Science.gov

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

    NASA Astrophysics Data System (ADS)

    Lu, Bin

    2012-06-01

    In this Letter, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations.

  3. 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

  4. A procedure to construct exact solutions of nonlinear fractional differential equations.

    PubMed

    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.

  5. 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.

  6. An effective analytic approach for solving nonlinear fractional partial differential equations

    NASA Astrophysics Data System (ADS)

    Ma, Junchi; Zhang, Xiaolong; Liang, Songxin

    2016-08-01

    Nonlinear fractional differential equations are widely used for modelling problems in applied mathematics. A new analytic approach with two parameters c1 and c2 is first proposed for solving nonlinear fractional partial differential equations. These parameters are used to improve the accuracy of the resulting series approximations. It turns out that much more accurate series approximations are obtained by choosing proper values of c1 and c2. To demonstrate the applicability and effectiveness of the new method, two typical fractional partial differential equations, the nonlinear gas dynamics equation and the nonlinear KdV-Burgers equation, are solved.

  7. Consistent Riccati Expansion Method and Its Applications to Nonlinear Fractional Partial Differential Equations

    NASA Astrophysics Data System (ADS)

    Huang, Qing; Wang, Li-Zhen; Zuo, Su-Li

    2016-02-01

    In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann-Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada-Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed. Supported by the National Natural Science Foundation of China under Grant Nos. 11101332, 11201371, 11371293 and the Natural Science Foundation of Shaanxi Province under Grant No. 2015JM1037

  8. Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

    PubMed

    Shah, Kamal; Khan, Rahmat Ali

    2016-01-01

    In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results. PMID:27478733

  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. 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.

  11. A Fractional Differential Kinetic Equation and Applications to Modelling Bursts in Turbulent Nonlinear Space Plasmas

    NASA Astrophysics Data System (ADS)

    Watkins, N. W.; Rosenberg, S.; Sanchez, R.; Chapman, S. C.; Credgington, D.

    2008-12-01

    Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototype) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold. This problem relates to the burst size measure introduced by Takalo and Consolini into solar-terrestrial physics and further studied by Freeman et al [PRE, 2000] on solar wind Poynting flux near L1. We test how expressions derived by other authors generalise to the non-Gaussian, constant threshold problem. Ongoing work on extension of these LFSM results to multifractals will also be discussed.

  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. Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line

    NASA Astrophysics Data System (ADS)

    Aslan, İsmail

    2016-09-01

    Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions (kink/antikink solitons, singular, periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.

  14. 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. PMID:27419212

  15. 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.

  16. 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.

  17. On the Singular Perturbations for Fractional Differential Equation

    PubMed Central

    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

  18. Fractional non-linear modelling of ultracapacitors

    NASA Astrophysics Data System (ADS)

    Bertrand, Nicolas; Sabatier, Jocelyn; Briat, Olivier; Vinassa, Jean-Michel

    2010-05-01

    In this paper, it is demonstrated that an ultracapacitor exhibits a non-linear behaviour in relation to the operating voltage. A set of fractional order linear systems resulting from a frequency analysis of the ultracapacitor at various operating points is first obtained. Then, a non-linear model is deduced from the linear systems set, so that its Taylor linearization around the considered operating points (for the frequency analysis), produces the linear system set. The resulting non-linear model is validated on a Hybrid Electric Vehicle (HEV) application.

  19. Similarity solutions to nonlinear heat conduction and Burgers/Korteweg-deVries fractional equations

    NASA Astrophysics Data System (ADS)

    Djordjevic, Vladan D.; Atanackovic, Teodor M.

    2008-12-01

    We analyze self-similar solutions to a nonlinear fractional diffusion equation and fractional Burgers/Korteweg-deVries equation in one spatial variable. By using Lie-group scaling transformation, we determined the similarity solutions. After the introduction of the similarity variables, both problems are reduced to ordinary nonlinear fractional differential equations. In two special cases exact solutions to the ordinary fractional differential equation, which is derived from the diffusion equation, are presented. In several other cases the ordinary fractional differential equations are solved numerically, for several values of governing parameters. In formulating the numerical procedure, we use special representation of a fractional derivative that is recently obtained.

  20. 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

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

    NASA Astrophysics Data System (ADS)

    Feng, Qing-Hua

    2014-08-01

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

  2. 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

  3. 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.

  4. 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

    2016-11-01

    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.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. Approximate controllability of nonlinear impulsive differential systems

    NASA Astrophysics Data System (ADS)

    Sakthivel, R.; Mahmudov, N. I.; Kim, J. H.

    2007-08-01

    Many practical systems in physical and biological sciences have impulsive dynamical be- haviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability issue for nonlinear impulsive differential and neutral functional differential equations in Hilbert spaces. Based on the semigroup theory and fixed point approach, sufficient conditions for approximate controllability of impulsive differential and neutral functional differential equations are established. Finally, two examples are presented to illustrate the utility of the proposed result. The results improve some recent results.

  13. Nonlinear self-adjointness through differential substitutions

    NASA Astrophysics Data System (ADS)

    Gandarias, M. L.

    2014-10-01

    It is known (Ibragimov, 2011; Galiakberova and Ibragimov, 2013) [14,18] that the property of nonlinear self-adjointness allows to associate conservation laws of the equations under study, with their symmetries. In this paper we show that, even when the equation is nonlinearly self-adjoint with a non differential substitution, finding the explicit form of the differential substitution can provide new conservation laws associated to its symmetries. By using the general theorem on conservation laws (Ibragimov, 2007) [11] and the property of nonlinear self-adjointness we find some new conservation laws for the modified Harry-Dym equation. By using a differential substitution we construct a conservation law for the Harry-Dym equation, which has not been derived before using Ibragimov method.

  14. 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.

  15. PREFACE: Fractional Differentiation and its Applications (FDA08) Fractional Differentiation and its Applications (FDA08)

    NASA Astrophysics Data System (ADS)

    Baleanu, Dumitru; Tenreiro Machado, J. A.

    2009-10-01

    The international workshop, Fractional Differentiation and its Applications (FDA08), held at Cankaya University, Ankara, Turkey on 5-7 November 2008, was the third in an ongoing series of conferences dedicated to exploring applications of fractional calculus in science, engineering, economics and finance. Fractional calculus, which deals with derivatives and integrals of any order, is now recognized as playing an important role in modeling multi-scale problems that span a wide range of time or length scales. Fractional calculus provides a natural link to the intermediate-order dynamics that often reflects the complexity of micro- and nanostructures through fractional-order differential equations. Unlike the more established techniques of mathematical physics, the methods of fractional differentiation are still under development; while it is true that the ideas of fractional calculus are as old as the classical integer-order differential operators, modern work is proceeding by both expanding the capabilities of this mathematical tool and by widening its range of applications. Hence, the interested reader will find papers here that focus on the underlying mathematics of fractional calculus, that extend fractional-order operators into new domains, and that apply well established methods to experimental and theoretical problems. The organizing committee invited presentations from experts representing the international community of scholars in fractional calculus and welcomed contributions from the growing number of researchers who are applying fractional differentiation to complex technical problems. The selection of papers in this topical issue of Physica Scripta reflects the success of the FDA08 workshop, with the emergence of a variety of novel areas of application. With these ideas in mind, the guest editors would like to honor the many distinguished scientists that have promoted the development of fractional calculus and, in particular, Professor George M

  16. 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.

  17. 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

  18. Nonlinear acoustic wave equations with fractional loss operators.

    PubMed

    Prieur, Fabrice; Holm, Sverre

    2011-09-01

    Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations.

  19. Modeling some real phenomena by fractional differential equations

    NASA Astrophysics Data System (ADS)

    Almeida, Ricardo; Bastos, Nuno R. O.; Monteiro, M. Teresa T.

    2016-11-01

    This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.

  20. 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

  1. Periodicity and positivity of a class of fractional differential equations.

    PubMed

    Ibrahim, Rabha W; Ahmad, M Z; Mohammed, M Jasim

    2016-01-01

    Fractional differential equations have been discussed in this study. We utilize the Riemann-Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is described in a fractional periodic Sobolev space. Positivity of outcomes is considered under certain requirements. We develop and extend some recent works. An example is constructed. PMID:27390664

  2. 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.

  3. 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.

  4. A short proof of Weyl's law for fractional differential operators

    SciTech Connect

    Geisinger, Leander

    2014-01-15

    We study spectral asymptotics for a large class of differential operators on an open subset of R{sup d} with finite volume. This class includes the Dirichlet Laplacian, the fractional Laplacian, and also fractional differential operators with non-homogeneous symbols. Based on a sharp estimate for the sum of the eigenvalues we establish the first term of the semiclassical asymptotics. This generalizes Weyl's law for the Laplace operator.

  5. High-order nonlinear differentiator and application to aircraft control

    NASA Astrophysics Data System (ADS)

    Wang, Xinhua; Shirinzadeh, Bijan

    2014-06-01

    In this paper, a high-order continuous nonlinear differentiator with lead compensation is presented based on finite-time stability. Not only the proposed high-order nonlinear differentiator can obtain the high-order derivatives of a signal, but also the chattering phenomenon can be reduced sufficiently. The parameters regulation is only required to be satisfied with Routh-Hurwitz Stability Criterion. The presented differentiator is a generalization of sliding mode differentiator and linear high-gain differentiator. The merits of the continuous differentiator include its simplicity, selecting parameters easily, restraining noises sufficiently, decreasing the phase shift and avoiding the chattering phenomenon. The theoretical results are confirmed by computer simulations and an experiment on a quadrotor aircraft: (i) the estimation of flying velocity and acceleration from the position measurement; (ii) a control law is designed based on the presented nonlinear differentiator to track a reference trajectory.

  6. 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.

  7. 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.

  8. Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

    PubMed Central

    Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

    2014-01-01

    In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns 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. PMID:25485293

  9. Numerical solutions of the nonlinear fractional-order brusselator system by Bernstein polynomials.

    PubMed

    Khan, Hasib; Jafari, Hossein; Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

    2014-01-01

    In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns 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. PMID:25485293

  10. A new fractional Chebyshev FDM: an application for solving the fractional differential equations generated by optimisation problem

    NASA Astrophysics Data System (ADS)

    Khader, M. M.

    2015-10-01

    In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method. The algorithm is based on a combination of the useful properties of Chebyshev polynomial approximation and finite difference method. We implement this technique to solve numerically the non-linear programming problem which are governed by fractional differential equations (FDEs). The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the Caputo fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The application of the method to the generated FDEs leads to algebraic systems which can be solved by an appropriate method. Two numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method. A comparison with the fourth-order Runge-Kutta method is given.

  11. Fuzzy fractional functional differential equations under Caputo gH-differentiability

    NASA Astrophysics Data System (ADS)

    Hoa, Ngo Van

    2015-05-01

    In this paper the fuzzy fractional functional differential equations (FFFDEs) under the Caputo generalized Hukuhara differentiability are introduced. We study the existence and uniqueness results of solutions for FFFDEs under some suitable conditions. Also the solution to fuzzy fractional functional initial value problem under Caputo-type fuzzy fractional derivatives by a modified Adams-Bashforth-Moulton method (MABMM) is presented. The method is illustrated by solving some examples.

  12. An efficient technique for higher order fractional differential equation.

    PubMed

    Ali, Ayyaz; Iqbal, Muhammad Asad; Ul-Hassan, Qazi Mahmood; Ahmad, Jamshad; Mohyud-Din, Syed Tauseef

    2016-01-01

    In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems. PMID:27047707

  13. Entropy and convexity for nonlinear partial differential equations.

    PubMed

    Ball, John M; Chen, Gui-Qiang G

    2013-12-28

    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.

  14. 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

  15. 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.

  16. A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

    NASA Astrophysics Data System (ADS)

    Simmons, Alex; Yang, Qianqian; Moroney, Timothy

    2015-04-01

    The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction-diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton-Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

  17. 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.

  18. A parareal method for time-fractional differential equations

    NASA Astrophysics Data System (ADS)

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

    2015-07-01

    In this paper, a parareal method is proposed for the parallel-in-time integration of time-fractional differential equations (TFDEs). It is a generalization of the original parareal method, proposed for classic differential equations. To match the global feature of fractional derivatives, the new method has in the correction step embraced the history part of the solution. We provide a convergence analysis under the assumption of Lipschitz stability conditions. We use a multi-domain spectral integrator to build the serial solvers and numerical results demonstrate the feasibility of the new approach and confirm the convergence analysis. Studies also show that both the coarse resolution and the nature of the differential operators can affect the performance.

  19. 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

  20. 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.

  1. 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.

  2. 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.

  3. Stability analysis and limit cycle in fractional system with Brusselator nonlinearities

    NASA Astrophysics Data System (ADS)

    Gafiychuk, V.; Datsko, B.

    2008-07-01

    The investigation of limit cycles in the fractional dynamical systems with Brusselator nonlinearities is considered. We present analysis of the stability domains as well as possible solutions realizing at different system parameters.

  4. 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.

  5. 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.

  6. Analysis of backward differentiation formula for nonlinear differential-algebraic equations with 2 delays.

    PubMed

    Sun, Leping

    2016-01-01

    This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true. PMID:27441132

  7. Sufficient conditions for oscillation of a nonlinear fractional nabla difference system.

    PubMed

    Li, Wei Nian; Sheng, Weihong

    2016-01-01

    In this paper, we study the oscillation of nonlinear fractional nabla difference equations of the form [Formula: see text]where c and α are constants, [Formula: see text] is the Riemann-Liouville fractional nabla difference operator of order [Formula: see text] is a real number, and [Formula: see text]. Some sufficient conditions for oscillation are established. PMID:27512637

  8. Stability, Boundedness, and Lagrange Stability of Fractional Differential Equations with Initial Time Difference

    PubMed Central

    Çiçek, Muhammed; Yakar, Coşkun; Oğur, Bülent

    2014-01-01

    Differential inequalities, comparison results, and sufficient conditions on initial time difference stability, boundedness, and Lagrange stability for fractional differential systems have been evaluated. PMID:24693255

  9. 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

  10. The exotic conformal Galilei algebra and nonlinear partial differential equations

    NASA Astrophysics Data System (ADS)

    Cherniha, Roman; Henkel, Malte

    2010-09-01

    The conformal Galilei algebra (CGA) and the exotic conformal Galilei algebra (ECGA) are applied to construct partial differential equations (PDEs) and systems of PDEs, which admit these algebras. We show that there are no single second-order PDEs invariant under the CGA but systems of PDEs can admit this algebra. Moreover, a wide class of nonlinear PDEs exists, which are conditionally invariant under CGA. It is further shown that there are systems of non-linear PDEs admitting ECGA with the realisation obtained very recently in [D. Martelli and Y. Tachikawa, arXiv:0903.5184v2 [hep-th] (2009)]. Moreover, wide classes of non-linear systems, invariant under two different 10-dimensional subalgebras of ECGA are explicitly constructed and an example with possible physical interpretation is presented.

  11. 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.

  12. 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.

  13. 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.

  14. Characterizing time dependent anomalous diffusion process: A survey on fractional derivative and nonlinear models

    NASA Astrophysics Data System (ADS)

    Wei, Song; Chen, Wen; Hon, Y. C.

    2016-11-01

    This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. A new perturbative approach to nonlinear partial differential equations

    SciTech Connect

    Bender, C.M.; Boettcher, S. ); Milton, K.A. )

    1991-11-01

    This paper shows how to solve some nonlinear wave equations as perturbation expansions in powers of a parameter that expresses the degree of nonlinearity. For the case of the Burgers equation {ital u}{sub {ital t}}+{ital uu}{sub {ital x}}={ital u}{sub {ital xx}}, the general nonlinear equation {ital u}{sub {ital t}}+{ital u}{sup {delta}}{ital u}{sub {ital x}}={ital u}{sub {ital xx}} is considered and expanded in powers of {delta}. The coefficients of the {delta} series to sixth order in powers of {delta} is determined and Pade summation is used to evaluate the perturbation series for large values of {delta}. The numerical results are accurate and the method is very general; it applies to other well-studied partial differential equations such as the Korteweg--de Vries equation, {ital u}{sub {ital t}}+{ital uu}{sub {ital x}} ={ital u}{sub {ital xxx}}.

  1. 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.

  2. Efficient implementation to numerically solve the nonlinear time fractional parabolic problems on unbounded spatial domain

    NASA Astrophysics Data System (ADS)

    Li, Dongfang; Zhang, Jiwei

    2016-10-01

    Anomalous diffusion behavior in many practical problems can be described by the nonlinear time-fractional parabolic problems on unbounded domain. The numerical simulation is a challenging problem due to the dependence of global information from time fractional operators, the nonlinearity of the problem and the unboundedness of the spacial domain. To overcome the unboundedness, conventional computational methods lead to extremely expensive costs, especially in high dimensions with a simple treatment of boundary conditions by making the computational domain large enough. In this paper, based on unified approach proposed in [25], we derive the efficient nonlinear absorbing boundary conditions (ABCs), which reformulates the problem on unbounded domain to an initial boundary value problem on bounded domain. To overcome nonlinearity, we construct a linearized finite difference scheme to solve the reduced nonlinear problem such that iterative methods become dispensable. And the stability and convergence of our linearized scheme are proved. Most important, we prove that the numerical solutions are bounded by the initial values with a constant coefficient, i.e., the constant coefficient is independent of the time. Overall, the computational cost can be significantly reduced comparing with the usual implicit schemes and a simple treatment of boundary conditions. Finally, numerical examples are given to demonstrate the efficiency of the artificial boundary conditions and theoretical results of the schemes.

  3. 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.

  4. Some properties for integro-differential operator defined by a fractional formal.

    PubMed

    Abdulnaby, Zainab E; Ibrahim, Rabha W; Kılıçman, Adem

    2016-01-01

    Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions. PMID:27386341

  5. Numerical solution of fractional-in-space nonlinear Schrödinger equation with the Riesz fractional derivative

    NASA Astrophysics Data System (ADS)

    Owolabi, Kolade M.; Atangana, Abdon

    2016-09-01

    In this paper, dynamics of time-dependent fractional-in-space nonlinear Schrödinger equation with harmonic potential V(x),x in R in one, two and three dimensions have been considered. We approximate the Riesz fractional derivative with the Fourier pseudo-spectral method and advance the resulting equation in time with both Strang splitting and exponential time-differencing methods. The Riesz derivative introduced in this paper is found to be so convenient to be applied in models that are connected with applied science, physics, and engineering. We must also report that the Riesz derivative introduced in this work will serve as a complementary operator to the commonly used Caputo or Riemann-Liouville derivatives in the higher-dimensional case. In the numerical experiments, one expects the travelling wave to evolve from such an initial function on an infinite computational domain (-∞, &infty); , which we truncate at some large, but finite values L. It is important that the value of L is chosen large enough to give enough room for the wave function to propagate. We observe a different distribution of complex wave functions for the focusing and defocusing cases.

  6. 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

  7. 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

  8. Influence of nonlinear sorption kinetics on the slow-desorbing organic contaminant fraction in soil

    SciTech Connect

    Schlebaum, W.; Schraa, G.; Van Riemsdijk, W.H.

    1999-05-01

    Release rates of hydrophobic organic compounds (HOCs) from the soil matrix influence the availability of HOCs in soils or sediments for microbial degradation or removal by physical means (e.g., soil washing or soil venting). In this study it was shown that the initial contaminant concentration influences the desorption rate. This was attributed to the presence of a limited number of high affinity sites that cause nonlinear sorption behavior. The experimental results could be described with a kinetic model composed of two separate compartments. One compartment was described with a Freundlich isotherm and corresponding kinetics and was assumed to represent sorption to high affinity sites. The second compartment was described with a linear sorption isotherm and first-order kinetics. The model was used to simulate the influence of purging strategies on removal of QCB. The simulations showed that after removal of a fast-desorbing fraction, the slow-desorbing fraction could be efficiently removed at very low purging rates. Intermittent purging reduced the total purging time but the simulations showed large fluctuations in the aqueous pentachlorobenzene concentration. For each subsequent purging interval, the purging efficiency decreased due to the nonlinear desorption kinetics of the slow-desorbing fraction of pentachlorobenzene.

