

    1995-01-01

    The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

  1. Fluid fractionation of tungsten during granite-pegmatite differentiation and the metal source of peribatholitic W quartz veins: Evidence from the Karagwe-Ankole Belt (Rwanda)

    NASA Astrophysics Data System (ADS)

    Hulsbosch, Niels; Boiron, Marie-Christine; Dewaele, Stijn; Muchez, Philippe

    2016-02-01

    The identification of a magmatic source for granite-associated rare metal (W, Nb, Ta and Sn) mineralisation in metasediment-hosted quartz veins is often obscured by intense fluid-rock interactions which metamorphically overprinted most source signatures in the vein system. In order to address this recurrent metal sourcing problem, we have studied the metasediment-hosted tungsten-bearing quartz veins of the Nyakabingo deposit of the Karagwe-Ankole belt in Central Rwanda. The vein system (992 ± 2 Ma) is spatiotemporal related to the well-characterised B-rich, F-poor G4 leucogranite-pegmatite suite (986 ± 10 Ma to 975 ± 8 Ma) of the Gatumba-Gitarama area which culminated in Nb-Ta-Sn mineralisation. Muscovite in the Nyakabingo veins is significantly enriched in granitophile elements (Rb, Cs, W and Sn) and show alkali metal signatures equivalent to muscovite of less-differentiated pegmatite zones of the Gatumba-Gitarama area. Pegmatitic muscovite records a decrease in W content with increasing differentiation proxies (Rb and Cs), in contrast to the continuous enrichment of other high field strength elements (Nb and Ta) and Sn. This is an indication of a selective redistribution for W by fluid exsolution and fluid fractionation. Primary fluid inclusions in tourmaline of these less-differentiated pegmatites demonstrate the presence of medium to low saline, H2O-NaCl-KCl-MgCl2-complex salt (e.g. Rb, Cs) fluids which started to exsolve at the G4 granite-pegmatite transition stage. Laser ablation inductively coupled plasma mass-spectrometry shows significant tungsten enrichment in these fluid phases (∼5-500 ppm). Fractional crystallisation has been identified previously as the driving mechanism for the transition from G4 granites, less-differentiated biotite, biotite-muscovite towards muscovite pegmatites and eventually columbite-tantalite mineralised pegmatites. The general absence of tungsten mineralisation in this magmatic suite, including the most differentiated

  2. A new 3D parallel high resolution electromagnetic nonlinear inversion based on new global magnetic integral and local differential decomposition (GILD)

    SciTech Connect

    Xie, G.; Li, J.

    1997-05-01

    A new 3D electromagnetic modeling and nonlinear inversion algorithm is presented based on global integral and local differential equations decomposition (GILD). The GILD parallel nonlinear inversion algorithm consists of five parts: (1) the domain is decomposed into subdomain SI and subdomain SII; (2) a new global magnetic integral equation in SI and the local magnetic differential equations IN SII will be used together to obtain the magnetic field in the modeling step; (3) the new global magnetic integral Jacobian equation in SI and the local magnetic differential Jacobian equations in SII will be used together to update the electric conductivity and permittivity from the magnetic field data in the inversion step; (4) the subdomain SII can naturally and uniformly be decomposed into 2{sup n} smaller sub-cubic-domains; the sparse matrix in each sub-cubic-domain can be eliminated separately, in parallel; (5) a new parallel multiple hierarchy substructure algorithm will be used to solve the smaller full matrices in SI, in parallel. The applications of the new 3D parallel GILD EM modeling and nonlinear inversion algorithm and software are: (1) to create high resolution controlled-source electric conductivity and permittivity imaging for interpreting electromagnetic field data acquired from cross hole, surface to borehole, surface to surface, single hole, and multiple holes; (2) to create the magnetotelluric high resolution imaging from the surface impedance and field data. The new GILD parallel nonlinear inversion will be a 3D/2.5D powerful imaging tool for the oil geophysical exploration and environmental remediation and monitoring.

  3. Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

    PubMed

    Kleinert, H; Zatloukal, V

    2013-11-01

    The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration. PMID:24329213

  4. FRACTIONAL INTEGRATION TOOLBOX

    PubMed Central

    Marinov, Toma M.; Ramirez, Nelson; Santamaria, Fidel

    2014-01-01

    The problems formulated in the fractional calculus framework often require numerical fractional integration/differentiation of large data sets. Several existing fractional control toolboxes are capable of performing fractional calculus operations, however, none of them can efficiently perform numerical integration on multiple large data sequences. We developed a Fractional Integration Toolbox (FIT), which efficiently performs fractional numerical integration/differentiation of the Riemann-Liouville type on large data sequences. The toolbox allows parallelization and is designed to be deployed on both CPU and GPU platforms. PMID:24812536

  5. Nonlinear waveguides

    NASA Astrophysics Data System (ADS)

    SjöBerg, Daniel

    2003-04-01

    We investigate the propagation of electromagnetic waves in a cylindrical waveguide with an arbitrary cross section filled with a nonlinear material. The electromagnetic field is expanded in the usual eigenmodes of the waveguide, and the coupling between the modes is quantified. We derive the wave equations governing each mode with special emphasis on the situation with a dominant TE mode. The result is a strictly hyperbolic system of nonlinear partial differential equations for the dominating mode, whereas the minor modes satisfy hyperbolic systems of linear, nonstationary, and partial differential equations. A growth estimate is given for the minor modes.

  6. Fractional vector calculus and fractional Maxwell's equations

    SciTech Connect

    Tarasov, Vasily E.

    2008-11-15

    The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered.

  7. Phase-Space Reconstruction: a Path Towards the Next Generation of Nonlinear Differential Equation Based Models and Its Implications Towards Non-Uniform Sampling Theory

    SciTech Connect

    Charles R. Tolle; Mark Pengitore

    2009-08-01

    This paper explores the overlaps between the Control community’s work on System Identification (SysID) and the Physics, Mathematics, Chaos, and Complexity communities’ work on phase-space reconstruction via time-delay embedding. There are numerous overlaps between the goals of each community. Nevertheless, the Controls community can gain new insight as well as some new very powerful tools for SysID from the latest developments within the Physics, Mathematics, Chaos, and Complexity communities. These insights are gained via the work on phase-space reconstruction of non-linear dynamics. New methods for discovering non-linear differential based equations that evolved from embedding operations can shed new light on hybrid-systems theory, Nyquest-Shannon’s Theories, and network based control theory. This paper strives to guide the Controls community towards a closer inspection of the tools and additional insights being developed within the Physics, Mathematics, Chaos, and Complexity communities for discovery of system dynamics, the first step in control system development. The paper introduces the concepts of phase-space reconstruction via time-delay embedding (made famous byWhitney, Takens, and Sauer’s Thoreoms), intergrate-and-fire embedding, and non-linear differential equation discovery based on Perona’s method.

  8. Endothelial Progenitor Cell Fraction Contained in Bone Marrow-Derived Mesenchymal Stem Cell Populations Impairs Osteogenic Differentiation

    PubMed Central

    Duttenhoefer, Fabian; Lara de Freitas, Rafael; Loibl, Markus; Bittermann, Gido; Geoff Richards, R.; Alini, Mauro; Verrier, Sophie

    2015-01-01

    In bone tissue engineering (TE) endothelial cell-osteoblast cocultures are known to induce synergies of cell differentiation and activity. Bone marrow mononucleated cells (BMCs) are a rich source of mesenchymal stem cells (MSCs) able to develop an osteogenic phenotype. Endothelial progenitor cells (EPCs) are also present within BMC. In this study we investigate the effect of EPCs present in the BMC population on MSCs osteogenic differentiation. Human BMCs were isolated and separated into two populations. The MSC population was selected through plastic adhesion capacity. EPCs (CD34+ and CD133+) were removed from the BMC population and the resulting population was named depleted MSCs. Both populations were cultured over 28 days in osteogenic medium (Dex+) or medium containing platelet lysate (PL). MSC population grew faster than depleted MSCs in both media, and PL containing medium accelerated the proliferation for both populations. Cell differentiation was much higher in Dex+ medium in both cases. Real-time RT-PCR revealed upregulation of osteogenic marker genes in depleted MSCs. Higher values of ALP activity and matrix mineralization analyses confirmed these results. Our study advocates that absence of EPCs in the MSC population enables higher osteogenic gene expression and matrix mineralization and therefore may lead to advanced bone neoformation necessary for TE constructs. PMID:26491682

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

    NASA Astrophysics Data System (ADS)

    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.

  10. Molecular size fractions of bay leaf (Laurus nobilis) exhibit differentiated regulation of colorectal cancer cell growth in vitro.

    PubMed

    Bennett, Louise; Abeywardena, Mahinda; Burnard, Sharon; Forsyth, Santina; Head, Richard; King, Kerryn; Patten, Glen; Watkins, Peter; Williams, Roderick; Zabaras, Dimitrios; Lockett, Trevor

    2013-01-01

    Numerous in vitro studies using solvent or aqueous extracts of raw dietary plant material have demonstrated modulation of colon cancer cell growth and apoptosis and effects on immune and nonimmune pathways of inflammation. We have developed a generic, 3-staged food-compatible process involving heating for conversion of dietary plants into food ingredients and report results on potential colon cancer-regulating properties of processed forms of Bay leaf (Laurus nobilis). In vitro studies demonstrated inhibition of cancer cell growth by processed Bay leaf products in HT-29, HCT-116, Caco-2, and SW-480 human cancer cell lines, which were accompanied by variable levels of elevated apoptosis. Bay leaf also exerted moderate inhibition of cycloxygenase 2 and 5 lipoxygenase enzymatic activity. In addition, these extracts significantly downregulated interferon-γ production in T helper Type 1-stimulated whole blood from healthy donors. Furthermore, size fractionation of the extracts revealed that antiproliferative and proapoptotic activities were associated with low mass (primarily polyphenolics and essential oils) and high mass (primarily proteins including polyphenol oxidase) chemical classes, respectively. Bay leaf exerted in vitro bioactivity that might be relevant to protecting against early events in sporadic colorectal cancer, with potential for further optimization of bioactivity by size-based fractionation. PMID:23859043

  11. The bi-Hamiltonian structure of some nonlinear fifth- and seventh-order differential equations and recursion formulas for their symmetries and conserved covariants

    NASA Astrophysics Data System (ADS)

    Fuchssteiner, Benno; Oevel, Walter

    1982-03-01

    Using a bi-Hamiltonian formulation we give explicit formulas for the conserved quantities and infinitesimal generators of symmetries for some nonlinear fifth- and seventh-order nonlinear partial differential equations; among them, the Caudrey-Dodd-Gibbon-Sawada-Kotera equation and the Kupershmidt equation. We show that the Lie algebras of the symmetry groups of these equations are of a very special form: Among the C∞ vector fields they are generated from two given commuting vector fields by a recursive application of a single operator. Furthermore, for some higher order equations, those multisoliton solutions, which for ||t||→∞ asymptotically decompose into traveling wave solutions, are characterized as eigenvector decompositions of certain operators.

  12. Fractionation of Zr and Hf during the differentiation of peralkaline magmatic system (Lovozero rare metal deposit, Kola Peninsula)

    NASA Astrophysics Data System (ADS)

    Kogarko, Liya

    2016-04-01

    Zirconium and hafnium are valuable strategic metals. We assessed principal features of the distribution of these elements in peralkaline rocks, ores and rock-forming and accessory minerals of Lovozero complex. The accumulation of these elements during the evolution of alkaline magma of Lovozero deposit up to extremely high concentrations in eudialyte ores (5-8% ZrO2 and 1200-1800 ppm Hf) has been established. These ores represent valuable complex raw material not only for Zr and Hf, but for REE as well. We evaluated partition coefficients of these elements in alkaline pyroxenes (aegirines) from porphyry-like agpaitic lujavrites of Lovozero massif which are 0.40 for zirconium and 0.58 for hafnium. We assessed variations of Zr/Hf ratio for all the rocks of Lovozero alkaline massif. The growth of this ratio in the course of the evolution of alkaline magma has been observed from 38 in the earliest magmatic phase, to 44 in the second phase and to 51-53 in the latest manifestation of alkaline magmatsm. On the basis of the obtained data and equations of equilibrium and fractional crystallization the model of the fractionation of zirconium and hafnium during the evolution of Lovozero intrusion has been constructed. We have demonstrated that the source of strongly enriched magmatic systems similar to Lovozero rare metal deposit is short-lived enriched reservoir - metasomatized and carbonatized mantle substrate. We investigated the fractionation of zirconium and hafnium in carbonatized mantle xenoliths from East Antarctica. The elevated Zr/Hf ratios (up to 125) in metasomatized xenoliths by comparison with the chondritic value have been found. The main reactions of carbonate metasomatism lead to the replacement of primary orthopyroxene by clinopyroxene 2Mg2Si2O6 + CaMg(CO3)2 = 2Mg2SiO4 + CaMgSi2O6 + 2CO2 3CaMg(CO3)2 + CaMgSi2O6 = 4CaCO3 + 2Mg2SiO4 + 2CO2 The substantial expansion of the clinopyroxene crystallization field results in increase of Zr/Hf ratio in equilibrium

  13. Polysaccharide characterization by hollow-fiber flow field-flow fractionation with on-line multi-angle static light scattering and differential refractometry.

    PubMed

    Pitkänen, Leena; Striegel, André M

    2015-02-01

    Accurate characterization of the molar mass and size of polysaccharides is an ongoing challenge, oftentimes due to architectural diversity but also to the broad molar mass (M) range over which a single polysaccharide can exist and to the ultra-high M of many polysaccharides. Because of the latter, many of these biomacromolecules experience on-column, flow-induced degradation during analysis by size-exclusion and, even, hydrodynamic chromatography (SEC and HDC, respectively). The necessity for gentler fractionation methods has, to date, been addressed employing asymmetric flow field-flow fractionation (AF4). Here, we introduce the coupling of hollow-fiber flow field-flow fractionation (HF5) to multi-angle static light scattering (MALS) and differential refractometry (DRI) detection for the analysis of polysaccharides. In HF5, less stresses are placed on the macromolecules during separation than in SEC or HDC, and HF5 can offer a higher sensitivity, with less propensity for system overloading and analyte aggregation, than generally found in AF4. The coupling to MALS and DRI affords the determination of absolute, calibration-curve-independent molar mass averages and dispersities. Results from the present HF5/MALS/DRI experiments with dextrans, pullulans, and larch arabinogalactan were augmented with hydrodynamic radius (RH) measurements from off-line quasi-elastic light scattering (QELS) and by RH distribution calculations and fractogram simulations obtained via a finite element analysis implementation of field-flow fractionation theory by commercially available software. As part of this study, we have investigated analyte recovery in HF5 and also possible reasons for discrepancies between calculated and simulated results vis-à-vis experimentally determined data. PMID:25578045

  14. [Value of Fractional Exhaled Nitric Oxide after Using a Beta-2 Bronchodilator in the Differential Diagnosis of Bronchial Asthma and Chronic Obstructive Pulmonary Disease].

    PubMed

    Ura, Midori; Tanaka, Hitomi; Takahashi, Kaori; Yamazaki, Haruna; Fujimoto, Keisaku

    2016-02-01

    It has been established that an increase in fractional exhaled nitric oxide (FeNO) is one of the indicators of bronchial asthma (BA) in clinical settings. However, the differential diagnosis of BA and chronic obstructive pulmonary disease (COPD) is difficult due to pathological similarities. Therefore, to determine if FeNO may be utilized in the differential diagnosis of BA and COPD, we compared FeNO values before and after inhalation of a short-acting beta-2 agonist (SABA). There were 3 groups of subjects recruited to this study: (1) 23 normal healthy controls, (2) 36 patients with BA, and (3) 13 patients with COPD. We measured FeNO, forced vital capacity, forced expiratory volume in 1 second (FEV1), and FEV1%, calculated using spirometry. Then, after the subjects inhaled the SABA, we measured these data after 10 and 30 minutes. Here we found that after inhalation of a SABA, 8 cases in the BA group who showed reversibility of airway obstruction demonstrated significantly increased FeNO values compared to the BA patients with non-reversible airway obstruction, those with COPD, and healthy subjects. This finding may be because the obstructed pulmonary peripheral airway was expanded by inhaling a SABA, and nitric oxide, which had been produced in the peripheral airway, was then exhaled. These results suggest the possibility that FeNO may be utilized in the differential diagnosis of BA and COPD. PMID:27311275

  15. Numerical investigation of mixed convective hydromagnetic nonlinear nanofluid flow past an inclined plate

    NASA Astrophysics Data System (ADS)

    Anjali Devi, S. P.; Suriyakumar, P.

    2013-09-01

    The nonlinear, steady, mixed convective, two-dimensional laminar hydromagnetic boundary layer flow of copper-water and alumina-water nanofluids over an inclined flat plate with an angle of inclination α in the presence of uniform transverse magnetic field is investigated in this work. The governing nonlinear partial differential equations of the problem are transformed into nonlinear ordinary differential equations by utilizing suitable similarity transformations and the resulting nonlinear ordinary differential equations are solved numerically using MATLAB. Numerical results for dimensionless velocity and temperature of the nanofluid flows are obtained and computations for the various values of Magnetic interaction parameter, angle of inclination, volume fraction, Prandtl number and mixed convection parameter. The range of volume fraction of nanofluids and the angle of inclination under study are as follows: 0.00 ≤ φ ≤ 0.10 and 0° ≤ α ≤ 60°. The results are displayed graphically to show the interesting aspects of the nanofluids.

  16. On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: A general approach

    NASA Astrophysics Data System (ADS)

    Van Gorder, Robert A.; Vajravelu, K.

    2009-12-01

    The Homotopy Analysis Method of Liao [Liao SJ. Beyond perturbation: introduction to the Homotopy Analysis Method. Boca Raton: Chapman & Hall/CRC Press; 2003] has proven useful in obtaining analytical solutions to various nonlinear differential equations. In this method, one has great freedom to select auxiliary functions, operators, and parameters in order to ensure the convergence of the approximate solutions and to increase both the rate and region of convergence. We discuss in this paper the selection of the initial approximation, auxiliary linear operator, auxiliary function, and convergence control parameter in the application of the Homotopy Analysis Method, in a fairly general setting. Further, we discuss various convergence requirements on solutions.

  17. Differentiation of lemon essential oil based on volatile and non-volatile fractions with various analytical techniques: a metabolomic approach.

    PubMed

    Mehl, Florence; Marti, Guillaume; Boccard, Julien; Debrus, Benjamin; Merle, Philippe; Delort, Estelle; Baroux, Lucie; Raymo, Vilfredo; Velazco, Maria Inés; Sommer, Horst; Wolfender, Jean-Luc; Rudaz, Serge

    2014-01-15

    Due to the importance of citrus lemon oil for the industry, fast and reliable analytical methods that allow the authentication and/or classification of such oil, using the origin of production or extraction process, are necessary. To evaluate the potential of volatile and non-volatile fractions for classification purposes, volatile compounds of cold-pressed lemon oils were analyzed, using GC-FID/MS and FT-MIR, while the non-volatile residues were studied, using FT-MIR, (1)H-NMR and UHPLC-TOF-MS. 64 Lemon oil samples from Argentina, Spain and Italy were considered. Unsupervised and supervised multivariate analyses were sequentially performed on various data blocks obtained by the above techniques. Successful data treatments led to statistically significant models that discriminated and classified cold-pressed lemon oils according to their geographic origin, as well as their production processes. Studying the loadings allowed highlighting of important classes of discriminant variables that corresponded to putative or identified chemical functions and compounds. PMID:24054247

  18. Λb→Λ ℓ+ℓ- form factors, differential branching fraction, and angular observables from lattice QCD with relativistic b quarks

    NASA Astrophysics Data System (ADS)

    Detmold, William; Meinel, Stefan

    2016-04-01

    Using (2 +1 )-flavor lattice QCD, we compute the 10 form factors describing the Λb→Λ matrix elements of the b →s vector, axial vector, and tensor currents. The calculation is based on gauge field ensembles generated by the RBC and UKQCD Collaborations with a domain-wall action for the u , d , and s quarks and the Iwasaki gauge action. The b quark is implemented using an anisotropic clover action, tuned nonperturbatively to the physical point, and the currents are renormalized with a mostly nonperturbative method. We perform simultaneous chiral, continuum, and kinematic extrapolations of the form factors through modified z expansions. Using our form factor results, we obtain precise predictions for the Λb→Λ (→p+π-)μ+μ- differential branching fraction and angular observables in the Standard Model.

  19. Quantification and parametrization of non-linearity effects by higher-order sensitivity terms in scattered light differential optical absorption spectroscopy

    NASA Astrophysics Data System (ADS)

    Puķīte, Jānis; Wagner, Thomas

    2016-05-01

    We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on

  20. Analytic solutions to nonlinear differential-difference equations by means of the extended (G'/G)-expansion method

    NASA Astrophysics Data System (ADS)

    Aslan, İsmail

    2010-10-01

    In this paper, a discrete extension of the (G'/G)-expansion method is applied to a relativistic Toda lattice system and a discrete nonlinear Schrödinger equation in order to obtain discrete traveling wave solutions. Closed form solutions with more arbitrary parameters, which reduce to solitary and periodic waves, are exhibited. New rational solutions are also obtained. The method is straightforward and concise, and its applications in physical sciences are promising.

