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

    PubMed

    Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

    2014-01-01

    We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

  3. Robust fast controller design via nonlinear fractional differential equations.

    PubMed

    Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

    2017-07-01

    A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  4. Some existence results on nonlinear fractional differential equations.

    PubMed

    Baleanu, Dumitru; Rezapour, Shahram; Mohammadi, Hakimeh

    2013-05-13

    In this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundary-value problem D(α)u(t)=f(t,u(t)) with a Riemann-Liouville fractional derivative via the different boundary-value problems u(0)=u(T), and the three-point boundary condition u(0)=β(1)u(η) and u(T)=β(2)u(η), where T>0, t∈I=[0,T], 0<α<1, 0<η

  5. Exact solutions and maximal dimension of invariant subspaces of time fractional coupled nonlinear partial differential equations

    NASA Astrophysics Data System (ADS)

    Sahadevan, R.; Prakash, P.

    2017-01-01

    We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter-Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman-Broer-Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.

  6. 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

  7. 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.

  8. 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.

  9. On invariant analysis of some time fractional nonlinear systems of partial differential equations. I

    NASA Astrophysics Data System (ADS)

    Singla, Komal; Gupta, R. K.

    2016-10-01

    An investigation of Lie point symmetries for systems of time fractional partial differential equations including Ito system, coupled Burgers equations, coupled Korteweg de Vries equations, Hirota-Satsuma coupled KdV equations, and coupled nonlinear Hirota equations has been done. Using the obtained symmetries, each one of the systems is reduced to the nonlinear system of fractional ordinary differential equations involving Erdélyi-Kober fractional differential operator depending on a parameter α.

  10. Analytical Approach for Nonlinear Partial Differential Equations of Fractional Order

    NASA Astrophysics Data System (ADS)

    Pradip, Roul

    2013-09-01

    The purpose of the paper is to present analytical and numerical solutions of a degenerate parabolic equation with time-fractional derivatives arising in the spatial diffusion of biological populations. The homotopy—perturbation method is employed for solving this class of equations, and the time-fractional derivatives are described in the sense of Caputo. Comparisons are made with those derived by Adomian's decomposition method, revealing that the homotopy perturbation method is more accurate and convenient than the Adomian's decomposition method. Furthermore, the results reveal that the approximate solution continuously depends on the time-fractional derivative and the proposed method incorporating the Caputo derivatives is a powerful and efficient technique for solving the fractional differential equations without requiring linearization or restrictive assumptions. The basis ideas presented in the paper can be further applied to solve other similar fractional partial differential equations.

  11. 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.

  12. On invariant analysis of space-time fractional nonlinear systems of partial differential equations. II

    NASA Astrophysics Data System (ADS)

    Singla, Komal; Gupta, R. K.

    2017-05-01

    In Paper I [Singla, K. and Gupta, R. K., J. Math. Phys. 57, 101504 (2016)], Lie symmetry method is developed for time fractional systems of partial differential equations. In this article, the Lie symmetry approach is proposed for space-time fractional systems of partial differential equations and applied to study some well-known physically significant space-time fractional nonlinear systems successfully.

  13. On the problem of convergence of series solution of non-linear fractional partial differential equation

    NASA Astrophysics Data System (ADS)

    Singh, Prince; Sharma, Dinkar

    2017-07-01

    Series solution is obtained on solving non-linear fractional partial differential equation using homotopy perturbation transformation method. First of all, we apply homotopy perturbation transformation method to obtain the series solution of non-linear fractional partial differential equation. In this case, the fractional derivative is described in Caputo sense. Then, we present the facts obtained by analyzing the convergence of this series solution. Finally, the established fact is supported by an example.

  14. The (G'/G)-expansion method for the nonlinear time fractional differential equations

    NASA Astrophysics Data System (ADS)

    Unsal, Omer; Guner, Ozkan; Bekir, Ahmet; Cevikel, Adem C.

    2017-01-01

    In this paper, we obtain exact solutions of two time fractional differential equations using Jumarie's modified Riemann-Liouville derivative which is encountered in mathematical physics and applied mathematics; namely (3 + 1)-dimensional time fractional KdV-ZK equation and time fractional ADR equation by using fractional complex transform and (G/'G )-expansion method. It is shown that the considered transform and method are very useful in solving nonlinear fractional differential equations.