  9. 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.

  10. 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.

  11. 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

  12. 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

  13. 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.

  14. Coherent states for N-component fractional quantum Hall systems and their nonlinear sigma models

    NASA Astrophysics Data System (ADS)

    Calixto, Manuel; Peón-Nieto, Carlos; Pérez-Romero, Emilio

    2016-10-01

    We revise the subject of N-component fractional quantum Hall systems and its field-theoretic description in terms of U(N) -invariant nonlinear sigma models under a group-theoretical perspective. The Berry Lagrangian, which determines the dynamics and encodes the quantum commutation relations for the order parameter, is quantized and the Hilbert space is interpreted in terms of states of N-component composite fermions (M electrons bound to f magnetic flux lines) for fractional filling factor ν = M / f, in accordance with Jain's picture. An explicit bosonic realization of coherent states on the Grassmannian manifold U(N) / [ U(M) × U(N - M) ] is provided, which describes coherent excitations of these composite fermions.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. A more fundamental approach to the derivation of nonlinear acoustic wave equations with fractional loss operators (L).

    PubMed

    Prieur, Fabrice; Vilenskiy, Gregory; Holm, Sverre

    2012-10-01

    A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["Nonlinear acoustic wave equations with fractional loss operators," J. Acoust. Soc. Am. 130(3), 1125-1132 (2011)]. The loss operator of the obtained nonlinear wave equations differs from the previous derivations as well as the dispersion equation, but when approximating for low frequencies the expressions for the frequency dependent attenuation and velocity dispersion remain unchanged.

  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. A modification of WKB method for fractional differential operators of Schrödinger's type

    NASA Astrophysics Data System (ADS)

    Sayevand, K.; Pichaghchi, K.

    2016-08-01

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

  2. Fractional Order Digital Differentiator Design Based on Power Function and Least squares

    NASA Astrophysics Data System (ADS)

    Kumar, Manjeet; Rawat, Tarun Kumar

    2016-10-01

    In this article, we propose the use of power function and least squares method for designing of a fractional order digital differentiator. The input signal is transformed into a power function by using Taylor series expansion, and its fractional derivative is computed using the Grunwald-Letnikov (G-L) definition. Next, the fractional order digital differentiator is modelled as a finite impulse response (FIR) system that yields fractional order derivative of the G-L type for a power function. The FIR system coefficients are obtained by using the least squares method. Two examples are used to demonstrate that the fractional derivative of the digital signals is computed by using the proposed technique. The results of the third and fourth examples reveal that the proposed technique gives superior performance in comparison with the existing techniques.

  3. 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.

  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. 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.

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

    PubMed

    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)]. 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.

  7. 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.

  8. The use of non-linear analysis for differentiating the biomagnetic activity in ovarian lesions.

    PubMed

    Anninos, P A; Anastasiadis, P; Kotini, A

    1999-05-01

    In this study we investigated the biomagnetic activity measured with the superconducting quantum interference device (SQUID) in benign and malignant ovarian lesions using non-linear analysis. We used a single channel biomagnetometer SQUID in order to measure the magnetic field emitted from benign and malignant ovarian lesions. We can differentiate such biomagnetic activities using non-linear analysis. Using the application of non-linear analysis in the ovarian lesions together with the use of dimensional calculations we have observed a clear saturation value for the dimension of malignant ovarian lesions and non-saturation for benign ovarian lesions. The biomagnetic measurements with the SQUID and the application of non-linear analysis in benign and malignant ovarian lesions, is a promising procedure in assessing and differentiating ovarian tumours. PMID:15512296

  9. On construction of solutions of linear fractional differential equations with constant coefficients

    NASA Astrophysics Data System (ADS)

    Borikhanov, Meiirkhan B.; Turmetov, Batirkhan Kh.

    2016-08-01

    One of the effective methods for finding exact solutions of differential equations is the method based on the operator representation of solutions. The essence of this method is to construct a series, whose members are the relevant iteration operators acting to some classes of sufficiently smooth functions. This method is widely used in the papers of Bondarenko for construction of solutions of differential equations of the integer order. In this paper, the operator method is applied to construct solutions of linear differential equations with constant coefficients and generalized Riemann-Liouville fractional derivative of order α and type γ. Then fundamental solutions are used to obtain the unique solution of the Cauchy problem.

  10. 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.

  11. Nonlocal Cauchy problems for semilinear differential inclusions with fractional order in Banach spaces

    NASA Astrophysics Data System (ADS)

    Wang, JinRong; Ibrahim, A. G.; Fečkan, Michal

    2015-10-01

    In this paper we present two existence results of nonlocal Cauchy problems for semilinear differential inclusions with fractional order in Banach spaces. The first result relies on a growth condition on the whole time interval. Our second result relies on a revised growth condition which is divided into two parts, one for the subintervals containing the points associated with the nonlocal conditions, and the other for the rest of the interval. The used technique is based on fractional calculus, the properties of the measure of noncompactness and a powerful fixed point theorem for multifunctions due to O'Regan-Precup. Finally, we apply the theoretical results to fractional differential inclusions on lattices with global neighborhood interactions.

  12. Computer algebra methods in the study of nonlinear differential systems

    NASA Astrophysics Data System (ADS)

    Irtegov, V. D.; Titorenko, T. N.

    2013-06-01

    Some issues concerning computer algebra methods as applied to the qualitative analysis of differential equations with first integrals are discussed. The problems of finding stationary sets and analyzing their stability and bifurcations are considered. Special attention is given to algorithms for finding and analyzing peculiar stationary sets. It is shown that computer algebra tools, combined with qualitative analysis methods for differential equations, make it possible not only to enhance the computational efficiency of classical algorithms, but also to implement new approaches to the solution of well-known problems and, in this way, to obtain new results.

  13. 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.

  14. 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

  15. Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method

    SciTech Connect

    Jerome L.V. Lewandowski

    2005-01-25

    A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.

  16. IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory.

    PubMed

    Romero, M; de Madrid, A P; Mañoso, C; Vinagre, B M

    2013-07-01

    This paper deals with the use of Chebyshev polynomials theory to achieve accurate discrete-time approximations to the fractional-order differentiator/integrator in terms of IIR filters. These filters are obtained using the Chebyshev-Padé and the Rational Chebyshev approximations, two highly accurate numerical methods that can be computed with ease using available software. They are compared against other highly accurate approximations proposed in the literature. It is also shown how the frequency response of the fractional-order integrator approximations can be easily improved at low frequencies. PMID:23507506

  17. 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

  18. The unified transform for linear, linearizable and integrable nonlinear partial differential equations

    NASA Astrophysics Data System (ADS)

    Fokas, A. S.; De Lillo, S.

    2014-03-01

    So-called inverse scattering provides a powerful method for analyzing the initial value problem for a large class of nonlinear evolution partial differential equations which are called integrable. In the late 1990s, the first author, motivated by inverse scattering, introduced a new method for analyzing boundary value problems. This method provides a unified treatment for linear, linearizable and integrable nonlinear partial differential equations. Here, this method, which is often referred to as the unified transform, is illustrated for the following concrete cases: the heat equation on the half-line; the nonlinear Schrödinger equation on the half-line; Burger's equation on the half-line; and Burger's equation on a moving boundary.

  19. 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.

  20. Numerical approximation of a nonlinear delay-advance functional differential equation by a finite element method

    NASA Astrophysics Data System (ADS)

    Teodoro, M. F.

    2012-09-01

    We are particularly interested in the numerical solution of the functional differential equations with symmetric delay and advance. In this work, we consider a nonlinear forward-backward equation, the Fitz Hugh-Nagumo equation. It is presented a scheme which extends the algorithm introduced in [1]. A computational method using Newton's method, finite element method and method of steps is developped.

  1. Differential polarization nonlinear optical microscopy with adaptive optics controlled multiplexed beams.

    PubMed

    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.

  2. Subcritical Hopf bifurcation in dynamical systems described by a scalar nonlinear delay differential equation.

    PubMed

    Larger, Laurent; Goedgebuer, Jean-Pierre; Erneux, Thomas

    2004-03-01

    A subcritical Hopf bifurcation in a dynamical system modeled by a scalar nonlinear delay differential equation is studied theoretically and experimentally. The subcritical Hopf bifurcation leads to a significant domain of bistability where stable steady and time-periodic states coexist.

  3. Multilevel Modeling of Two Cyclical Processes: Extending Differential Structural Equation Modeling to Nonlinear Coupled Systems

    ERIC Educational Resources Information Center

    Butner, Jonathan; Amazeen, Polemnia G.; Mulvey, Genna M.

    2005-01-01

    The authors present a dynamical multilevel model that captures changes over time in the bidirectional, potentially asymmetric influence of 2 cyclical processes. S. M. Boker and J. Graham's (1998) differential structural equation modeling approach was expanded to the case of a nonlinear coupled oscillator that is common in bimanual coordination…

  4. 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.

  5. 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.

  6. Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

    PubMed

    Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

    2016-06-27

    We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power. PMID:27410594

  7. 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

  8. 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.).

  9. Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods.

    PubMed

    Calderhead, Ben; Girolami, Mark

    2011-12-01

    Mechanistic models based on systems of nonlinear differential equations can help provide a quantitative understanding of complex physical or biological phenomena. The use of such models to describe nonlinear interactions in molecular biology has a long history; however, it is only recently that advances in computing have allowed these models to be set within a statistical framework, further increasing their usefulness and binding modelling and experimental approaches more tightly together. A probabilistic approach to modelling allows us to quantify uncertainty in both the model parameters and the model predictions, as well as in the model hypotheses themselves. In this paper, the Bayesian approach to statistical inference is adopted and we examine the significant challenges that arise when performing inference over nonlinear ordinary differential equation models describing cell signalling pathways and enzymatic circadian control; in particular, we address the difficulties arising owing to strong nonlinear correlation structures, high dimensionality and non-identifiability of parameters. We demonstrate how recently introduced differential geometric Markov chain Monte Carlo methodology alleviates many of these issues by making proposals based on local sensitivity information, which ultimately allows us to perform effective statistical analysis. Along the way, we highlight the deep link between the sensitivity analysis of such dynamic system models and the underlying Riemannian geometry of the induced posterior probability distributions. PMID:23226584

  10. Unveiling hidden properties of young star clusters: differential reddening, star-formation spread, and binary fraction

    NASA Astrophysics Data System (ADS)

    Bonatto, C.; Lima, E. F.; Bica, E.

    2012-04-01

    Context. Usually, important parameters of young, low-mass star clusters are very difficult to obtain by means of photometry, especially when differential reddening and/or binaries occur in large amounts. Aims: We present a semi-analytical approach (ASAmin) that, when applied to the Hess diagram of a young star cluster, is able to retrieve the values of mass, age, star-formation spread, distance modulus, foreground and differential reddening, and binary fraction. Methods: The global optimisation method known as adaptive simulated annealing (ASA) is used to minimise the residuals between the observed and simulated Hess diagrams of a star cluster. The simulations are realistic and take the most relevant parameters of young clusters into account. Important features of the simulations are a normal (Gaussian) differential reddening distribution, a time-decreasing star-formation rate, the unresolved binaries, and the smearing effect produced by photometric uncertainties on Hess diagrams. Free parameters are cluster mass, age, distance modulus, star-formation spread, foreground and differential reddening, and binary fraction. Results: Tests with model clusters built with parameters spanning a broad range of values show that ASAmin retrieves the input values with a high precision for cluster mass, distance modulus, and foreground reddening, but they are somewhat lower for the remaining parameters. Given the statistical nature of the simulations, several runs should be performed to obtain significant convergence patterns. Specifically, we find that the retrieved (absolute minimum) parameters converge to mean values with a low dispersion as the Hess residuals decrease. When applied to actual young clusters, the retrieved parameters follow convergence patterns similar to the models. We show how the stochasticity associated with the early phases may affect the results, especially in low-mass clusters. This effect can be minimised by averaging out several twin clusters in the

  11. 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

  12. Boundary layer fractionation constrained by differential information from the Kutsugata lava flow, Rishiri volcano, Japan

    NASA Astrophysics Data System (ADS)

    Kuritani, Takeshi

    1999-12-01

    Detailed investigation of an erupted magma with limited compositional diversity provides instantaneous information on incremental magma differentiation processes in a magma chamber. Kutsugata lava, a suitable target of such study, is a Quaternary alkali basalt (51.3-53.2 wt% in SiO2) from Rishiri Volcano, northern Japan. Despite the narrow range in the whole rock compositional variation, chemical and modal compositions of mineral phases crystallized in the magma chamber vary systematically with the whole rock composition. In the North lava (51.3-51.9 wt% in SiO2) the less differentiated portion of the Kutsugata lava, most crystals which include low-Ni olivine and plagioclase were derived from the mushy boundary layer. The main part of the magma body was principally aphyric (<0.5 vol% crystals). Estimated chemical compositions of fractionated mineral phases during differentiation of the magma coincide with the observed compositions of low-Ni olivine and plagioclase crystals. This indicates that the main magma was differentiated by separation of crystals grown in the mush zone. The low-density interstitial melt is suggested to have been extracted from the floor mush zone with average crystallinity of >30 vol% by such mechanisms as compaction and compositional convection. This fractionated melt was mixed with the overlying main magma, causing differentiation of the Kutsugata magma. The average temperature of the extracted melt is 1010°C, significantly lower than 1100°C estimated for the main magma. A quantitative model of magmatic differentiation, which includes thermal and compositional evolution of a mushy boundary layer, can successfully reproduce the observed compositional trends of the North lava.

  13. 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.

  14. New exact solutions of fractional Davey-Stewartson equation with power-law nonlinearity and new integrable Davey-Stewartson-type equation

    NASA Astrophysics Data System (ADS)

    Saha Ray, S.

    2016-09-01

    In this article, the Jacobi elliptic function method viz. the mixed dn-sn method has been presented for finding the travelling wave solutions of the Davey-Stewartson equations. As a result, some solitary wave solutions and doubly periodic solutions are obtained in terms of Jacobi elliptic functions. Moreover, solitary wave solutions are obtained as simple limits of doubly periodic functions. These solutions can be useful to explain some physical phenomena, viz. evolution of a three-dimensional wave packet on water of finite depth. The proposed Jacobi elliptic function method is efficient, powerful and can be used in order to establish newer exact solutions for other kinds of nonlinear fractional partial differential equations arising in mathematical physics.

  15. Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding.

    PubMed

    Wang, Xiaogang; Chen, Wen; Chen, Xudong

    2014-09-22

    We present a novel image hiding method based on phase retrieval algorithm under the framework of nonlinear double random phase encoding in fractional Fourier domain. Two phase-only masks (POMs) are efficiently determined by using the phase retrieval algorithm, in which two cascaded phase-truncated fractional Fourier transforms (FrFTs) are involved. No undesired information disclosure, post-processing of the POMs or digital inverse computation appears in our proposed method. In order to achieve the reduction in key transmission, a modified image hiding method based on the modified phase retrieval algorithm and logistic map is further proposed in this paper, in which the fractional orders and the parameters with respect to the logistic map are regarded as encryption keys. Numerical results have demonstrated the feasibility and effectiveness of the proposed algorithms.

  16. 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.

  17. 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

  18. 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.

  19. 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

  20. 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

  1. 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.

  2. 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.

  3. 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)

  4. 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

  5. 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.

  6. THE WEIGHTED SPACES L_{p,r}^\\alpha(\\rho_1,\\,\\rho_2) OF DIFFERENTIABLE FUNCTIONS OF FRACTIONAL SMOOTHNESS

    NASA Astrophysics Data System (ADS)

    Nogin, V. A.

    1988-02-01

    This is an investigation of weighted spaces of differentiable functions of fractional smoothness consisting of functions f(x) which are r-integrable with a weight \\rho_1 and have "fractional derivatives" which are p-integrable with a weight \\rho_2.Bibliography: 20 titles.

  7. 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.

  8. Global series solutions of nonlinear differential equations with shocks using Walsh functions

    NASA Astrophysics Data System (ADS)

    Gnoffo, Peter A.

    2014-02-01

    An orthonormal basis set composed of Walsh functions is used for deriving global solutions (valid over the entire domain) to nonlinear differential equations that include discontinuities. Function gn(x) of the set, a scaled Walsh function in sequency order, is comprised of n piecewise constant values (square waves) across the domain xa⩽x⩽xb. Only two square wave lengths are allowed in any function and a new derivation of the basis functions applies a fractal-like algorithm (infinitely self-similar) focused on the distribution of wave lengths. This distribution is determined by a recursive folding algorithm that propagates fundamental symmetries to successive values of n. Functions, including those with discontinuities, may be represented on the domain as a series in gn(x) with no occurrence of a Gibbs phenomenon (ringing) across the discontinuity. A much more powerful, self-mapping characteristic of the series is closure under multiplication - the product of any two Walsh functions is also a Walsh function. This self-mapping characteristic transforms the solution of nonlinear differential equations to the solution of systems of polynomial equations if the original nonlinearities can be represented as products of the dependent variables and the convergence of the series for n→∞ can be demonstrated. Fundamental operations (reciprocal, integral, derivative) on Walsh function series representations of functions with discontinuities are defined. Examples are presented for solution of the time dependent Burger's equation and for quasi-one-dimensional nozzle flow including a shock.

  9. 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.

  10. 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

  11. 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.

  12. 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.

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

    DOE PAGES

    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

  14. 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

  15. On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions

    NASA Astrophysics Data System (ADS)

    Antoine, Xavier; Tang, Qinglin; Zhang, Yong

    2016-11-01

    In this paper, we propose some efficient and robust numerical methods to compute the ground states and dynamics of Fractional Schrödinger Equation (FSE) with a rotation term and nonlocal nonlinear interactions. In particular, a newly developed Gaussian-sum (GauSum) solver is used for the nonlocal interaction evaluation [31]. To compute the ground states, we integrate the preconditioned Krylov subspace pseudo-spectral method [4] and the GauSum solver. For the dynamics simulation, using the rotating Lagrangian coordinates transform [14], we first reformulate the FSE into a new equation without rotation. Then, a time-splitting pseudo-spectral scheme incorporated with the GauSum solver is proposed to simulate the new FSE. In parallel to the numerical schemes, we also prove some existence and nonexistence results for the ground states. Dynamical laws of some standard quantities, including the mass, energy, angular momentum and the center of mass, are stated. The ground states properties with respect to the fractional order and/or rotating frequencies, dynamics involving decoherence and turbulence together with some interesting phenomena are reported.

  16. Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions

    NASA Astrophysics Data System (ADS)

    Lin, Yezhi; Liu, Yinping; Li, Zhibin

    2012-01-01

    The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. Program summaryProgram title: NAPA Catalogue identifier: AEJZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJZ_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.: 4060 No. of bytes in distributed program, including test data, etc.: 113 498 Distribution format: tar.gz Programming language: MAPLE R13 Computer: PC Operating system: Windows XP/7 RAM: 2 Gbytes Classification: 4.3 Nature of problem: Solve nonlinear differential equations with initial conditions. Solution method: Adomian decomposition method and Padé technique. Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.

  17. Zirconium and hafnium fractionation in differentiation of alkali carbonatite magmatic systems

    NASA Astrophysics Data System (ADS)

    Kogarko, L. N.