  1. Cyclohexane-1,2-dicarboxylic acid diisononyl ester and metabolite effects on rat epididymal stromal vascular fraction differentiation of adipose tissue.

    PubMed

    Campioli, Enrico; Duong, Tam B; Deschamps, François; Papadopoulos, Vassilios

    2015-07-01

    Plastics are generally mixed with additives like plasticizers to enhance their flexibility, pliability, and elasticity proprieties. Plasticizers are easily released into the environment and are absorbed mainly through ingestion, dermal contact, and inhalation. One of the main classes of plasticizers, phthalates, has been associated with endocrine and reproductive diseases. In 2002, 1,2-cyclohexane dicarboxylic acid diisononyl ester (DINCH) was introduced in the market for use in plastic materials and articles intended to come into contact with food, and it received final approval from the European Food Safety Authority in 2006. At present, there is limited knowledge about the safety and potential metabolic and endocrine-disrupting properties of DINCH and its metabolites. The purpose of this study was to evaluate the biological effects of DINCH and its active metabolites, cyclohexane-1,2-dicarboxylic acid (CHDA) and cyclohexane-1,2-dicarboxylic acid mono isononyl ester (MINCH), on rat primary stromal vascular fraction (SVF) of adipose tissue. DINCH and its metabolite, CHDA, were not able to directly affect SVF differentiation. However, exposure of SVF to 50 μM and 100 μM concentrations of MINCH affected the expression of Cebpa and Fabp4, thus inducing SVF preadipocytes to accumulate lipids and fully differentiate into mature adipocytes. The effect of MINCH was blocked by the specific peroxisome proliferator-activated receptor (PPAR)-α antagonist, GW6471. Taken together, these results suggest that MINCH is a potent PPAR-α agonist and a metabolic disruptor, capable of inducing SVF preadipocyte differentiation, that may interfere with the endocrine system in mammals. PMID:25863588

  2. Cyclohexane-1,2-dicarboxylic acid diisononyl ester and metabolite effects on rat epididymal stromal vascular fraction differentiation of adipose tissue

    SciTech Connect

    Campioli, Enrico; Duong, Tam B.; Deschamps, François; Papadopoulos, Vassilios

    2015-07-15

    Plastics are generally mixed with additives like plasticizers to enhance their flexibility, pliability, and elasticity proprieties. Plasticizers are easily released into the environment and are absorbed mainly through ingestion, dermal contact, and inhalation. One of the main classes of plasticizers, phthalates, has been associated with endocrine and reproductive diseases. In 2002, 1,2-cyclohexane dicarboxylic acid diisononyl ester (DINCH) was introduced in the market for use in plastic materials and articles intended to come into contact with food, and it received final approval from the European Food Safety Authority in 2006. At present, there is limited knowledge about the safety and potential metabolic and endocrine-disrupting properties of DINCH and its metabolites. The purpose of this study was to evaluate the biological effects of DINCH and its active metabolites, cyclohexane-1,2-dicarboxylic acid (CHDA) and cyclohexane-1,2-dicarboxylic acid mono isononyl ester (MINCH), on rat primary stromal vascular fraction (SVF) of adipose tissue. DINCH and its metabolite, CHDA, were not able to directly affect SVF differentiation. However, exposure of SVF to 50 μM and 100 μM concentrations of MINCH affected the expression of Cebpa and Fabp4, thus inducing SVF preadipocytes to accumulate lipids and fully differentiate into mature adipocytes. The effect of MINCH was blocked by the specific peroxisome proliferator-activated receptor (PPAR)-α antagonist, GW6471. Taken together, these results suggest that MINCH is a potent PPAR-α agonist and a metabolic disruptor, capable of inducing SVF preadipocyte differentiation, that may interfere with the endocrine system in mammals. - Highlights: • DINCH and CHDA did not affect the adipogenesis of the SVF. • MINCH affected the adipogenesis of the SVF. • MINCH effect was blocked by the specific PPAR-α antagonist GW6471. • MINCH exerted a similar effect as MEHP on SVF adipogenesis. • DINCH/MINCH are potential metabolic

  3. The nonlinear relationship between albedo and cloud fraction on near-global, monthly mean scale in observations and in the CMIP5 model ensemble

    NASA Astrophysics Data System (ADS)

    Engström, A.; Bender, F. A.-M.; Charlson, R. J.; Wood, R.

    2015-11-01

    We study the relation between monthly mean albedo and cloud fraction over ocean, 60°S-60°N. Satellite observations indicate that these clouds all fall on the same near-exponential curve, with a monotonic distribution over the ranges of cloud fractions and albedo. Using these observational data as a reference, we examine the degree to which 26 climate models capture this feature of the near-global marine cloud population. Models show a general increase in albedo with increasing cloud fraction, but none of them display a relation that is as well defined as that characterizing the observations. Models typically display larger albedo variability at a given cloud fraction, larger sensitivity in albedo to changes in cloud fraction, and lower cloud fractions. Several models also show branched distributions, contrasting with the smooth observational relation. In the models the present-day cloud scenes are more reflective than the preindustrial, demonstrating the simulated impact of anthropogenic aerosols on planetary albedo.

  4. Cubication of Conservative Nonlinear Oscillators

    ERIC Educational Resources Information Center

    Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada

    2009-01-01

    A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…

  5. Exact solutions of the Liénard- and generalized Liénard-type ordinary nonlinear differential equations obtained by deforming the phase space coordinates of the linear harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Harko, Tiberiu; Liang, Shi-Dong

    2016-06-01

    We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\\'enard and generalized Li\\'enard type, which physically describe important oscillator systems. By using a method inspired by quantum mechanics, and which consist on the deformation of the phase space coordinates of the harmonic oscillator, we generalize the equation of motion of the classical linear harmonic oscillator to several classes of strongly non-linear differential equations. The first integrals, and a number of exact solutions of the corresponding equations are explicitly obtained. The devised method can be further generalized to derive explicit general solutions of nonlinear second order differential equations unrelated to the harmonic oscillator. Applications of the obtained results for the study of the travelling wave solutions of the reaction-convection-diffusion equations, and of the large amplitude free vibrations of a uniform cantilever beam are also presented.

  6. NONLINEAR-APPROXIMATION TECHNIQUE FOR DETERMINING VERTICAL OZONE-CONCENTRATION PROFILES WITH A DIFFERENTIAL-ABSORPTION LIDAR

    EPA Science Inventory

    A new technique is presented for the retrieval of ozone concentration profiles from backscattered signals obtained by a multi-wavelength differential-absorption lidar (DIAL). The technique makes it possible to reduce erroneous local fluctuations induced in the ozone-concentration...

  7. A high-order and unconditionally stable scheme for the modified anomalous fractional sub-diffusion equation with a nonlinear source term

    NASA Astrophysics Data System (ADS)

    Mohebbi, Akbar; Abbaszadeh, Mostafa; Dehghan, Mehdi

    2013-05-01

    The aim of this paper is to study the high order difference scheme for the solution of modified anomalous fractional sub-diffusion equation. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grünwald-Letnikov discretization of the Riemann-Liouville derivative to obtain a fully discrete implicit scheme. We analyze the solvability, stability and convergence of the proposed scheme using the Fourier method. The convergence order of method is O(τ+h4). Numerical examples demonstrate the theoretical results and high accuracy of the proposed scheme.

  8. Algebro-Geometric Solutions with Characteristics of a Nonlinear Partial Differential Equation with Three-Potential Functions

    NASA Astrophysics Data System (ADS)

    Zhang, Yu-Feng; Feng, Bin-Lu; Rui, Wen-Juan; Zhang, Xiang-Zhi

    2015-07-01

    With the help of a simple Lie algebra, an isospectral Lax pair, whose feature presents decomposition of element (1, 2) into a linear combination in the temporal Lax matrix, is introduced for which a new integrable hierarchy of evolution equations is obtained, whose Hamiltonian structure is also derived from the trace identity in which contains a constant γ to be determined. In the paper, we obtain a general formula for computing the constant γ. The reduced equations of the obtained hierarchy are the generalized nonlinear heat equation containing three-potential functions, the mKdV equation and a generalized linear KdV equation. The algebro-geometric solutions (also called finite band solutions) of the generalized nonlinear heat equation are obtained by the use of theory on algebraic curves. Finally, two kinds of gauge transformations of the spatial isospectral problem are produced. Supported by the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014) and the National Natural Science Foundation of China under Grant No. 11371361, the Fundamental Research Funds for the Central Universities (2013XK03) as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016

  9. A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm.

    PubMed

    El-Qulity, Said Ali; Mohamed, Ali Wagdy

    2016-01-01

    This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness. PMID:26819583

  10. A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm

    PubMed Central

    El-Qulity, Said Ali; Mohamed, Ali Wagdy

    2016-01-01

    This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness. PMID:26819583

  11. Effects of the dichloromethane fraction of Dipsaci Radix on the osteoblastic differentiation of human alveolar bone marrow-derived mesenchymal stem cells.

    PubMed

    Kim, Beom-Su; Kim, Yoon-Chul; Zadeh, Homa; Park, Yoon-Jeong; Pi, Sung-Hee; Shin, Hyung-Shik; You, Hyung-Keun

    2011-01-01

    Dipsaci Radix is the dried root of Dipsacus asper Wall. It has been used in Korean herbal medicine to treat bone fractures. In this study, we examined the effect of the dichloromethane fraction of Dipsaci Radix (DR(DM)) on the osteoblastic differentiation of human alveolar bone marrow-derived MSCs (ABM-MSCs). The ABM-MSCs were isolated from healthy subjects and cultured in vitro, followed by phenotypic characterization. They showed a fibroblast-like morphology and expressed CD29, CD44, CD73, and CD105, but not CD34. Calcified nodules were generated in response to both dexamethasone (DEX) and DR(DM). There was a significant increase in the alkaline phosphatase (ALP) activity and protein expression of bone sialoprotein (BSP) and osteocalcin (OC) in response to DEX and DR(DM) as compared to control. These results provide evidence for the osteogenic potential of cultured ABM-MSCs in response to DR(DM). Also, an active single compound was additionally isolated from DR(DM). The single compound (hederagenin 3-O-(2-O-acetyl)-α-L-arabinopyranoside) also significantly increased ALP activity and the level of protein expression of BSP and OC. These results highlight the possible clinical applications of DR(DM) and hederagenin 3-O-(2-O-acetyl)-α-L-arabinopyranoside in bone regeneration. PMID:21228489

  12. Nonlinear Differential Equations and Feedback Control Design for the Urban-Rural Resident Pension Insurance in China

    NASA Astrophysics Data System (ADS)

    Wang, Lijian

    2015-12-01

    Facing many problems of the urban-rural resident pension insurance system in China, one should firstly make sure that this system can be optimized. This paper, based on the modern control theory, sets up differential equations as models to describe the urban-rural resident pension insurance system, and discusses the globally asymptotic stability in the sense of Liapunov for the urban-rural resident pension insurance system in the new equilibrium point. This research sets the stage for our further discussion, and it is theoretically important and convenient for optimizing the urban-rural resident pension insurance system.

  13. Trigonometric Integrals via Partial Fractions

    ERIC Educational Resources Information Center

    Chen, H.; Fulford, M.

    2005-01-01

    Parametric differentiation is used to derive the partial fractions decompositions of certain rational functions. Those decompositions enable us to integrate some new combinations of trigonometric functions.

  14. Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada-Kotera-Ito equation

    NASA Astrophysics Data System (ADS)

    Yaşar, Emrullah; Yıldırım, Yakup; Khalique, Chaudry Masood

    In this paper Lie symmetry analysis of the seventh-order time fractional Sawada-Kotera-Ito (FSKI) equation with Riemann-Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi-Kober sense. Furthermore, adapting the Ibragimov's nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method.

  15. Nonlinear-approximation technique for determining vertical ozone-concentration profiles with a differential-absorption lidar

    NASA Astrophysics Data System (ADS)

    Kovalev, Vladimir A.; Bristow, Michael P.; McElroy, James L.

    1996-08-01

    A new technique is presented for the retrieval of ozone-concentration profiles (O 3 ) from backscattered signals obtained by a multiwavelength differential-absorption lidar (DIAL). The technique makes it possible to reduce erroneous local fluctuations induced in the ozone-concentration profiles by signal noise and other phenomena such as aerosol inhomogeneity. Before the O 3 profiles are derived, the dominant measurement errors are estimated and uncertainty boundaries for the measured profiles are established. The off- to on-line signal ratio is transformed into an intermediate function, and analytical approximations of the function are then determined. The separation of low- and high-frequency constituents of the measured ozone profile is made by the application of different approximation fits to appropriate intermediate functions. The low-frequency constituents are approximated with a low-order polynomial fit, whereas the high-frequency constituents are approximated with a trigonometric fit. The latter fit makes it possible to correct the measured O 3 profiles in zones of large ozone-concentration gradients where the low-order polynomial fit is found to be insufficient. Application of this technique to experimental data obtained in the lower troposphere shows that erroneous fluctuations induced in the ozone-concentration profile by signal noise and aerosol inhomogeneity undergo a significant reduction in comparison with the results from the conventional technique based on straightforward numerical differentiation.

  16. Nonlinear-approximation technique for determining vertical ozone-concentration profiles with a differential-absorption lidar.

    PubMed

    Kovalev, V A; Bristow, M P; McElroy, J L

    1996-08-20

    A new technique is presented for the retrieval of ozone-concentration profiles (O(3)) from backscattered signals obtained by a multiwavelength differential-absorption lidar (DIAL). The technique makes it possible to reduce erroneous local fluctuations induced in the ozone-concentration profiles by signal noise and other phenomena such as aerosol inhomogeneity. Before the O(3) profiles are derived, the dominant measurement errors are estimated and uncertainty boundaries for the measured profiles are established. The off- to on-line signal ratio is transformed into an intermediate function, and analytical approximations of the function are then determined. The separation of low- and high-frequency constituents of the measured ozone profile is made by the application of different approximation fits to appropriate intermediate functions. The low-frequency constituents are approximated with a low-order polynomial fit, whereas the high-frequency constituents are approximated with a trigonometric fit. The latter fit makes it possible to correct the measured O(3) profiles in zones of large ozone-concentration gradients where the low-order polynomial fit is found to be insufficient. Application of this technique to experimental data obtained in the lower troposphere shows that erroneous fluctuations induced in the ozone-concentration profile by signal noise and aerosol inhomogeneity undergo a significant reduction in comparison with the results from the conventional technique based on straightforward numerical differentiation. PMID:21102905

  17. Comments on Riemann-Christoffel Tensor in Differential Geometry of Fractional Order Application to Fractal Space-Time [FRACTALS 21 (2013) 1350004

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2015-04-01

    We prove that main properties represented by Eq. (4.2) for fractional derivative of power function and the non-fractional Leibniz rule in the form (4.3) of the considered paper, cannot hold together for derivatives of non-integer order. As a result, we prove that the usual Leibniz rule (4.3) cannot hold for fractional derivatives.

  18. Chaotic and hyperchaotic attractors of a complex nonlinear system

    NASA Astrophysics Data System (ADS)

    Mahmoud, Gamal M.; Al-Kashif, M. A.; Farghaly, A. A.

    2008-02-01

    In this paper, we introduce a complex nonlinear hyperchaotic system which is a five-dimensional system of nonlinear autonomous differential equations. This system exhibits both chaotic and hyperchaotic behavior and its dynamics is very rich. Based on the Lyapunov exponents, the parameter values at which this system has chaotic, hyperchaotic attractors, periodic and quasi-periodic solutions and solutions that approach fixed points are calculated. The stability analysis of these fixed points is carried out. The fractional Lyapunov dimension of both chaotic and hyperchaotic attractors is calculated. Some figures are presented to show our results. Hyperchaos synchronization is studied analytically as well as numerically, and excellent agreement is found.

  19. On Fractional Model Reference Adaptive Control

    PubMed Central

    Shi, Bao; Dong, Chao

    2014-01-01

    This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapunov theory. Moreover, numerical simulations of both linear and nonlinear systems are performed to exhibit the viability and effectiveness of the proposed methodology. PMID:24574897

  20. On fractional Model Reference Adaptive Control.

    PubMed

    Shi, Bao; Yuan, Jian; Dong, Chao

    2014-01-01

    This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapunov theory. Moreover, numerical simulations of both linear and nonlinear systems are performed to exhibit the viability and effectiveness of the proposed methodology. PMID:24574897

  1. Fractional diffusion on bounded domains

    DOE PAGESBeta

    Defterli, Ozlem; D'Elia, Marta; Du, Qiang; Gunzburger, Max Donald; Lehoucq, Richard B.; Meerschaert, Mark M.

    2015-03-13

    We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

  2. Accessible solitons of fractional dimension

    NASA Astrophysics Data System (ADS)

    Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi

    2016-05-01

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  4. Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet

    PubMed Central

    2012-01-01

    In this work, we study the flow and heat transfer characteristics of a viscous nanofluid over a nonlinearly stretching sheet in the presence of thermal radiation, included in the energy equation, and variable wall temperature. A similarity transformation was used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme was used to obtain the solution of the boundary value problem. The variations of dimensionless surface temperature, as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include the nanoparticle volume fraction ϕ, the nonlinearly stretching sheet parameter n, the thermal radiation parameter NR, and the viscous dissipation parameter Ec, were graphed and tabulated. Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell for local Nusselt number without taking the effect of nanoparticles. PMID:22520273

  5. Differential protection among fractionated blueberry polyphenolic families against DA-, Aβ42 and LPS-induced decrements in Ca2+ buffering in primary hippocampal cells

    PubMed Central

    Joseph, James A.; Shukitt-Hale, Barbara; Brewer, Gregory J.; Weikel, Karen A.; Kalt, Wilhelmina; Fisher, Derek R.

    2011-01-01

    It has been postulated that at least part of the loss of cognitive function in aging may be the result of deficits in Ca2+ recovery (CAR) and increased oxidative/inflammatory (OX/INF) stress signaling. However, previous research showed that aged animals supplemented with blueberry (BB) extract, showed fewer deficits in CAR, as well as motor and cognitive functional deficits. A recent subsequent experiment has shown that DA- or Aβ42-induced deficits in CAR in primary hippocampal neuronal cells (HNC) were antagonized by BB extract, and (OX/INF) signaling was reduced. Present experiments assessed the most effective BB polyphenol fraction that could protect against OX/INF-induced deficits in CAR, ROS generation, or viability. HNCs treated with BB extract, BB fractions (e.g., proanthocyanidin, PAC), or control medium were exposed to dopamine (DA, 0.1mM), amyloid beta (Aβ42, 25 µM) or lipopolysaccharide (LPS, 1µg/ml). Results indicated that the degree of protection against deficits in CAR varied as a function of the stressor and was generally greater against Aβ42 and LPS than DA. The whole BB, anthocyanin (ANTH) and pre-C18 fractions offered the greatest protection, while chlorogenic acid offered the lowest protection. Protective capabilities of the various fractions against ROS depended upon the stressor, where the BB extract and the combined PAC (high and low m.w.) fraction offered the best protection against LPS and Aβ42 but were less effective against DA-induced ROS. The high and low m.w. PACs and the ANTH fractions enhanced ROS production regardless of the stressor used and this reflected increased activation of stress signals (e.g., P38 MAPK). The viability data indicated that the whole BB and combined PAC fraction showed greater protective effects against the stressors than the more fractionated polyphenolic components. Thus, these results suggest that, except for a few instances, the lesser the polyphenolic fractionation the greater the effects, especially

  6. A Class of Integer Order and Fractional Order Hyperchaotic Systems via the Chen System

    NASA Astrophysics Data System (ADS)

    Xu, Fei

    2016-06-01

    In this article, we investigate the generation of a class of hyperchaotic systems via the Chen chaotic system using both integer order and fractional order differential equation systems. Based on the Chen chaotic system, we designed a system with four nonlinear ordinary differential equations. For different parameter sets, the trajectory of the system may diverge or display a hyperchaotic attractor with double wings. By linearizing the ordinary differential equation system with divergent trajectory and designing proper switching controls, we obtain a chaotic attractor. Similar phenomenon has also been observed in linearizing the hyperchaotic system. The corresponding fractional order systems are also considered. Our investigation indicates that, switching control can be applied to either linearized chaotic or nonchaotic differential equation systems to create chaotic attractor.

  7. Effect of Bee Venom and Its Fractions on the Release of Pro-Inflammatory Cytokines in PMA-Differentiated U937 Cells Co-Stimulated with LPS.