  15. Soliton solution and other solutions to a nonlinear fractional differential equation

    NASA Astrophysics Data System (ADS)

    Guner, Ozkan; Unsal, Omer; Bekir, Ahmet; Kadem, Abdelouahab

    2017-01-01

    In this paper, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the ansatz method and the functional variable method are used to construct exact solutions for (3+1)-dimensional time fractional KdV-Zakharov-Kuznetsov (KdV-ZK) equation. This fractional equation is turned into another nonlinear ordinary differential equation by fractional complex transform then these methods are applied to solve it. As a result, some new exact solutions obtained.

  16. Bright and dark soliton solutions for some nonlinear fractional differential equations

    NASA Astrophysics Data System (ADS)

    Ozkan, Guner; Ahmet, Bekir

    2016-03-01

    In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona-Mahoney (mBBM) equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann-Liouville sense.

  17. Analytical approaches for the approximate solution of a nonlinear fractional ordinary differential equation

    NASA Astrophysics Data System (ADS)

    Basak, K. C.; Ray, P. C.; Bera, R. K.

    2009-10-01

    The aim of the present analysis is to apply the Adomian decomposition method and He's variational method for the approximate analytical solution of a nonlinear ordinary fractional differential equation. The solutions obtained by the above two methods have been numerically evaluated and presented in the form of tables and also compared with the exact solution. It was found that the results obtained by the above two methods are in excellent agreement with the exact solution. Finally, a surface plot of the approximate solutions of the fractional differential equation by the above two methods is drawn for 0<=t<=2 and 1<α<=2.

  18. 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.

  19. Existence of positive periodic solutions of some nonlinear fractional differential equations

    NASA Astrophysics Data System (ADS)

    Cabada, Alberto; Kisela, Tomáš

    2017-09-01

    The paper is devoted to study of existence and uniqueness of periodic solutions for a particular class of nonlinear fractional differential equations admitting its right-hand side with certain singularities. Our approach is based on Krasnosel'skiĭ and Schauder fixed point theorems and monotone iterative technique which enable us to extend some previously known results. The discussed problems are characterized by a Green's function which has integrable singularities disallowing a direct use of classical techniques known from theory of ordinary differential equations, therefore proper modifications are proposed. Furher, the paper presents simple numerical algorithms directly built on the iterative technique used in theoretical proofs. Illustrative examples conclude the paper.

  20. 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

  1. Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation

    NASA Astrophysics Data System (ADS)

    Du, Yanwei; Liu, Yang; Li, Hong; Fang, Zhichao; He, Siriguleng

    2017-09-01

    In this article, a fully discrete local discontinuous Galerkin (LDG) method with high-order temporal convergence rate is presented and developed to look for the numerical solution of nonlinear time-fractional fourth-order partial differential equation (PDE). In the temporal direction, for approximating the fractional derivative with order α ∈ (0 , 1), the weighted and shifted Grünwald difference (WSGD) scheme with second-order convergence rate is introduced and for approximating the integer time derivative, two step backward Euler method with second-order convergence rate is used. For the spatial direction, the LDG method is used. For the numerical theories, the stability is derived and a priori error results are proved. Further, some error results and convergence rates are calculated by numerical procedure to illustrate the effectiveness of proposed method.

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

    NASA Astrophysics Data System (ADS)

    Isah, Abdulnasir; Chang, Phang

    2016-06-01

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

  3. Robust and adaptive techniques for numerical simulation of nonlinear partial differential equations of fractional order

    NASA Astrophysics Data System (ADS)

    Owolabi, Kolade M.

    2017-03-01

    In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE) on a finite but large spatial domain x ∈ [0, L], x = x(x , y , z) and t ∈ [0, T] are considered. Also in this work, the standard reaction-diffusion system with boundary conditions is generalized by replacing the second-order spatial derivatives with Riemann-Liouville space-fractional derivatives of order α, for 0 < α < 2. Fourier spectral method is introduced as a better alternative to existing low order schemes for the integration of fractional in space reaction-diffusion problems in conjunction with an adaptive exponential time differencing method, and solve a range of one-, two- and three-components SFORDE numerically to obtain patterns in one- and two-dimensions with a straight forward extension to three spatial dimensions in a sub-diffusive (0 < α < 1) and super-diffusive (1 < α < 2) scenarios. It is observed that computer simulations of SFORDE give enough evidence that pattern formation in fractional medium at certain parameter value is practically the same as in the standard reaction-diffusion case. With application to models in biology and physics, different spatiotemporal dynamics are observed and displayed.