    2016-05-01

    Zirconium and hafnium are valuable strategic metals which are in high demand in industry. The Zr and Hf contents are elevated in the final products of magmatic differentiation of alkali carbonatite rocks in the Polar Siberia region (Guli Complex) and Ukraine (Chernigov Massif). Early pyroxene fractionation led to an increase in the Zr/Hf ratio in the evolution of the ultramafic-alkali magmatic system due to a higher distribution coefficient of Hf in pyroxene with respect to Zr. The Rayleigh equation was used to calculate a quantitative model of variation in the Zr/Hf ratio in the development of the Guli magmatic system. Alkali carbonatite rocks originated from rare element-rich mantle reservoirs, in particular, the metasomatized mantle. Carbonated mantle xenoliths are characterized by a high Zr/Hf ratio due to clinopyroxene development during metasomatic replacement of orthopyroxene by carbonate fluid melt.

  18. 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

  19. 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.

  20. 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.

  1. 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

  2. Simultaneous nonlinear encryption of grayscale and color images based on phase-truncated fractional Fourier transform and optical superposition principle.

    PubMed

    Wang, Xiaogang; Zhao, Daomu

    2013-09-01

    A nonlinear color and grayscale images cryptosystem based on phase-truncated fractional Fourier transform and optical superposition principle is proposed. In order to realize simultaneous encryption of color and grayscale images, each grayscale image is first converted into two phase masks by using an optical coherent superposition, one of which is treated as a part of input information that will be fractional Fourier transformed while the other in the form of a chaotic random phase mask (CRPM) is used as a decryption key. For the purpose of optical performance, all the processes are performed through three channels, i.e., red, green, and blue. Different from most asymmetric encryption methods, the decryption process is designed to be linear for the sake of effective decryption. The encryption level of a double random phase encryption based on phase-truncated Fourier transform is enhanced by extending it into fractional Fourier domain and the load of the keys management and transmission is lightened by using CRPMs. The security of the proposed cryptosystem is discussed and computer simulation results are presented to verify the validity of the proposed method.

  3. 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.

  4. 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.

  5. Statistically Differentiating between Interaction and Nonlinearity in Multiple Regression Analysis: A Monte Carlo Investigation of a Recommended Strategy.

    ERIC Educational Resources Information Center

    Kromrey, Jeffrey D.; Foster-Johnson, Lynn

    1999-01-01

    Shows that the procedure recommended by D. Lubinski and L. Humphreys (1990) for differentiating between moderated and nonlinear regression models evidences statistical problems characteristic of stepwise procedures. Interprets Monte Carlo results in terms of the researchers' need to differentiate between exploratory and confirmatory aspects of…

  6. Remarks on the Non-Linear Differential Equation the Second Derivative of Theta Plus A Sine Theta Equals 0.

    ERIC Educational Resources Information Center

    Fay, Temple H.; O'Neal, Elizabeth A.

    1985-01-01

    The authors draw together a variety of facts concerning a nonlinear differential equation and compare the exact solution with approximate solutions. Then they provide an expository introduction to the elliptic sine function suitable for presentation in undergraduate courses on differential equations. (MNS)

  7. Solution of nonlinear partial differential equations using the Chebyshev spectral method

    NASA Astrophysics Data System (ADS)

    Kapania, R. K.; Eldred, L. B.

    1991-05-01

    The spectral method is a powerful numerical technique for solving engineering differential equations. The method is a specialization of the method of weighted residuals. Trial functions that are easily and exactly differentiable are used. Often the functions used also satisfy an orthogonality equation, which can improve the efficiency of the approximation. Generally, the entire domain is modeled, but multiple sub-domains may be used. A Chebyshev-Collocation Spectral method is used to solve a two-dimensional, highly nonlinear, two parameter Bratu's equation. This equation previously assumed to have only symmetric solutions are shown to have regions where solutions that are non-symmetric in x and y are valid. Away from these regions an accurate and efficient technique for tracking the equation's multi-valued solutions was developed. It is found that the accuracy of the present method is very good, with a significant improvement in computer time.

  8. 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

  9. Experimental demonstration of fractional order differentiation using a long-period grating-based in-fiber modal interferometer

    NASA Astrophysics Data System (ADS)

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

    2016-12-01

    In this work we demonstrate both, experimentally and theoretically, that a long-period grating-based in-fiber modal interferometer can perform an all-optical arbitrary-order fractional differentiation. Experimentally, we fractionally differentiated to the 0.5th order a secant hyperbolic-like pulse of 23 ps time width provided by a 1039.5 nm emission wavelength modelocked fiber laser, with a chirp parameter of -30. An analytical expression relating the fractional order of differentiation n with the characteristics of the modal interferometer was also derived, with the purpose to simplify the design procedure. The proposal was corroborated also numerically. This device may find applications in real time phase recovery.

  10. 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.

  11. 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.

  12. 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

  13. 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).

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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

  19. 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.

  20. 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.

  1. 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

  2. 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

  3. 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.

  4. Sensitivity analysis and model reduction of nonlinear differential-algebraic systems. Final progress report

    SciTech Connect

    Petzold, L.R.; Rosen, J.B.

    1997-12-30

    Differential-algebraic equations arise in a wide variety of engineering and scientific problems. Relatively little work has been done regarding sensitivity analysis and model reduction for this class of problems. Efficient methods for sensitivity analysis are required in model development and as an intermediate step in design optimization of engineering processes. Reduced order models are needed for modelling complex physical phenomena like turbulent reacting flows, where it is not feasible to use a fully-detailed model. The objective of this work has been to develop numerical methods and software for sensitivity analysis and model reduction of nonlinear differential-algebraic systems, including large-scale systems. In collaboration with Peter Brown and Alan Hindmarsh of LLNL, the authors developed an algorithm for finding consistent initial conditions for several widely occurring classes of differential-algebraic equations (DAEs). The new algorithm is much more robust than the previous algorithm. It is also very easy to use, having been designed to require almost no information about the differential equation, Jacobian matrix, etc. in addition to what is already needed to take the subsequent time steps. The new algorithm has been implemented in a version of the software for solution of large-scale DAEs, DASPK, which has been made available on the internet. The new methods and software have been used to solve a Tokamak edge plasma problem at LLNL which could not be solved with the previous methods and software because of difficulties in finding consistent initial conditions. The capability of finding consistent initial values is also needed for the sensitivity and optimization efforts described in this paper.

  5. Automatic versus manual model differentiation to compute sensitivities and solve non-linear inverse problems

    NASA Astrophysics Data System (ADS)

    Elizondo, D.; Cappelaere, B.; Faure, Ch.

    2002-04-01

    Emerging tools for automatic differentiation (AD) of computer programs should be of great benefit for the implementation of many derivative-based numerical methods such as those used for inverse modeling. The Odyssée software, one such tool for Fortran 77 codes, has been tested on a sample model that solves a 2D non-linear diffusion-type equation. Odyssée offers both the forward and the reverse differentiation modes, that produce the tangent and the cotangent models, respectively. The two modes have been implemented on the sample application. A comparison is made with a manually-produced differentiated code for this model (MD), obtained by solving the adjoint equations associated with the model's discrete state equations. Following a presentation of the methods and tools and of their relative advantages and drawbacks, the performances of the codes produced by the manual and automatic methods are compared, in terms of accuracy and of computing efficiency (CPU and memory needs). The perturbation method (finite-difference approximation of derivatives) is also used as a reference. Based on the test of Taylor, the accuracy of the two AD modes proves to be excellent and as high as machine precision permits, a good indication of Odyssée's capability to produce error-free codes. In comparison, the manually-produced derivatives (MD) sometimes appear to be slightly biased, which is likely due to the fact that a theoretical model (state equations) and a practical model (computer program) do not exactly coincide, while the accuracy of the perturbation method is very uncertain. The MD code largely outperforms all other methods in computing efficiency, a subject of current research for the improvement of AD tools. Yet these tools can already be of considerable help for the computer implementation of many numerical methods, avoiding the tedious task of hand-coding the differentiation of complex algorithms.

  6. 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

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Fractionation of fluorine, chlorine and other trace elements during differentiation of a tholeiitic magma.

    NASA Technical Reports Server (NTRS)

    Greenland, L.; Lovering, J. F.

    1966-01-01

    Fluorine, chlorine and other trace elements determined through differentiated tholeiitic dolerite sill from Tasmania using statistical techniques, showing hydroxyl lattice sites by chlorine and fluorine

  19. On a solution of the nonlinear differential equation for transonic flow past a wave-shaped wall

    NASA Technical Reports Server (NTRS)

    Kaplan, Carl

    1952-01-01

    The Prandtl-Busemann small-perturbation method is utilized to obtain the flow of a compressible fluid past an infinitely long wave-shaped wall. When the essential assumption for transonic flow (that all Mach numbers in the region of flow are nearly unity) is introduced, the expression for the velocity potential takes the form of a power series in the transonic similarity parameter. On the basis of this form of the solution, an attempt is made to solve the nonlinear differential equation for transonic flow past the wavy wall. The analysis utilized exhibits clearly the difficulties inherent in nonlinear-flow problems.

  20. 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.

  1. 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.

  2. 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.

  3. Phenolic-rich leaf carbon fractions differentially influence microbial respiration and plant growth.

    PubMed

    Meier, Courtney L; Bowman, William D

    2008-11-01

    Phenolics can reduce soil nutrient availability, either indirectly by stimulating microbial nitrogen (N) immobilization or directly by enhancing physical protection within soil. Phenolic-rich plants may therefore negatively affect neighboring plant growth by restricting the N supply. We used a slow-growing, phenolic-rich alpine forb, Acomastylis rossii, to test the hypothesis that phenolic-rich carbon (C) fractions stimulate microbial population growth and reduce plant growth. We generated low-molecular-weight (LMW) fractions, tannin fractions, and total soluble C fractions from A. rossii and measured their effects on soil respiration and growth of Deschampsia caespitosa, a fast-growing, co-dominant grass. Fraction effects fell into two distinct categories: (1) fractions did not increase soil respiration and killed D. caespitosa plants, or (2) fractions stimulated soil respiration and reduced plant growth and plant N concentration while simultaneously inhibiting root growth. The LMW phenolic-rich fractions increased soil respiration and reduced plant growth more than tannins. These results suggest that phenolic compounds can inhibit root growth directly as well as indirectly affect growth by reducing pools of plant available N by stimulating soil microbes. Both mechanisms illustrate how below-ground phenolic effects may influence the growth of neighboring plants. We also examined patterns of foliar phenolic concentrations among populations of A. rossii across a natural productivity gradient (productivity was used as a proxy for competition intensity). Concentrations of some LMW phenolics increased significantly in more productive sites where A. rossii is a competitive equal with the faster growing D. caespitosa. Taken together, our results contribute important information to the growing body of evidence indicating that the quality of C moving from plants to soils can have significant effects on neighboring plant performance, potentially associated with phytoxic

  4. 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

  5. Gain determination of non-linear IR detectors with the differential photon transfer curve (dPTC) method

    NASA Astrophysics Data System (ADS)

    Rest, Armin; Hilbert, Bryan; Leisenring, Jarron M.; Misselt, Karl; Rieke, Marcia; Robberto, Massimo

    2016-07-01

    Conversion gain is a basic detector property which relates the raw counts in a pixel in data numbers (DN) to the number of electrons detected. The standard method for determining the gain is called the Photon Transfer Curve (PTC) method and involves the measurement the change in variance as a function of signal level. For non-linear IR detectors, this method depends strongly on the non-linearity correction and is therefore susceptible to systematic biases due to calibration issues. We have developed a new, robust, and fast method, the differential Photon Transfer Curve (dPTC) method, which is independent of non-linearity corrections, but still delivers gain values similar in precision but higher in accuracy.

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

    PubMed Central

    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

  7. 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.

  8. 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

  9. State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

    PubMed

    Korayem, M H; Nekoo, S R

    2015-07-01

    This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data.

  10. 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

  11. 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.

  12. Carotenoids of aleurone, germ, and endosperm fractions of barley, corn and wheat differentially inhibit oxidative stress.

    PubMed

    Masisi, Kabo; Diehl-Jones, William L; Gordon, Joseph; Chapman, Donald; Moghadasian, Mohammed H; Beta, Trust

    2015-03-18

    The antioxidant potential of carotenoids from aleurone, germ, and endosperm fractions of barley, corn, and wheat has been evaluated. HPLC analysis confirmed the presence of lutein and zeaxanthin carotenoids (nd-15139 μg/kg) in extracts of cereal grain fractions. The antioxidant properties using 2,2-diphenyl-1-picrylhydrazyl, oxygen radical absorbance capacity, 2,2'-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) assays revealed significantly higher (P<0.001) antioxidant activity in the germ than in the aleurone and endosperm fractions. Using 3-(4,5-dimethylthiazolyl-2)-2,5-diphenyltetrazolium bromide (MTT) assay, 2,2'azobis (2-amidinopropane)dihydrochloride (AAPH)-induced cell loss was effectively reduced by preincubating Caco-2, HT-29, and FHs 74 Int cells with carotenoid extracts. Moreover, carotenoid extracts reduced (P<0.001) AAPH-induced intracellular oxidation in the cell lines, suggesting antioxidant activity. Of the 84 antioxidant pathway genes included in microarray array analysis (HT-29 cells), the expressions of 28 genes were enhanced (P<0.05). Our findings suggest that carotenoids of germ, aleurone, and endosperm fractions improved antioxidant capacity and thus have the potential to mitigate oxidative stress.

  13. Differential response of human nasal and bronchial epithelial cells upon exposure to size-fractionated dairy dust.

    PubMed

    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 proinflammatory transcripts (interleukin [IL]-8, IL-6, and tumor necrosis factor [TNF]-α) were measured 2 h 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 proinflammatory 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 that the two cell types need to be considered separately in airway cell models of agricultural dust toxicity. PMID:25965193

  14. 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.

  15. 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

  16. 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

  17. 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.

  18. Modeling the compositional evolution of recharging, evacuating, and fractionating (REFC) magma chambers: Implications for differentiation of arc magmas

    NASA Astrophysics Data System (ADS)

    Lee, Cin-Ty A.; Lee, Tien Chang; Wu, Chi-Tang

    2014-10-01

    are high and warm country rock decrease the cooling rates of magma chambers. By contrast, REFC should be less significant in shallow crustal magma chambers, which erupt and cool more efficiently due to lower confining pressures, colder country rock, and the cooling effects of hydrothermal systems. We thus speculate that the effects of REFC will be small in mid-ocean ridge settings and most pronounced in arc settings, particularly mature island arcs or continental arcs, where magma chambers >10 km depth are possible. This begs the question of whether high Fe3+, H2O and CO2 (all of which can be treated as incompatible “elements”) in arc basalts could be enhanced by REFC processes and thus not just reflect inheritance from the mantle source. We show that REFC can plausibly explain observed enrichments in Fe3+ and H2O in arc melts without significant depletion in MgO. Because the difference between calc-alkaline and tholeiitic differentiation series is mostly likely due to higher water and oxygen fugacity in the former, it may be worth considering the effects of REFC. Thus, if REFC is more pronounced in deep crustal magma chambers, mature island arcs and continental arcs would tend towards calc-alkaline differentiation, whereas juvenile island arcs would be more tholeiitic. To fully test the significance of REFC will require detailed analysis of other highly incompatible elements, but presently the relative differences in bulk D of such elements may not be constrained well enough. The equations presented here provide a framework for evaluating whether REFC should be considered when interpreting geochemical data in differentiated magmas. For completeness, we have also provided the more general equations for a magma chamber undergoing recharge (R), evacuation (E), crustal assimilation (A) and fractional crystallization (FC), e.g., REAFC, for constant mass, growing and dying magma chambers.

  19. Differential branching fractions and isospin asymmetries of B → K (*) μ + μ - decays

    NASA Astrophysics Data System (ADS)