    PubMed

    Tusiimire, Jonans; Wallace, Jennifer; Woods, Nicola; Dufton, Mark J; Parkinson, John A; Abbott, Grainne; Clements, Carol J; Young, Louise; Park, Jin Kyu; Jeon, Jong Woon; Ferro, Valerie A; Watson, David G

    2016-01-01

    The venom of Apis mellifera (honey bee) has been reported to play a role in immunotherapy, but existing evidence to support its immuno-modulatory claims is insufficient. Four fractions from whole bee venom (BV) were separated using medium pressure liquid chromatography. Their ability to induce the production of cytokines TNFα, IL-1β and IL-6 in phorbol-12-myristate-13-acetate (PMA)-treated U937 cells was assessed. The levels of the three cytokines produced by stimulation with the four fractions and crude BV without LPS were not significantly different from negative control values. However, co-stimulation of the cells with LPS and Fraction 4 (F-4) induced a 1.6-fold increase in TNF-α level (p < 0.05) compared to LPS alone. Likewise, LPS-induced IL-1β production was significantly synergised in the presence of F-1 (nine-fold), F-2 (six-fold), F-3 (four-fold) and F-4 (two-fold) fractions, but was only slightly enhanced with crude BV (1.5-fold) relative to LPS. Furthermore, the LPS-stimulated production of IL-6 was not significantly increased in cells co-treated with F-2 and F-3, but the organic fraction (F-4) showed an inhibitory effect (p < 0.05) on IL-6 production. The latter was elucidated by NMR spectroscopy and found to contain(Z)-9-eicosen-1-ol. The effects observed with the purified BV fractions were more marked than those obtained with the crude sample. PMID:27104574

  8. Effect of Bee Venom and Its Fractions on the Release of Pro-Inflammatory Cytokines in PMA-Differentiated U937 Cells Co-Stimulated with LPS

    PubMed Central

    Tusiimire, Jonans; Wallace, Jennifer; Woods, Nicola; Dufton, Mark J.; Parkinson, John A.; Abbott, Grainne; Clements, Carol J.; Young, Louise; Park, Jin Kyu; Jeon, Jong Woon; Ferro, Valerie A.; Watson, David G.

    2016-01-01

    The venom of Apis mellifera (honey bee) has been reported to play a role in immunotherapy, but existing evidence to support its immuno-modulatory claims is insufficient. Four fractions from whole bee venom (BV) were separated using medium pressure liquid chromatography. Their ability to induce the production of cytokines TNFα, IL-1β and IL-6 in phorbol-12-myristate-13-acetate (PMA)-treated U937 cells was assessed. The levels of the three cytokines produced by stimulation with the four fractions and crude BV without LPS were not significantly different from negative control values. However, co-stimulation of the cells with LPS and Fraction 4 (F-4) induced a 1.6-fold increase in TNF-α level (p < 0.05) compared to LPS alone. Likewise, LPS-induced IL-1β production was significantly synergised in the presence of F-1 (nine-fold), F-2 (six-fold), F-3 (four-fold) and F-4 (two-fold) fractions, but was only slightly enhanced with crude BV (1.5-fold) relative to LPS. Furthermore, the LPS-stimulated production of IL-6 was not significantly increased in cells co-treated with F-2 and F-3, but the organic fraction (F-4) showed an inhibitory effect (p < 0.05) on IL-6 production. The latter was elucidated by NMR spectroscopy and found to contain(Z)-9-eicosen-1-ol. The effects observed with the purified BV fractions were more marked than those obtained with the crude sample. PMID:27104574

  9. New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method

    NASA Astrophysics Data System (ADS)

    Tasbozan, Orkun; Çenesiz, Yücel; Kurt, Ali

    2016-07-01

    In this paper, the Jacobi elliptic function expansion method is proposed for the first time to construct the exact solutions of the time conformable fractional two-dimensional Boussinesq equation and the combined KdV-mKdV equation. New exact solutions are found. This method is based on Jacobi elliptic functions. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.

  10. Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

    PubMed Central

    Zeng, Caibin; Yang, Qigui; Cao, Junfei

    2014-01-01

    This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t) = A(X(t))dt+Φ(t)dBH(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation. PMID:24574903

  11. Fractional calculus in bioengineering.

    PubMed

    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

  12. On the design of experiments for determining ternary mixture free energies from static light scattering data using a nonlinear partial differential equation

    PubMed Central

    Wahle, Chris W.; Ross, David S.; Thurston, George M.

    2012-01-01

    We mathematically design sets of static light scattering experiments to provide for model-independent measurements of ternary liquid mixing free energies to a desired level of accuracy. A parabolic partial differential equation (PDE), linearized from the full nonlinear PDE [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008)10.1063/1.2937902], describes how data noise affects the free energies to be inferred. The linearized PDE creates a net of spacelike characteristic curves and orthogonal, timelike curves in the composition triangle, and this net governs diffusion of information coming from light scattering measurements to the free energy. Free energy perturbations induced by a light scattering perturbation diffuse along the characteristic curves and towards their concave sides, with a diffusivity that is proportional to the local characteristic curvature radius. Consequently, static light scattering can determine mixing free energies in regions with convex characteristic curve boundaries, given suitable boundary data. The dielectric coefficient is a Lyapunov function for the dynamical system whose trajectories are PDE characteristics. Information diffusion is heterogeneous and system-dependent in the composition triangle, since the characteristics depend on molecular interactions and are tangent to liquid-liquid phase separation coexistence loci at critical points. We find scaling relations that link free energy accuracy, total measurement time, the number of samples, and the interpolation method, and identify the key quantitative tradeoffs between devoting time to measuring more samples, or fewer samples more accurately. For each total measurement time there are optimal sample numbers beyond which more will not improve free energy accuracy. We estimate the degree to which many-point interpolation and optimized measurement concentrations can improve accuracy and save time. For a modest light scattering setup, a sample calculation shows that

  13. Automatic differentiation bibliography

    SciTech Connect

    Corliss, G.F.

    1992-07-01

    This is a bibliography of work related to automatic differentiation. Automatic differentiation is a technique for the fast, accurate propagation of derivative values using the chain rule. It is neither symbolic nor numeric. Automatic differentiation is a fundamental tool for scientific computation, with applications in optimization, nonlinear equations, nonlinear least squares approximation, stiff ordinary differential equation, partial differential equations, continuation methods, and sensitivity analysis. This report is an updated version of the bibliography which originally appeared in Automatic Differentiation of Algorithms: Theory, Implementation, and Application.

  14. Nonlinear dynamics of initially imperfect functionally graded circular cylindrical shell under complex loads

    NASA Astrophysics Data System (ADS)

    Liu, Y. Z.; Hao, Y. X.; Zhang, W.; Chen, J.; Li, S. B.

    2015-07-01

    The nonlinear vibration of a simply supported FGM cylindrical shell with small initial geometric imperfection under complex loads is studied. The effects of radial harmonic excitation, compressive in-plane force combined with supersonic aerodynamic and thermal loads are considered. The small initial geometric imperfection of the cylindrical shell is characterized in the form of the sine-type trigonometric functions. The effective material properties of this FGM cylindrical shell are graded in the radial direction according to a simple power law in terms of the volume fractions. Based on Reddy's third-order shear deformation theory, von Karman-type nonlinear kinematics and Hamilton's principle, the nonlinear partial differential equation that controls the shell dynamics is derived. Both axial symmetric and driven modes of the cylindrical shell deflection pattern are included. Furthermore, the equations of motion can be reduced into a set of coupled nonlinear ordinary differential equations by applying Galerkin's method. In the study of the nonlinear dynamics responses of small initial geometric imperfect FGM cylindrical shell under complex loads, the 4th order Runge-Kutta method is used to obtain time history, phase portraits, bifurcation diagrams and Poincare maps with different parameters. The effects of external loads, geometric imperfections and volume fractions on the nonlinear dynamics of the system are discussed.

  15. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

    1991-01-01

    Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

  16. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

    1990-01-01

    Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

  17. PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena

    NASA Astrophysics Data System (ADS)

    Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo

    2010-10-01

    according to the standards of the journal. The selection of papers in this issue aims to bring together recent developments and findings, even though it consists of only a fraction of the impressive developments in recent years which have affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete geometry, among others. The special issue begins with four review papers: Integrable models in nonlinear optics and soliton solutions Degasperis [1] reviews integrable models in nonlinear optics. He presents a number of approximate models which are integrable and illustrates the links between the mathematical and applicative aspects of the theory of integrable dynamical systems. In particular he discusses the recent impact of boomeronic-type wave equations on applications arising in the context of the resonant interaction of three waves. Hamiltonian PDEs: deformations, integrability, solutions Dubrovin [2] presents classification results for systems of nonlinear Hamiltonian partial differential equations (PDEs) in one spatial dimension. In particular he uses a perturbative approach to the theory of integrability of these systems and discusses their solutions. He conjectures universality of the critical behaviour for the solutions, where the notion of universality refers to asymptotic independence of the structure of solutions (at the point of gradient catastrophe) from the choice of generic initial data as well as from the choice of a generic PDE. KP solitons in shallow water Kodama [3] presents a survey of recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. A large variety of exact soliton solutions of the KP equation are presented and classified. The study includes numerical analysis of the stability of the found solution as well as numerical simulations of the initial value problems which

  18. Approximate Solution to the Fractional Second-Type Lane-Emden Equation

    NASA Astrophysics Data System (ADS)

    Abdel-Salam, E. A.-B.; Nouh, M. I.

    2016-09-01

    The spherical isothermal Lane-Emden equation is a second-order nonlinear differential equation that models many configurations in astrophysics. Using the fractal index technique and the power series expansion, we solve the fractional Lane-Emden equation involving the modified Riemann-Liouville derivative. The results indicate that the series converges over the range of radii 0≤ x< 2200 for a wide spread of values for the fractional parameter α. Comparison with the numerical solution reveals good agreement with a maximum relative error of 0.05.

  19. Fractional Dynamics of Globally Slow Transcription and Its Impact on Deterministic Genetic Oscillation

    PubMed Central

    Wei, Kun; Gao, Shilong; Zhong, Suchuan; Ma, Hong

    2012-01-01

    In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models – the Goodwin oscillator and the Rössler oscillator. By constructing a “dual memory” oscillator – the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically. PMID:22679500

  20. The pecan nut (Carya illinoinensis) and its oil and polyphenolic fractions differentially modulate lipid metabolism and the antioxidant enzyme activities in rats fed high-fat diets.

    PubMed

    Domínguez-Avila, Jesús A; Alvarez-Parrilla, Emilio; López-Díaz, José A; Maldonado-Mendoza, Ignacio E; Gómez-García, María Del Consuelo; de la Rosa, Laura A

    2015-02-01

    Tree nuts such as pecans (Carya illinoinensis) contain mostly oil but are also a source of polyphenols. Nut consumption has been linked to a reduction in serum lipid levels and oxidative stress. These effects have been attributed to the oil while overlooking the potential contribution of the polyphenols. Because the evidence regarding each fraction's bioactivity is scarce, we administered high-fat (HF) diets to male Wistar rats, supplementing them with pecan oil (HF+PO), pecan polyphenols (HF+PP) or whole pecans (HF+WP), and analysed the effects of each fraction. The HF diet increased the serum leptin and total cholesterol (TC) with respect to the control levels. The HF+WP diet prevented hyperleptinemia and decreased the TC compared with the control. The HF+WP diet upregulated the hepatic expression of apolipoprotein B and LDL receptor mRNAs with respect to the HF levels. The HF+PO diet reduced the level of triacylglycerols compared with the control. The HF+PP diet stimulated the hepatic expression of liver X receptor alpha mRNA. The HF+WP diet increased the activities of hepatic catalase, glutathione peroxidase and glutathione S transferase compared with the control, and decreased the degree of lipid peroxidation compared with the HF diet. The most bioactive diet was the WP diet. PMID:25172744

  1. Can the Non-linear Ballooning Model describe ELMs?

    NASA Astrophysics Data System (ADS)

    Henneberg, S. A.; Cowley, S. C.; Wilson, H. R.

    2015-11-01

    The explosive, filamentary plasma eruptions described by the non-linear ideal MHD ballooning model is tested quantitatively against experimental observations of ELMs in MAST. The equations describing this model were derived by Wilson and Cowley for tokamak-like geometry which includes two differential equations: the linear ballooning equation which describes the spatial distribution along the field lines and the non-linear ballooning mode envelope equation, which is a two-dimensional, non-linear differential equation which can involve fractional temporal-derivatives, but is often second-order in time and space. To employ the second differential equation for a specific geometry one has to evaluate the coefficients of the equation which is non-trivial as it involves field line averaging of slowly converging functions. We have solved this system for MAST, superimposing the solutions of both differential equations and mapping them onto a MAST plasma. Comparisons with the evolution of ELM filaments in MAST will be reported in order to test the model. The support of the EPSRC for the FCDT (Grant EP/K504178/1), of Euratom research and training programme 2014-2018 (No 633053) and of the RCUK Energy Programme [grant number EP/I501045] is gratefully acknowledged.

  2. Fractional oscillator.

    PubMed

    Stanislavsky, A A

    2004-11-01

    We consider a fractional oscillator which is a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by a stochastic time arrow. The intrinsic absorption of the fractional oscillator results from the full contribution of the harmonic oscillator ensemble: these oscillators differ a little from each other in frequency so that each response is compensated by an antiphase response of another harmonic oscillator. This allows one to draw a parallel in the dispersion analysis for media described by a fractional oscillator and an ensemble of ordinary harmonic oscillators with damping. The features of this analysis are discussed. PMID:15600586

  3. ``Once Nonlinear, Always Nonlinear''

    NASA Astrophysics Data System (ADS)

    Blackstock, David T.

    2006-05-01

    The phrase "Once nonlinear, always nonlinear" is attributed to David F. Pernet. In the 1970s he noticed that nonlinearly generated higher harmonic components (both tones and noise) don't decay as small signals, no matter how far the wave propagates. Despite being out of step with the then widespread notion that small-signal behavior is restored in "old age," Pernet's view is supported by the Burgers-equation solutions of the early 1960s. For a plane wave from a sinusoidally vibrating source in a thermoviscous fluid, the old-age decay of the nth harmonic is e-nαx, not e-n2αx (small-signal expectation), where α is the absorption coefficient at the fundamental frequency f and x is propagation distance. Moreover, for spherical waves (r the distance) the harmonic diminishes as e-nαx/rn, not e-n2αx/r. While not new, these results have special application to aircraft noise propagation, since the large propagation distances of interest imply old age. The virtual source model may be used to explain the "anomalous" decay rates. In old age most of the nth harmonic sound comes from virtual sources close to the receiver. Their strength is proportional to the nth power of the local fundamental amplitude, and that sets the decay law for the nth harmonic.

  4. A Robust e-Epidemiology Tool in Phenotyping Heart Failure with Differentiation for Preserved and Reduced Ejection Fraction: the Electronic Medical Records and Genomics (eMERGE) Network.

    PubMed

    Bielinski, Suzette J; Pathak, Jyotishman; Carrell, David S; Takahashi, Paul Y; Olson, Janet E; Larson, Nicholas B; Liu, Hongfang; Sohn, Sunghwan; Wells, Quinn S; Denny, Joshua C; Rasmussen-Torvik, Laura J; Pacheco, Jennifer Allen; Jackson, Kathryn L; Lesnick, Timothy G; Gullerud, Rachel E; Decker, Paul A; Pereira, Naveen L; Ryu, Euijung; Dart, Richard A; Peissig, Peggy; Linneman, James G; Jarvik, Gail P; Larson, Eric B; Bock, Jonathan A; Tromp, Gerard C; de Andrade, Mariza; Roger, Véronique L

    2015-11-01

    Identifying populations of heart failure (HF) patients is paramount to research efforts aimed at developing strategies to effectively reduce the burden of this disease. The use of electronic medical record (EMR) data for this purpose is challenging given the syndromic nature of HF and the need to distinguish HF with preserved or reduced ejection fraction. Using a gold standard cohort of manually abstracted cases, an EMR-driven phenotype algorithm based on structured and unstructured data was developed to identify all the cases. The resulting algorithm was executed in two cohorts from the Electronic Medical Records and Genomics (eMERGE) Network with a positive predictive value of >95 %. The algorithm was expanded to include three hierarchical definitions of HF (i.e., definite, probable, possible) based on the degree of confidence of the classification to capture HF cases in a whole population whereby increasing the algorithm utility for use in e-Epidemiologic research. PMID:26195183

  5. Numerical solution of the one-dimensional fractional convection diffusion equations based on Chebyshev operational matrix.

    PubMed

    Xie, Jiaquan; Huang, Qingxue; Yang, Xia

    2016-01-01

    In this paper, we are concerned with nonlinear one-dimensional fractional convection diffusion equations. An effective approach based on Chebyshev operational matrix is constructed to obtain the numerical solution of fractional convection diffusion equations with variable coefficients. The principal characteristic of the approach is the new orthogonal functions based on Chebyshev polynomials to the fractional calculus. The corresponding fractional differential operational matrix is derived. Then the matrix with the Tau method is utilized to transform the solution of this problem into the solution of a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via examples. It is shown that the proposed algorithm yields better results. Finally, error analysis shows that the algorithm is convergent. PMID:27504247

  6. Toward lattice fractional vector calculus

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2014-09-01

    An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

  7. Fractional Galilean symmetries

    NASA Astrophysics Data System (ADS)

    Hosseiny, Ali; Rouhani, Shahin

    2016-09-01

    We generalize the differential representation of the operators of the Galilean algebras to include fractional derivatives. As a result a whole new class of scale invariant Galilean algebras are obtained. The first member of this class has dynamical index z = 2 similar to the Schrödinger algebra. The second member of the class has dynamical index z = 3 / 2, which happens to be the dynamical index Kardar-Parisi-Zhang equation.

  8. Radiating subdispersive fractional optical solitons.

    PubMed

    Fujioka, J; Espinosa, A; Rodríguez, R F; Malomed, B A

    2014-09-01

    It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy. PMID:25273201

  9. Radiating subdispersive fractional optical solitons

    NASA Astrophysics Data System (ADS)

    Fujioka, J.; Espinosa, A.; Rodríguez, R. F.; Malomed, B. A.

    2014-09-01

    It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.

  10. Radiating subdispersive fractional optical solitons

    SciTech Connect

    Fujioka, J. Espinosa, A.; Rodríguez, R. F.; Malomed, B. A.

    2014-09-01

    It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.

  11. A semi-alternating direction method for a 2-D fractional FitzHugh-Nagumo monodomain model on an approximate irregular domain

    NASA Astrophysics Data System (ADS)

    Liu, F.; Zhuang, P.; Turner, I.; Anh, V.; Burrage, K.

    2015-07-01

    A FitzHugh-Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh-Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction-diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Second, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction-diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Third, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional FitzHugh-Nagumo model on both an approximate circular and an approximate irregular domain.

  12. [Nonlinear magnetohydrodynamics

    SciTech Connect

    Not Available

    1994-01-01

    Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday`s law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm`s law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile.

  13. Anti-inflammatory/Anti-oxidative stress activities and differential regulation of Nrf2-mediated genes by non-polar fractions of tea Chrysanthemum zawadskii and licorice Glycyrrhiza uralensis.

    PubMed

    Wu, Tien-Yuan; Khor, Tin Oo; Saw, Constance Lay Lay; Loh, Stephanie C; Chen, Alvin I; Lim, Soon Sung; Park, Jung Han Yoon; Cai, Li; Kong, Ah-Ng Tony

    2011-03-01

    Accumulating evidence from epidemiological studies indicates that chronic inflammation and oxidative stress play critical roles in neoplastic development. The aim of this study was to investigate the anti-inflammatory, anti-oxidative stress activities, and differential regulation of Nrf2-mediated genes by tea Chrysanthemum zawadskii (CZ) and licorice Glycyrrhiza uralensis (LE) extracts. The anti-inflammatory and anti-oxidative stress activities of hexane/ethanol extracts of CZ and LE were investigated using in vitro and in vivo approaches, including quantitative real-time PCR (qPCR) and microarray. Additionally, the role of the transcriptional factor Nrf2 (nuclear erythroid-related factor 2) signaling pathways was examined. Our results show that CZ and LE extracts exhibited potent anti-inflammatory activities by suppressing the mRNA and protein expression levels of pro-inflammatory biomarkers IL-1β, IL-6, COX-2 and iNOS in LPS-stimulated murine RAW 264.7 macrophage cells. CZ and LE also significantly suppressed the NO production of LPS-stimulated RAW 264.7 cells. Additionally, CZ and LE suppressed the NF-κB luciferase activity in human HT-29 colon cancer cells. Both extracts also showed strong Nrf2-mediated antioxidant/Phase II detoxifying enzymes induction. CZ and LE induced NQO1, Nrf2, and UGT and antioxidant response element (ARE)-luciferase activity in human hepatoma HepG2 C8 cells. Using Nrf2 knockout [Nrf2 (-/-)] and Nrf2 wild-type (+/+) mice, LE and CZ showed Nrf2-dependent transactivation of Nrf2-mediated antioxidant and phase II detoxifying genes. In summary, CZ and LE possess strong inhibitory effects against NF-κB-mediated inflammatory as well as strong activation of the Nrf2-ARE-anti-oxidative stress signaling pathways, which would contribute to their overall health promoting pharmacological effects against diseases including cancer. PMID:20967519

  14. One adaptive synchronization approach for fractional-order chaotic system with fractional-order 1 < q < 2.

    PubMed

    Zhou, Ping; Bai, Rongji

    2014-01-01

    Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme. PMID:25247207

  15. Fraction Reduction through Continued Fractions

    ERIC Educational Resources Information Center

    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.