  4. Comments on “Application of generalized differential transform method to multi-order fractional differential equations”, Vedat Suat Erturk, Shaher Momani, Zaid Odibat [Commun Nonlinear Sci Numer Simul 2008;13:1642 54

    NASA Astrophysics Data System (ADS)

    Arikoglu, Aytac; Ozkol, Ibrahim

    2008-10-01

    In this note, we would like to point some similarities between the study [Erturk VS, Momani S, Odibat Z. Application of generalized differential transform method to multi-order fractional differential equations. Commun Nonlinear Sci Numer Simul. doi:10.1016/j.cnsns.2007.02.006] with the already existing one [Arikoglu A, Ozkol I. Solution of fractional differential equations by using differential transform method. Chaos Soliton Fract. 10.1016/j.chaos.2006.09.004].

  5. Controllability of Nonlinear Fractional Delay Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Nirmala, R. Joice; Balachandran, K.; Rodríguez-Germa, L.; Trujillo, J. J.

    2016-02-01

    This paper is concerned with controllability of nonlinear fractional delay dynamical systems with delay in state variables. The solution representations of fractional delay differential equations have been established by using the Laplace transform technique and the Mittag-Leffler function. Necessary and sufficient conditions for the controllability criteria of linear fractional delay systems are established. Further sufficient condition for the controllability of nonlinear fractional delay dynamical system are obtained by using the fixed point argument. Examples and numerical simulation are presented to illustrate the results.

  6. Multiple positive solutions to nonlinear boundary value problems of a system for fractional differential equations.

    PubMed

    Zhai, Chengbo; Hao, Mengru

    2014-01-01

    By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D(0+)(ν1)y1(t) = λ1a1(t)f(y1(t), y2(t)), - D(0+)(ν2)y2(t) = λ2a2(t)g(y1(t), y2(t)), where D(0+)(ν) is the standard Riemann-Liouville fractional derivative, ν1, ν2 ∈ (n - 1, n] for n > 3 and n ∈ N, subject to the boundary conditions y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = 0 = [D(0+ (α)y2(t)] t=1, for 1 ≤ α ≤ n - 2, or y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = ϕ1(y1), [D(0+)(α)y2(t)] t=1 = ϕ2(y2), for 1 ≤ α ≤ n - 2, ϕ1, ϕ2 ∈ C([0,1], R). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.

  7. Augmented nonlinear differentiator design

    NASA Astrophysics Data System (ADS)

    Shao, Xingling; Liu, Jun; Yang, Wei; Tang, Jun; Li, Jie

    2017-06-01

    This paper presents a sigmoid function based augmented nonlinear differentiator (AND) for calculating the noise-less time derivative from a noisy measurement. The prominent advantages of the present differentiation technique are: (i) compared to the existing tracking differentiators, better noise suppression ability can be achieved without appreciable delay; (ii) the enhanced noise-filtering mechanism not only can be applied to the designed differentiator, but also can be extended for improving noise-tolerance capability of the available differentiators. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, applications on autopilot design and displacement following for nonlinear mass spring mechanical system are given to demonstrate the effectiveness and applicability of the proposed AND technique.

  8. Perturbed nonlinear differential equations

    NASA Technical Reports Server (NTRS)

    Proctor, T. G.

    1974-01-01

    For perturbed nonlinear systems, a norm, other than the supremum norm, is introduced on some spaces of continuous functions. This makes possible the study of new types of behavior. A study is presented on a perturbed nonlinear differential equation defined on a half line, and the existence of a family of solutions with special boundedness properties is established. The ideas developed are applied to the study of integral manifolds, and examples are given.

  9. 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.

  10. Solving systems of fractional differential equations using differential transform method

    NASA Astrophysics Data System (ADS)

    Erturk, Vedat Suat; Momani, Shaher

    2008-05-01

    This paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. Some examples are solved as illustrations, using symbolic computation. The numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations.

  11. Perturbed nonlinear differential equations

    NASA Technical Reports Server (NTRS)

    Proctor, T. G.

    1972-01-01

    The existence of a solution defined for all t and possessing a type of boundedness property is established for the perturbed nonlinear system y = f(t,y) + F(t,y). The unperturbed system x = f(t,x) has a dichotomy in which some solutions exist and are well behaved as t increases to infinity, and some solution exists and are well behaved as t decreases to minus infinity. A similar study is made for a perturbed nonlinear differential equation defined on a half line, R+, and the existence of a family of solutions with special boundedness properties is established. The ideas are applied to integral manifolds.

  12. 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.