    Aaij, R.; Adeva, B.; Adinolfi, M.; Affolder, A.; Ajaltouni, Z.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Cartelle, P. Alvarez; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; An, L.; Anderlini, L.; Anderson, J.; Andreassen, R.; Andreotti, M.; Andrews, J. E.; Appleby, R. B.; Gutierrez, O. Aquines; Archilli, F.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Baalouch, M.; Bachmann, S.; Back, J. J.; Badalov, A.; Balagura, V.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Batozskaya, V.; Bauer, Th.; Bay, A.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Belogurov, S.; Belous, K.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Benton, J.; Berezhnoy, A.; Bernet, R.; Bettler, M.-O.; van Beuzekom, M.; Bien, A.; Bifani, S.; Bird, T.; Bizzeti, A.; Bjørnstad, P. M.; Blake, T.; Blanc, F.; Blouw, J.; Blusk, S.; Bocci, V.; Bondar, A.; Bondar, N.; Bonivento, W.; Borghi, S.; Borgia, A.; Borsato, M.; Bowcock, T. J. V.; Bowen, E.; Bozzi, C.; Brambach, T.; van den Brand, J.; Bressieux, J.; Brett, D.; Britsch, M.; Britton, T.; Brook, N. H.; Brown, H.; Bursche, A.; Busetto, G.; Buytaert, J.; Cadeddu, S.; Calabrese, R.; Callot, O.; Calvi, M.; Gomez, M. Calvo; Camboni, A.; Campana, P.; Perez, D. Campora; Carbone, A.; Carboni, G.; Cardinale, R.; Cardini, A.; Carranza-Mejia, H.; Carson, L.; Akiba, K. Carvalho; Casse, G.; Cassina, L.; Garcia, L. Castillo; Cattaneo, M.; Cauet, Ch.; Cenci, R.; Charles, M.; Charpentier, Ph.; Cheung, S.-F.; Chiapolini, N.; Chrzaszcz, M.; Ciba, K.; Vidal, X. Cid; Ciezarek, G.; Clarke, P. E. L.; Clemencic, M.; Cliff, H. V.; Closier, J.; Coca, C.; Coco, V.; Cogan, J.; Cogneras, E.; 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.; Torres, M. Cruz; Cunliffe, S.; Currie, R.; D'Ambrosio, C.; Dalseno, J.; David, P.; 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.; Decamp, D.; Deckenhoff, M.; Del Buono, L.; Déléage, N.; Derkach, D.; Deschamps, O.; Dettori, F.; Di Canto, A.; Dijkstra, H.; Donleavy, S.; Dordei, F.; Dorigo, M.; Suárez, A. Dosil; Dossett, D.; Dovbnya, A.; 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.; Esen, S.; Evans, T.; Falabella, A.; Färber, C.; Farinelli, C.; Farry, S.; Ferguson, D.; Albor, V. Fernandez; Rodrigues, F. Ferreira; Ferro-Luzzi, M.; Filippov, S.; Fiore, M.; Fiorini, M.; Firlej, M.; Fitzpatrick, C.; Fiutowski, T.; Fontana, M.; Fontanelli, F.; Forty, R.; Francisco, O.; Frank, M.; Frei, C.; Frosini, M.; Fu, J.; Furfaro, E.; Torreira, A. Gallas; Galli, D.; Gallorini, S.; Gambetta, S.; Gandelman, M.; Gandini, P.; Gao, Y.; Garofoli, J.; Tico, J. Garra; Garrido, L.; Gaspar, C.; Gauld, R.; Gavardi, L.; Gersabeck, E.; Gersabeck, M.; Gershon, T.; Ghez, Ph.; Gianelle, A.; Giani', S.; Gibson, V.; Giubega, L.; Gligorov, V. V.; Göbel, C.; Golubkov, D.; Golutvin, A.; Gomes, A.; Gordon, H.; Gotti, C.; Gándara, M. Grabalosa; Diaz, R. Graciani; Cardoso, L. A. Granado; Graugés, 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.; Hartmann, T.; He, J.; Head, T.; Heijne, V.; Hennessy, K.; Henrard, P.; Henry, L.; Morata, J. A. Hernando; van Herwijnen, E.; Heß, M.; Hicheur, A.; Hill, D.; Hoballah, M.; Hombach, C.; Hulsbergen, W.; Hunt, P.; Hussain, N.; Hutchcroft, D.; Hynds, D.; Idzik, M.; Ilten, P.; Jacobsson, R.; Jaeger, A.; Jalocha, J.; Jans, E.; Jaton, P.; Jawahery, A.; Jezabek, M.; Jing, F.; John, M.; Johnson, D.; Jones, C. R.; Joram, C.; Jost, B.; Jurik, N.; Kaballo, M.; Kandybei, S.; Kanso, W.; Karacson, M.; Karbach, T. M.; Kelsey, M.; Kenyon, I. R.; Ketel, T.; Khanji, B.; Khurewathanakul, C.; Klaver, S.; Kochebina, O.; Kolpin, M.; Komarov, I.; Koopman, R. F.; Koppenburg, P.; Korolev, M.; Kozlinskiy, A.; Kravchuk, L.; Kreplin, K.; Kreps, M.; Krocker, G.; Krokovny, P.; Kruse, F.; Kucharczyk, M.; Kudryavtsev, V.; Kurek, K.; Kvaratskheliya, T.; La Thi, V. N.; Lacarrere, D.; Lafferty, G.; Lai, A.; Lambert, D.; Lambert, R. W.; Lanciotti, E.; 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.; Leo, S.; Leroy, O.; Lesiak, T.; Leverington, B.; Li, Y.; Liles, M.; Lindner, R.; Linn, C.; Lionetto, F.; Liu, B.; Liu, G.; Lohn, S.; Longstaff, I.; Lopes, J. H.; Lopez-March, N.; Lowdon, P.; Lu, H.; Lucchesi, D.; Luo, H.; Lupato, A.; Luppi, E.; Lupton, O.; Machefert, F.; Machikhiliyan, I. V.; Maciuc, F.; Maev, O.; Malde, S.; Manca, G.; Mancinelli, G.; Manzali, M.; Maratas, J.; Marchand, J. F.; Marconi, U.; Benito, C. Marin; Marino, P.; Märki, R.; Marks, J.; Martellotti, G.; Martens, A.; Sánchez, A. Martín; Martinelli, M.; Santos, D. Martinez; Vidal, F. Martinez; Tostes, D. Martins; Massafferri, A.; Matev, R.; Mathe, Z.; Matteuzzi, C.; Mazurov, A.; McCann, M.; McCarthy, J.; McNab, A.; McNulty, R.; McSkelly, B.; Meadows, B.; Meier, F.; Meissner, M.; Merk, M.; Milanes, D. A.; Minard, M.-N.; Rodriguez, J. Molina; Monteil, S.; Moran, D.; Morandin, M.; Morawski, P.; Mordà, A.; Morello, M. J.; Moron, J.; Mountain, R.; Muheim, F.; Müller, K.; Muresan, R.; 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.; Nicol, M.; Niess, V.; Niet, R.; Nikitin, N.; Nikodem, T.; Novoselov, A.; Oblakowska-Mucha, A.; Obraztsov, V.; Oggero, S.; Ogilvy, S.; Okhrimenko, O.; Oldeman, R.; Onderwater, G.; Orlandea, M.; Goicochea, J. M. Otalora; Owen, P.; Oyanguren, A.; Pal, B. K.; Palano, A.; Palombo, F.; Palutan, M.; Panman, J.; Papanestis, A.; Pappagallo, M.; Parkes, C.; Parkinson, C. J.; Passaleva, G.; Patel, G. D.; Patel, M.; Patrignani, C.; Alvarez, A. Pazos; Pearce, A.; Pellegrino, A.; Altarelli, M. Pepe; Perazzini, S.; Trigo, E. Perez; Perret, P.; Perrin-Terrin, M.; Pescatore, L.; Pesen, E.; Petridis, K.; Petrolini, A.; Olloqui, E. Picatoste; Pietrzyk, B.; Pilař, T.; Pinci, D.; Pistone, A.; Playfer, S.; Casasus, M. Plo; Polci, F.; Poluektov, A.; Polycarpo, E.; Popov, A.; Popov, D.; Popovici, B.; Potterat, C.; Powell, A.; Prisciandaro, J.; Pritchard, A.; Prouve, C.; Pugatch, V.; Navarro, A. Puig; Punzi, G.; Qian, W.; Rachwal, B.; Rademacker, J. H.; Rakotomiaramanana, B.; Rama, M.; Rangel, M. S.; Raniuk, I.; Rauschmayr, N.; Raven, G.; Reichert, S.; Reid, M. M.; dos Reis, A. C.; Ricciardi, S.; Richards, A.; Rinnert, K.; Molina, V. Rives; Romero, D. A. Roa; Robbe, P.; Rodrigues, A. B.; Rodrigues, E.; Perez, P. Rodriguez; Roiser, S.; Romanovsky, V.; Vidal, A. Romero; Rotondo, M.; Rouvinet, J.; Ruf, T.; Ruffini, F.; Ruiz, H.; Valls, P. Ruiz; Sabatino, G.; Silva, J. J. Saborido; Sagidova, N.; Sail, P.; Saitta, B.; Guimaraes, V. Salustino; Mayordomo, C. Sanchez; Sedes, B. Sanmartin; Santacesaria, R.; Rios, C. Santamarina; Santovetti, E.; Sapunov, M.; Sarti, A.; Satriano, C.; Satta, A.; Savrie, 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.; Seco, M.; Semennikov, A.; Senderowska, K.; Sepp, I.; Serra, N.; Serrano, J.; Sestini, L.; Seyfert, P.; Shapkin, M.; Shapoval, I.; Shcheglov, Y.; Shears, T.; Shekhtman, L.; Shevchenko, V.; Shires, A.; Coutinho, R. Silva; Simi, G.; Sirendi, M.; Skidmore, N.; 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.; De Paula, B. Souza; Spaan, B.; Sparkes, A.; Spinella, F.; Spradlin, P.; Stagni, F.; Stahl, S.; Steinkamp, O.; Stenyakin, O.; Stevenson, S.; Stoica, S.; Stone, S.; Storaci, B.; Stracka, S.; Straticiuc, M.; Straumann, U.; Stroili, R.; Subbiah, V. K.; Sun, L.; Sutcliffe, W.; Swientek, K.; Swientek, S.; Syropoulos, V.; Szczekowski, M.; Szczypka, P.; Szilard, D.; Szumlak, T.; T'Jampens, S.; Teklishyn, M.; Tellarini, G.; Teodorescu, E.; Teubert, F.; Thomas, C.; Thomas, E.; van Tilburg, J.; Tisserand, V.; Tobin, M.; Tolk, S.; Tomassetti, L.; Tonelli, D.; Topp-Joergensen, S.; Torr, N.; Tournefier, E.; Tourneur, S.; Tran, M. T.; Tresch, M.; Tsaregorodtsev, A.; Tsopelas, P.; Tuning, N.; Garcia, M. Ubeda; Ukleja, A.; Ustyuzhanin, A.; Uwer, U.; Vagnoni, V.; Valenti, G.; Vallier, A.; Gomez, R. Vazquez; Regueiro, P. Vazquez; Sierra, C. Vázquez; 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.; Voss, H.; de Vries, J. A.; Waldi, R.; Wallace, C.; Wallace, R.; Walsh, J.; Wandernoth, S.; Wang, J.; Ward, D. R.; Watson, N. K.; Webber, A. D.; Websdale, D.; Whitehead, M.; Wicht, J.; Wiedner, D.; Wilkinson, G.; Williams, M. P.; Williams, M.; Wilson, F. F.; Wimberley, J.; Wishahi, J.; Wislicki, W.; Witek, M.; Wormser, G.; Wotton, S. A.; Wright, S.; Wu, S.; Wyllie, K.; Xie, Y.; Xing, Z.; Xu, Z.; Yang, Z.; Yuan, X.; Yushchenko, O.; Zangoli, M.; Zavertyaev, M.; Zhang, F.; Zhang, L.; Zhang, W. C.; Zhang, Y.; Zhelezov, A.; Zhokhov, A.; Zhong, L.; Zvyagin, A.

    2014-06-01

    The isospin asymmetries of B → Kμ + μ - and B → K * μ + μ - decays and the partial branching fractions of the B 0 → K 0 μ + μ -, B + → K + μ + μ - and B + → K *+ μ + μ - decays are measured as functions of the dimuon mass squared, q 2. The data used correspond to an integrated luminosity of 3 fb-1 from proton-proton collisions collected with the LHCb detector at centre-of-mass energies of 7 TeV and 8 TeV in 2011 and 2012, respectively. The isospin asymmetries are both consistent with the Standard Model expectations. The three measured branching fractions favour lower values than their respective theoretical predictions, however they are all individually consistent with the Standard Model. [Figure not available: see fulltext.

  20. Study of the fractional order proportional integral controller for the permanent magnet synchronous motor based on the differential evolution algorithm.

    PubMed

    Zheng, Weijia; Pi, Youguo

    2016-07-01

    A tuning method of the fractional order proportional integral speed controller for a permanent magnet synchronous motor is proposed in this paper. Taking the combination of the integral of time and absolute error and the phase margin as the optimization index, the robustness specification as the constraint condition, the differential evolution algorithm is applied to search the optimal controller parameters. The dynamic response performance and robustness of the obtained optimal controller are verified by motor speed-tracking experiments on the motor speed control platform. Experimental results show that the proposed tuning method can enable the obtained control system to achieve both the optimal dynamic response performance and the robustness to gain variations.

  1. 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

  2. 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.

  3. Approximate Controllability of Fractional Neutral Stochastic System with Infinite Delay

    NASA Astrophysics Data System (ADS)

    Sakthivel, R.; Ganesh, R.; Suganya, S.

    2012-12-01

    The concept of controllability plays an important role in analysis and design of linear and nonlinear control systems. Further, fractional differential equations have wide applications in engineering and science. In this paper, the approximate controllability of neutral stochastic fractional integro-differential equation with infinite delay in a Hilbert space is studied. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.

  4. Continuous Time Random Walks in periodic systems: fluid limit and fractional differential equations on the circle

    SciTech Connect

    Calvo, Ivan; Carreras, Benjamin A; Sanchez, Raul; van Milligen, B. Ph.

    2007-01-01

    In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out the fluid limit equation, formulated in terms of the periodic version of the fractional Riemann-Liouville operators, for which we provide explicit expressions. Finally, we compute the propagator in some simple cases. The analysis presented herein should be relevant when investigating anomalous transport phenomena in systems with periodic dimensions.

  5. 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.

  6. Nonlinear gain-scheduling output-feedback control for polynomial nonlinear systems subject to actuator saturation

    NASA Astrophysics Data System (ADS)

    Wu, Fen; Hays, Scott

    2013-09-01

    This paper investigates nonlinear gain-scheduling control approaches for a class of polynomial nonlinear systems, containing an output-dependent vector field with input saturation. Using the polytopic differential inclusion and norm-bounded differential inclusion (NDI) of saturation and dead-zone functions, the nonlinear plants are transformed into systems with measurable parameters. For the polytopic differential inclusion description, a quasi-linear parameter varying (quasi-LPV) output-feedback controller will be sought for saturation control. On the other hand, the NDI model leads to a nonlinear fractional transformation (NFT) output-feedback controller for saturated nonlinear systems. The quasi-LPV and NFT output-feedback control synthesis conditions are derived in the forms of output-dependent matrix inequalities. They can be reformulated as sum-of-squares (SOS) optimisations and solved efficiently using SOS programming. The proposed nonlinear gain-scheduling saturation control approaches will be demonstrated using the Van der Pol equation.

  7. Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients

    NASA Astrophysics Data System (ADS)

    Mao, Zhiping; Shen, Jie

    2016-02-01

    Efficient spectral-Galerkin algorithms are developed to solve multi-dimensional fractional elliptic equations with variable coefficients in conserved form as well as non-conserved form. These algorithms are extensions of the spectral-Galerkin algorithms for usual elliptic PDEs developed in [24]. More precisely, for separable FPDEs, we construct a direct method by using a matrix diagonalization approach, while for non-separable FPDEs, we employ a preconditioned BICGSTAB method with a suitable separable FPDE with constant-coefficients as preconditioner. The cost of these algorithms is of O (N d + 1) flops where d is the space dimension. We derive rigorous weighted error estimates which provide more precise convergence rate for problems with singularities at boundaries. We also present ample numerical results to validate the algorithms and error estimates.

  8. Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. Kh; Avdonina, E. D.

    2013-10-01

    The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions. Bibliography: 23 titles.

  9. Crossover regime of optical vortices generation via electro-optic nonlinearity: the problem of optical vortices with the fractional charge generated by crystals.

    PubMed

    Vasylkiv, Yurij; Skab, Ihor; Vlokh, Rostyslav

    2014-09-01

    In this work, we analyze the behavior of topological defects of optical indicatrix orientation induced by a conically shaped electric field in crystals in a crossover regime that appears at intermediate fields separating the regimes of prevailing Pockels and Kerr electro-optic nonlinearities. We have found that increases in the electric voltage applied to a crystal induce neither topological defects, with the strengths being not multiples of ½, or the optical vortices with fractional charges. Instead, there appear some additional topological defects of the optical indicatrix orientation, the behavior of which we have studied in detail.

  10. Mango (Mangifera indica L.) peel extract fractions from different cultivars differentially affect lipid accumulation in 3T3-L1 adipocyte cells.

    PubMed

    Taing, Meng-Wong; Pierson, Jean-Thomas; Shaw, Paul N; Dietzgen, Ralf G; Roberts-Thomson, Sarah J; Gidley, Michael J; Monteith, Gregory R

    2013-02-26

    Plant phytochemicals are increasingly recognised as sources of bioactive molecules which may have potential benefit in many health conditions. In mangoes, peel extracts from different cultivars exhibit varying effects on adipogenesis in the 3T3-L1 adipocyte cell line. In this study, the effects of preparative HPLC fractions of methanol peel extracts from Irwin, Nam Doc Mai and Kensington Pride mangoes were evaluated. Fraction 1 contained the most hydrophilic components while subsequent fractions contained increasingly more hydrophobic components. High content imaging was used to assess mango peel fraction effects on lipid accumulation, nuclei count and nuclear area in differentiating 3T3-L1 cells. For all three mango cultivars, the more hydrophilic peel fractions 1-3 inhibited lipid accumulation with greater potency than the more hydrophobic peel fractions 4. For all three cultivars, the more lipophilic fraction 4 had concentrations that enhanced lipid accumulation greater than fractions 1-3 as assessed by lipid droplet integrated intensity. The potency of this fraction 4 varied significantly between cultivars. Using mass spectrometry, five long chain free fatty acids were detected in fraction 4; these were not present in any other peel extract fractions. Total levels varied between cultivars, with Irwin fraction 4 containing the highest levels of these free fatty acids. Lipophilic components appear to be responsible for the lipid accumulation promoting effects of some mango extracts and are the likely cause of the diverse effects of peel extracts from different mango cultivars on lipid accumulation.

  11. 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

  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.

  13. 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)

  14. 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.

  15. 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.

  16. Study of the fractional order proportional integral controller for the permanent magnet synchronous motor based on the differential evolution algorithm.

    PubMed

    Zheng, Weijia; Pi, Youguo

    2016-07-01

    A tuning method of the fractional order proportional integral speed controller for a permanent magnet synchronous motor is proposed in this paper. Taking the combination of the integral of time and absolute error and the phase margin as the optimization index, the robustness specification as the constraint condition, the differential evolution algorithm is applied to search the optimal controller parameters. The dynamic response performance and robustness of the obtained optimal controller are verified by motor speed-tracking experiments on the motor speed control platform. Experimental results show that the proposed tuning method can enable the obtained control system to achieve both the optimal dynamic response performance and the robustness to gain variations. PMID:27129766

  17. 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…

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. Importance of fractional exhaled nitric oxide in the differentiation of asthma–COPD overlap syndrome, asthma, and COPD

    PubMed Central

    Chen, Feng-jia; Huang, Xin-yan; Liu, Yang-li; Lin, Geng-peng; Xie, Can-mao

    2016-01-01

    Background Fractional exhaled nitric oxide (FeNO) is an easy, sensitive, reproducible, and noninvasive marker of eosinophilic airway inflammation. Accordingly, FeNO is extensively used to diagnose and manage asthma. Patients with COPD who share some of the features of asthma have a condition called asthma–COPD overlap syndrome (ACOS). The feasibility of using FeNO to differentiate ACOS patients from asthma and COPD patients remains unclear. Methods From February 2013 to May 2016, patients suspected with asthma and COPD through physician’s opinion were subjected to FeNO measurement, pulmonary function test (PFT), and bronchial hyperresponsiveness or bronchodilator test. Patients were divided into asthma alone group, COPD alone group, and ACOS group according to a clinical history, PFT values, and bronchial hyperresponsiveness or bronchodilator test. Receiver operating characteristic (ROC) curves were obtained to elucidate the clinical functions of FeNO in diagnosing ACOS. The optimal operating point was also determined. Results A total of 689 patients were enrolled in this study: 500 had asthma, 132 had COPD, and 57 had ACOS. The FeNO value in patients with ACOS was 27 (21.5) parts per billion (ppb; median [interquartile range]), which was significantly higher than that in the COPD group (18 [11] ppb). The area under the ROC curve was estimated to be 0.783 for FeNO. Results also revealed an optimal cutoff value of >22.5 ppb FeNO for differentiating ACOS from COPD patients (sensitivity 70%, specificity 75%). Conclusion FeNO measurement is an easy, noninvasive, and sensitive method for differentiating ACOS from COPD. This technique is a new perspective for the management of COPD patients. PMID:27713629

  3. 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.

  4. 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

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. A new Differential Equation for Anomalous Diffusion with Potential Applications to Nonlinear Space Plasmas

    NASA Astrophysics Data System (ADS)

    Watkins, N. W.; Credgington, D.; Sanchez, R.; Chapman, S. C.

    2007-12-01

    Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototpe) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in indices quantifying Earth's auroral currents and in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work [1] in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects. I will discuss how this resolves some contradictions seen in earlier work. Such Noah-Joseph hybrid ("ambivalent" [2]) behaviour is highly topical in physics but is typically studied in the paradigm of the continuous time random walk (CTRW) [2,3] rather than LFSM. I will clarify the physical differences between these two pictures and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm [4] with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time (c.f. [2,3]). Intriguingly the self-similarity exponent extracted from the CTRW differs from that seen in LFSM. In the CTRW it is the ratio of μ to a temporal exponent, in LFSM it is an additive function of them. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold-related to the burst size measure introduced by Takalo and Consolini into solar- terrestrial physics

  11. 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.

  12. 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.

  13. 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

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

    PubMed

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

    2015-12-11

    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.

  15. 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…

  16. 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.

  17. 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.