  16. Spline approximations for nonlinear hereditary control systems

    NASA Technical Reports Server (NTRS)

    Daniel, P. L.

    1982-01-01

    A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

  17. Differential Association of the Na+/H+ Exchanger Regulatory Factor (NHERF) Family of Adaptor Proteins with the Raft-and the Non-Raft Brush Border Membrane Fractions of NHE3

    PubMed Central

    Sultan, Ayesha; Luo, Min; Yu, Qin; Riederer, Brigitte; Xia, Weiliang; Chen, Mingmin; Lissner, Simone; Gessner, Johannes E.; Donowitz, Mark; Yun, C. Chris; deJonge, Hugo; Lamprecht, Georg; Seidler, Ursula

    2014-01-01

    Background/Aims Trafficking, brush border membrane (BBM) retention, and signal-specific regulation of the Na+/H+ exchanger NHE3 is regulated by the Na+/H+ Exchanger Regulatory Factor (NHERF) family of PDZ-adaptor proteins, which enable the formation of multiprotein complexes. It is unclear, however, what determines signal specificity of these NHERFs. Thus, we studied the association of NHE3, NHERF1 (EBP50), NHERF2 (E3KARP), and NHERF3 (PDZK1) with lipid rafts in murine small intestinal BBM. Methods Detergent resistant membranes (“lipid rafts”) were isolated by floatation of Triton X-incubated small intestinal BBM from a variety of knockout mouse strains in an Optiprep step gradient. Acid-activated NHE3 activity was measured fluorometrically in BCECF-loaded microdissected villi, or by assessment of CO2/HCO3− mediated increase in fluid absorption in perfused jejunal loops of anethetized mice. Results NHE3 was found to partially associate with lipid rafts in the native BBM, and NHE3 raft association had an impact on NHE3 transport activity and regulation in vivo. NHERF1, 2 and 3 were differentially distributed to rafts and non-rafts, with NHERF2 being most raft-associated and NHERF3 entirely non-raft associated. NHERF2 expression enhanced the localization of NHE3 to membrane rafts. The use of acid sphingomyelinase-deficient mice, which have altered membrane lipid as well as lipid raft composition, allowed us to test the validity of the lipid raft concept in vivo. Conclusions The differential association of the NHERFs with the raft-associated and the non-raft fraction of NHE3 in the brush border membrane is one component of the differential and signal-specific NHE3 regulation by the different NHERFs. PMID:24297041

  18. Global Phase Portraits of Kukles Differential Systems with Homogeneous Polynomial Nonlinearities of Degree 6 Having a Center and Their Small Limit Cycles

    NASA Astrophysics Data System (ADS)

    Llibre, Jaume; da Silva, Maurício Fronza

    We provide the nine topological global phase portraits in the Poincaré disk of the family of the centers of Kukles polynomial differential systems of the form ẋ = ‑y, ẏ = x + ax5y + bx3y3 + cxy5, where x,y ∈ ℝ and a,b,c are real parameters satisfying a2 + b2 + c2≠0. Using averaging theory up to sixth order we determine the number of limit cycles which bifurcate from the origin when we perturb this system first inside the class of all homogeneous polynomial differential systems of degree 6, and second inside the class of all polynomial differential systems of degree 6.

  19. Equation of motion using fractional calculus

    SciTech Connect

    Kihong, Kwon.

    1991-01-01

    One-dimensional motion of a particle was studied using fractional calculus, which is the differentiation and the integration of arbitrary order. By fractional differentiation, equation of motion could be written in compact form. Fractional parameters were numerically calculated by using the known solutions of general relativistic free fall motion. Also, from the approximate forms for fractional parameters, the physical meanings were found. The fractional parameters depended on the proper time, the mass of gravitating body, and the initial radial coordinate of the particle.

  20. Nonlinear systems in medicine.

    PubMed Central

    Higgins, John P.

    2002-01-01

    Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107

  1. Nonlinear focusing of DNA macromolecules

    NASA Astrophysics Data System (ADS)

    Frumin, Leonid L.; Peltek, Sergey E.; Zilberstein, Gleb V.

    2001-08-01

    The present paper reports the nonlinear electrophoretic focusing techniques developed after an original idea by Chacron and Slater [Phys. Rev. E 56, 3436 (1997)]. Focusing of DNA molecules is achieved in an alternating nonuniform electric field, created in a wedge gel with hyperbolic boundaries. The fractions separated on such a wedge retained their rectilinear shape during the electrophoresis. Experiments with gel electrophoresis confirm the possibility of a noticeable nonlinear focusing of DNA molecules.

  2. Numerical studies of the nonlinear properties of composites

    NASA Astrophysics Data System (ADS)

    Zhang, X.; Stroud, D.

    1994-01-01

    Using both numerical and analytical techniques, we investigate various ways to enhance the cubic nonlinear susceptibility χe of a composite material. We start from the exact relation χe =tsumipiχi<(E.E)2>i,lin/ E40, where χi and pi are the cubic nonlinear susceptibility and volume fraction of the ith component, E0 is the applied electric field, and i,lin is the expectation value of the electric field in the ith component, calculated in the linear limit where χi=0. In our numerical work, we represent the composite by a random resistor or impedance network, calculating the electric-field distributions by a generalized transfer-matrix algorithm. Under certain conditions, we find that χe is greatly enhanced near the percolation threshold. We also find a large enhancement for a linear fractal in a nonlinear host. In a random Drude metal-insulator composite χe is hugely enhanced especially near frequencies which correspond to the surface-plasmon resonance spectrum of the composite. At zero frequency, the random composite results are reasonably well described by a nonlinear effective-medium approximation. The finite-frequency enhancement shows very strong reproducible structure which is nearly undetectable in the linear response of the composite, and which may possibly be described by a generalized nonlinear effective-medium approximation. The fractal results agree qualitatively with a nonlinear differential effective-medium approximation. Finally, we consider a suspension of coated spheres embedded in a host. If the coating is nonlinear, we show that χe/χcoat>>1 near the surface-plasmon resonance frequency of the core particle.

  3. Differentiation between Focal Malignant Marrow-Replacing Lesions and Benign Red Marrow Deposition of the Spine with T2*-Corrected Fat-Signal Fraction Map Using a Three-Echo Volume Interpolated Breath-Hold Gradient Echo Dixon Sequence

    PubMed Central

    Kim, Yong Pyo; Kannengiesser, Stephan; Paek, Mun-Young; Chung, Tae-Sub; Yoo, Yeon Hwa; Yoon, Choon-Sik; Song, Ho-Taek; Lee, Young Han; Suh, Jin-Suck

    2014-01-01

    Objective To assess the feasibility of T2*-corrected fat-signal fraction (FF) map by using the three-echo volume interpolated breath-hold gradient echo (VIBE) Dixon sequence to differentiate between malignant marrow-replacing lesions and benign red marrow deposition of vertebrae. Materials and Methods We assessed 32 lesions from 32 patients who underwent magnetic resonance imaging after being referred for assessment of a known or possible vertebral marrow abnormality. The lesions were divided into 21 malignant marrow-replacing lesions and 11 benign red marrow depositions. Three sequences for the parameter measurements were obtained by using a 1.5-T MR imaging scanner as follows: three-echo VIBE Dixon sequence for FF; conventional T1-weighted imaging for the lesion-disc ratio (LDR); pre- and post-gadolinium enhanced fat-suppressed T1-weighted images for the contrast-enhancement ratio (CER). A region of interest was drawn for each lesion for parameter measurements. The areas under the curve (AUC) of the parameters and their sensitivities and specificities at the most ideal cutoff values from receiver operating characteristic curve analysis were obtained. AUC, sensitivity, and specificity were respectively compared between FF and CER. Results The AUCs of FF, LDR, and CER were 0.96, 0.80, and 0.72, respectively. In the comparison of diagnostic performance between the FF and CER, the FF showed a significantly larger AUC as compared to the CER (p = 0.030), although the difference of sensitivity (p = 0.157) and specificity (p = 0.157) were not significant. Conclusion Fat-signal fraction measurement using T2*-corrected three-echo VIBE Dixon sequence is feasible and has a more accurate diagnostic performance, than the CER, in distinguishing benign red marrow deposition from malignant bone marrow-replacing lesions. PMID:25469090

  4. Numerical study for multi-strain tuberculosis (TB) model of variable-order fractional derivatives.

    PubMed

    Sweilam, Nasser H; Al-Mekhlafi, Seham M

    2016-03-01

    In this paper, we presented a novel multi-strain TB model of variable-order fractional derivatives, which incorporates three strains: drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), as an extension for multi-strain TB model of nonlinear ordinary differential equations which developed in 2014 by Arino and Soliman [1]. Numerical simulations for this variable-order fractional model are the main aim of this work, where the variable-order fractional derivative is defined in the sense of Grünwald-Letnikov definition. Two numerical methods are presented for this model, the standard finite difference method (SFDM) and nonstandard finite difference method (NSFDM). Numerical comparison between SFDM and NSFDM is presented. It is concluded that, NSFDM preserves the positivity of the solutions and numerically stable in large regions than SFDM. PMID:26966568

  5. Numerical study for multi-strain tuberculosis (TB) model of variable-order fractional derivatives

    PubMed Central

    Sweilam, Nasser H.; AL-Mekhlafi, Seham M.

    2015-01-01

    In this paper, we presented a novel multi-strain TB model of variable-order fractional derivatives, which incorporates three strains: drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), as an extension for multi-strain TB model of nonlinear ordinary differential equations which developed in 2014 by Arino and Soliman [1]. Numerical simulations for this variable-order fractional model are the main aim of this work, where the variable-order fractional derivative is defined in the sense of Grünwald–Letnikov definition. Two numerical methods are presented for this model, the standard finite difference method (SFDM) and nonstandard finite difference method (NSFDM). Numerical comparison between SFDM and NSFDM is presented. It is concluded that, NSFDM preserves the positivity of the solutions and numerically stable in large regions than SFDM. PMID:26966568

  6. Automatic Differentiation Package

    Energy Science and Technology Software Center (ESTSC)

    2007-03-01

    Sacado is an automatic differentiation package for C++ codes using operator overloading and C++ templating. Sacado provide forward, reverse, and Taylor polynomial automatic differentiation classes and utilities for incorporating these classes into C++ codes. Users can compute derivatives of computations arising in engineering and scientific applications, including nonlinear equation solving, time integration, sensitivity analysis, stability analysis, optimization and uncertainity quantification.

  7. A functional realization of 𝔰𝔩(3, ℝ) providing minimal Vessiot-Guldberg-Lie algebras of nonlinear second-order ordinary differential equations as proper subalgebras

    NASA Astrophysics Data System (ADS)

    Campoamor-Stursberg, R.

    2016-06-01

    A functional realization of the Lie algebra s l (" separators=" 3 , R) as a Vessiot-Guldberg-Lie algebra of second order differential equation (SODE) Lie systems is proposed. It is shown that a minimal Vessiot-Guldberg-Lie algebra L V G is obtained from proper subalgebras of s l (" separators=" 3 , R) for each of the SODE Lie systems of this type by particularization of one functional and two scalar parameters of the s l (" separators=" 3 , R) -realization. The relation between the various Vessiot-Guldberg-Lie algebras by means of a limiting process in the scalar parameters further allows to define a notion of contraction of SODE Lie systems.

  8. Approximate solution of two-term fractional-order diffusion, wave-diffusion, and telegraph models arising in mathematical physics using optimal homotopy asymptotic method

    NASA Astrophysics Data System (ADS)

    Sarwar, S.; Rashidi, M. M.

    2016-07-01

    This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.

  9. Nonlinear vibrations of functionally graded doubly curved shallow shells

    NASA Astrophysics Data System (ADS)

    Alijani, F.; Amabili, M.; Karagiozis, K.; Bakhtiari-Nejad, F.

    2011-03-01

    Nonlinear forced vibrations of FGM doubly curved shallow shells with a rectangular base are investigated. Donnell's nonlinear shallow-shell theory is used and the shell is assumed to be simply supported with movable edges. The equations of motion are reduced using the Galerkin method to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities. Using the multiple scales method, primary and subharmonic resonance responses of FGM shells are fully discussed and the effect of volume fraction exponent on the internal resonance conditions, softening/hardening behavior and bifurcations of the shallow shell when the excitation frequency is (i) near the fundamental frequency and (ii) near two times the fundamental frequency is shown. Moreover, using a code based on arclength continuation method, a bifurcation analysis is carried out for a special case with two-to-one internal resonance between the first and second doubly symmetric modes with respect to the panel's center ( ω13≈2 ω11). Bifurcation diagrams and Poincaré maps are obtained through direct time integration of the equations of motion and chaotic regions are shown by calculating Lyapunov exponents and Lyapunov dimension.

  10. Fractional Adams-Bashforth/Moulton methods: An application to the fractional Keller-Segel chemotaxis system

    NASA Astrophysics Data System (ADS)

    Zayernouri, Mohsen; Matzavinos, Anastasios

    2016-07-01

    We first formulate a fractional class of explicit Adams-Bashforth (A-B) and implicit Adams-Moulton (A-M) methods of first- and second-order accuracy for the time-integration of τ 0 CDt u (x , t) = g (t ; u), τ ∈ (0 , 1 ], where τ 0 CDt denotes the fractional derivative in the Caputo sense. In this fractional setting and in contrast to the standard Adams methods, an extra history load term emerges and the associated weight coefficients are τ-dependent. However when τ = 1, the developed schemes reduce to the well-known A-B and A-M methods with standard coefficients. Hence, in terms of scientific computing, our approach constitutes a minimal modification of the existing Adams libraries. Next, we develop an implicit-explicit (IMEX) splitting scheme for linear and nonlinear fractional PDEs of a general advection-reaction-diffusion type, and we apply our scheme to the time-space fractional Keller-Segel chemotaxis system. In this context, we evaluate the nonlinear advection term explicitly, employing the fractional A-B method in the prediction step, and we treat the corresponding diffusion term implicitly in the correction step using the fractional A-M scheme. Moreover, we perform the corresponding spatial discretization by employing an efficient and spectrally-accurate fractional spectral collocation method. Our numerical experiments exhibit the efficiency of the proposed IMEX scheme in solving nonlinear fractional PDEs.

  11. Fractional Adams-Bashforth/Moulton methods: An application to the fractional Keller-Segel chemotaxis system

    NASA Astrophysics Data System (ADS)

    Zayernouri, Mohsen; Matzavinos, Anastasios

    2016-07-01

    We first formulate a fractional class of explicit Adams-Bashforth (A-B) and implicit Adams-Moulton (A-M) methods of first- and second-order accuracy for the time-integration of 0 CD t τ u (x , t) = g (t ; u), τ ∈ (0 , 1 ], where 0 CD t τ denotes the fractional derivative in the Caputo sense. In this fractional setting and in contrast to the standard Adams methods, an extra history load term emerges and the associated weight coefficients are τ-dependent. However when τ = 1, the developed schemes reduce to the well-known A-B and A-M methods with standard coefficients. Hence, in terms of scientific computing, our approach constitutes a minimal modification of the existing Adams libraries. Next, we develop an implicit-explicit (IMEX) splitting scheme for linear and nonlinear fractional PDEs of a general advection-reaction-diffusion type, and we apply our scheme to the time-space fractional Keller-Segel chemotaxis system. In this context, we evaluate the nonlinear advection term explicitly, employing the fractional A-B method in the prediction step, and we treat the corresponding diffusion term implicitly in the correction step using the fractional A-M scheme. Moreover, we perform the corresponding spatial discretization by employing an efficient and spectrally-accurate fractional spectral collocation method. Our numerical experiments exhibit the efficiency of the proposed IMEX scheme in solving nonlinear fractional PDEs.

  12. Complex step derivative approximation of consistent tangent operators for viscoelasticity based on fractional calculus

    NASA Astrophysics Data System (ADS)

    Hürkamp, André; Tanaka, Masato; Kaliske, Michael

    2015-12-01

    In this contribution, the convergence behaviour of simulations with nonlinear viscoelastic models for rubber-like materials using fractional derivatives is investigated. Based on the complex step derivative approximation, numerical approximation schemes for tangent operators on the local and global algorithmic level are analysed. Material models including fractional derivatives usually exhibit numerical difficulties, since the entire stress history of the material has to be considered for the current stress state. Non-classical methods can help to reduce the numerical effort, but the convergence behaviour is not perfect. In this paper, a classical and a non-classical fractional element based viscoelastic material formulation are analysed. The local and the global convergence rate using analytically and numerically derived tangents are investigated and compared to the convergence behaviour of a standard nonlinear viscoelastic model. Numerical examples on rubber materials are exploited, showing the performance of the proposed methods. It can be proven that the outlined numerical differentiation schemes improve the convergence rate, as well as reduce the computation time for the fractional element based material models.

  13. The Vertical Linear Fractional Initialization Problem

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.

    1999-01-01

    This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.

  14. Legendre Wavelet Operational Matrix of fractional Derivative through wavelet-polynomial transformation and its Applications in Solving Fractional Order Brusselator system

    NASA Astrophysics Data System (ADS)

    Chang, Phang; Isah, Abdulnasir

    2016-02-01

    In this paper we propose the wavelet operational method based on shifted Legendre polynomial to obtain the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. The operational matrices of fractional derivative and collocation method turn the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.

  15. A Fractional Variational Approach to the Fractional Basset-Type Equation

    NASA Astrophysics Data System (ADS)

    Baleanu, Dumitru; Garra, Roberto; Petras, Ivo

    2013-08-01

    In this paper we discuss an application of fractional variational calculus to the Basset-type fractional equations. It is well known that the unsteady motion of a sphere immersed in a Stokes fluid is described by an integro-differential equation involving derivative of real order. Here we study the inverse problem, i.e. we consider the problem from a Lagrangian point of view in the framework of fractional variational calculus. In this way we find an application of fractional variational methods to a classical physical model, finding a Basset-type fractional equation starting from a Lagrangian depending on derivatives of fractional order.

  16. Forward model nonlinearity versus inverse model nonlinearity

    USGS Publications Warehouse

    Mehl, S.

    2007-01-01

    The issue of concern is the impact of forward model nonlinearity on the nonlinearity of the inverse model. The question posed is, "Does increased nonlinearity in the head solution (forward model) always result in increased nonlinearity in the inverse solution (estimation of hydraulic conductivity)?" It is shown that the two nonlinearities are separate, and it is not universally true that increased forward model nonlinearity increases inverse model nonlinearity. ?? 2007 National Ground Water Association.

  17. Possible isotopic fractionation effects in sputtered minerals

    NASA Technical Reports Server (NTRS)

    Haff, P. K.; Watson, C. C.; Tombrello, T. A.

    1980-01-01

    A model which makes definite predictions for the fractionation of isotopes in sputtered material is discussed. The fractionation patterns are nonlinear, and the pattern for a particular set of isotopes depends on the chemical matrix within which those isotopes are contained. Calculations are presented for all nonmonoisotopic elements contained in the minerals perovskite, anorthite, ackermanite, enstatite, and troilite. All isotopes are fractionated at the level of approximately 4-6 deg/o per atomic mass unit. Oxygen is always positively fractionated (heavier isotopes sputtered preferentially), and heavier elements are generally negatively fractioned (light isotopes sputtered preferentially). The value of Delta (O-18:O-16) is always less by about 1.8 deg/o than a linear extrapolation based upon the calculated delta (O-17:O-16) value would suggest. The phenomenon of both negative and positive fractionation patterns from a single target mineral are used to make an experimental test of the proposed model.

  18. SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

    DOEpatents

    Collier, D.M.; Meeks, L.A.; Palmer, J.P.

    1960-05-10

    A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

  19. Nonlinear Dynamics: Maps, Integrators and Solitons

    SciTech Connect

    Parsa, Z.

    1998-10-01

    For many physical systems of interest in various disciplines, the solution to nonlinear differential equations describing the physical systems can be generated using maps, symplectic integrators and solitons. We discuss these methods and apply them for various examples.

  20. 10 ps resolution, 160 ns full scale range and less than 1.5% differential non-linearity time-to-digital converter module for high performance timing measurements.