  13. A Novel Effective Approach for Solving Fractional Nonlinear PDEs

    PubMed Central

    Aminikhah, Hossein; Malekzadeh, Nasrin; Rezazadeh, Hadi

    2014-01-01

    The present work introduces an effective modification of homotopy perturbation method for the solution of nonlinear time-fractional biological population model and a system of three nonlinear time-fractional partial differential equations. In this approach, the solution is considered a series expansion that converges to the nonlinear problem. The new approximate analytical procedure depends only on two iteratives. The analytical approximations to the solution are reliable and confirm the ability of the new homotopy perturbation method as an easy device for computing the solution of nonlinear equations. PMID:27419212

  14. A Novel Effective Approach for Solving Fractional Nonlinear PDEs.

    PubMed

    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.

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

    PubMed

    Zheng, Bin

    2013-01-01

    We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

  16. Exp-Function Method for Solving Fractional Partial Differential Equations

    PubMed Central

    2013-01-01

    We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established. PMID:23818823

  17. Sequential fractional differential equations with Hadamard derivative

    NASA Astrophysics Data System (ADS)

    Klimek, M.

    2011-12-01

    A class of nonlinear sequential fractional differential equations dependent on the basic fractional operator involving a Hadamard derivative is studied for arbitrary real noninteger order α∈R+. The existence and uniqueness of the solution is proved using the contraction principle and a new, equivalent norm and metric, introduced in the paper. As an example, a linear nonhomogeneous FDE is solved explicitly in arbitrary interval [ a, b] and for a nonhomogeneous term given as an arbitrary Fox function. The general solution consists of the solution of a homogeneous counterpart equation and a particular solution corresponding to the nonhomogeneous term and is given as a linear combination of the respective Fox functions series.

  18. 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.

  19. 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.

  20. (N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations

    NASA Astrophysics Data System (ADS)

    Arshad, Muhammad; Lu, Dianchen; Wang, Jun

    2017-07-01

    In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.

  1. Fractional Differential Equations and Multifractality

    NASA Astrophysics Data System (ADS)

    Larcheveque, M.; Schertzer, D. J.; Schertzer, D. J.; Duan, J.; Lovejoy, S.

    2001-12-01

    There has been a mushrooming interest in the linear Fokker-Planck Equation (FPPE) which corresponds to the generating equation of Lévy's anomalous diffusion. We already pointed out some theoretical and empirical limitations of the linear FPPE for various geophysical problems: the medium is in fact considered as homogeneous and the exponent of the power law of the pdf tails should be smaller than 2. We showed that a nonlinear extension based on a nonlinear Langevin equation forced by a Lévy stable motion overcomes these limitations. We show that in order to generate multifractal diffusion, and more generally multifractal fields, we need to furthermore consider fractional time derivatives in the Langevin equation and in FPPE. We compare our approach with the Continuous-Time Random Walk (CTWR) approach.

  2. On the singular perturbations for fractional differential equation.

    PubMed

    Atangana, Abdon

    2014-01-01

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

  3. Numerical approach to differential equations of fractional order

    NASA Astrophysics Data System (ADS)

    Momani, Shaher; Odibat, Zaid

    2007-10-01

    In this paper, the variational iteration method and the Adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. This paper presents a numerical comparison between the two methods for solving systems of fractional differential equations. Numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order.

  4. Fractional nonlinear dynamics of DNA breathing

    NASA Astrophysics Data System (ADS)

    Mvogo, Alain; Ben-Bolie, Germain H.; Kofané, Timoléon C.

    2017-07-01

    The classical Lagrangian formulation for the nonlinear dynamics of a homogeneous Peyrard-Bishop DNA molecular chain is reviewed and extended to include coordinates with time derivative of fractional order γ (0 < 2γ < 2), which can be viewed as memory effect. We obtain the equations of motion depending on γ. The analytical procedure for obtaining nonlinear waves solutions is performed through the application of a powerful fractional perturbation technique. The results show that both the amplitude and the velocity of waves increase when γ decreases. Accordingly, for low values of γ, the system exhibits highly localized waves with high amplitude and velocity. The numerical results agree with the theoretical ones and show that the system can support fractional breather-like modes.

  5. Solving fuzzy fractional differential equations using Zadeh's extension principle.

    PubMed

    Ahmad, M Z; Hasan, M K; Abbasbandy, S

    2013-01-01

    We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided.

  6. Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

    PubMed Central

    Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.

    2013-01-01

    We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853

  7. 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.

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

    SciTech Connect

    Deng, Mao-Lin; Zhu, Wei-Qiu

    2016-08-15

    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.