  18. Differentiating the extent of cartilage repair in rabbit ears using nonlinear optical microscopy.

    PubMed

    Zhu, X Q; Xu, Y H; Liao, C X; Liu, W G; Cheng, K K; Chen, J X

    2015-11-01

    Nonlinear optical microscopy (NLOM) was used as a noninvasive and label-free tool to detect and quantify the extent of the cartilage recovery. Two cartilage injury models were established in the outer ears of rabbits that created a different extent of cartilage recovery based on the presence or absence of the perichondrium. High-resolution NLOM images were used to measure cartilage repair, specifically through spectral analysis and image texture. In contrast to a wound lacking a perichondrium, wounds with intact perichondria demonstrated significantly larger TPEF signals from cells and matrix, coarser texture indicating the more deposition of type I collagen. Spectral analysis of cells and matrix can reveal the matrix properties and cell growth. In addition, texture analysis of NLOM images showed significant differences in the distribution of cells and matrix of repaired tissues with or without perichondrium. Specifically, the decay length of autocorrelation coefficient based on TPEF images is 11.2 ± 1.1 in Wound 2 (with perichondrium) and 7.5 ± 2.0 in Wound 1 (without perichondrium), indicating coarser image texture and faster growth of cells in repaired tissues with perichondrium (p < 0.05). Moreover, the decay length of autocorrelation coefficient based on collagen SHG images also showed significant difference between Wound 2 and 1 (16.2 ± 1.2 vs. 12.2 ± 2.1, p < 0.05), indicating coarser image texture and faster deposition of collagen in repaired tissues with perichondrium (Wound 2). These findings suggest that NLOM is an ideal tool for studying cartilage repair, with potential applications in clinical medicine. NLOM can capture macromolecular details and distinguish between different extents of cartilage repair without the need for labelling agents.

  19. New iterative method for fractional gas dynamics and coupled Burger's equations.

    PubMed

    Al-Luhaibi, Mohamed S

    2015-01-01

    This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger's equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.

  20. New Iterative Method for Fractional Gas Dynamics and Coupled Burger's Equations

    PubMed Central

    2015-01-01

    This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger's equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations. PMID:25884018

  1. 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

  2. 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.

  3. 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}

  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. 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).

  6. 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

  7. Analytical and numerical validation for solving the fractional Klein-Gordon equation using the fractional complex transform and variational iteration methods

    NASA Astrophysics Data System (ADS)

    Khader, M. M.; Adel, M.

    2016-09-01

    In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given.

  8. Universal fractional map and cascade of bifurcations type attractors.

    PubMed

    Edelman, M

    2013-09-01

    We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal α-Family of Maps depending on a single parameter α>0, which is the order of the fractional derivative in the nonlinear fractional differential equation describing a system experiencing periodic kicks. We consider two particular α-families corresponding to the Standard and Logistic Maps. For fractional α<2 in the area of parameter values of the transition through the period doubling cascade of bifurcations from regular to chaotic motion in regular dynamics corresponding fractional systems demonstrate a new type of attractors--cascade of bifurcations type trajectories.

  9. 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

  10. 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.

  11. Free spectral range optimization of return-to-zero differential phase-shift keyed demodulation in 40 Gbit/s nonlinear transmission.

    PubMed

    Li, Xiaolin; Zhang, Fan; Zhang, Xiaoru; Zhang, Dechao; Chen, Zhangyuan; Xu, Anshi

    2008-02-01

    For differential decoding, direct detection of DPSK signal needs a delay line interferometer with a free spectral range normally equal to the transmitted bit-rate. We numerically demonstrate that free spectral range optimization can increase tolerance to fiber Kerr nonlinearities for 40 Gbit/s RZ-DPSK transmission, especially for multi-format (RZ-DPSK and RZ-OOK) systems, in which Kerr nonlinearities is quite serious mainly due to cross-phase modulation. The optimal delay time of the delay line interferometer in DPSK signal demodulation is shorter than one bit-period. Joint optimization of free spectral range and optical filter bandwidth will further enhance system tolerance to nonlinear transmission.

  12. 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

  13. 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.

  14. 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.

  15. Existence and uniqueness of solutions to a class of nonlinear-operator-differential equations arising in automated spaceship navigation

    NASA Technical Reports Server (NTRS)

    Bogdan, V. M.

    1981-01-01

    A proof is given of the existence and uniqueness of the solution to the automatic control problem with a nonlinear state equation of the form y' = f(t,y,u) and nonlinear operator controls u = U(y) acting onto the state function y which satisfies the initial condition y(t) = x(t) for t or = 0.

  16. 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.

  17. 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.

  18. Differential sensitivity of two predominant stromal progenitor cell subpopulations in bone marrow to single and fractionated radiation doses

    SciTech Connect

    Kolesnikova, A.I.; Konoplyannikov, A.G.; Hendry, J.H.

    1995-12-01

    The sensitivity of fibroblastoid precursor cells in rat bone marrow to single and fractionated doses of {gamma} rays delivered in vivo was measured. In vitro colonies were classified as being compact or diffuse, and the progenitor cells for both types were slowly cycling in vivo (survival levels after exposure to hydroxyurea were 90 {+-} 6% and 93 {+-} 11%, respectively). The progenitor cells forming diffuse colonies were more resistant (D{sub o} = 1.39 Gy) than those forming compact colonies (D{sub o} = 0.76 Gy). The fractionation sensitivities were characterized by an {alpha}/{beta} ratio of 12.7 {+-} 5.5 Gy for diffuse colonies and 4.5 {+-} 3.0 Gy for compact colonies, respectively. The progenitor cells forming diffuse colonies may contribute more to long-term regeneration after high doses in vivo. 15 refs., 2 figs., 1 tab.

  19. 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

  20. 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.

  1. Establishment of subcellular fractionation techniques to monitor the intracellular fate of polymer therapeutics I. Differential centrifugation fractionation B16F10 cells and use to study the intracellular fate of HPMA copolymer - doxorubicin.

    PubMed

    Seib, F Philipp; Jones, Arwyn T; Duncan, Ruth

    2006-07-01

    Polymer therapeutics are being designed for lysosomotropic, endosomotropic and transcellular drug delivery. Their appropriate intracellular routing is thus crucial for successful use. For example, polymer-anticancer drug conjugates susceptible to lysosomal enzyme degradation will never deliver their drug payload unless they encounter the appropriate activating enzymes. Many studies use confocal microscopy to monitor intracellular fate, but there is a pressing need for more quantitative methods able to define intracellular compartmentation over time. Only then will it be possible to optimise the next generation of polymer therapeutics for specific applications. The aim of this study was to establish a subcellular fractionation method for B16F10 murine melanoma cells and subsequently to use it to define the intracellular trafficking of N-(2-hydroxyproplylmethacrylamide) (HPMA) copolymer-bound doxorubicin (PK1). Free doxorubicin was used as a reference. The cell cracker method was used to achieve cell breakage and optimised to reproducibly achieve approximately 90% breakage efficiency. This ensured that subsequent subcellular fractionation experiments were representative for the whole cell population. To characterise the subcellular fractions obtained by differential centrifugation, DNA (nuclei), succinate dehydrogenase (mitochondria), N-acetyl-beta-glucosaminidase (lysosomes), alkaline phosphatase (plasma membrane) and lactate dehydrogenase (cytosol) were selected as markers and their assay was carefully validated. The relative specific activity (RSA) of the fractions obtained from B16F10 cells were: nuclei (2.2), mitochondria (4.1), lysosomes (3.7) and cytosol (2.5). When used to study the intracellular distribution at non-toxic concentrations of PK1 and doxorubicin, time-dependent accumulation of PK1 in lysosomes was evident and the expected nuclear localisation of free doxorubicin was seen. Live cell fluorescence microscopy and confocal co-localisation studies

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

    PubMed

    Duttenhoefer, Fabian; de Freitas, Rafael Lara; Loibl, Markus; Bittermann, Gido; Richards, R Geoff; 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

  3. 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

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. 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

  9. 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.

  10. 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

  11. Microbial communities in liquid and fiber fractions of food waste digestates are differentially resistant to inhibition by ammonia.

    PubMed

    Peng, Wei; Lü, Fan; Shao, Liming; He, Pinjing

    2015-04-01

    The effect of different concentrations of ammonia (1.0-7.0 g/L) during mesophilic anaerobic digestion with fiber or liquid digestate as inoculum was examined. Evolution of microbial community within fiber and liquid digestates was quantitatively assessed by the intact lipid analysis methods and qualitatively by DNA fingerprint methods in order to determine their resistance to ammonia inhibition. The results showed that an increased level of total ammonia nitrogen prolonged the lag phase of fiber digestates while reduced the metabolic rate of liquid digestates. Fiber digestates had 19.6-50.9-fold higher concentrations of phospholipid fatty acids (PLFA) compared to liquid digestates, whereas concentrations of phospholipid ether lipids (PLEL) in the fiber digestates were only 2.91-17.6-fold higher compared to liquid digestates. Although the cell concentration in liquid fraction was far lower than that in the fiber one, the ammonia-resistant ability and the methanization efficiency of the liquid digestate was superior to the fiber digestate. The bacterial profiles were affected more by the type of digestate inoculum compared to the concentration of ammonia. Principal component analysis indicated that the lipids technique was superior to the DNA technique for bacterial quantification but detected less archaeal diversity. PMID:25661818

  12. 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.

  13. 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.

  14. 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

  15. Measurement of the Differential Branching Fraction and Forward-Backward Asymmetry for B->K{sup (*)}l{sup +}l{sup -}

    SciTech Connect

    Wei, J.-T.; Chang, P.; Chang, Y.-W.; Chao, Y.; Chen, K.-F.; Chiang, C.-C.; Hou, W.-S.; Shiu, J.-G.; Wang, C. C.; Wang, M.-Z.; Adachi, I.; Dalseno, J.; Hazumi, M.; Itoh, R.; Iwasaki, Y.; Katayama, N.; Kichimi, H.; Krokovny, P.; Nakao, M.; Nishida, S.

    2009-10-23

    We study B->K{sup (*)}l{sup +}l{sup -} decays (l=e, mu) based on a data sample of 657x10{sup 6} BB pairs collected with the Belle detector at the KEKB e{sup +}e{sup -} collider. We report the differential branching fraction, isospin asymmetry, K* polarization, and the forward-backward asymmetry (A{sub FB}) as functions of q{sup 2}=M{sub ll}{sup 2}c{sup 2}. The fitted A{sub FB} spectrum exceeds the standard model expectation by 2.7 standard deviations. The measured branching fractions are B(B->K*l{sup +}l{sup -})=(10.7{sub -1.0}{sup +1.1}+-0.9)x10{sup -7} and B(B->Kl{sup +}l{sup -})=(4.8{sub -0.4}{sup +0.5}+-0.3)x10{sup -7}, where the first errors are statistical and the second are systematic, with the muon to electron ratios R{sub K*}=0.83+-0.17+-0.08 and R{sub K}=1.03+-0.19+-0.06.

  16. 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.

  17. Chemical and isotopic fractionation of wet andesite in a temperature gradient: Experiments and models suggesting a new mechanism of magma differentiation

    NASA Astrophysics Data System (ADS)

    Huang, F.; Lundstrom, C. C.; Glessner, J.; Ianno, A.; Boudreau, A.; Li, J.; Ferré, E. C.; Marshak, S.; DeFrates, J.

    2009-02-01

    Piston-cylinder experiments were conducted to investigate the behavior of partially molten wet andesite held within an imposed temperature gradient at 0.5 GPa. In one experiment, homogenous andesite powder (USGS rock standard AGV-1) with 4 wt.% H 2O was sealed in a double capsule assembly for 66 days. The temperature at one end of this charge was held at 950 °C, and the temperature at the other end was kept at 350 °C. During the experiment, thermal migration (i.e., diffusion in a thermal gradient) took place, and the andesite underwent compositional and mineralogical differentiation. The run product can be broadly divided into three portions: (1) the top third, at the hot end, contained 100% melt; (2) the middle-third contained crystalline phases plus progressively less melt; and (3) the bottom third, at the cold end, consisted of a fine-grained, almost entirely crystalline solid of granitic composition. Bulk major- and trace-element compositions change down temperature gradient, reflecting the systematic change in modal mineralogy. These changes mimic differentiation trends produced by fractional crystallization. The change in composition throughout the run product indicates that a fully connected hydrous silicate melt existed throughout the charge, even in the crystalline, cold bottom region. Electron Backscatter Diffraction analysis of the run product indicates that no preferred crystallographic orientation of minerals developed in the run product. However, a significant anisotropy of magnetic susceptibility was observed, suggesting that new crystals of magnetite were elongated in the direction of the thermal gradient. Further, petrographic observation reveals alignment of hornblende parallel to the thermal gradient. Finally, the upper half of the run product shows large systematic variations in Fe-Mg isotopic composition reflecting thermal diffusion, with the hot end systematically enriched in light isotopes. The overall δ 56Fe IRMM-14 and δ 26Mg DSM-3

  18. 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…

  19. 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

  20. 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.

  1. Bifurcation characteristics of fractional reaction-diffusion systems

    NASA Astrophysics Data System (ADS)

    Datsko, Bohdan; Gafiychuk, Vasyl; Luchko, Yuri

    2012-11-01

    Anomalous behavior of many complex heterogeneous systems is known to be adequate modeled with the fractional differential equations and in particular with the fractional reaction-diffusion systems (FRDS). In this article, a generalized reaction-diffusion model in form of a system of nonlinear fractional partial differential equations is considered. It is shown that orders of the fractional derivatives contained in the FRDS are new bifurcation parameters that can change stability both of the spatially-homogeneous and of the spatially-nonhomogeneous stationary solutions. A general principle of linear stability for FRDS is formulated. The results of linear stability analysis are confirmed by computer simulations of some basic FRDS with classical nonlinearities. It is shown that stability of steady state solutions of FRDS and their evolution are mainly determined by the orders of the fractional derivatives and the eigenvalue spectrum of the linearized systems. Moreover, new types of spatiotemporal solutions and new mechanisms of pattern formation can be observed in FRDS because of new bifurcation types. Characteristic plots of evolution of steady state solutions for basic time-fractional reaction-diffusion systems are presented.

  2. 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...

  3. 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

  4. Measurement of the D0→π-e+νe differential decay branching fraction as a function of q2 and study of form factor parametrizations

    NASA Astrophysics Data System (ADS)

    Lees, J. P.; Poireau, V.; Tisserand, V.; Grauges, E.; Palano, A.; Eigen, G.; Stugu, B.; Brown, D. N.; Kerth, L. T.; Kolomensky, Yu. G.; Lee, M. J.; Lynch, G.; Koch, H.; Schroeder, T.; Hearty, C.; Mattison, T. S.; McKenna, J. A.; So, R. Y.; Khan, A.; Blinov, V. E.; Buzykaev, A. R.; Druzhinin, V. P.; Golubev, V. B.; Kravchenko, E. A.; Onuchin, A. P.; Serednyakov, S. I.; Skovpen, Yu. I.; Solodov, E. P.; Todyshev, K. Yu.; Lankford, A. J.; Mandelkern, M.; Dey, B.; Gary, J. W.; Long, O.; Campagnari, C.; Franco Sevilla, M.; Hong, T. M.; Kovalskyi, D.; Richman, J. D.; West, C. A.; Eisner, A. M.; Lockman, W. S.; Panduro Vazquez, W.; Schumm, B. A.; Seiden, A.; Chao, D. S.; Cheng, C. H.; Echenard, B.; Flood, K. T.; Hitlin, D. G.; Miyashita, T. S.; Ongmongkolkul, P.; Porter, F. C.; Röhrken, M.; Andreassen, R.; Huard, Z.; Meadows, B. T.; Pushpawela, B. G.; Sokoloff, M. D.; Sun, L.; Bloom, P. C.; Ford, W. T.; Gaz, A.; Smith, J. G.; Wagner, S. R.; Ayad, R.; Toki, W. H.; Spaan, B.; Bernard, D.; Verderi, M.; Playfer, S.; Bettoni, D.; Bozzi, C.; Calabrese, R.; Cibinetto, G.; Fioravanti, E.; Garzia, I.; Luppi, E.; Piemontese, L.; Santoro, V.; Calcaterra, A.; de Sangro, R.; Finocchiaro, G.; Martellotti, S.; Patteri, P.; Peruzzi, I. M.; Piccolo, M.; Rama, M.; Zallo, A.; Contri, R.; Lo Vetere, M.; Monge, M. R.; Passaggio, S.; Patrignani, C.; Robutti, E.; Bhuyan, B.; Prasad, V.; Adametz, A.; Uwer, U.; Lacker, H. M.; Dauncey, P. D.; Mallik, U.; Chen, C.; Cochran, J.; Prell, S.; Ahmed, H.; Gritsan, A. V.; Arnaud, N.; Davier, M.; Derkach, D.; Grosdidier, G.; Le Diberder, F.; Lutz, A. M.; Malaescu, B.; Roudeau, P.; Stocchi, A.; Wormser, G.; Lange, D. J.; Wright, D. M.; Coleman, J. P.; Fry, J. R.; Gabathuler, E.; Hutchcroft, D. E.; Payne, D. J.; Touramanis, C.; Bevan, A. J.; di Lodovico, F.; Sacco, R.; Cowan, G.; Bougher, J.; Brown, D. N.; Davis, C. L.; Denig, A. G.; Fritsch, M.; Gradl, W.; Griessinger, K.; Hafner, A.; Schubert, K. R.; Barlow, R. J.; Lafferty, G. D.; Cenci, R.; Hamilton, B.; Jawahery, A.; Roberts, D. A.; Cowan, R.; Sciolla, G.; Cheaib, R.; Patel, P. M.; Robertson, S. H.; Neri, N.; Palombo, F.; Cremaldi, L.; Godang, R.; Sonnek, P.; Summers, D. J.; Simard, M.; Taras, P.; de Nardo, G.; Onorato, G.; Sciacca, C.; Martinelli, M.; Raven, G.; Jessop, C. P.; Losecco, J. M.; Honscheid, K.; Kass, R.; Feltresi, E.; Margoni, M.; Morandin, M.; Posocco, M.; Rotondo, M.; Simi, G.; Simonetto, F.; Stroili, R.; Akar, S.; Ben-Haim, E.; Bomben, M.; Bonneaud, G. R.; Briand, H.; Calderini, G.; Chauveau, J.; Leruste, Ph.; Marchiori, G.; Ocariz, J.; Biasini, M.; Manoni, E.; Pacetti, S.; Rossi, A.; Angelini, C.; Batignani, G.; Bettarini, S.; Carpinelli, M.; Casarosa, G.; Cervelli, A.; Chrzaszcz, M.; Forti, F.; Giorgi, M. A.; Lusiani, A.; Oberhof, B.; Paoloni, E.; Perez, A.; Rizzo, G.; Walsh, J. J.; Lopes Pegna, D.; Olsen, J.; Smith, A. J. S.; Faccini, R.; Ferrarotto, F.; Ferroni, F.; Gaspero, M.; Li Gioi, L.; Pilloni, A.; Piredda, G.; Bünger, C.; Dittrich, S.; Grünberg, O.; Hess, M.; Leddig, T.; Voß, C.; Waldi, R.; Adye, T.; Olaiya, E. O.; Wilson, F. F.; Emery, S.; Vasseur, G.; Anulli, F.; Aston, D.; Bard, D. J.; Cartaro, C.; Convery, M. R.; Dorfan, J.; Dubois-Felsmann, G. P.; Dunwoodie, W.; Ebert, M.; Field, R. C.; Fulsom, B. G.; Graham, M. T.; Hast, C.; Innes, W. R.; Kim, P.; Leith, D. W. G. S.; Lewis, P.; Lindemann, D.; Luitz, S.; Luth, V.; Lynch, H. L.; Macfarlane, D. B.; Muller, D. R.; Neal, H.; Perl, M.; Pulliam, T.; Ratcliff, B. N.; Roodman, A.; Salnikov, A. A.; Schindler, R. H.; Snyder, A.; Su, D.; Sullivan, M. K.; Va'Vra, J.; Wisniewski, W. J.; Wulsin, H. W.; Purohit, M. V.; White, R. M.; Wilson, J. R.; Randle-Conde, A.; Sekula, S. J.; Bellis, M.; Burchat, P. R.; Puccio, E. M. T.; Alam, M. S.; Ernst, J. A.; Gorodeisky, R.; Guttman, N.; Peimer, D. R.; Soffer, A.; Spanier, S. M.; Ritchie, J. L.; Ruland, A. M.; Schwitters, R. F.; Wray, B. C.; Izen, J. M.; Lou, X. C.; Bianchi, F.; de Mori, F.; Filippi, A.; Gamba, D.; Lanceri, L.; Vitale, L.; Martinez-Vidal, F.; Oyanguren, A.; Villanueva-Perez, P.; Albert, J.; Banerjee, Sw.; Beaulieu, A.; Bernlochner, F. U.; Choi, H. H. F.; King, G. J.; Kowalewski, R.; Lewczuk, M. J.; Lueck, T.; Nugent, I. M.; Roney, J. M.; Sobie, R. J.; Tasneem, N.; Gershon, T. J.; Harrison, P. F.; Latham, T. E.; Band, H. R.; Dasu, S.; Pan, Y.; Prepost, R.; Wu, S. L.; Babar Collaboration

    2015-03-01

    Based on a sample of 500 million e+e-→c c ¯ events recorded by the BABAR detector at c.m. energies of close to 10.6 GeV, we report on a study of the decay D0→π-e+νe. We measure the ratio of branching fractions, RD=B (D0→π-e+νe)/B (D0→K-π+)=0.0713 ±0.001 7stat±0.002 4syst , and use the present world average for B (D0→K-π+) to obtain B (D0→π-e+νe)=(2.770 ±0.06 8stat±0.09 2syst±0.03 7ext)×1 0-3 where the third error accounts for the uncertainty on the branching fraction for the reference channel. The measured dependence of the differential branching fraction on q2, the four-momentum transfer squared between the D and the π meson, is compared to various theoretical predictions for the hadronic form factor, f+,Dπ(q2), and the normalization |Vc d| ×f+,Dπ(q2=0 )=0.1374 ±0.003 8stat±0.002 2syst±0.000 9ext . is extracted from a fit to data. Using the most recent LQCD prediction of f+,Dπ(q2=0 )=0.666 ±0.029 , we obtain |Vc d| =0.206 ±0.00 7exp±0.00 9LQCD . Assuming, instead, |Vc d| =|Vu s| =0.2252 ±0.0009 , we obtain f+,Dπ(q2=0 )=0.610 ±0.02 0exp±0.00 5ext . The q2 dependence of f+,Dπ(q2) is compared to a variety of multipole parametrizations. This information is applied to B0→π-e+νe decays and, combined with an earlier B0→π-e+νe measurement by BABAR, is used to derive estimates of |Vu b|.