    PubMed

    Markovic, B; Tamborini, D; Villa, F; Tisa, S; Tosi, A; Zappa, F

    2012-07-01

    We present a compact high performance time-to-digital converter (TDC) module that provides 10 ps timing resolution, 160 ns dynamic range and a differential non-linearity better than 1.5% LSB(rms). The TDC can be operated either as a general-purpose time-interval measurement device, when receiving external START and STOP pulses, or in photon-timing mode, when employing the on-chip SPAD (single photon avalanche diode) detector for detecting photons and time-tagging them. The instrument precision is 15 ps(rms) (i.e., 36 ps(FWHM)) and in photon timing mode it is still better than 70 ps(FWHM). The USB link to the remote PC allows the easy setting of measurement parameters, the fast download of acquired data, and their visualization and storing via an user-friendly software interface. The module proves to be the best candidate for a wide variety of applications such as: fluorescence lifetime imaging, time-of-flight ranging measurements, time-resolved positron emission tomography, single-molecule spectroscopy, fluorescence correlation spectroscopy, diffuse optical tomography, optical time-domain reflectometry, quantum optics, etc. PMID:22852708

  1. 10 ps resolution, 160 ns full scale range and less than 1.5% differential non-linearity time-to-digital converter module for high performance timing measurements

    NASA Astrophysics Data System (ADS)

    Markovic, B.; Tamborini, D.; Villa, F.; Tisa, S.; Tosi, A.; Zappa, F.

    2012-07-01

    We present a compact high performance time-to-digital converter (TDC) module that provides 10 ps timing resolution, 160 ns dynamic range and a differential non-linearity better than 1.5% LSBrms. The TDC can be operated either as a general-purpose time-interval measurement device, when receiving external START and STOP pulses, or in photon-timing mode, when employing the on-chip SPAD (single photon avalanche diode) detector for detecting photons and time-tagging them. The instrument precision is 15 psrms (i.e., 36 psFWHM) and in photon timing mode it is still better than 70 psFWHM. The USB link to the remote PC allows the easy setting of measurement parameters, the fast download of acquired data, and their visualization and storing via an user-friendly software interface. The module proves to be the best candidate for a wide variety of applications such as: fluorescence lifetime imaging, time-of-flight ranging measurements, time-resolved positron emission tomography, single-molecule spectroscopy, fluorescence correlation spectroscopy, diffuse optical tomography, optical time-domain reflectometry, quantum optics, etc.

  2. 10 ps resolution, 160 ns full scale range and less than 1.5% differential non-linearity time-to-digital converter module for high performance timing measurements

    SciTech Connect

    Markovic, B.; Tamborini, D.; Villa, F.; Tisa, S.; Tosi, A.; Zappa, F.

    2012-07-15

    We present a compact high performance time-to-digital converter (TDC) module that provides 10 ps timing resolution, 160 ns dynamic range and a differential non-linearity better than 1.5% LSB{sub rms}. The TDC can be operated either as a general-purpose time-interval measurement device, when receiving external START and STOP pulses, or in photon-timing mode, when employing the on-chip SPAD (single photon avalanche diode) detector for detecting photons and time-tagging them. The instrument precision is 15 ps{sub rms} (i.e., 36 ps{sub FWHM}) and in photon timing mode it is still better than 70 ps{sub FWHM}. The USB link to the remote PC allows the easy setting of measurement parameters, the fast download of acquired data, and their visualization and storing via an user-friendly software interface. The module proves to be the best candidate for a wide variety of applications such as: fluorescence lifetime imaging, time-of-flight ranging measurements, time-resolved positron emission tomography, single-molecule spectroscopy, fluorescence correlation spectroscopy, diffuse optical tomography, optical time-domain reflectometry, quantum optics, etc.

  3. Investigation of a Nonlinear Control System

    NASA Technical Reports Server (NTRS)

    Flugge-Lotz, I; Taylor, C F; Lindberg, H E

    1958-01-01

    A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

  4. Complex order fractional derivatives in viscoelasticity

    NASA Astrophysics Data System (ADS)

    Atanacković, Teodor M.; Konjik, Sanja; Pilipović, Stevan; Zorica, Dušan

    2016-06-01

    We introduce complex order fractional derivatives in models that describe viscoelastic materials. This cannot be carried out unrestrictedly, and therefore we derive, for the first time, real valued compatibility constraints, as well as physical constraints that lead to acceptable models. As a result, we introduce a new form of complex order fractional derivative. Also, we consider a fractional differential equation with complex derivatives, and study its solvability. Results obtained for stress relaxation and creep are illustrated by several numerical examples.

  5. Information geometric nonlinear filtering

    NASA Astrophysics Data System (ADS)

    Newton, Nigel J.

    2015-06-01

    This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on a Hilbert information manifold. This supports the Fisher metric as a pseudo-Riemannian metric. Flows of Shannon information are shown to be connected with the quadratic variation of the process of posterior distributions in this metric. Apart from providing a suitable setting in which to study such information-theoretic properties, the Hilbert manifold has an appropriate topology from the point of view of multi-objective filter approximations. A general class of finite-dimensional exponential filters is shown to fit within this framework, and an intrinsic evolution equation, involving Amari's -1-covariant derivative, is developed for such filters. Three example systems, one of infinite dimension, are developed in detail.

  6. Fractionation of Subcellular Organelles.

    PubMed

    Graham, John M

    2015-01-01

    This unit provides both a theoretical and a practical background to all the techniques associated with the application of differential and density gradient centrifugation for the analysis of subcellular membranes. The density gradient information focuses on the use of the modern gradient solute iodixanol, chosen for its ease of use, versatility, and compatibility with biological particles. Its use in both pre-formed discontinuous and continuous gradients and in self-generated gradients is discussed. Considerable emphasis is given to selection of the appropriate centrifuge rotors and tubes and their influence on the methods used for creation, fractionation, and analysis of density gradients. Without proper consideration of these critical ancillary procedures, the resolving power of the gradient can be easily compromised. PMID:26621372

  7. Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control

    NASA Astrophysics Data System (ADS)

    Yu, Zhiyong; Jiang, Haijun; Hu, Cheng; Yu, Juan

    2015-09-01

    In this paper, the leader-following consensus problem of fractional-order multi-agent systems is considered via adaptive pinning control. The dynamics of leader and all followers with linear and nonlinear functions are investigated, respectively. We assume that the node should be pinned if its in-degree is less than its out-degree in the paper. Under this assumption and based on the stability theory of fractional-order differential systems, some leader-following consensus criteria are derived, which are easily obtained by matrix inequalities. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and the Riccati inequality. Several simulation examples are presented to demonstrate the effectiveness of the proposed method.

  8. Fractional characteristic times and dissipated energy in fractional linear viscoelasticity

    NASA Astrophysics Data System (ADS)

    Colinas-Armijo, Natalia; Di Paola, Mario; Pinnola, Francesco P.

    2016-08-01

    In fractional viscoelasticity the stress-strain relation is a differential equation with non-integer operators (derivative or integral). Such constitutive law is able to describe the mechanical behavior of several materials, but when fractional operators appear, the elastic and the viscous contribution are inseparable and the characteristic times (relaxation and retardation time) cannot be defined. This paper aims to provide an approach to separate the elastic and the viscous phase in the fractional stress-strain relation with the aid of an equivalent classical model (Kelvin-Voigt or Maxwell). For such equivalent model the parameters are selected by an optimization procedure. Once the parameters of the equivalent model are defined, characteristic times of fractional viscoelasticity are readily defined as ratio between viscosity and stiffness. In the numerical applications, three kinds of different excitations are considered, that is, harmonic, periodic, and pseudo-stochastic. It is shown that, for any periodic excitation, the equivalent models have some important features: (i) the dissipated energy per cycle at steady-state coincides with the Staverman-Schwarzl formulation of the fractional model, (ii) the elastic and the viscous coefficients of the equivalent model are strictly related to the storage and the loss modulus, respectively.

  9. Constructing general partial differential equations using polynomial and neural networks.

    PubMed

    Zjavka, Ladislav; Pedrycz, Witold

    2016-01-01

    Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. PMID:26547244

  10. Isolation of differentiated membrane domains from Escherichia coli and Salmonella typhimurium, including a fraction containing sites between the inner and outer membranes and Murein skeleton of the cell envelope

    SciTech Connect

    Not Available

    1986-01-05

    Cell envelopes of Salmonella typhimurium and Escherichia coli were disrupted in a French pressure cell and fractionated by successive cycles of sedimentation and floatation density gradient centrifugation. This permitted the identification and isolation of several membrane fractions in addition to the major inner membrane and murein-outer membrane fractions. One of these fractions (fraction OM/sub L/) accounted for about 10% of the total cell envelope protein, and is likely to include the murein-membrane adhesion zones that are seen in electron micrographs of plasmolyzed cells. Fraction OM/sub L/ contained inner membrane, murein, and outer membrane in an apparently normal configuration, was capable of synthesizing murein from UDP-(/sup 3/H)N-acetylglucosamine and UDP-N-acetylmuramyl-pentapeptide and covalently linking it to the endogenous murein of the preparation. It showed a labeling pattern in (/sup 3/H)galactose pulse-chase experiments that was consistent with its acting as an intermediate in the movement of newly synthesized lipopolysaccharide from inner membrane to outer membrane.

  11. Initialized Fractional Calculus

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.

    2000-01-01

    This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

  12. Quantum disorder, duality, and fractional statistics in 2 + 1 dimensions

    NASA Technical Reports Server (NTRS)

    Wen, X. G.; Zee, A.

    1989-01-01

    A low-energy equivalence between two apparently unrelated Lagrangians with fractional statistics is reported. Exploiting this equivalence, it is possible to study the quantum disordered phase of the nonlinear sigma model with Hopf term. It is found that the quasi-particles in the disordered phase also have fractional statistics. There appears to be a dual relationship between the ordered and disordered phases.

  13. Solving Fractional Programming Problems based on Swarm Intelligence

    NASA Astrophysics Data System (ADS)

    Raouf, Osama Abdel; Hezam, Ibrahim M.

    2014-04-01

    This paper presents a new approach to solve Fractional Programming Problems (FPPs) based on two different Swarm Intelligence (SI) algorithms. The two algorithms are: Particle Swarm Optimization, and Firefly Algorithm. The two algorithms are tested using several FPP benchmark examples and two selected industrial applications. The test aims to prove the capability of the SI algorithms to solve any type of FPPs. The solution results employing the SI algorithms are compared with a number of exact and metaheuristic solution methods used for handling FPPs. Swarm Intelligence can be denoted as an effective technique for solving linear or nonlinear, non-differentiable fractional objective functions. Problems with an optimal solution at a finite point and an unbounded constraint set, can be solved using the proposed approach. Numerical examples are given to show the feasibility, effectiveness, and robustness of the proposed algorithm. The results obtained using the two SI algorithms revealed the superiority of the proposed technique among others in computational time. A better accuracy was remarkably observed in the solution results of the industrial application problems.

  14. Tempered fractional calculus

    NASA Astrophysics Data System (ADS)

    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

    SciTech Connect

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

    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.

  16. Fermentation and dry fractionation increase bioactivity of cloudberry (Rubus chamaemorus).

    PubMed

    Puupponen-Pimiä, Riitta; Nohynek, Liisa; Juvonen, Riikka; Kössö, Tuija; Truchado, Pilar; Westerlund-Wikström, Benita; Leppänen, Tiina; Moilanen, Eeva; Oksman-Caldentey, Kirsi-Marja

    2016-04-15

    Phenolic composition and bioactivity of cloudberry was modified by bioprocessing, and highly bioactive fractions were produced by dry fractionation of the press cake. During fermentation polymeric ellagitannins were partly degraded into ellagic acid derivatives. Phenolic compounds were differentially distributed in seed coarse and fine fractions after dry fractionation process. Tannins concentrated in fine fraction, and flavonol derivatives were mainly found in coarse fraction. Ellagic acid derivatives were equally distributed between the dry fractions. Fermentation and dry fractionation increased statistically significantly anti-adhesion and anti-inflammatory activity of cloudberry. The seed fine fraction showed significant inhibition of P fimbria-mediated haemagglutination assay of uropathogenic Escherichia coli. The seed coarse fraction significantly reduced NO and IL-6 production and iNOS expression in activated macrophages. Fermentation did not affect antimicrobial activity, but slight increase in activity was detected in dry fractions. The results indicate the potential of cloudberry in pharma or health food applications. PMID:26617039

  17. Nonlinear ac stationary response and dynamic magnetic hysteresis of quantum uniaxial superparamagnets

    NASA Astrophysics Data System (ADS)

    Kalmykov, Yuri P.; Titov, Serguey V.; Coffey, William T.

    2015-11-01

    The nonlinear ac stationary response of uniaxial paramagnets and superparamagnets—nanoscale solids or clusters with spin number S ˜100-104 —in superimposed uniform ac and dc bias magnetic fields of arbitrary strength, each applied along the easy axis of magnetization, is determined by solving the evolution equation for the reduced density matrix represented as a finite set of three-term differential-recurrence relations for its diagonal matrix elements. The various harmonic components arising from the nonlinear response of the magnetization, dynamic magnetic hysteresis loops, etc., are then evaluated via matrix continued fractions indicating a pronounced dependence of the response on S arising from the quantum spin dynamics, which differ markedly from the magnetization dynamics of classical nanomagnets. In the linear response approximation, the results concur with existing solutions.

  18. Nonlinear frequency shift of electrostatic waves in general collisionless plasma: Unifying theory of fluid and kinetic nonlinearities

    SciTech Connect

    Liu, Chang; Dodin, Ilya Y.

    2015-08-15

    The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.

  19. On the origins of generalized fractional calculus

    NASA Astrophysics Data System (ADS)

    Kiryakova, Virginia

    2015-11-01

    In Fractional Calculus (FC), as in the (classical) Calculus, the notions of derivatives and integrals (of first, second, etc. or arbitrary, incl. non-integer order) are basic and co-related. One of the most frequent approach in FC is to define first the Riemann-Liouville (R-L) integral of fractional order, and then by means of suitable integer-order differentiation operation applied over it (or under its sign) a fractional derivative is defined - in the R-L sense (or in Caputo sense). The first mentioned (R-L type) is closer to the theoretical studies in analysis, but has some shortages - from the point of view of interpretation of the initial conditions for Cauchy problems for fractional differential equations (stated also by means of fractional order derivatives/ integrals), and also for the analysts' confusion that such a derivative of a constant is not zero in general. The Caputo (C-) derivative, arising first in geophysical studies, helps to overcome these problems and to describe models of applied problems with physically consistent initial conditions. The operators of the Generalized Fractional Calculus - GFC (integrals and derivatives) are based on commuting m-tuple (m = 1, 2, 3, …) compositions of operators of the classical FC with power weights (the so-called Erdélyi-Kober operators), but represented in compact and explicit form by means of integral, integro-differential (R-L type) or differential-integral (C-type) operators, where the kernels are special functions of most general hypergeometric kind. The foundations of this theory are given in Kiryakova 18. In this survey we present the genesis of the definitions of the GFC - the generalized fractional integrals and derivatives (of fractional multi-order) of R-L type and Caputo type, analyze their properties and applications. Their special cases are all the known operators of classical FC, their generalizations introduced by other authors, the hyper-Bessel differential operators of higher integer

  20. Highly nonlinear stress-relaxation response of articular cartilage in indentation: Importance of collagen nonlinearity.

    PubMed

    Mäkelä, J T A; Korhonen, R K

    2016-06-14

    Modern fibril-reinforced computational models of articular cartilage can include inhomogeneous tissue composition and structure, and nonlinear mechanical behavior of collagen, proteoglycans and fluid. These models can capture well experimental single step creep and stress-relaxation tests or measurements under small strains in unconfined and confined compression. Yet, it is known that in indentation, especially at high strain velocities, cartilage can express highly nonlinear response. Different fibril reinforced poroelastic and poroviscoelastic models were used to assess measured highly nonlinear stress-relaxation response of rabbit articular cartilage in indentation. Experimentally measured depth-dependent volume fractions of different tissue constituents and their mechanical nonlinearities were taken into account in the models. In particular, the collagen fibril network was modeled using eight separate models that implemented five different constitutive equations to describe the nonlinearity. These consisted of linear elastic, nonlinear viscoelastic and multiple nonlinear elastic representations. The model incorporating the most nonlinearly increasing Young׳s modulus of collagen fibrils as a function of strain captured best the experimental data. Relative difference between the model and experiment was ~3%. Surprisingly, the difference in the peak forces between the experiment and the model with viscoelastic collagen fibrils was almost 20%. Implementation of the measured volume fractions did not improve the ability of the model to capture the measured mechanical data. These results suggest that a highly nonlinear formulation for collagen fibrils is needed to replicate multi-step stress-relaxation response of rabbit articular cartilage in indentation with high strain rates. PMID:27130474

  1. TEMPERED FRACTIONAL CALCULUS

    PubMed Central

    MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; CHEN, JINGHUA

    2014-01-01

    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 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. PMID:26085690

  2. Lipschitz regularity of solutions for mixed integro-differential equations

    NASA Astrophysics Data System (ADS)

    Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril

    We establish new Hölder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hölder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one.

  3. A fractional-order infectivity SIR model

    NASA Astrophysics Data System (ADS)

    Angstmann, C. N.; Henry, B. I.; McGann, A. V.

    2016-06-01

    Fractional-order SIR models have become increasingly popular in the literature in recent years, however unlike the standard SIR model, they often lack a derivation from an underlying stochastic process. Here we derive a fractional-order infectivity SIR model from a stochastic process that incorporates a time-since-infection dependence on the infectivity of individuals. The fractional derivative appears in the generalised master equations of a continuous time random walk through SIR compartments, with a power-law function in the infectivity. We show that this model can also be formulated as an infection-age structured Kermack-McKendrick integro-differential SIR model. Under the appropriate limit the fractional infectivity model reduces to the standard ordinary differential equation SIR model.

  4. On fractional order of an oscillatory system

    NASA Astrophysics Data System (ADS)

    David, S. A.; Valentim, C. A., Jr.

    2013-10-01

    In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional nonlinear dynamic equations involving the classical physical application "Spring-Mass-Dumper System" to both, integer order calculus (IOC) and fractional order calculus (FOC) approaches. After the numerical simulations, we outlined the main results through time histories and the investigation of phase portraits. Thereafter, we believe that the results showed on this paper are pertinent enough to be thoroughly analyzed and maybe it can be the very beginning of a stride towards more realistic and more precise results about fractional-order models when compared to the integer order models in these applications.

  5. New Exact Solutions of Fractional Zakharov—Kuznetsov and Modified Zakharov—Kuznetsov Equations Using Fractional Sub-Equation Method

    NASA Astrophysics Data System (ADS)

    Saha, Ray S.; Sahoo, S.

    2015-01-01

    In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov—Kuznetsov (ZK) and modified Zakharov—Kuznetsov (mZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie' modified Riemann—Liouville sense.

  6. FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

    2010-11-01

    In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

  7. A Technique for Determining Non-Linear Circuit Parameters from Ring Down Data

    SciTech Connect

    ROMERO, LOUIS; DICKEY, FRED M.; DISON, HOLLY

    2003-01-01

    We present a technique for determining non-linear resistances, capacitances, and inductances from ring down data in a non-linear RLC circuit. Although the governing differential equations are non-linear, we are able to solve this problem using linear least squares without doing any sort of non-linear iteration.

  8. Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. Part 1: Theory

    NASA Technical Reports Server (NTRS)

    Padovan, Joe

    1986-01-01

    In a three part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modelled by fractional integro-differential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator. In the second and third parts of the paper, 3-D extensions are developed along with transient contact strategies enabling the handling of impacts with obstructions. Overall, the various developments are benchmarked via comprehensive 2- and 3-D simulations. These are correlated with experimental data to define modelling capabilities.

  9. Nonlinear dynamics of axially moving plates

    NASA Astrophysics Data System (ADS)

    Ghayesh, Mergen H.; Amabili, Marco; Païdoussis, Michael P.

    2013-01-01

    The nonlinear dynamics for forced motions of an axially moving plate is numerically investigated using Von Kármán plate theory and retaining in-plane displacements and inertia. The equations of motion are obtained via an energy method based on Lagrange equations. This yields a set of second-order nonlinear ordinary differential equations with coupled terms. The equations are transformed into a set of first-order nonlinear ordinary differential equations and are solved via the pseudo-arclength continuation technique. The near-resonance nonlinear dynamics is examined via plotting the frequency-response curves of the system. Results are shown through frequency-response curves, time histories, and phase-plane diagrams. The effect of system parameters, such as the axial speed and the pretension, on the resonant responses is also highlighted.

  10. DIY Fraction Pack.

    ERIC Educational Resources Information Center

    Graham, Alan; Graham, Louise

    2003-01-01

    Describes a very successful attempt to teach fractions to year 5 pupils based on pupils making their own fraction pack. Children decided for themselves how to make the fractional slices used in the activity using colored cardboard sheets and templates of a paper circle consisting of 24 equal slices. (Author/NB)

  11. New Nonlinear Multigrid Analysis

    NASA Technical Reports Server (NTRS)

    Xie, Dexuan

    1996-01-01

    The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.

  12. Nonlinear axisymmetric flexural vibration of spherical shells

    NASA Technical Reports Server (NTRS)

    Kunieda, H.

    1972-01-01

    Axisymmetric responses are presented of a nonshallow thin-walled spherical shell on the basis of nonlinear bending theory. An ordinary differential equation with nonlinearity of quadratic as well as cubic terms associated with variable time is derived. The derivation is based on the assumption that the deflection mode is the sum of four Legendre polynomials, and the Galerkin procedure is applied. The equation is solved by asymptotic expansion, and a first approximate solution is adopted. Unstable regions of this solution are discussed.

  13. General purpose nonlinear system solver based on Newton-Krylov method.

    Energy Science and Technology Software Center (ESTSC)

    2013-12-01

    KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].

  14. Fractional-order variational optical flow model for motion estimation.

    PubMed

    Chen, Dali; Sheng, Hu; Chen, YangQuan; Xue, Dingyü

    2013-05-13

    A new class of fractional-order variational optical flow models, which generalizes the differential of optical flow from integer order to fractional order, is proposed for motion estimation in this paper. The corresponding Euler-Lagrange equations are derived by solving a typical fractional variational problem, and the numerical implementation based on the Grünwald-Letnikov fractional derivative definition is proposed to solve these complicated fractional partial differential equations. Theoretical analysis reveals that the proposed fractional-order variational optical flow model is the generalization of the typical Horn and Schunck (first-order) variational optical flow model and the second-order variational optical flow model, which provides a new idea for us to study the optical flow model and has an important theoretical implication in optical flow model research. The experiments demonstrate the validity of the generalization of differential order. PMID:23547225

  15. PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena

    NASA Astrophysics Data System (ADS)

    Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo

    2010-10-01

    according to the standards of the journal. The selection of papers in this issue aims to bring together recent developments and findings, even though it consists of only a fraction of the impressive developments in recent years which have affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete geometry, among others. The special issue begins with four review papers: Integrable models in nonlinear optics and soliton solutions Degasperis [1] reviews integrable models in nonlinear optics. He presents a number of approximate models which are integrable and illustrates the links between the mathematical and applicative aspects of the theory of integrable dynamical systems. In particular he discusses the recent impact of boomeronic-type wave equations on applications arising in the context of the resonant interaction of three waves. Hamiltonian PDEs: deformations, integrability, solutions Dubrovin [2] presents classification results for systems of nonlinear Hamiltonian partial differential equations (PDEs) in one spatial dimension. In particular he uses a perturbative approach to the theory of integrability of these systems and discusses their solutions. He conjectures universality of the critical behaviour for the solutions, where the notion of universality refers to asymptotic independence of the structure of solutions (at the point of gradient catastrophe) from the choice of generic initial data as well as from the choice of a generic PDE. KP solitons in shallow water Kodama [3] presents a survey of recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. A large variety of exact soliton solutions of the KP equation are presented and classified. The study includes numerical analysis of the stability of the found solution as well as numerical simulations of the initial value problems which

  16. Nonlinear behavior of electrodynamic loudspeaker suspension at low frequencies

    NASA Astrophysics Data System (ADS)

    Feng, ZiXin; Shen, Yong; Heng, Wei; Liu, YunFeng

    2013-07-01

    The suspension of electrodynamic loudspeakers includes a surround of the cone and a spider, and it is characterized by the mechanic stiffness in the lumped-parameter model. By solving the nonlinear differential equation of motion which considers the nonlinearity of suspension at low frequencies numerically and measuring different kinds of surrounds and spiders, the nonlinear behavior of suspension is theoretically and experimentally studied. Since the nonlinear stiffness of spiders and surrounds can be measured and fitted respectively before assembled into loudspeakers, which spider works best with which surround is studied. The performance of loudspeakers such as harmonic distortion based on the nonlinear parameters can be predicted.

  17. Relativistic equations with fractional and pseudodifferential operators

    SciTech Connect

    Babusci, D.; Dattoli, G.; Quattromini, M.

    2011-06-15

    In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with noninteger exponents. We apply the method to equations resembling generalizations of the heat equations and discuss the possibility of extending the procedure to the relativistic Schroedinger and Dirac equations.

  18. Dividing Fractions: A Pedagogical Technique

    ERIC Educational Resources Information Center

    Lewis, Robert

    2016-01-01

    When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions it is turned into an easy multiplication of…

  19. Fractional calculus in bioengineering, part 3.

    PubMed

    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

  20. Geometrically nonlinear vibrations of beams supported by a nonlinear elastic foundation with variable discontinuity

    NASA Astrophysics Data System (ADS)

    Stojanović, Vladimir

    2015-11-01

    Geometrically nonlinear vibrations of a Timoshenko beam resting on a nonlinear Winkler and Pasternak elastic foundation with variable discontinuity are investigated in this paper. A p-version finite element method is developed for geometric nonlinear vibrations of a shear deformable beam resting on a nonlinear foundation with discontinuity. The elastic foundation has cubic nonlinearity with the shearing layer. In the study the p-element which comes from the use of explored special displacement shape functions for damaged beams is used and applied to a model with nonlinear foundation. The novelty of the present study lies in the easy generalisation of the approach of natural frequencies, general mode shapes (transverse and rotations of cross sections), and maximal deflections in nonlinear steady state vibrations of the shear deformable beam for any size and location of discontinuity of the nonlinear elastic support. A new set of nonlinear partial differential equations is developed, and they are solved in the time domain using the Newmark method for obtaining the amplitudes and deformed shapes of a beam in the steady state forced vibration regime. The present work consists of the comparison of the results with various stiffnesses of nonlinear elastic supports of the Winkler and Pasternak type.

  1. Bayesian Estimation of Panel Data Fractional Response Models with Endogeneity: An Application to Standardized Test Rates

    ERIC Educational Resources Information Center

    Kessler, Lawrence M.

    2013-01-01

    In this paper I propose Bayesian estimation of a nonlinear panel data model with a fractional dependent variable (bounded between 0 and 1). Specifically, I estimate a panel data fractional probit model which takes into account the bounded nature of the fractional response variable. I outline estimation under the assumption of strict exogeneity as…

  2. FRACTIONAL PEARSON DIFFUSIONS

    PubMed Central

    Leonenko, Nikolai N.; Meerschaert, Mark M.

    2013-01-01

    Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change. PMID:23626377

  3. Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation.

    PubMed

    Mustafa, M; Mushtaq, A; Hayat, T; Alsaedi, A

    2016-01-01

    Present study explores the MHD three-dimensional rotating flow and heat transfer of ferrofluid induced by a radiative surface. The base fluid is considered as water with magnetite-Fe3O4 nanoparticles. Novel concept of non-linear radiative heat flux is considered which produces a non-linear energy equation in temperature field. Conventional transformations are employed to obtain the self-similar form of the governing differential system. The arising system involves an interesting temperature ratio parameter which is an indicator of small/large temperature differences in the flow. Numerical simulations with high precision are determined by well-known shooting approach. Both uniform stretching and rotation have significant impact on the solutions. The variation in velocity components with the nanoparticle volume fraction is non-monotonic. Local Nusselt number in Fe3O4-water ferrofluid is larger in comparison to the pure fluid even at low particle concentration. PMID:26894690

  4. Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation

    PubMed Central

    Mustafa, M.; Mushtaq, A.; Hayat, T.; Alsaedi, A.

    2016-01-01

    Present study explores the MHD three-dimensional rotating flow and heat transfer of ferrofluid induced by a radiative surface. The base fluid is considered as water with magnetite-Fe3O4 nanoparticles. Novel concept of non-linear radiative heat flux is considered which produces a non-linear energy equation in temperature field. Conventional transformations are employed to obtain the self-similar form of the governing differential system. The arising system involves an interesting temperature ratio parameter which is an indicator of small/large temperature differences in the flow. Numerical simulations with high precision are determined by well-known shooting approach. Both uniform stretching and rotation have significant impact on the solutions. The variation in velocity components with the nanoparticle volume fraction is non-monotonic. Local Nusselt number in Fe3O4–water ferrofluid is larger in comparison to the pure fluid even at low particle concentration. PMID:26894690

  5. Canonical forms for nonlinear systems

    NASA Technical Reports Server (NTRS)

    Su, R.; Hunt, L. R.; Meyer, G.

    1983-01-01

    Necessary and sufficient conditions for transforming a nonlinear system to a controllable linear system have been established, and this theory has been applied to the automatic flight control of aircraft. These transformations show that the nonlinearities in a system are often not intrinsic, but are the result of unfortunate choices of coordinates in both state and control variables. Given a nonlinear system (that may not be transformable to a linear system), we construct a canonical form in which much of the nonlinearity is removed from the system. If a system is not transformable to a linear one, then the obstructions to the transformation are obvious in canonical form. If the system can be transformed (it is called a linear equivalent), then the canonical form is a usual one for a controllable linear system. Thus our theory of canonical forms generalizes the earlier transformation (to linear systems) results. Our canonical form is not unique, except up to solutions of certain partial differential equations we discuss. In fact, the important aspect of this paper is the constructive procedure we introduce to reach the canonical form. As is the case in many areas of mathematics, it is often easier to work with the canonical form than in arbitrary coordinate variables.

  6. Fractional calculus in bioengineering, part 2.

    PubMed

    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

  7. On the implementation of automatic differentiation tools.

    SciTech Connect

    Bischof, C. H.; Hovland, P. D.; Norris, B.; Mathematics and Computer Science; Aachen Univ. of Technology

    2008-01-01

    Automatic differentiation is a semantic transformation that applies the rules of differential calculus to source code. It thus transforms a computer program that computes a mathematical function into a program that computes the function and its derivatives. Derivatives play an important role in a wide variety of scientific computing applications, including numerical optimization, solution of nonlinear equations, sensitivity analysis, and nonlinear inverse problems. We describe the forward and reverse modes of automatic differentiation and provide a survey of implementation strategies. We describe some of the challenges in the implementation of automatic differentiation tools, with a focus on tools based on source transformation. We conclude with an overview of current research and future opportunities.

  8. An Appetite for Fractions

    ERIC Educational Resources Information Center

    Wilkerson, Trena L.; Bryan, Tommy; Curry, Jane

    2012-01-01

    This article describes how using candy bars as models gives sixth-grade students a taste for learning to represent fractions whose denominators are factors of twelve. Using paper models of the candy bars, students explored and compared fractions. They noticed fewer different representations for one-third than for one-half. The authors conclude…

  9. Can Kindergartners Do Fractions?

    ERIC Educational Resources Information Center

    Cwikla, Julie

    2014-01-01

    Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems…

  10. The Future of Fractions

    ERIC Educational Resources Information Center

    Usiskin, Zalman P.

    2007-01-01

    In the 1970s, the movement to the metric system (which has still not completely occurred in the United States) and the advent of hand-held calculators led some to speculate that decimal representation of numbers would render fractions obsolete. This provocative proposition stimulated Zalman Usiskin to write "The Future of Fractions" in 1979. He…

  11. (Carbon isotope fractionation inplants)

    SciTech Connect

    O'Leary, M.H.

    1990-01-01

    The objectives of this research are: To develop a theoretical and experimental framework for understanding isotope fractionations in plants; and to develop methods for using this isotope fractionation for understanding the dynamics of CO{sub 2} fixation in plants. Progress is described.

  12. Differentiator design and performance for edge sharpening

    USGS Publications Warehouse

    Pan, Jeng-Jong; Domingue, Julia O.

    1990-01-01

    A two-dimensional differentiator is useful for edge sharpening in digital image processing. In the design of a differentiator, differentiator coefficients that satisfy the specification of frequency response must be approximated. Four mathematical techniques - the minimax method, least-squares method, nonlinear programming, and linear programming - can be applied to solve the approximation problem. Results indicated that the differentiator derived from linear programming gives the highest resolution. -from Authors

  13. Nonlinear Acoustics in Fluids

    NASA Astrophysics Data System (ADS)

    Lauterborn, Werner; Kurz, Thomas; Akhatov, Iskander

    At high sound intensities or long propagation distances at in fluids sufficiently low damping acoustic phenomena become nonlinear. This chapter focuses on nonlinear acoustic wave properties in gases and liquids. The origin of nonlinearity, equations of state, simple nonlinear waves, nonlinear acoustic wave equations, shock-wave formation, and interaction of waves are presented and discussed. Tables are given for the nonlinearity parameter B/A for water and a range of organic liquids, liquid metals and gases. Acoustic cavitation with its nonlinear bubble oscillations, pattern formation and sonoluminescence (light from sound) are modern examples of nonlinear acoustics. The language of nonlinear dynamics needed for understanding chaotic dynamics and acoustic chaotic systems is introduced.

  14. Isotopomers as a method for differentiating between bacterial and fungal production of nitrous oxide

    NASA Astrophysics Data System (ADS)

    Sutka, R. L.; Adams, G.; Ostrom, N.; Ostrom, P.

    2007-12-01

    In order to study the importance of fungi to nitrous oxide (N2O) production in the environment it is critical to have a non-intrusive method for differentiating between fungal and bacterial N2O production. Site preference (SP), the difference in d15N between the central and outer N atoms in N2O, has been used to differentiate between bacterial nitrification and denitrification. In this study we compare the SP, d15N and d18O of N2O produced by the two best-studied fungal denitrifiers, Fusarium oxysporum and Cylindrocarpon tonkinense, to data from our previous bacterial studies. Both d18O and SP values remained fairly constant during the course of nitrite reduction which likely reflects isotopic exchange with water in the case of d18O and conservative behavior in SP that has been observed previously (Sutka et al., 2006). We observed a wide range of fractionation factors for fungal denitrification, -74.7 to -6.6 ‰, and non-linear behavior indicating that fractionation was controlled by more than one step. We interpret the small degree of fractionation as reflecting fractionation during diffusion and the more negative values as being controlled by enzymatic fractionation. Data from this and our previous study of bacterial production (Sutka et al., 2006) reveals that N2O produced via nitrification by fungi can be differentiated from N2O produced by bacterial denitrification primarily on the basis of d18O. The site preference of N2O produced by F. oxysporum and C. tonkinense was 37.1 ± 2.5 ‰ and 36.9 ± 2.8 ‰, respectively. These results indicate that isotopomers can be used as a basis for differentiating bacterial and fungal denitrification. Our work further reveals the role that fungal and bacterial nitric oxide reductases have in determining site preference during N2O production.

  15. Non-linearity in clinical practice.

    PubMed

    Petros, Peter

    2003-05-01

    The whole spectrum of medicine consists of complex non-linear systems that are balanced and interact with each other. How non-linearity confers stability on a system and explains variation and uncertainty in clinical medicine is discussed. A major theme is that a small alteration in initial conditions may have a major effect on the end result. In the context of non-linearity, it is argued that 'evidence-based medicine' (EBM) as it exists today can only ever be relevant to a small fraction of the domain of medicine, that the 'art of medicine' consists of an intuitive 'tuning in' to these complex systems and as such is not so much an art as an expression of non-linear science. The main cause of iatrogenic disease is interpreted as a failure to understand the complexity of the systems being treated. Case study examples are given and analysed in non-linear terms. It is concluded that good medicine concerns individualized treatment of an individual patient whose body functions are governed by non-linear processes. EBM as it exists today paints with a broad and limited brush, but it does promise a fresh new direction. In this context, we need to expand the spectrum of scientific medicine to include non-linearity, and to look upon the 'art of medicine' as a historical (but unstated) legacy in this domain. PMID:12787180

  16. Some nonlinear space decomposition algorithms

    SciTech Connect

    Tai, Xue-Cheng; Espedal, M.

    1996-12-31

    Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.

  17. Nonlinear control in fusion reactors

    NASA Astrophysics Data System (ADS)

    Schuster, Eugenio

    There is consensus in the fusion reactor community that active control will be one of the key enabling technologies. With further advancements in reduced-order fusion modeling, advances in control systems for fusion will continue, including vertical and shape control, kinetic and current profile control, MHD (magnetohydrodynamic) stabilization and plasma transport reduction. This dissertation addresses different control problems in tokamaks using as common denominator a nonlinear control approach. Contributions are made in the areas of kinetic control, magnetic control, and MHD flow control. In the area of kinetic control, we approach the problem of nonlinear control of burn instability in fission reactors, where a lumped-parameter nonlinear model involving approximate conservation equations for the energy and the densities of the species is used to synthesize a nonlinear feedback controller (backstepping, feedback linearization, passivity and input to state stability) for stabilizing the thermally unstable burn condition of a fusion reactor. In addition, the problem of control of kinetic profiles in non-burning plasmas, where a set of nonlinear partial differential equations (PDE's) describing approximately the dynamics of the density and energy was considered as the plant model used to synthesize a boundary controller (infinite-dimensional nonlinear backstepping) whose goal was the control of the density and energy spatial distributions, is also considered. In the area of magnetic control, the problem of plasma vertical position stabilization and shape control under actuation saturation in the DIII-D Tokamak at General Atomics is approached. In this case, modifications of the nominal control loops (nonlinear anti-windup augmentation) are proposed to ensure stability of the plant and good behavior of the nominal controller under the presence of voltage saturation in the coils that are used to vertically position and shape the plasma inside the tokamak. In the area

  18. Application of the Homotopy Perturbation Method to the Nonlinear Pendulum

    ERIC Educational Resources Information Center

    Belendez, A.; Hernandez, A.; Belendez, T.; Marquez, A.

    2007-01-01

    The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as…

  19. Biochemical characterization of three mycobacterial ribosomal fractions.

    PubMed

    Portelance, V; Beaudet, R

    1983-02-01

    The induction of antituberculous immunity by crude ribosomal fractions isolated from Mycobacterium tuberculosis strain H37Ra, M. bovis strain BCG, and M. smegmatis was studied in CF-1 mice. Levels of antituberculous immunity similar to that induced by live BCG were induced by the BCG and H37Ra ribosomal fractions whereas that isolated from M. smegmatis was found to be inactive. Electrophoresis of the three ribosomal fractions in sodium dodecyl sulfate - polyacylamide gels followed by differential staining showed the two active ribosomal fractions to be similar in their proteins, carbohydrate-containing substances, and lipid profiles. The inactive smegmatis ribosomal fraction differed mainly from the active ones on the basis of its carbohydrate-containing substances profile and by the absence of lipids. The polysaccharides and the ribosomes present in the H37Ra ribosomal fractions were purified by affinity chromatography on concanavalin A - Sepharose 4B. Each purified preparation showed no or only low antituberculous activity when injected separately, but when mixed together a high protection was observed. The formation of complexes between the ribosomes and the polysaccharide fraction was suggested and appears to be necessary for the induction of antituberculous immunity. PMID:6189570

  20. Fractional Modeling of Viscoelasticity in Brain Aneurysms

    NASA Astrophysics Data System (ADS)

    Yu, Yue; Karniadakis, George

    2014-11-01

    We develop fundamental new numerical methods for fractional order PDEs, and investigate corresponding models for arterial walls. Specifically, the arterial wall is a heterogeneous soft tissue with complex biomechanical properties, and its constitutive laws are typically derived using integer-order differential equations. However, recent simulations on 1D model have indicated that fractional order models may offer a more powerful alternative for describing arterial wall mechanics, because they are less sensitive to the parameter estimation compared with the integer-calculus-based models. We study the specific fractional PDEs that better model the properties of the 3D arterial walls, and for the first time employ them in simulating flow structure interactions for patient-specific brain aneurysms. A comparison study indicates that for the integer order models, the viscous behavior strongly depends on the relaxation parameters while the fractional order models are less sensitive. This finding is consistent with what is observed in the 1D models for arterial networks (Perdikaris & Karniadakis, 2014), except that when the fractional order is small, the 3D fractional-order models are more sensitive to the fractional order compared to the 1D models.