  5. Experimental observation of fractional echoes

    NASA Astrophysics Data System (ADS)

    Karras, G.; Hertz, E.; Billard, F.; Lavorel, B.; Siour, G.; Hartmann, J.-M.; Faucher, O.; Gershnabel, Erez; Prior, Yehiam; Averbukh, Ilya Sh.

    2016-09-01

    We report the observation of fractional echoes in a double-pulse excited nonlinear system. Unlike standard echoes, which appear periodically at delays which are integer multiples of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of CO2 molecules excited by a pair of femtosecond laser pulses.

  6. Fractional anisotropy shows differential reduction in frontal-subcortical fiber bundles—A longitudinal MRI study of 76 middle-aged and older adults

    PubMed Central

    Vik, Alexandra; Hodneland, Erlend; Haász, Judit; Ystad, Martin; Lundervold, Astri J.; Lundervold, Arvid

    2015-01-01

    Motivated by the frontal- and white matter (WM) retrogenesis hypotheses and the assumptions that fronto-striatal circuits are especially vulnerable in normal aging, the goal of the present study was to identify fiber bundles connecting subcortical nuclei and frontal areas and obtain site-specific information about age related fractional anisotropy (FA) changes. Multimodal magnetic resonance image acquisitions [3D T1-weighted and diffusion weighted imaging (DWI)] were obtained from healthy older adults (N = 76, range 49–80 years at inclusion) at two time points, 3 years apart. A subset of the participants (N = 24) was included at a third time-point. In addition to the frontal-subcortical fibers, the anterior callosal fiber (ACF) and the corticospinal tract (CST) was investigated by its mean FA together with tract parameterization analysis. Our results demonstrated fronto-striatal structural connectivity decline (reduced FA) in normal aging with substantial inter-individual differences. The tract parameterization analysis showed that the along tract FA profiles were characterized by piece-wise differential changes along their extension rather than being uniformly affected. To the best of our knowledge, this is the first longitudinal study detecting age-related changes in frontal-subcortical WM connections in normal aging. PMID:26029102

  7. 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.

  8. 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.

  9. 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.

  10. Wavelet operational matrix method for solving the Riccati differential equation

    NASA Astrophysics Data System (ADS)

    Li, Yuanlu; Sun, Ning; Zheng, Bochao; Wang, Qi; Zhang, Yingchao

    2014-03-01

    A Haar wavelet operational matrix method (HWOMM) was derived to solve the Riccati differential equations. As a result, the computation of the nonlinear term was simplified by using the Block pulse function to expand the Haar wavelet one. The proposed method can be used to solve not only the classical Riccati differential equations but also the fractional ones. The capability and the simplicity of the proposed method was demonstrated by some examples and comparison with other methods.

  11. On the influence of local fluctuations in volume fraction of constituents on the effective properties of nonlinear composites. Application to porous materials

    NASA Astrophysics Data System (ADS)

    Gărăjeu, M.; Suquet, P.

    2007-04-01

    Composite materials often exhibit local fluctuations in the volume fraction of their individual constituents. This paper studies the influence of such small fluctuations on the effective properties of composites. A general asymptotic expansion of these properties in terms of powers of the amplitude of the fluctuations is given first. Then, this general result is applied to porous materials. As is well-known, the effective yield surface of ductile voided materials is accurately described by Gurson's criterion. Suitable extensions for viscoplastic solids have also been proposed. The question addressed in the present study pertains to nonuniform distributions of voids in a typical volume element or in other words to the presence of matrix-rich and pore-rich zones in the material. It is shown numerically and analytically that such deviations from a uniform distribution result in a weakening of the macroscopic carrying capacity of the material.

  12. Sieve Estimation of Constant and Time-Varying Coefficients in Nonlinear Ordinary Differential Equation Models by Considering Both Numerical Error and Measurement Error

    PubMed Central

    Xue, Hongqi; Miao, Hongyu; Wu, Hulin

    2010-01-01

    This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is investigated in this study. A numerical algorithm such as the Runge–Kutta method is used to approximate the ODE solution. The asymptotic properties are established for the proposed estimators considering both numerical error and measurement error. The B-spline is used to approximate the time-varying coefficients, and the corresponding asymptotic theories in this case are investigated under the framework of the sieve approach. Our results show that if the maximum step size of the p-order numerical algorithm goes to zero at a rate faster than n−1/(p∧4), the numerical error is negligible compared to the measurement error. This result provides a theoretical guidance in selection of the step size for numerical evaluations of ODEs. Moreover, we have shown that the numerical solution-based NLS estimator and the sieve NLS estimator are strongly consistent. The sieve estimator of constant parameters is asymptotically normal with the same asymptotic co-variance as that of the case where the true ODE solution is exactly known, while the estimator of the time-varying parameter has the optimal convergence rate under some regularity conditions. The theoretical results are also developed for the case when the step size of the ODE numerical solver does not go to zero fast enough or the numerical error is comparable to the measurement error. We illustrate our approach with both simulation studies and clinical data on HIV viral dynamics. PMID:21132064

  13. 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

  14. Technical Note: A measure of watershed nonlinearity II: re-introducing an IFP inverse fractional power transform for streamflow recession analysis

    NASA Astrophysics Data System (ADS)

    Ding, J. Y.

    2013-12-01

    This note illustrates, in the context of Brutsaert-Nieber (1977) model: -dQ/dt = aQb, the utility of a newly rediscovered inverse fractional power (IFP) transform of the flow rates. This method of streamflow recession analysis dates back a half-century. The IFP transform Δb on an operand Q is defined as Δb Q = 1/Qb-1. Brutsaert-Nieber model by IFP transform thus becomes: ΔbQ(t) = ΔbQ(0) + (b-1) at, if b ≠ 1. The IFP transformed recession curve appears as a straight line on a semi-IFP plot. The method has both the advantage of being independent of the size of computational time step, and the disadvantage of being depending on the parameter b value. This is used to calibrate the Brutsaert-Nieber recession flow model in which b is a slope (or shape) parameter, and a is an intercept (or a scale parameter). It is applied to four observed events on the Spoon River in Illinois (4237 km2). The results show that the IFP transform method gives a narrower range of parameter b values than the regression method in a recession plot. Theoretically, an IFP transformed recession curve for large watersheds falls between those performed by the reciprocal of the cubic root (RoCR) transform and the reciprocal of the square root (RoSR) one. In general, the forgotten IFP transform method merits a fresh look, especially for hillslopes and zero-order catchments, the building blocks of a watershed system. In particular, because of its origin in hillslope hydrology, the 1-parameter RoSR transform need be falsified or verified for application to headwater catchments.

  15. A Novel Scheme for Optimal Control of a Nonlinear Delay Differential Equations Model to Determine Effective and Optimal Administrating Chemotherapy Agents in Breast Cancer

    PubMed Central

    Ramezanpour, HR; Setayeshi, S; Akbari, ME

    2011-01-01

    Background Determining the optimal and effective scheme for administrating the chemotherapy agents in breast cancer is the main goal of this scientific research. The most important issue here is the amount of drug or radiation administrated in chemotherapy and radiotherapy for increasing patient's survival. This is because in these cases, the therapy not only kills the tumor cells, but also kills some of the healthy tissues and causes serious damages. In this paper we investigate optimal drug scheduling effect for breast cancer model which consist of nonlinear ordinary differential time-delay equations. Methods In this paper, a mathematical model of breast cancer tumors is discussed and then optimal control theory is applied to find out the optimal drug adjustment as an input control of system. Finally we use Sensitivity Approach (SA) to solve the optimal control problem. Results The goal of this paper is to determine optimal and effective scheme for administering the chemotherapy agent, so that the tumor is eradicated, while the immune systems remains above a suitable level. Simulation results confirm the effectiveness of our proposed procedure. Conclusion In this paper a new scheme is proposed to design a therapy protocol for chemotherapy in Breast Cancer. In contrast to traditional pulse drug delivery, a continuous process is offered and optimized, according to the optimal control theory for time-delay systems. PMID:26322192

  16. MORE: mixed optimization for reverse engineering--an application to modeling biological networks response via sparse systems of nonlinear differential equations.

    PubMed

    Sambo, Francesco; de Oca, Marco A Montes; Di Camillo, Barbara; Toffolo, Gianna; Stützle, Thomas

    2012-01-01

    Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.

  17. Fractional diffusion on bounded domains

    SciTech Connect

    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.

  18. 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.

  19. Fractional randomness

    NASA Astrophysics Data System (ADS)

    Tapiero, Charles S.; Vallois, Pierre

    2016-11-01

    The premise of this paper is that a fractional probability distribution is based on fractional operators and the fractional (Hurst) index used that alters the classical setting of random variables. For example, a random variable defined by its density function might not have a fractional density function defined in its conventional sense. Practically, it implies that a distribution's granularity defined by a fractional kernel may have properties that differ due to the fractional index used and the fractional calculus applied to define it. The purpose of this paper is to consider an application of fractional calculus to define the fractional density function of a random variable. In addition, we provide and prove a number of results, defining the functional forms of these distributions as well as their existence. In particular, we define fractional probability distributions for increasing and decreasing functions that are right continuous. Examples are used to motivate the usefulness of a statistical approach to fractional calculus and its application to economic and financial problems. In conclusion, this paper is a preliminary attempt to construct statistical fractional models. Due to the breadth and the extent of such problems, this paper may be considered as an initial attempt to do so.

  20. The residue harmonic balance for fractional order van der Pol like oscillators

    NASA Astrophysics Data System (ADS)

    Leung, A. Y. T.; Yang, H. X.; Guo, Z. J.

    2012-02-01

    When seeking a solution in series form, the number of terms needed to satisfy some preset requirements is unknown in the beginning. An iterative formulation is proposed so that when an approximation is available, the number of effective terms can be doubled in one iteration by solving a set of linear equations. This is a new extension of the Newton iteration in solving nonlinear algebraic equations to solving nonlinear differential equations by series. When Fourier series is employed, the method is called the residue harmonic balance. In this paper, the fractional order van der Pol oscillator with fractional restoring and damping forces is considered. The residue harmonic balance method is used for generating the higher-order approximations to the angular frequency and the period solutions of above mentioned fractional oscillator. The highly accurate solutions to angular frequency and limit cycle of the fractional order van der Pol equations are obtained analytically. The results that are obtained reveal that the proposed method is very effective for obtaining asymptotic solutions of autonomous nonlinear oscillation systems containing fractional derivatives. The influence of the fractional order on the geometry of the limit cycle is investigated for the first time.

  1. Differential protection among fractionated blueberry polyphenolic families against DA-, Abeta(42)- and LPS-induced decrements in Ca(2+) buffering in primary hippocampal cells.

    PubMed

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

    2010-07-28

    It has been postulated that at least part of the loss of cognitive function in aging may be the result of deficits in Ca(2+) 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 Abeta(42)-induced deficits in CAR in primary hippocampal neuronal cells (HNC) were antagonized by BB extract, and (OX/INF) signaling was reduced. The 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, 0.1 mM), amyloid beta (Abeta(42), 25 muM) or lipopolysaccharide (LPS, 1 microg/mL). The results indicated that the degree of protection against deficits in CAR varied as a function of the stressor and was generally greater against Abeta(42) and LPS than DA. The whole BB, anthocyanin (ANTH), and PRE-C18 fractions offered the greatest protection, whereas 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 molecular weight) fraction offered the best protection against LPS and Abeta(42) but were less effective against DA-induced ROS. The high and low molecular weight 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

  2. Lyapunov functions for fractional order systems

    NASA Astrophysics Data System (ADS)

    Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A.; Gallegos, Javier A.

    2014-09-01

    A new lemma for the Caputo fractional derivatives, when 0<α<1, is proposed in this paper. This result has proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the stability of many fractional order systems, which can be nonlinear and time varying.

  3. A general fractional-order dynamical network: Synchronization behavior and state tuning

    NASA Astrophysics Data System (ADS)

    Wang, Junwei; Xiong, Xiaohua

    2012-06-01

    A general fractional-order dynamical network model for synchronization behavior is proposed. Different from previous integer-order dynamical networks, the model is made up of coupled units described by fractional differential equations, where the connections between individual units are nondiffusive and nonlinear. We show that the synchronous behavior of such a network cannot only occur, but also be dramatically different from the behavior of its constituent units. In particular, we find that simple behavior can emerge as synchronized dynamics although the isolated units evolve chaotically. Conversely, individually simple units can display chaotic attractors when the network synchronizes. We also present an easily checked criterion for synchronization depending only on the eigenvalues distribution of a decomposition matrix and the fractional orders. The analytic results are complemented with numerical simulations for two networks whose nodes are governed by fractional-order Lorenz dynamics and fractional-order Rössler dynamics, respectively.

  4. 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

  5. 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

  6. 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.

  7. Stability Analysis of Distributed Order Fractional Chen System

    PubMed Central

    Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.

    2013-01-01

    We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508

  8. 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.

  9. 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

  10. 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

  11. 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

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

    PubMed

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

    2012-07-21

    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)], 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 less than two

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation.

    PubMed

    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.

  19. 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.

  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. Linearization of Conservative Nonlinear Oscillators

    ERIC Educational Resources Information Center

    Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.

    2009-01-01

    A linearization method 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 which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

  2. Generalized Nonlinear Yule Models

    NASA Astrophysics Data System (ADS)

    Lansky, Petr; Polito, Federico; Sacerdote, Laura

    2016-10-01

    With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

  3. 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.

  4. 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

  5. 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.

  6. 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.

  7. [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.

  8. One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1 < q < 2

    PubMed Central

    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

  9. 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

  10. 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.

  11. 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.

  12. 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

  13. 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

  14. 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.

  15. [Fractionated P-bilirubins].

    PubMed

    Schou, C S; Mortensen, H

    1989-08-14

    A diazo-based dry film technique for the estimation of different bilirubins in plasma is now available. This procedure separates bilirubins from icteric sera into three separate fractions: bilirubin (unconjugated), bilirubin-glucuronides (mono + diglucuronide) and bilirubin-albumin. In newborns with prolonged jaundice classification of hyperbilirubinemia is of importance for choice of treatment. While binding of bilirubin and bilirubin-glucuronides to albumin is non covalent, reversible, bilirubin-albumin appears to be firmly associated with albumin by covalent bonds. This causes delayed clearance of this bilirubin fraction from plasma as the half-life of albumin is approximately 18 days. Hence the substance concentration of bilirubin-albumin will decrease at a slower rate than will bilirubin and bilirubin-glucuronide, despite hepatobiliary recovery. Bilirubin-albumin may therefore prove of value in the differentiation between different clinical entities with hyperbilirubinemia. PMID:2773134

  16. 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

  17. Review of Some Promising Fractional Physical Models

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2013-04-01

    Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law nonlocality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods in the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of noninteger order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.

  18. 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.

  19. 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.

  20. Automatic Differentiation Package

    SciTech Connect

    Gay, David M.; Phipps, Eric; Bratlett, Roscoe

    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.

  1. Lie symmetry theorem of fractional nonholonomic systems

    NASA Astrophysics Data System (ADS)

    Sun, Yi; Chen, Ben-Yong; Fu, Jing-Li

    2014-11-01

    The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is established, and the fractional Lagrange equations are obtained by virtue of the d'Alembert—Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal transformations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.

  2. Nonlinear optics and nonlinear dynamics

    NASA Astrophysics Data System (ADS)

    Chen, C. H.

    1990-08-01

    The author was invited by the Institute of Atomic and Molecular Sciences, Academia Sinica, in Taiwan to give six lectures on nonlinear optics. The participants included graduate students, postdoctoral fellows, research staff, and professors from several research organizations and universities. Extensive discussion followed each lecture. Since both the Photophysics Group at Oak Ridge National Laboratory (ORNL) and Institute of Atomic and Molecular Sciences in Taiwan have been actively participating in nonlinear optics research, the discussions are very beneficial to ORNL programs. The author also visited several laboratories at IAMS to exchange research ideas on nonlinear optics.

  3. 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.

  4. Computing a numerical solution of two dimensional non-linear Schrödinger equation on complexly shaped domains by RBF based differential quadrature method

    NASA Astrophysics Data System (ADS)

    Golbabai, Ahmad; Nikpour, Ahmad

    2016-10-01

    In this paper, two-dimensional Schrödinger equations are solved by differential quadrature method. Key point in this method is the determination of the weight coefficients for approximation of spatial derivatives. Multiquadric (MQ) radial basis function is applied as test functions to compute these weight coefficients. Unlike traditional DQ methods, which were originally defined on meshes of node points, the RBFDQ method requires no mesh-connectivity information and allows straightforward implementation in an unstructured nodes. Moreover, the calculation of coefficients using MQ function includes a shape parameter c. A new variable shape parameter is introduced and its effect on the accuracy and stability of the method is studied. We perform an analysis for the dispersion error and different internal parameters of the algorithm are studied in order to examine the behavior of this error. Numerical examples show that MQDQ method can efficiently approximate problems in complexly shaped domains.

  5. 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.

  6. Nonlinear channelizer.

    PubMed

    In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D; Leung, Daniel; Liu, Norman; Meadows, Brian K; Gordon, Frank; Bulsara, Adi R; Palacios, Antonio

    2012-12-01

    The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.