  1. Fractional Dynamics of Network Growth Constrained by Aging Node Interactions

    PubMed Central

    Safdari, Hadiseh; Zare Kamali, Milad; Shirazi, Amirhossein; Khalighi, Moein; Jafari, Gholamreza; Ausloos, Marcel

    2016-01-01

    In many social complex systems, in which agents are linked by non-linear interactions, the history of events strongly influences the whole network dynamics. However, a class of “commonly accepted beliefs” seems rarely studied. In this paper, we examine how the growth process of a (social) network is influenced by past circumstances. In order to tackle this cause, we simply modify the well known preferential attachment mechanism by imposing a time dependent kernel function in the network evolution equation. This approach leads to a fractional order Barabási-Albert (BA) differential equation, generalizing the BA model. Our results show that, with passing time, an aging process is observed for the network dynamics. The aging process leads to a decay for the node degree values, thereby creating an opposing process to the preferential attachment mechanism. On one hand, based on the preferential attachment mechanism, nodes with a high degree are more likely to absorb links; but, on the other hand, a node’s age has a reduced chance for new connections. This competitive scenario allows an increased chance for younger members to become a hub. Simulations of such a network growth with aging constraint confirm the results found from solving the fractional BA equation. We also report, as an exemplary application, an investigation of the collaboration network between Hollywood movie actors. It is undubiously shown that a decay in the dynamics of their collaboration rate is found, even including a sex difference. Such findings suggest a widely universal application of the so generalized BA model. PMID:27171424

  2. Fractional Dynamics of Network Growth Constrained by Aging Node Interactions.

    PubMed

    Safdari, Hadiseh; Zare Kamali, Milad; Shirazi, Amirhossein; Khalighi, Moein; Jafari, Gholamreza; Ausloos, Marcel

    2016-01-01

    In many social complex systems, in which agents are linked by non-linear interactions, the history of events strongly influences the whole network dynamics. However, a class of "commonly accepted beliefs" seems rarely studied. In this paper, we examine how the growth process of a (social) network is influenced by past circumstances. In order to tackle this cause, we simply modify the well known preferential attachment mechanism by imposing a time dependent kernel function in the network evolution equation. This approach leads to a fractional order Barabási-Albert (BA) differential equation, generalizing the BA model. Our results show that, with passing time, an aging process is observed for the network dynamics. The aging process leads to a decay for the node degree values, thereby creating an opposing process to the preferential attachment mechanism. On one hand, based on the preferential attachment mechanism, nodes with a high degree are more likely to absorb links; but, on the other hand, a node's age has a reduced chance for new connections. This competitive scenario allows an increased chance for younger members to become a hub. Simulations of such a network growth with aging constraint confirm the results found from solving the fractional BA equation. We also report, as an exemplary application, an investigation of the collaboration network between Hollywood movie actors. It is undubiously shown that a decay in the dynamics of their collaboration rate is found, even including a sex difference. Such findings suggest a widely universal application of the so generalized BA model. PMID:27171424

  3. Effects of model sensitivity and nonlinearity on nonlinear regression of ground water flow

    USGS Publications Warehouse

    Yager, R.M.

    2004-01-01

    Nonlinear regression is increasingly applied to the calibration of hydrologic models through the use of perturbation methods to compute the Jacobian or sensitivity matrix required by the Gauss-Newton optimization method. Sensitivities obtained by perturbation methods can be less accurate than those obtained by direct differentiation, however, and concern has arisen that the optimal parameter values and the associated parameter covariance matrix computed by perturbation could also be less accurate. Sensitivities computed by both perturbation and direct differentiation were applied in nonlinear regression calibration of seven ground water flow models. The two methods gave virtually identical optimum parameter values and covariances for the three models that were relatively linear and two of the models that were relatively nonlinear, but gave widely differing results for two other nonlinear models. The perturbation method performed better than direct differentiation in some regressions with the nonlinear models, apparently because approximate sensitivities computed for an interval yielded better search directions than did more accurately computed sensitivities for a point. The method selected to avoid overshooting minima on the error surface when updating parameter values with the Gauss-Newton procedure appears for nonlinear models to be more important than the method of sensitivity calculation in controlling regression convergence.

  4. Multiple daily fractionation schedules

    SciTech Connect

    Peschel, R.E.; Fischer, J.J.

    1982-10-01

    Although conventional fractionation schedules have been satisfactory for the treatment of some tumors, there is reason to believe that the results of radiation therapy could be improved in some cases by appropriate alterations in treatment schedules. The pharmacological characteristics of some of the electron affinic radiation sensitizers have provided added incentive to investigate newer fractionation schemes, particularly ones which deliver the majority of the radiation dose in short periods of time. This editorial discusses three papers describing preliminary clinical studies using multi-daily fractionated (MDF) radiation therapy. Two of these studies also make use of the radiation sensitizer misonidazole. (KRM)

  5. The valuation of currency options by fractional Brownian motion.

    PubMed

    Shokrollahi, Foad; Kılıçman, Adem

    2016-01-01

    This research aims to investigate a model for pricing of currency options in which value governed by the fractional Brownian motion model (FBM). The fractional partial differential equation and some Greeks are also obtained. In addition, some properties of our pricing formula and simulation studies are presented, which demonstrate that the FBM model is easy to use. PMID:27504243

  6. Nonlinear Acoustical Assessment of Precipitate Nucleation

    NASA Technical Reports Server (NTRS)

    Cantrell, John H.; Yost, William T.

    2004-01-01

    The purpose of the present work is to show that measurements of the acoustic nonlinearity parameter in heat treatable alloys as a function of heat treatment time can provide quantitative information about the kinetics of precipitate nucleation and growth in such alloys. Generally, information on the kinetics of phase transformations is obtained from time-sequenced electron microscopical examination and differential scanning microcalorimetry. The present nonlinear acoustical assessment of precipitation kinetics is based on the development of a multiparameter analytical model of the effects on the nonlinearity parameter of precipitate nucleation and growth in the alloy system. A nonlinear curve fit of the model equation to the experimental data is then used to extract the kinetic parameters related to the nucleation and growth of the targeted precipitate. The analytical model and curve fit is applied to the assessment of S' precipitation in aluminum alloy 2024 during artificial aging from the T4 to the T6 temper.

  7. Discrete time learning control in nonlinear systems

    NASA Technical Reports Server (NTRS)

    Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh

    1992-01-01

    In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.

  8. Pricing currency options in the mixed fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Sun, Lin

    2013-08-01

    This paper deals with the problem of pricing European currency options in the mixed fractional Brownian environment. Both the pricing formula and the mixed fractional partial differential equation for European call currency options are obtained. Some Greeks and the estimator of volatility are also provided. Empirical studies and simulation results confirm the theoretical findings and show that the mixed fractional Brownian pricing model is a reasonable one.

  9. Power-law spatial dispersion from fractional Liouville equation

    SciTech Connect

    Tarasov, Vasily E.

    2013-10-15

    A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

  10. Differential morphology and image processing.

    PubMed

    Maragos, P

    1996-01-01

    Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision. PMID:18285181

  11. Nonlinear Analysis Of Rotor Dynamics

    NASA Technical Reports Server (NTRS)

    Day, William B.; Zalik, Richard

    1988-01-01

    Study explores analytical consequences of nonlinear Jeffcott equations of rotor dynamics. Section 1: Summary of previous studies. Section 2: Jeffcott Equations. Section 3: Proves two theorems that provide inequalities on coefficients of differential equations and magnitude of forcing function in absence of side force. Section 4: Numerical investigation of multiple-forcing-function problem by introducing both side force and mass imbalance. Section 5: Examples of numberical solutions of complex generalized Jeffcott equation with two forcing functions of different frequencies f1 and f2. Section 6: Boundedness and stability of solutions.Section 7: Concludes report reviewing analytical results and significance.

  12. Nonlinear Hysteretic Torsional Waves.

    PubMed

    Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V

    2015-07-31

    We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters. PMID:26274421

  13. Nonlinear Hysteretic Torsional Waves

    NASA Astrophysics Data System (ADS)

    Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.

    2015-07-01

    We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

  14. Complex geometrical optics of nonlinear inhomogeneous fibres

    NASA Astrophysics Data System (ADS)

    Berczynski, Pawel

    2011-03-01

    This paper analyses the Gaussian beam (GB) evolution in nonlinear fibres with special attention given to the influence of the initial curvature of the wavefront and to the fibres' permittivity profile. The analysis is performed in the framework of paraxial complex geometrical optics (PCGO). This method reduces the problem of GB evolution in nonlinear and inhomogeneous media to the solution of ordinary differential equations, which can be easily solved either analytically or numerically. It is shown that the PCGO approach radically simplifies modelling of nonlinear phenomena in fibres as compared with standard methods of nonlinear optics such as the variational method approach and the method of moments. It is shown that the PCGO method readily supplies the solution of the nonlinear Schrödinger equation (NLS) for a self-focusing fibre with a focusing permittivity profile and provides a number of new results. The discussion on the interplay between the nonlinear (self-focusing and self-defocusing) and linear (focusing and defocusing) components of the total permittivity demonstrates the new possibilities to limit the collapse phenomenon in nonlinear fibres of Kerr type taking into account the effect of initial beam divergence.

  15. Geometrically nonlinear behavior of piezoelectric laminated plates

    NASA Astrophysics Data System (ADS)

    Rabinovitch, Oded

    2005-08-01

    The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.

  16. FCC main fractionator revamps

    SciTech Connect

    Golden, S.W.; Martin, G.R.; Sloley, A.W. )

    1993-03-01

    Structured packing use in fluid catalytic cracker (FCC) main fractionators significantly impacts unit pressure profile. Unit pressure balance links the FCC main fractionator, reactor, regenerator, air compressor and wet gas compressor. Unit pressure balance should be viewed as a design variable when evaluating FCC unit revamps. Depending upon limitations of the particular FCC unit, capacity increases of 12.5% to 22.5% have been achieved without modifications to major rotating equipment, by revamping FCC main fractionators with structured packing. An examination of three FCC main fractionator revamps show improvements to pressure profiles and unit capacity. The three revamps described included a wet gas compressor volume limit; an air blower limitation; and a wet gas compressor motor limitation.

  17. Nonlinear microscopy of collagen fibers

    NASA Astrophysics Data System (ADS)

    Strupler, M.; Pena, A.-M.; Hernest, M.; Tharaux, P.-L.; Fabre, A.; Marchal-Somme, J.; Crestani, B.; Débarre, D.; Martin, J.-L.; Beaurepaire, E.; Schanne-Klein, M.-C.

    2007-02-01

    We used intrinsic Second Harmonic Generation (SHG) by fibrillar collagen to visualize the three-dimensional architecture of collagen fibrosis at the micrometer scale using laser scanning nonlinear microscopy. We showed that SHG signals are highly specific to fibrillar collagen and provide a sensitive probe of the micrometer-scale structural organization of collagen in tissues. Moreover, recording simultaneously other nonlinear optical signals in a multimodal setup, we visualized the tissue morphology using Two-Photon Excited Fluorescence (2PEF) signals from endogenous chromophores such as NADH or elastin. We then compared different methods to determine accurate indexes of collagen fibrosis using nonlinear microscopy, given that most collagen fibrils are smaller than the microscope resolution and that second harmonic generation is a coherent process. In order to define a robust method to process our three-dimensional images, we either calculated the fraction of the images occupied by a significant SHG signal, or averaged SHG signal intensities. We showed that these scores provide an estimation of the extension of renal and pulmonary fibrosis in murine models, and that they clearly sort out the fibrotic mice.

  18. Intracellular Cadmium Isotope Fractionation

    NASA Astrophysics Data System (ADS)

    Horner, T. J.; Lee, R. B.; Henderson, G. M.; Rickaby, R. E.

    2011-12-01

    Recent stable isotope studies into the biological utilization of transition metals (e.g. Cu, Fe, Zn, Cd) suggest several stepwise cellular processes can fractionate isotopes in both culture and nature. However, the determination of fractionation factors is often unsatisfactory, as significant variability can exist - even between different organisms with the same cellular functions. Thus, it has not been possible to adequately understand the source and mechanisms of metal isotopic fractionation. In order to address this problem, we investigated the biological fractionation of Cd isotopes within genetically-modified bacteria (E. coli). There is currently only one known biological use or requirement of Cd, a Cd/Zn carbonic anhydrase (CdCA, from the marine diatom T. weissfloggii), which we introduce into the E. coli genome. We have also developed a cleaning procedure that allows for the treating of bacteria so as to study the isotopic composition of different cellular components. We find that whole cells always exhibit a preference for uptake of the lighter isotopes of Cd. Notably, whole cells appear to have a similar Cd isotopic composition regardless of the expression of CdCA within the E. coli. However, isotopic fractionation can occur within the genetically modified E. coli during Cd use, such that Cd bound in CdCA can display a distinct isotopic composition compared to the cell as a whole. Thus, the externally observed fractionation is independent of the internal uses of Cd, with the largest Cd isotope fractionation occurring during cross-membrane transport. A general implication of these experiments is that trace metal isotopic fractionation most likely reflects metal transport into biological cells (either actively or passively), rather than relating to expression of specific physiological function and genetic expression of different metalloenzymes.

  19. Symmetric continued fractions

    SciTech Connect

    Panprasitwech, Oranit; Laohakosol, Vichian; Chaichana, Tuangrat

    2010-11-11

    Explicit formulae for continued fractions with symmetric patterns in their partial quotients are constructed in the field of formal power series. Similar to the work of Cohn in 1996, which generalized the so-called folding lemma to {kappa}-fold symmetry, the notion of {kappa}-duplicating symmetric continued fractions is investigated using a modification of the 1995 technique due to Clemens, Merrill and Roeder.

  20. Solitary travelling auto-waves in fractional reaction-diffusion systems

    NASA Astrophysics Data System (ADS)

    Datsko, Bohdan; Gafiychuk, Vasyl; Podlubny, Igor

    2015-06-01

    In this article we study properties of solitary auto-waves in nonlinear fractional reaction-diffusion systems. As an example, the generalised FitzHugh-Nagumo model with time-fractional derivatives is considered. By a linear stability analysis and computer simulation it is shown that the order of the fractional derivative can substantially change the properties of solitary auto-waves and significantly enrich nonlinear system dynamics. The main properties of solitary travelling wave solutions, including the shape of the waves, the domain of their existence, as well as the parameters of their propagation in fractional reaction-diffusion systems, are investigated.

  1. Using Numerical Solutions in the Fourier Method for the Fokker-Planck-Kolmogorov Equation in the Analysis of First-Order Stochastic Nonlinear Systems for Nonlinear Detectors

    NASA Astrophysics Data System (ADS)

    Nevolin, V. I.

    2003-04-01

    We present a method for analyzing the characteristics of nonlinear detectors using the algorithms of first-order nonlinear differential equations. This method is based on numerical solutions of the Fokker-Planck-Kolmogorov (FPK) equations in the form of series of functions over Hermite-Chebyshev polynomials for both nonlinear systems and their linear counterparts. The results of the solutions for the linear case are extended to nonlinear systems in a recurrent way.

  2. Stability analysis of impulsive functional systems of fractional order

    NASA Astrophysics Data System (ADS)

    Stamova, Ivanka; Stamov, Gani

    2014-03-01

    In this paper, a class of impulsive fractional functional differential systems is investigated. Sufficient conditions for stability of the zero solution are proved, extending the corresponding theory of impulsive functional differential equations. The investigations are carried out by using the comparison principle, coupled with the Lyapunov function method. We apply our results to an impulsive single species model of Lotka-Volterra type.

  3. Analytical periodic motions in a parametrically excited, nonlinear rotating blade

    NASA Astrophysics Data System (ADS)

    Wang, F.; Luo, A. C. J.

    2013-09-01

    The stability and bifurcation analyses of periodic motions in a rotating blade subject to a torsional excitation are investigated. For high speed rotations, cubic geometric nonlinearity and gyroscopic effects of the rotating blade are considered. From the Galerkin method, the partial differential equation of the nonlinear rotating blade is simplified to the ordinary differential equations, and periodic motions and stability of the rotating blade are studied by the generalized harmonic balance method. The analytical and numerical results of periodic solutions are compared. The rich dynamics and co-existing periodic solutions of the nonlinear rotating blades are investigated.

  4. Systematic Computation of Nonlinear Cellular and Molecular Dynamics with Low-Power CytoMimetic Circuits: A Simulation Study

    PubMed Central

    Papadimitriou, Konstantinos I.; Stan, Guy-Bart V.; Drakakis, Emmanuel M.

    2013-01-01

    This paper presents a novel method for the systematic implementation of low-power microelectronic circuits aimed at computing nonlinear cellular and molecular dynamics. The method proposed is based on the Nonlinear Bernoulli Cell Formalism (NBCF), an advanced mathematical framework stemming from the Bernoulli Cell Formalism (BCF) originally exploited for the modular synthesis and analysis of linear, time-invariant, high dynamic range, logarithmic filters. Our approach identifies and exploits the striking similarities existing between the NBCF and coupled nonlinear ordinary differential equations (ODEs) typically appearing in models of naturally encountered biochemical systems. The resulting continuous-time, continuous-value, low-power CytoMimetic electronic circuits succeed in simulating fast and with good accuracy cellular and molecular dynamics. The application of the method is illustrated by synthesising for the first time microelectronic CytoMimetic topologies which simulate successfully: 1) a nonlinear intracellular calcium oscillations model for several Hill coefficient values and 2) a gene-protein regulatory system model. The dynamic behaviours generated by the proposed CytoMimetic circuits are compared and found to be in very good agreement with their biological counterparts. The circuits exploit the exponential law codifying the low-power subthreshold operation regime and have been simulated with realistic parameters from a commercially available CMOS process. They occupy an area of a fraction of a square-millimetre, while consuming between 1 and 12 microwatts of power. Simulations of fabrication-related variability results are also presented. PMID:23393550

  5. soil organic matter fractionation

    NASA Astrophysics Data System (ADS)

    Osat, Maryam; Heidari, Ahmad

    2010-05-01

    Carbon is essential for plant growth, due to its effects on other soil properties like aggregation. Knowledge of dynamics of organic matter in different locations in the soil matrix can provide valuable information which affects carbon sequestration and soil the other soil properties. Extraction of soil organic matter (SOM) fractions has been a long standing approach to elucidating the roles of soil organic matter in soil processes. Several kind fractionation methods are used and all provide information on soil organic matter function. Physical fractionation capture the effects on SOM dynamics of the spatial arrangement of primary and secondary organomineral particles in soil while chemical fractionation can not consider the spatial arrangement but their organic fractions are suitable for advanced chemical characterization. Three method of physical separation of soil have been used, sieving, sedimentation and densitometry. The distribution of organic matter within physical fractions of the soil can be assessed by sieving. Sieving separates soil particles based strictly on size. The study area is located on north central Iran, between 35° 41'- 36° 01' N and 50° 42'- 51° 14' E. Mean annual precipitation about 243.8 mm and mean annual air temperature is about 14.95 °C. The soil moisture and temperature regime vary between aridic-thermic in lower altitudes to xeric-mesic in upper altitudes. More than 36 surface soil samples (0-20 cm) were collected according to land-use map units. After preliminary analyzing of samples 10 samples were selected for further analyses in five size fractions and three different time intervals in September, January and April 2008. Fractionation carried out by dry sieving in five classes, 1-2 mm, 0.5-1 mm, 270 μm-0.5mm, 53-270 μm and <53 μm. Organic matter and C/N ratio were determined for all fractions at different time intervals. Chemical fractionation of organic matter also carried out according to Tan (2003), also Mineralogical

  6. Modern plasma fractionation.

    PubMed

    Burnouf, Thierry

    2007-04-01

    Protein products fractionated from human plasma are an essential class of therapeutics used, often as the only available option, in the prevention, management, and treatment of life-threatening conditions resulting from trauma, congenital deficiencies, immunologic disorders, or infections. Modern plasma product production technology remains largely based on the ethanol fractionation process, but much has evolved in the last few years to improve product purity, to enhance the recovery of immunoglobulin G, and to isolate new plasma proteins, such as alpha1-protease inhibitor, von Willebrand factor, and protein C. Because of the human origin of the starting material and the pooling of 10,000 to 50,000 donations required for industrial processing, the major risk associated to plasma products is the transmission of blood-borne infectious agents. A complete set of measures--and, most particularly, the use of dedicated viral inactivation and removal treatments--has been implemented throughout the production chain of fractionated plasma products over the last 20 years to ensure optimal safety, in particular, and not exclusively, against HIV, hepatitis B virus, and hepatitis C virus. In this review, we summarize the practices of the modern plasma fractionation industry from the collection of the raw plasma material to the industrial manufacture of fractionated products. We describe the quality requirements of plasma for fractionation and the various treatments applied for the inactivation and removal of blood-borne infectious agents and provide examples of methods used for the purification of the various classes of plasma protein therapies. We also highlight aspects of the good manufacturing practices and the regulatory environment that govern the whole chain of production. In a regulated and professional environment, fractionated plasma products manufactured by modern processes are certainly among the lowest-risk therapeutic biological products in use today. PMID:17397761

  7. Excitons in the Fractional Quantum Hall Effect

    DOE R&D Accomplishments Database

    Laughlin, R. B.

    1984-09-01

    Quasiparticles of charge 1/m in the Fractional Quantum Hall Effect form excitons, which are collective excitations physically similar to the transverse magnetoplasma oscillations of a Wigner crystal. A variational exciton wavefunction which shows explicitly that the magnetic length is effectively longer for quasiparticles than for electrons is proposed. This wavefunction is used to estimate the dispersion relation of these excitons and the matrix elements to generate them optically out of the ground state. These quantities are then used to describe a type of nonlinear conductivity which may occur in these systems when they are relatively clean.

  8. A discrete fractional random transform

    NASA Astrophysics Data System (ADS)

    Liu, Zhengjun; Zhao, Haifa; Liu, Shutian

    2005-11-01

    We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of the fractional Fourier transform along with some fantastic features of its own. As a primary application, the discrete fractional random transform has been used for image encryption and decryption.

  9. Sharp nonlinear stability for centrifugal filtration convection in magnetizable media.

    PubMed

    Saravanan, S; Brindha, D

    2011-11-01

    A nonlinear stability theory is adopted to study centrifugal thermal convection in a magnetic-fluid-saturated and differentially heated porous layer placed in a zero-gravity environment. The axis of rotation of the layer is placed within its boundaries that leads to an alternating direction of the centrifugal body force. An analysis through the variational principles is made to find the unconditional and sharp nonlinear limits. The compound matrix method is employed to solve the eigenvalue problems of the nonlinear and corresponding linear theories. The importance of nonlinear theory is established by demonstrating the failure of the linear theory in capturing the physics of the onset of convection. PMID:22181509

  10. Subcellular fractionation of human liver reveals limits in global proteomic quantification from isolated fractions.

    PubMed

    Wiśniewski, Jacek R; Wegler, Christine; Artursson, Per

    2016-09-15

    The liver plays an important role in metabolism and elimination of xenobiotics, including drugs. Determination of concentrations of proteins involved in uptake, distribution, metabolism, and excretion of xenobiotics is required to understand and predict elimination mechanisms in this tissue. In this work, we have fractionated homogenates of snap-frozen human liver by differential centrifugation and performed quantitative mass spectrometry-based proteomic analysis of each fraction. Concentrations of proteins were calculated by the "total protein approach". A total of 4586 proteins were identified by at least five peptides and were quantified in all fractions. We found that the xenobiotics transporters of the canalicular and basolateral membranes were differentially enriched in the subcellular fractions and that phase I and II metabolizing enzymes, the cytochrome P450s and the UDP-glucuronyl transferases, have complex subcellular distributions. These findings show that there is no simple way to scale the data from measurements in arbitrarily selected membrane fractions using a single scaling factor for all the proteins of interest. This study also provides the first absolute quantitative subcellular catalog of human liver proteins obtained from frozen tissue specimens. Our data provide quantitative insights into the subcellular distribution of proteins and can be used as a guide for development of fractionation procedures. PMID:27311553

  11. Fractional calculus in hydrologic modeling: A numerical perspective

    PubMed Central

    Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

    2013-01-01

    Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

  12. Fractional calculus in hydrologic modeling: A numerical perspective.

    PubMed

    Benson, David A; Meerschaert, Mark M; Revielle, Jordan

    2013-01-01

    Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

  13. Fractional Calculus in Hydrologic Modeling: A Numerical Perspective

    SciTech Connect

    David A. Benson; Mark M. Meerschaert; Jordan Revielle

    2012-01-01

    Fractional derivatives can be viewed either as a handy extension of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Levy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Levy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.

  14. Modeling of Electromagnetic Phenomenon in Fractional Dimensional Space

    NASA Astrophysics Data System (ADS)

    Zubair, Muhammad; Ang, L. K.

    Fractional dimensional space has emerged as an extremely useful concept in many areas of physics, including electromagnetic (EM) theory. The development made in the area of fractional calculus has made it possible to study the most important physical phenomenon in a generalized D-dimensional fractional space. It is worthwhile to mention that many natural objects, such as clouds, snowflakes, rough surfaces, cracks, turbulence in fluids, are aptly described by dimensions of fractional order. Therefore, EM wave propagation in such fractal media is best characterized by considering an effective space of non-integer (fractional) dimensions. Here we present the recent developments in the study of differential Maxwell equations in a D-dimensional fractional space, where D is a non-integer value. Same examples will be used in order to show the transition to the traditional non-fractional conditions or settings.

  15. A Nonlinear Modal Aeroelastic Solver for FUN3D

    NASA Technical Reports Server (NTRS)

    Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.

    2016-01-01

    A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.

  16. Vibration suppression of composite laminated plate with nonlinear energy sink

    NASA Astrophysics Data System (ADS)

    Zhang, Ye-Wei; Zhang, Hao; Hou, Shuai; Xu, Ke-Fan; Chen, Li-Qun

    2016-06-01

    The composite laminated plate is widely used in supersonic aircraft. So, there are many researches about the vibration suppression of composite laminated plate. In this paper, nonlinear energy sink (NES) as an effective method to suppress vibration is studied. The coupled partial differential governing equations of the composite laminated plate with the nonlinear energy sink (NES) are established by using the Hamilton principle. The fourth-order Galerkin discrete method is used to truncate the partial differential equations, which are solved by numerical integration method. Meanwhile study about the precise effectiveness of the nonlinear energy sink (NES) by discussing the different installation location of the nonlinear energy sink (NES) at the same speed. The results indicate that the nonlinear energy sink (NES) can significantly suppress the severe vibration of the composite laminated plate with speed wind loadings in to protect the composite laminated plate from excessive vibration.

  17. Differential geometric methods in system theory.

    NASA Technical Reports Server (NTRS)

    Brockett, R. W.

    1971-01-01

    Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.

  18. Radiotherapy Dose Fractionation under Parameter Uncertainty

    NASA Astrophysics Data System (ADS)

    Davison, Matt; Kim, Daero; Keller, Harald

    2011-11-01

    In radiotherapy, radiation is directed to damage a tumor while avoiding surrounding healthy tissue. Tradeoffs ensue because dose cannot be exactly shaped to the tumor. It is particularly important to ensure that sensitive biological structures near the tumor are not damaged more than a certain amount. Biological tissue is known to have a nonlinear response to incident radiation. The linear quadratic dose response model, which requires the specification of two clinically and experimentally observed response coefficients, is commonly used to model this effect. This model yields an optimization problem giving two different types of optimal dose sequences (fractionation schedules). Which fractionation schedule is preferred depends on the response coefficients. These coefficients are uncertainly known and may differ from patient to patient. Because of this not only the expected outcomes but also the uncertainty around these outcomes are important, and it might not be prudent to select the strategy with the best expected outcome.

  19. Radiotherapy Dose Fractionation under Parameter Uncertainty

    SciTech Connect

    Davison, Matt; Kim, Daero; Keller, Harald

    2011-11-30

    In radiotherapy, radiation is directed to damage a tumor while avoiding surrounding healthy tissue. Tradeoffs ensue because dose cannot be exactly shaped to the tumor. It is particularly important to ensure that sensitive biological structures near the tumor are not damaged more than a certain amount. Biological tissue is known to have a nonlinear response to incident radiation. The linear quadratic dose response model, which requires the specification of two clinically and experimentally observed response coefficients, is commonly used to model this effect. This model yields an optimization problem giving two different types of optimal dose sequences (fractionation schedules). Which fractionation schedule is preferred depends on the response coefficients. These coefficients are uncertainly known and may differ from patient to patient. Because of this not only the expected outcomes but also the uncertainty around these outcomes are important, and it might not be prudent to select the strategy with the best expected outcome.

  20. EVOLUTION OF THE BINARY FRACTION IN DENSE STELLAR SYSTEMS

    SciTech Connect

    Fregeau, John M.; Ivanova, Natalia; Rasio, Frederic A.

    2009-12-20

    Using our recently improved Monte Carlo evolution code, we study the evolution of the binary fraction in globular clusters. In agreement with previous N-body simulations, we find generally that the hard binary fraction in the core tends to increase with time over a range of initial cluster central densities for initial binary fractions approx<90%. The dominant processes driving the evolution of the core binary fraction are mass segregation of binaries into the cluster core and preferential destruction of binaries there. On a global scale, these effects and the preferential tidal stripping of single stars tend to roughly balance, leading to overall cluster binary fractions that are roughly constant with time. Our findings suggest that the current hard binary fraction near the half-mass radius is a good indicator of the hard primordial binary fraction. However, the relationship between the true binary fraction and the fraction of main-sequence stars in binaries (which is typically what observers measure) is nonlinear and rather complicated. We also consider the importance of soft binaries, which not only modify the evolution of the binary fraction, but can also drastically change the evolution of the cluster as a whole. Finally, we briefly describe the recent addition of single and binary stellar evolution to our cluster evolution code.

  1. Gaussian beam evolution in nonlinear inhomogeneous plasma

    NASA Astrophysics Data System (ADS)

    Berczynski, P.; Kravtsov, Yu. A.; Tikhonchuk, V.; Tikhonchuk

    2014-04-01

    The method of nonlinear complex geometrical optics (NCGO) is proposed in this paper for description of the evolution of a spatially narrow Gaussian beam (GB) in an inhomogeneous nonlinear plasma. NCGO method deals with first-order ordinary differential equations for the complex curvature of the wave front and for GB amplitude and for second-order ordinary differential equation for GB width. Thus, NCGO simplifies the description of GB diffraction and self-focusing effects as compared to the known methods of plasma physics and this way it can be assumed to be attractive and comprehensive approach in problems of plasma heating by electromagnetic waves. Moreover, we demonstrate in this paper some regularity for nonlinear inhomogeneous plasma in the framework of which central ray of a GB is not subjected to nonlinear refraction within NCGO method boundary applicability. On the contrary, the beam width, wave front curvature, and GB amplitude are modified by diffraction and self-focusing processes. General properties of the beam propagation are illustrated with results of numerical modeling for two particular cases: GB diffraction and self-focusing along curvilinear trajectory with torsion in axially symmetric plasma column and GB reflection from nonlinear inhomogeneous plasma layer. We prove in this paper that NCGO is new effective method of plasma physics, which can be applied for improvement of ray tracing techniques and plasma diagnostics.

  2. A Stochastic Differential Equation Approach To Multiphase Flow In Porous Media

    NASA Astrophysics Data System (ADS)

    Dean, D.; Russell, T.

    2003-12-01

    The motivation for using stochastic differential equations in multiphase flow systems stems from our work in developing an upscaling methodology for single phase flow. The long term goals of this project include: I. Extending this work to a nonlinear upscaling methodology II. Developing a macro-scale stochastic theory of multiphase flow and transport that accounts for micro-scale heterogeneities and interfaces. In this talk, we present a stochastic differential equation approach to multiphase flow, a typical example of which is flow in the unsaturated domain. Specifically, a two phase problem is studied which consists of a wetting phase and a non-wetting phase. The approach given results in a nonlinear stochastic differential equation describing the position of the non-wetting phase fluid particle. Our fundamental assumption is that the flow of fluid particles is described by a stochastic process and that the positions of the fluid particles over time are governed by the law of the process. It is this law which we seek to determine. The nonlinearity in the stochastic differential equation arises because both the drift and diffusion coefficients depend on the volumetric fraction of the phase which in turn depends on the position of the fluid particles in the experimental domain. The concept of a fluid particle is central to the development of the model described in this talk. Expressions for both saturation and volumetric fraction are developed using the fluid particle concept. Darcy's law and the continuity equation are then used to derive a Fokker-Planck equation using these expressions. The Ito calculus is then applied to derive a stochastic differential equation for the non-wetting phase. This equation has both drift and diffusion terms which depend on the volumetric fraction of the non-wetting phase. Standard stochastic theories based on the Ito calculus and the Wiener process and the equivalent Fokker-Planck PDE's are typically used to model dispersion

  3. Periodic boundary value problem for a system of ordinary differential equations with impulse effects

    NASA Astrophysics Data System (ADS)

    Tleulesova, Agila

    2016-08-01

    In this work, we investigated a nonlinear periodic boundary value problem with impulse effects. We have found some sufficient conditions for existence of isolated solution to periodic boundary value problem for system of nonlinear differential equations with impulse effects.

  4. R-Function Relationships for Application in the Fractional Calculus

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.

    2000-01-01

    The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

  5. FRACTIONAL CRYSTALLIZATION FEED ENVELOPE

    SciTech Connect

    HERTING DL

    2008-03-19

    Laboratory work was completed on a set of evaporation tests designed to establish a feed envelope for the fractional crystallization process. The feed envelope defines chemical concentration limits within which the process can be operated successfully. All 38 runs in the half-factorial design matrix were completed successfully, based on the qualitative definition of success. There is no feed composition likely to be derived from saltcake dissolution that would cause the fractional crystallization process to not meet acceptable performance requirements. However, some compositions clearly would provide more successful operation than other compositions.

  6. Multipartite Fully Entangled Fraction

    NASA Astrophysics Data System (ADS)

    Xu, Jianwei

    2016-06-01

    Fully entangled fraction is a definition for bipartite states, which is tightly related to bipartite maximally entangled states, and has clear experimental and theoretical significance. In this work, we generalize it to multipartite case, we call the generalized version multipartite fully entangled fraction (MFEF). MFEF measures the closeness of a state to GHZ states. The analytical expressions of MFEF are very difficult to obtain except for very special states, however, we show that, the MFEF of any state is determined by a system of finite-order polynomial equations. Therefore, the MFEF can be efficiently numerically computed.

  7. Release Fraction Evaluation

    SciTech Connect

    Bamberger, Judith A.; Glissmeyer, John A.

    2004-01-01

    This document presents results of experiments conducted to measure release fractions during certain tank retrieval processes. The tests were performed in a 1/4 scale model of a waste storage tank. The retrieval processes simulated were: (1) Discharging liquid or slurry from the mouth of a vertically oriented two-in. Schedule 40 pipe. The discharging material was in free-fall from the mouth of the pipe near the top of the tank into a liquid or slurry pool at the bottom of the tank. (2) The jet from a 9/16-in.-diameter nozzle transferring liquid or slurry waste from one side of the tank to the other. The discharging liquid was aimed at the opposite side of the tank from the nozzle and either impacted the tank wall or fell into a liquid or slurry pool in the bottom of the tank. (3) A high pressure fan jet of liquid striking a steel plate or simulated waste from a stand-off distance of a few inches. For each process, a water-soluble fluorescent dye was added to the liquid fraction as a tracer. Kaolin clay was used to represent the solids. The tank was covered and there was no forced ventilation in the tank during the tests. Six air samples were collected during each test. The air samples were collected at fixed positions in the tank. The air sample filters were dried and weighed to determine the solids collection. The fluorescent dye was then leached from each filter and quantified with a fluorometer to determine the collection of liquid. Samples of the slurry and liquid simulants were also collected to determine the quantities of simulant used in each test. To calculate the release fraction, the quantity collected on each air sample was adjusted for the fraction of the tank volume sampled and divided by the quantity of material exposed in the simulation. The method was not as sensitive for the solids content as it was for the liquid content, but in those instances where a solids release fraction was determined, it was in relatively good agreement with that of the

  8. Performance analysis of fractional order extremum seeking control.

    PubMed

    Malek, Hadi; Dadras, Sara; Chen, YangQuan

    2016-07-01

    Extremum-seeking scheme is a powerful adaptive technique to optimize steady-state system performance. In this paper, a novel extremum-seeking scheme for the optimization of nonlinear plants using fractional order calculus is proposed. The fractional order extremum-seeking algorithm only utilizes output measurements of the plant, however, it performs superior in many aspects such as convergence speed and robustness. A detailed stability analysis is given to not only guarantee a faster convergence of the system to an adjustable neighborhood of the optimum but also confirm a better robustness for proposed algorithm. Furthermore, simulation and experimental results demonstrate that the fractional order extremum-seeking scheme for nonlinear systems outperforms the traditional integer order one. PMID:27000632

  9. Fractional dynamics of coupled oscillators with long-range interaction

    SciTech Connect

    Tarasov, Vasily E.; Zaslavsky, George M.

    2006-06-15

    We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1/|n-m|{sup {alpha}}{sup +1}. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order {alpha}, when 0<{alpha}<2. We consider a few models of coupled oscillators and show how their synchronization can appear as a result of bifurcation, and how the corresponding solutions depend on {alpha}. The presence of a fractional derivative also leads to the occurrence of localized structures. Particular solutions for fractional time-dependent complex Ginzburg-Landau (or nonlinear Schroedinger) equation are derived. These solutions are interpreted as synchronized states and localized structures of the oscillatory medium.

  10. Generalized Functions for the Fractional Calculus

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.

    1999-01-01

    Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

  11. Forced oscillations with linear and nonlinear damping

    NASA Astrophysics Data System (ADS)

    Li, Aijun; Ma, Li; Keene, David; Klingel, Joshua; Payne, Marvin; Wang, Xiao-jun

    2016-01-01

    A general solution is derived for the differential equations of forced oscillatory motion with both linear damping ( ˜v ) and nonlinear damping ( ˜v2 ). Experiments with forced oscillators are performed using a flat metal plate with a drag force due to eddy currents and a flat piece of stiffened cardboard with a drag force due to air resistance serving as the linear and nonlinear damping, respectively. Resonance of forced oscillations for different damping forces and quality factors is demonstrated. The experimental measurements and theoretical calculations are in good agreement, and damping constants are determined.

  12. Robust nonlinear control of vectored thrust aircraft

    NASA Technical Reports Server (NTRS)

    Doyle, John C.; Murray, Richard; Morris, John

    1993-01-01

    An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.

  13. Robust outer synchronization between two complex networks with fractional order dynamics.

    PubMed

    Asheghan, Mohammad Mostafa; Míguez, Joaquín; Hamidi-Beheshti, Mohammad T; Tavazoei, Mohammad Saleh

    2011-09-01

    Synchronization between two coupled complex networks with fractional-order dynamics, hereafter referred to as outer synchronization, is investigated in this work. In particular, we consider two systems consisting of interconnected nodes. The state variables of each node evolve with time according to a set of (possibly nonlinear and chaotic) fractional-order differential equations. One of the networks plays the role of a master system and drives the second network by way of an open-plus-closed-loop (OPCL) scheme. Starting from a simple analysis of the synchronization error and a basic lemma on the eigenvalues of matrices resulting from Kronecker products, we establish various sets of conditions for outer synchronization, i.e., for ensuring that the errors between the state variables of the master and response systems can asymptotically vanish with time. Then, we address the problem of robust outer synchronization, i.e., how to guarantee that the states of the nodes converge to common values when the parameters of the master and response networks are not identical, but present some perturbations. Assuming that these perturbations are bounded, we also find conditions for outer synchronization, this time given in terms of sets of linear matrix inequalities (LMIs). Most of the analytical results in this paper are valid both for fractional-order and integer-order dynamics. The assumptions on the inner (coupling) structure of the networks are mild, involving, at most, symmetry and diffusivity. The analytical results are complemented with numerical examples. In particular, we show examples of generalized and robust outer synchronization for networks whose nodes are governed by fractional-order Lorenz dynamics. PMID:21974656

  14. Sweet Work with Fractions

    ERIC Educational Resources Information Center

    Vinogradova, Natalya; Blaine, Larry

    2013-01-01

    Almost everyone loves chocolate. However, the same cannot be said about fractions, which are loved by markedly fewer. Middle school students tend to view them with wary respect, but little affection. The authors attempt to sweeten the subject by describing a type of game involving division of chocolate bars. The activity they describe provides a…

  15. Momentum fractionation on superstrata

    NASA Astrophysics Data System (ADS)

    Bena, Iosif; Martinec, Emil; Turton, David; Warner, Nicholas P.

    2016-05-01

    Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in high-degree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifold singularities. Upon taking the AdS3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions.

  16. Fraction collector for electrophoresis

    NASA Technical Reports Server (NTRS)

    Bier, M.

    1977-01-01

    Rotating-tube electrophoresis apparatus employs rotating jet of eluting buffer to reduce effects of convection during separation. Designed for separation of microorganisms and biological species, system combines gravity/gradient compensating of lumen with buffer flush at fraction outlet to increase separation efficiency.

  17. Fractionation of Soil Phosphorus

    Technology Transfer Automated Retrieval System (TEKTRAN)

    An understanding of the qualitative and quantitative information provided by soil phosphorus (P) fractionation methods is important for addressing agronomic and water quality problems, as well as evaluating P biogeochemistry in extreme environments. This chapter provides a schematic overview of and ...

  18. Field-Flow Fractionation.

    ERIC Educational Resources Information Center

    Caldwell, Karin D.

    1988-01-01

    Describes a technique for separating samples that range over 15 orders of magnitude in molecular weight. Discusses theory, apparatus, and sample preparation techniques. Lists several types of field-flow fractionation (FFF) and their uses: sedimentation FFF, thermal FFF, flow FFF, electrical FFF, and steric FFF. (ML)

  19. Fractional statistics and confinement

    NASA Astrophysics Data System (ADS)

    Gaete, P.; Wotzasek, C.

    2005-02-01

    It is shown that a pointlike composite having charge and magnetic moment displays a confining potential for the static interaction while simultaneously obeying fractional statistics in a pure gauge theory in three dimensions, without a Chern-Simons term. This result is distinct from the Maxwell-Chern-Simons theory that shows a screening nature for the potential.

  20. Focused optical and acoustic beams in media with nonlinear absorption

    NASA Astrophysics Data System (ADS)

    Rudenko, O. V.; Sukhorukov, A. A.

    1996-11-01

    Optical and acoustic beams are known to be useful for medical and biological applications, such as diagnostics, surgery, etc. At high intensities both nonlinear lens effects and nonlinear absorption can be significant for the beams. The nonlinear absorption arises due to two-photon optical processes or acoustic shock wave formation. The present work is devoted to the theoretical description of nonlinear beam propagation and focal spot formation taking into account the competition between focusing, diffraction and absorption. We derived a new nonlinear integro- differential equation describing the spatial evolution of the beam width. The general analytical solution of this equation is obtained for arbitrary boundary conditions. The simple formulas are derived for the angle divergence in the far field, as well as for beam width at nonlinear waist. The results of the analysis of these key parameters in different situations are presented.