  7. 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.

  8. Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

    NASA Astrophysics Data System (ADS)

    Wu, Yimin; Lv, Hui

    2016-08-01

    In this paper, we consider the control problem of a class of uncertain fractional-order chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm. We model the hysteresis by using a differential equation. Based on the fractional Lyapunov stability criterion and the backstepping algorithm procedures, an adaptive neural network controller is driven. No knowledge of the upper bound of the disturbance and system uncertainty is required in our controller, and the asymptotical convergence of the tracking error can be guaranteed. Finally, we give two simulation examples to confirm our theoretical results.

  9. 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.

  10. Adaptive fractionation therapy: II. Biological effective dose

    NASA Astrophysics Data System (ADS)

    Chen, Mingli; Lu, Weiguo; Chen, Quan; Ruchala, Kenneth; Olivera, Gustavo

    2008-10-01

    Radiation therapy is fractionized to differentiate the cell killing between the tumor and organ at risk (OAR). Conventionally, fractionation is done by dividing the total dose into equal fraction sizes. However, as the relative positions (configurations) between OAR and the tumor vary from fractions to fractions, intuitively, we want to use a larger fraction size when OAR and the tumor are far apart and a smaller fraction size when OAR and the tumor are close to each other. Adaptive fractionation accounts for variations of configurations between OAR and the tumor. In part I of this series, the adaptation minimizes the OAR (physical) dose and maintains the total tumor (physical) dose. In this work, instead, the adaptation is based on the biological effective dose (BED). Unlike the linear programming approach in part I, we build a fraction size lookup table using mathematical induction. The lookup table essentially describes the fraction size as a function of the remaining tumor BED, the OAR/tumor dose ratio and the remaining number of fractions. The lookup table is calculated by maximizing the expected survival of OAR and preserving the tumor cell kill. Immediately before the treatment of each fraction, the OAR-tumor configuration and thus the dose ratio can be obtained from the daily setup image, and then the fraction size can be determined by the lookup table. Extensive simulations demonstrate the effectiveness of our method compared with the conventional fractionation method.

  11. 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.

  12. 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.

  13. Nonlinear Systems.

    ERIC Educational Resources Information Center

    Seider, Warren D.; Ungar, Lyle H.

    1987-01-01

    Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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

  19. Fractionation of Subcellular Organelles.

    PubMed

    Graham, John M

    2015-12-01

    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.

  20. Fractional Derivatives in Dengue Epidemics

    NASA Astrophysics Data System (ADS)

    Pooseh, Shakoor; Rodrigues, Helena Sofia; Torres, Delfim F. M.

    2011-09-01

    We introduce the use of fractional calculus, i.e., the use of integrals and derivatives of non-integer (arbitrary) order, in epidemiology. The proposed approach is illustrated with an outbreak of dengue disease, which is motivated by the first dengue epidemic ever recorded in the Cape Verde islands off the coast of west Africa, in 2009. Numerical simulations show that in some cases the fractional models fit better the reality when compared with the standard differential models. The classical results are obtained as particular cases by considering the order of the derivatives to take an integer value.

  1. 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.

  2. Varieties of operator manipulation. [for solving differential equations and calculating finite differences

    NASA Technical Reports Server (NTRS)

    Doohovskoy, A.

    1977-01-01

    A change in MACSYMA syntax is proposed to accommodate the operator manipulators necessary to implement direct and indirect methods for the solution of differential equations, calculus of finite differences, and the fractional calculus, as well as their modern counterparts. To illustrate the benefits and convenience of this syntax extension, an example is given to show how MACSYMA's pattern-matching capability can be used to implement a particular set of operator identities which can then be used to obtain exact solutions to nonlinear differential equations.

  3. 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.

  4. Clinical Nonlinear Laser Imaging of Human Skin: A Review

    PubMed Central

    Pavone, Francesco Saverio

    2014-01-01

    Nonlinear optical microscopy has the potential of being used in vivo as a noninvasive imaging modality for both epidermal and dermal imaging. This paper reviews the capabilities of nonlinear microscopy as a noninvasive high-resolution tool for clinical skin inspection. In particular, we show that two-photon fluorescence microscopy can be used as a diagnostic tool for characterizing epidermal layers by means of a morphological examination. Additional functional information on the metabolic state of cells can be provided by measuring the fluorescence decay of NADH. This approach allows differentiating epidermal layers having different structural and cytological features and has the potential of diagnosing pathologies in a very early stage. Regarding therapy follow-up, we demonstrate that nonlinear microscopy could be successfully used for monitoring the effect of a treatment. In particular, combined two-photon fluorescence and second-harmonic generation microscopy were used in vivo for monitoring collagen remodeling after microablative fractional laser resurfacing and for quantitatively monitoring psoriasis on the basis of the morphology of epidermal cells and dermal papillae. We believe that the described microscopic modalities could find in the near future a stable place in a clinical dermatological setting for quantitative diagnostic purposes and as a monitoring method for various treatments. PMID:25250337

  5. Matrix fractional systems

    NASA Astrophysics Data System (ADS)

    Tenreiro Machado, J. A.

    2015-08-01

    This paper addresses the matrix representation of dynamical systems in the perspective of fractional calculus. Fractional elements and fractional systems are interpreted under the light of the classical Cole-Cole, Davidson-Cole, and Havriliak-Negami heuristic models. Numerical simulations for an electrical circuit enlighten the results for matrix based models and high fractional orders. The conclusions clarify the distinction between fractional elements and fractional systems.

  6. Nonlinear self-adjointness and conservation laws

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. H.

    2011-10-01

    The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness (definition 1) and quasi-self-adjointness introduced earlier by the author. It is shown that the equations possessing nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint form. For example, the heat equation ut - Δu = 0 becomes strictly self-adjoint after multiplying by u-1. Conservation laws associated with symmetries are given in an explicit form for all nonlinearly self-adjoint partial differential equations and systems.

  7. 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.

  8. 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.

  9. On abstract degenerate neutral differential equations

    NASA Astrophysics Data System (ADS)

    Hernández, Eduardo; O'Regan, Donal

    2016-10-01

    We introduce a new abstract model of functional differential equations, which we call abstract degenerate neutral differential equations, and we study the existence of strict solutions. The class of problems and the technical approach introduced in this paper allow us to generalize and extend recent results on abstract neutral differential equations. Some examples on nonlinear partial neutral differential equations are presented.

  10. 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.

  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. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  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. 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.

  20. 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

  1. Disordered Interactions and Fractional Quantum Hall States

    NASA Astrophysics Data System (ADS)

    Degottardi, Wade; Hafezi, Mohammad

    The possibility that topological ordered states may be realized in photonic systems has recently attracted a great deal of attention. Given the rich phenomenology of the fractional quantum Hall effect, the bosonic Laughlin states have been of particular focus in this context. These states are known to arise in strongly nonlinear photonic lattices with artificial gauge fields, where nonlinearities associated with the resonators mimic on-site interactions. These effective interaction strengths are not universal and are subject to spatial disorder. We present a detailed study of the stability of these states and what implications they have for experiments.

  2. 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

  3. 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

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  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 ring resonator: spatial pattern generation

    NASA Astrophysics Data System (ADS)

    Ivanov, Vladimir Y.; Lachinova, Svetlana L.; Irochnikov, Nikita G.

    2000-03-01

    We consider theoretically spatial pattern formation processes in a unidirectional ring cavity with thin layer of Kerr-type nonlinear medium. Our method is based on studying of two coupled equations. The first is a partial differential equation for temporal dynamics of phase modulation of light wave in the medium. It describes nonlinear interaction in the Kerr-type lice. The second is a free propagation equation for the intracavity field complex amplitude. It involves diffraction effects of light wave in the cavity.

  10. Concurrent processing in nonlinear structural stability

    NASA Technical Reports Server (NTRS)

    Darbhamulla, S. P.; Razzaq, Z.; Storaasli, O. O.

    1986-01-01

    A concurrent processing algorithm is developed for materially nonlinear stability analysis of imperfect columns with biaxial partial rotational end restraints. The algorithm for solving the governing nonlinear ordinary differential equations is implemented on a multiprocessor computer called the 'Finite Element Machine', developed at the NASA Langley Research Center. Numerical results are obtained on up to nine concurrent processors. A substantial computational gain is achieved in using the parallel processing approach.

  11. General purpose nonlinear system solver based on Newton-Krylov method.

    SciTech Connect

    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].

  12. 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

  13. The relative roles of boundary layer fractionation and homogeneous fractionation in cooling basaltic magma chambers

    NASA Astrophysics Data System (ADS)

    Kuritani, Takeshi

    2009-06-01

    In a cooling magma chamber, magmatic differentiation can proceed both by fractionation of crystals from the main molten part of the magma body (homogeneous fractionation) and by mixing of the main magma with fractionated melt derived from low-temperature mush zones (boundary layer fractionation). In this study, the relative roles of boundary layer fractionation and homogeneous fractionation in basaltic magma bodies were examined using a thermodynamics-based mass balance model. Model calculations show that boundary layer fractionation cannot be a dominant fractionation mechanism when magma chambers are located at low pressures (< ~ 50 MPa) or when magmas are less hydrous (< ~ 1 wt.%), such as mid-ocean ridge basalt and intraplate basalt, because of the low efficiency of melt transport from the mush zones to the main magma. Therefore, magmas evolve principally by homogeneous fractionation. If crystal-melt separation does not occur effectively in the main magma, the magma becomes crystal-rich in the early stages of magmatic evolution. On the other hand, boundary layer fractionation can occur effectively when magmas are hydrous (> ~ 2 wt.%), such as arc basalt, and the magma chambers are located at depth (> ~ 100 MPa). Because the melt derived from mush zones is enriched in alkalis and H 2O, crystallization from the main magma is suppressed by mixing with the mush melt as a consequence of depression of the liquidus temperature. Therefore, homogeneous fractionation is more effectively suppressed in magma chambers in which boundary layer fractionation is more active. If magmatic differentiation proceeds primarily by boundary layer fractionation, magmas can remain free of crystals for long periods during magmatic evolution.

  14. Fractional kinetics in multi-compartmental systems.

    PubMed

    Dokoumetzidis, Aristides; Magin, Richard; Macheras, Panos

    2010-10-01

    Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems. PMID

  15. Control design for a class of nonlinear parameter varying systems

    NASA Astrophysics Data System (ADS)

    Cai, Xiushan; Liu, Yang; Zhang, Wei

    2015-07-01

    Stabilisation for a class of one-sided Lipschitz nonlinear parameter varying systems is dealt with in this paper. First, the nonlinear parameter varying system is represented as a subsystem of a differential inclusion. Sufficient conditions for exponential stabilisation for the differential inclusion are given by solving linear matrix inequalities. Then a continuous control law is designed to stabilise the differential inclusion. It leads to stabilising the nonlinear parameter varying system. Finally, a simulation example is presented to show the validity and advantages of the proposed method.

  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. 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.

  18. State space approximation for general fractional order dynamic systems

    NASA Astrophysics Data System (ADS)

    Liang, Shu; Peng, Cheng; Liao, Zeng; Wang, Yong

    2014-10-01

    Approximations for general fractional order dynamic systems are of much theoretical and practical interest. In this paper, a new approximate method for fractional order integrator is proposed. The poles of the approximate model are unrelated to the order of integrator. This feature shows benefits on extending the algorithm to the systems containing various fractional orders. Then a unified approximate method is derived for general fractional order linear or nonlinear dynamic systems via combining the proposed new method with the distributed frequency model approach. Numerical examples are given to show the wide applicability of our method and to illustrate the acceptable accuracy for approximations as well.

  19. 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…

  20. Boundary induced amplification and nonlinear instability of interchange modes

    SciTech Connect

    Bagaipo, Jupiter; Hassam, A. B.

    2013-02-15

    It is shown that small distortions on the boundaries are amplified in the core of a magnetized plasma if the system is close to marginal stability for the ideal magnetohydrodynamic interchange mode. It is also shown that such marginal systems can be nonlinearly unstable. The combination of boundary amplification and nonlinearity is shown to result in a nonlinear instability. The induced instability is highly sensitive to the boundary in that, if the fractional deviation from marginality is a small parameter b, the system can go unstable from fractional boundary distortions of O(b{sup 3/2}).

  1. 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

  2. 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

  3. On controllability of nonlinear stochastic systems

    NASA Astrophysics Data System (ADS)

    Sakthivel, R.; Kim, J.-H.; Mahmudov, N. I.

    2006-12-01

    In this paper, complete controllability for nonlinear stochastic systems is studied. First this paper addresses the problem of complete controllability of nonlinear stochastic systems with standard Brownian motion. Then this result is extended to establish complete controllability criterion for stochastic systems with fractional Brownian motion. A fixed point approach is employed for achieving the required result. The solutions are given by a variation of constants formula which allows us to study the complete controllability for nonlinear stochastic systems. In this paper, we prove the complete controllability of nonlinear stochastic system under the natural assumption that the associated linear control system is completely controllable. Finally, an illustrative example is provided to show the usefulness of the proposed technique.

  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. 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

  6. 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.

  7. Milk fat and primary fractions obtained by dry fractionation 1. Chemical composition and crystallisation properties.

    PubMed

    Lopez, Christelle; Bourgaux, Claudie; Lesieur, Pierre; Riaublanc, Alain; Ollivon, Michel

    2006-10-01

    The chemical composition and crystallisation properties of milk fat and its primary fractions, obtained by dry fractionation at 21 degrees C, were investigated. The solid fraction (stearin) and the liquid fraction (olein) displayed a different triacylglycerol (TG) composition. Stearin fraction was enriched in long-chain fatty acids, whereas olein fraction was enriched in short-chain and unsaturated fatty acids. Crystallisation properties of milk fat, and both the stearin and olein fractions were studied on cooling at |dT/dt|=1 degrees C min(-1) by differential scanning calorimetry and time-resolved synchrotron X-ray diffraction (XRD) at small and wide angles. Two main types of crystals corresponding to double chain length structures were characterised in the stearin fraction: alpha 2L(1) (47.5 Angstrom) and beta' 2L(2) (41.7 Angstrom). A triple chain length structure was formed in the olein fraction: alpha 3L (72.1 Angstrom). Crystallization of milk fat showed the formation of two 2L (47.3 and 41.6 Angstrom) and one 3L (72.1 Angstrom) lamellar structures with an hexagonal packing (alpha form). A schematic representation of the 3L packing of olein fraction was proposed to explain how a wide diversity of TG can accommodate to form a lamellar structure with a thickness of 72 Angstrom. Furthermore, the sharpness of the small-angle XRD lines associated to the alpha form was explained by the formation of liquid crystals of smectic type.

  8. Double resonant processes in 1D nonlinear periodic media

    NASA Astrophysics Data System (ADS)

    Kuzmiak, Vladimir; Konotop, Vladimir

    2001-03-01

    We consider one-dimensional periodic structure consisting of alternating layers fabricated from the materials possessing \\chi^(2) nonlinearity and assume that the filling fraction and the dielectric permittivities of the slabs are chosen in such a way that resonant contions for the generation for the second and third harmonic are satisfied simultaneously. The possibility of such process is demonstrated in the structure consisting of the alternating slabs of AlGaAs and InSb. The wave evolution is described in terms of envelope function approach. By taking account three resonant waves one obtains a system of coupled-mode differential equations. One of the solutions which is of special importance is that of having a constant amplitude and the first and third harmonic having zero amplitude. We analyze the stability of the solutions and show that the use of the double resonance allows one to obtain difference generation. A particular example of such a process is fractional conversion ω arrow (2/3)ω which takes place with the participation of the mode with the frequency ω/3.

  9. Transport equations for subdiffusion with nonlinear particle interaction.

    PubMed

    Straka, P; Fedotov, S

    2015-02-01

    We show how the nonlinear interaction effects 'volume filling' and 'adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with anomalous trapping and systematically derive generic non-Markovian and nonlinear governing equations for the mean concentrations of the subdiffusive cells or organisms. We uncover an interesting interaction between the nonlinearities and the non-Markovian nature of the transport. In the subdiffusive case, this interaction manifests itself in a nontrivial combination of nonlinear terms with fractional derivatives. In the long time limit, however, these equations simplify to a form without fractional operators. This provides an easy method for the study of aggregation phenomena. In particular, this enables us to show that volume filling can prevent "anomalous aggregation," which occurs in subdiffusive systems with a spatially varying anomalous exponent.

  10. Multiobjective optimization design of a fractional order PID controller for a gun control system.

    PubMed

    Gao, Qiang; Chen, Jilin; Wang, Li; Xu, Shiqing; Hou, Yuanlong

    2013-01-01

    Motion control of gun barrels is an ongoing topic for the development of gun control equipments possessing excellent performances. In this paper, a typical fractional order PID control strategy is employed for the gun control system. To obtain optimal parameters of the controller, a multiobjective optimization scheme is developed from the loop-shaping perspective. To solve the specified nonlinear optimization problem, a novel Pareto optimal solution based multiobjective differential evolution algorithm is proposed. To enhance the convergent rate of the optimization process, an opposition based learning method is embedded in the chaotic population initialization process. To enhance the robustness of the algorithm for different problems, an adapting scheme of the mutation operation is further employed. With assistance of the evolutionary algorithm, the optimal solution for the specified problem is selected. The numerical simulation results show that the control system can rapidly follow the demand signal with high accuracy and high robustness, demonstrating the efficiency of the proposed controller parameter tuning method.

  11. Nonlinearities in vegetation functioning

    NASA Astrophysics Data System (ADS)

    Ceballos-Núñez, Verónika; Müller, Markus; Metzler, Holger; Sierra, Carlos

    2016-04-01

    Given the current drastic changes in climate and atmospheric CO2 concentrations, and the role of vegetation in the global carbon cycle, there is increasing attention to the carbon allocation component in biosphere terrestrial models. Improving the representation of C allocation in models could be the key to having better predictions of the fate of C once it enters the vegetation and is partitioned to C pools of different residence times. C allocation has often been modeled using systems of ordinary differential equations, and it has been hypothesized that most models can be generalized with a specific form of a linear dynamical system. However, several studies have highlighted discrepancies between empirical observations and model predictions, attributing these differences to problems with model structure. Although efforts have been made to compare different models, the outcome of these qualitative assessments has been a conceptual categorization of them. In this contribution, we introduce a new effort to identify the main properties of groups of models by studying their mathematical structure. For this purpose, we performed a literature research of the relevant models of carbon allocation in vegetation and developed a database with their representation in symbolic mathematics. We used the Python package SymPy for symbolic mathematics as a common language and manipulated the models to calculate their Jacobian matrix at fixed points and their eigenvalues, among other mathematical analyses. Our preliminary results show a tendency of inverse proportionality between model complexity and size of time/space scale; complex interactions between the variables controlling carbon allocation in vegetation tend to operate at shorter time/space scales, and vice-versa. Most importantly, we found that although the linear structure is common, other structures with non-linearities have been also proposed. We, therefore, propose a new General Model that can accommodate these

  12. 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

  13. 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

  14. 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.

  15. Solving nonlinear heat transfer constant area fin problems

    NASA Technical Reports Server (NTRS)

    1968-01-01

    Tables and graphs were compiled for solving nonlinear heat transfer constant area fin problems. The differential equation describing one-dimensional steady-state temperature distribution and heat flow under three modes of heat transfer with heat generation was investigated.

  16. 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…

  17. (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.

  18. 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…

  19. 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…

  20. Nonlinearities distribution Laplace transform-homotopy perturbation method.

    PubMed

    Filobello-Nino, Uriel; Vazquez-Leal, Hector; Benhammouda, Brahim; Hernandez-Martinez, Luis; Hoyos-Reyes, Claudio; Perez-Sesma, Jose Antonio Agustin; Jimenez-Fernandez, Victor Manuel; Pereyra-Diaz, Domitilo; Marin-Hernandez, Antonio; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus; Cervantes-Perez, Juan

    2014-01-01

    This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures between approximate and exact solutions we show the effectiveness of the proposed method.

  1. A fucose containing polymer-rich fraction from the brown alga Ascophyllum nodosum mediates lifespan increase and thermal-tolerance in Caenorhabditis elegans, by differential effects on gene and protein expression.

    PubMed

    Kandasamy, Saveetha; Khan, Wajahatullah; Evans, Franklin D; Critchley, Alan T; Zhang, Junzeng; Fitton, J H; Stringer, Damien N; Gardiner, Vicki-Anne; Prithiviraj, Balakrishnan

    2014-02-01

    The extracts of the brown alga, Ascophyllum nodosum, which contains several bioactive compounds, have been shown to impart biotic and abiotic stress tolerance properties when consumed by animals. However, the physiological, biochemical and molecular mechanism underlying such effects remain elusive. We investigated the effect of A. nodosum fucose-containing polymer (FCP) on tolerance to thermally induced stress using the invertebrate animal model, Caenorhabditis elegans. FCP at a concentration of 150 μg mL(-1) significantly improved the life span and tolerance against thermally induced stress in C. elegans. The treatment increased the C. elegans survival by approximately 24%, when the animals were under severe thermally induced stress (i.e. 35 °C) and 27% under mild stress (i.e. 30 °C) conditions. The FCP induced differential expression of genes and proteins is associated with stress response pathways. Under thermal stress, FCP treatment significantly altered the expression of 65 proteins (54 up-regulated & 11 down-regulated). Putative functional analysis of FCP-induced differential proteins signified an association of altered proteins in stress-related molecular and biochemical pathways of the model worm. PMID:24323434

  2. A fucose containing polymer-rich fraction from the brown alga Ascophyllum nodosum mediates lifespan increase and thermal-tolerance in Caenorhabditis elegans, by differential effects on gene and protein expression.

    PubMed

    Kandasamy, Saveetha; Khan, Wajahatullah; Evans, Franklin D; Critchley, Alan T; Zhang, Junzeng; Fitton, J H; Stringer, Damien N; Gardiner, Vicki-Anne; Prithiviraj, Balakrishnan

    2014-02-01

    The extracts of the brown alga, Ascophyllum nodosum, which contains several bioactive compounds, have been shown to impart biotic and abiotic stress tolerance properties when consumed by animals. However, the physiological, biochemical and molecular mechanism underlying such effects remain elusive. We investigated the effect of A. nodosum fucose-containing polymer (FCP) on tolerance to thermally induced stress using the invertebrate animal model, Caenorhabditis elegans. FCP at a concentration of 150 μg mL(-1) significantly improved the life span and tolerance against thermally induced stress in C. elegans. The treatment increased the C. elegans survival by approximately 24%, when the animals were under severe thermally induced stress (i.e. 35 °C) and 27% under mild stress (i.e. 30 °C) conditions. The FCP induced differential expression of genes and proteins is associated with stress response pathways. Under thermal stress, FCP treatment significantly altered the expression of 65 proteins (54 up-regulated & 11 down-regulated). Putative functional analysis of FCP-induced differential proteins signified an association of altered proteins in stress-related molecular and biochemical pathways of the model worm.

  3. 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.

  4. A nonlinear oscillator

    SciTech Connect

    Tomlin, R.

    1990-01-27

    A nonlinear oscillator design was imported from Cornell modified, and built for the purpose of simulating the chaotic states of a forced pendulum. Similar circuits have been investigated in the recent nonlinear explosion.

  5. 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.

  6. 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.

  7. 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

  8. 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

  9. 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.

  10. 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.

  11. 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.

  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. 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

  14. 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.

  15. 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.

  16. Stable Chlorine Isotope Fractionation

    NASA Astrophysics Data System (ADS)

    Sharp, Z.

    2006-12-01

    Chlorine isotope partitioning between different phases is not well understood. Pore fluids can have δ37Cl values as low as -8‰, with neoform sediments having strongly positive values. Most strikingly, volcanic gases have δ37Cl values that cover a range in excess of 14‰ (Barnes et al., this meeting). The large range is difficult to explain in terms of equilibrium fractionation, which, although calculated to be very large for Cl in different oxidation states, should be less than 2‰ between chloride species (Schauble et al., 2003, GCA). To address the discrepancy between Nature and theory, we have measured Cl isotope fractionation for selected equilibrium and disequilibrium experiments in order to identify mechanisms that might lead to large fractionations. 1) NaCl (s,l) NaCl (v): NaCl was sealed in an evacuated silica tube and heated at one end, causing vaporization and reprecipitation of NaCl (v) at the cool end of the tube. The fractionation is 0.2‰ at 700°C (halite-vapor) and 0.7‰ at 800°C (liquid-vapor), respectively. The larger fractionation at higher temperature may be related to equilibrium fractionation between liquid and gas vs. `stripping' of the solid in the lower T experiments. 2) Sodalite NaCl(l): Nepheline and excess NaCl were sealed in a Pt crucible at 825°C for 48 hrs producing sodalite. The measured newly-formed sodalite-NaCl fractionation is -0.2‰. 3) Volatilization of HCl: Dry inert gas was bubbled through HCl solutions and the vapor was collected in a downstream water trap. There was no fractionation for 12.4M HCl (HCl fuming) vapor at 25°C. For a 1 M boiling HCl solution, the HCl-vapor fractionation was ~9‰. The difference is probably related to the degree of dissociation in the acid, with HCl dissolved in water for the highly acidic solutions, and dissociated H3O+ and Cl- for lower concentrations. The HCl volatilization experiments are in contrast to earlier vapor-liquid experiments in NaCl-H2O system, where fractionation was

  17. 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.

  18. Chromatographic methods of fractionation.

    PubMed

    Friesen, A D

    1987-01-01

    Chromatography's functional versatility, separation efficiency, gentle non-denaturing separating process and ease of automation and scale-up make it attractive for industrial scale protein purification. The Winnipeg Rh Institute's new Plasma Fractionation facility is an example of the use of chromatography for the large scale purification of plasma protein fractions. The fractionation facility has a capacity to process 800 litres of plasma per batch into blood clotting factor VIII and IX, albumin and intravenous immune serum globulin (i.v. ISG). Albumin and i.v. ISG are purified using ion exchange columns of DEAE-Sepharose (230 litre size), DEAE-Biogel (150 litre size) and CM-Sepharose (150 litre size). The chromatographic process is automated using a Modicon 584 Programmable Logic Controller to regulate valves, pumps and sensors which control plasma flow during fractionation. The stainless steel tanks and piping are automatically cleaned-in-place. The high degree of automation and cleaning provides efficient operation and sanitary processing. Chromatographic methods (DEAE-Sepharose and metal chelation) are also being used at the pilot scale to purify the human blood products superoxide dismutase and hemoglobin from outdated red blood cells. Characterization of the protein fractions produced by chromatography has shown them to be of equal or higher quality than fractions produced by other techniques.

  19. Nonlinear vibration of thick stiff fabric with small flexural stiffness

    NASA Astrophysics Data System (ADS)

    Chen, J.-P.; Wang, S.-Z.; Wu, W.-Y.; Gu, H.-B.

    2008-02-01

    Dynamic behaviour of fabric is very complex during weaving, dyeing and finishing processes. Thick stiff fabric vibration has great influence not only on the fabric itself but also on the performance of machine. The theoretic analysis for the nonlinear free vibration of thick stiff fabric with small flexural stiffness is put forward in the paper. The nonlinear partial differential equation is derived by applying the flexible thin plate theory, and then transformed into nonlinear ordinary differential equation by the Galerkin method. The approximate analytical solution is obtained by the homotopy perturbation method.

  20. 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.

  1. 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

  2. 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.

  3. Fractional resonances between waves and energetic particles in tokamak plasmas.

    PubMed

    Kramer, G J; Chen, L; Fisher, R K; Heidbrink, W W; Nazikian, R; Pace, D C; Van Zeeland, M A

    2012-07-20

    From numerical simulation and analytical modeling it is shown that fast ions can resonate with plasma waves at fractional values of the particle drift-orbit transit frequency when the plasma wave amplitude is sufficiently large. The fractional resonances, which are caused by a nonlinear interaction between the particle orbit and the wave, give rise to an increased density of resonances in phase space which reduces the threshold for stochastic transport. The effects of the fractional resonances on spatial and energy transport are illustrated for an energetic particle geodesic acoustic mode but they apply equally well to other types of MHD activity.

  4. 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

  5. Approximate analytic solutions for singular non-linear oscillators

    NASA Technical Reports Server (NTRS)

    Bota, K. B.; Mickens, R. E.

    1984-01-01

    Mickens (1981, 1984) has considered analytic techniques for obtaining approximate solutions to one-dimensional nonlinear oscillatory systems x(double-dot) + x = lambda f(x, x/dot/, lambda) where lambda is a small positive parameter and f is a nonlinear polynomial function of its arguments. However, in certain cases there is interest in the analysis of physical systems for which the nonlinear function f(x, x/dot/, lambda) is singular for finite values of x or x(dot). The present investigation is concerned with the use of existing approximate analytic schemes to obtain solutions to singular nonlinear oscillatory differential equations.

  6. 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.

  7. Fractional field equations for highly improbable events

    NASA Astrophysics Data System (ADS)

    Kleinert, H.

    2013-06-01

    Free and weakly interacting particles perform approximately Gaussian random walks with collisions. They follow a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. By contrast, the fields of strongly interacting particles extremize more involved effective actions obeying fractional wave equations with anomalous dimensions. Their particle orbits perform universal Lévy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong windgusts, monster or rogue waves, earthquakes, and financial crashes. While earthquakes may destroy entire cities, the latter have the potential of devastating entire economies.

  8. 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

  9. Challenges in nonlinear gravitational clustering

    NASA Astrophysics Data System (ADS)

    Padmanabhan, Thanu

    2006-04-01

    This article addresses some issues related to the statistical description of gravitating systems in an expanding backgrounds. In particular, I describe (a) how the nonlinear mode-mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale and (b) what are the asymptotic characteristics of gravitational clustering that are independent of the initial conditions. The analysis uses a new approach based on an integro-differential equation for the evolution of the gravitational potential in the Fourier space. I show how this equation allows one to understand several aspects of nonlinear gravitational clustering and provides insight in to the transfer of power from one scale to another through nonlinear mode coupling. Numerical simulations as well as analytic work shows that power transfer leads to a universal power spectrum at late times, somewhat reminiscent of the existence of Kolmogorov spectrum in fluid turbulence. To cite this article: T. Padmanabhan, C. R. Physique 7 (2006).

  10. 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.

  11. 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.

  12. Fractional Noether Theorem Based on Extended Exponentially Fractional Integral

    NASA Astrophysics Data System (ADS)

    Long, Zi-Xuan; Zhang, Yi

    2013-10-01

    Based on the new type of fractional integral definition, namely extended exponentially fractional integral introduced by EI-Nabulsi, we study the fractional Noether symmetries and conserved quantities for both holonomic system and nonholonomic system. First, the fractional variational problem under the sense of extended exponentially fractional integral is established, the fractional d'Alembert-Lagrange principle is deduced, then the fractional Euler-Lagrange equations of holonomic system and the fractional Routh equations of nonholonomic system are given; secondly, the invariance of fractional Hamilton action under infinitesimal transformations of group is also discussed, the corresponding definitions and criteria of fractional Noether symmetric transformations and quasi-symmetric transformations are established; finally, the fractional Noether theorems for both holonomic system and nonholonomic system are explored. What's more, the relationship between the fractional Noether symmetry and conserved quantity are revealed.

  13. 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.

  14. Connectance and stability of nonlinear symplectic systems

    NASA Astrophysics Data System (ADS)

    Laveder, D.; Cosentino, M.; Lega, Elena; Froeschlé, C.

    2008-09-01

    We have revisited the problem of the transition from ordered to chaotic motion for increasing number of degrees of freedom in nonlinear symplectic maps. Following the pioneer work of Froeschlé (Phys. Rev. A 18, 277 281, 1978) we investigate such systems as a function of the number of couplings among the equations of motion, i.e. as a function of a parameter called connectance since the seminal paper of Gardner and Ashby (Nature 228, 784, 1970) about linear systems. We compare two different models showing that in the nonlinear case the connectance has to be intended as the fraction of explicit dynamical couplings among degrees of freedom, rather than the fraction of non-zero elements in a given matrix. The chaoticity increases then with the connectance until the system is fully coupled.

  15. Nonlinear analysis of a simply-supported composite beam under random excitations

    SciTech Connect

    Eslami, H.; Gudmundson, S.

    1994-12-31

    Nonlinear analysis of composite laminated beams subjected-to random excitation is studied here. The forcing function is a stationary Gaussian type random excitation. The governing partial differential equations of motion are obtained by considering the Von Karman type geometrical nonlinearity. These partial differential equations are transformed into nonlinear Ordinary differential equations of Duffing type by applying the Galerkin`s method. The resulting nonlinear ODE are first solved by using the equivalent linearization method and the numerical integration (Runge Kutta) method. The equations are reduced to that of isotropic beam and results are also compared with the previously published ones.

  16. 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.

  17. 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.

  18. Fractional Schrödinger dynamics and decoherence

    NASA Astrophysics Data System (ADS)

    Kirkpatrick, Kay; Zhang, Yanzhi

    2016-10-01

    We study the dynamics of the Schrödinger equation with a fractional Laplacian (- Δ) α, and the decoherence of the solution is observed. Analytically, we obtain equations of motion for the expected position and momentum in the fractional Schödinger equation, equations that are the fractional counterpart of the well-known Newtonian equations of motion for the standard (α = 1) Schrödinger equation. Numerically, we propose an explicit, effective numerical method for solving the time-dependent fractional nonlinear Schrödinger equation-a method that has high order spatial accuracy, requires little memory, and has low computational cost. We apply our method to study the dynamics of fractional Schrödinger equation and find that the nonlocal interactions from the fractional Laplacian introduce decoherence into the solution. The local nonlinear interactions can however reduce or delay the emergence of decoherence. Moreover, we find that the solution of the standard NLS behaves more like a particle, but the solution of the fractional NLS behaves more like a wave with interference effects.

  19. 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.

  20. 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.

  1. Spectral decomposition of nonlinear systems with memory

    NASA Astrophysics Data System (ADS)

    Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.

    2016-02-01

    We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

  2. Spectral decomposition of nonlinear systems with memory.

    PubMed

    Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J

    2016-02-01

    We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

  3. Intrinsic nonlinearities in the mechanics of hard sphere suspensions.

    PubMed

    Kumar, Mansi A; Ewoldt, Randy H; Zukoski, Charles F

    2016-09-28

    The onset of nonlinear responses in near hard sphere suspensions is characterized as a function of oscillatory frequency and strain amplitude. At low frequencies where the viscous behavior dominates, the onset of nonlinearities is driven by increases in rate of strain. At high deformation frequency, where suspension mechanics is dominated by an elastic response, the nonlinear responses occur when deformation exceeds a characteristic strain. This strain is associated with the transient confinement of particles by nearest neighbors and its volume fraction dependence is through cage parameters derived from the high frequency elastic modulus. The onset of nonlinear responses takes on a universal behavior when deformation frequency is normalized by the characteristic time governing the shift from viscous to elastic behavior indicating that this transition is associated with transient particle localization and is expected to be observed for all volume fractions where pair interactions are important. PMID:27530863

  4. 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.

  5. 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

  6. Diamond nonlinear photonics

    NASA Astrophysics Data System (ADS)

    Hausmann, B. J. M.; Bulu, I.; Venkataraman, V.; Deotare, P.; Lončar, M.

    2014-05-01

    Despite progress towards integrated diamond photonics, studies of optical nonlinearities in diamond have been limited to Raman scattering in bulk samples. Diamond nonlinear photonics, however, could enable efficient, in situ frequency conversion of single photons emitted by diamond's colour centres, as well as stable and high-power frequency microcombs operating at new wavelengths. Both of these applications depend crucially on efficient four-wave mixing processes enabled by diamond's third-order nonlinearity. Here, we have realized a diamond nonlinear photonics platform by demonstrating optical parametric oscillation via four-wave mixing using single-crystal ultrahigh-quality-factor (1 × 106) diamond ring resonators operating at telecom wavelengths. Threshold powers as low as 20 mW are measured, and up to 20 new wavelengths are generated from a single-frequency pump laser. We also report the first measurement of the nonlinear refractive index due to the third-order nonlinearity in diamond at telecom wavelengths.

  7. Nonlinear rotordynamics analysis

    NASA Technical Reports Server (NTRS)

    Day, W. B.

    1985-01-01

    The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.

  8. 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.

  9. 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

  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. Stationary nonlinear Airy beams

    SciTech Connect

    Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.

    2011-08-15

    We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.

  12. 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.

  13. Topologies for neutral functional differential equations.

    NASA Technical Reports Server (NTRS)

    Melvin, W. R.

    1973-01-01

    Bounded topologies are considered for functional differential equations of the neutral type in which present dynamics of the system are influenced by its past behavior. A special bounded topology is generated on a collection of absolutely continuous functions with essentially bounded derivatives, and an application to a class of nonlinear neutral functional differential equations due to Driver (1965) is presented.

  14. Organic nonlinear optical materials

    NASA Technical Reports Server (NTRS)

    Umegaki, S.

    1987-01-01

    Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.

  15. Nonlinear optics at interfaces

    SciTech Connect

    Chen, C.K.

    1980-12-01

    Two aspects of surface nonlinear optics are explored in this thesis. The first part is a theoretical and experimental study of nonlinear intraction of surface plasmons and bulk photons at metal-dielectric interfaces. The second part is a demonstration and study of surface enhanced second harmonic generation at rough metal surfaces. A general formulation for nonlinear interaction of surface plasmons at metal-dielectric interfaces is presented and applied to both second and third order nonlinear processes. Experimental results for coherent second and third harmonic generation by surface plasmons and surface coherent antiStokes Raman spectroscopy (CARS) are shown to be in good agreement with the theory.

  16. Momentum fractionation on superstrata

    DOE PAGES

    Bena, Iosif; Martinec, Emil; Turton, David; Warner, Nicholas P.

    2016-05-11

    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 highdegree 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 orbifoldmore » 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. Lastly, 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.« less

  17. Understanding Fraction Multiplication.

    ERIC Educational Resources Information Center

    Bezuk, Nadine S.; Armstrong, Barbara E.

    1992-01-01

    Presents five activities to help students construct meaning for multiplying fractions through real-world problem contexts, physical or pictorial models, the recognition of patterns, and the use of calculators. In the context of a garden plot, worksheets examine various aspects of parts of plots, patterns in plots, and a maximization problem.…

  18. Fractions through Fruit Salad.

    ERIC Educational Resources Information Center

    Lincoln, Lisa

    1987-01-01

    The mathematics concept of fractions was taught to a group of learning disabled, dyslexic, and multiply handicapped students (15-20 years old) by preparing a fruit salad. Enthusiastic student participation and enhanced knowledge illustrated the effectiveness of employing several sensory modes in learning activities. (CB)

  19. 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)

  20. Avoidance of Fractions.

    ERIC Educational Resources Information Center

    Hart, Kathleen; Kerslake, Daphne

    The Concepts in Secondary Mathematics and Science (CSMS) and Strategies and Errors in Secondary Mathematics (SESM) research projects based at Chelsa College, England, have shown the marked reluctance of secondary school students to use fractions when solving mathematical problems, even though they have been taught the topic for a number of years.…