  9. Analytical approximate solution for nonlinear space—time fractional Klein—Gordon equation

    NASA Astrophysics Data System (ADS)

    Khaled, A. Gepreel; Mohamed, S. Mohamed

    2013-01-01

    The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space—time fractional derivatives Klein—Gordon equation. The numerical results show that the approaches are easy to implement and accurate when applied to the nonlinear space—time fractional derivatives Klein—Gordon equation. This method introduces a promising tool for solving many space—time fractional partial differential equations. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.

  10. 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

  11. An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics.

    PubMed

    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.

  12. Numerical solutions and solitary wave solutions of fractional KDV equations using modified fractional reduced differential transform method

    NASA Astrophysics Data System (ADS)

    Saha Ray, S.

    2013-12-01

    In this paper, the modified fractional reduced differential transform method (MFRDTM) has been proposed and it is implemented for solving fractional KdV (Korteweg-de Vries) equations. The fractional derivatives are described in the Caputo sense. In this paper, the reduced differential transform method is modified to be easily employed to solve wide kinds of nonlinear fractional differential equations. In this new approach, the nonlinear term is replaced by its Adomian polynomials. Thus the nonlinear initial-value problem can be easily solved with less computational effort. In order to show the power and effectiveness of the present modified method and to illustrate the pertinent features of the solutions, several fractional KdV equations with different types of nonlinearities are considered. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of fractional KdV equations.

  13. On the solution of the fractional nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Rida, S. Z.; El-Sherbiny, H. M.; Arafa, A. A. M.

    2008-01-01

    We present the nonlinear Schrödinger (NLS) equation of fractional order. The fractional derivatives are described in the Caputo sense. The Adomian decomposition method (ADM) in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution constructed in power series with easily computable components.

  14. Numerical approaches to fractional calculus and fractional ordinary differential equation

    NASA Astrophysics Data System (ADS)

    Li, Changpin; Chen, An; Ye, Junjie

    2011-05-01

    Nowadays, fractional calculus are used to model various different phenomena in nature, but due to the non-local property of the fractional derivative, it still remains a lot of improvements in the present numerical approaches. In this paper, some new numerical approaches based on piecewise interpolation for fractional calculus, and some new improved approaches based on the Simpson method for the fractional differential equations are proposed. We use higher order piecewise interpolation polynomial to approximate the fractional integral and fractional derivatives, and use the Simpson method to design a higher order algorithm for the fractional differential equations. Error analyses and stability analyses are also given, and the numerical results show that these constructed numerical approaches are efficient.

  15. Numerical solution of distributed order fractional differential equations

    NASA Astrophysics Data System (ADS)

    Katsikadelis, John T.

    2014-02-01

    In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

  16. Nonlinear scalar field equations involving the fractional Laplacian

    NASA Astrophysics Data System (ADS)

    Byeon, Jaeyoung; Kwon, Ohsang; Seok, Jinmyoung

    2017-04-01

    In this paper we study the existence, regularity, radial symmetry and decay property of a mountain pass solution for nonlinear scalar field equations involving the fractional Laplacian under an almost optimal class of continuous nonlinearities.

  17. 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.

  18. A study of impulsive multiterm fractional differential equations with single and multiple base points and applications.

    PubMed

    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.

  19. 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

  20. 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.

  1. 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.

  2. The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations

    NASA Astrophysics Data System (ADS)

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

    2012-11-01

    In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems.

  3. Systems of Nonlinear Hyperbolic Partial Differential Equations

    DTIC Science & Technology

    1997-12-01

    McKinney) Travelling wave solutions of the modified Korteweg - deVries -Burgers Equation . J. Differential Equations , 116 (1995), 448-467. 4. (with D.G...SUBTITLE Systems of Nonlinear Hyperbolic Partial Differential Equations 6. AUTHOR’S) Michael Shearer PERFORMING ORGANIZATION NAMES(S) AND...DISTRIBUTION CODE 13. ABSTRACT (Maximum 200 words) This project concerns properties of wave propagation in partial differential equations that are nonlinear

  4. Fractional differentiation by neocortical pyramidal neurons

    PubMed Central

    Lundstrom, Brian Nils; Higgs, Matthew H; Spain, William J; Fairhall, Adrienne L

    2008-01-01

    Neural systems adapt to changes in stimulus statistics. However, it is not known how stimuli with complex temporal dynamics drive the dynamics of adaptation and the resulting firing rate. For single neurons, it has often been assumed that adaptation has a single time scale. Here, we show that single rat neocortical pyramidal neurons adapt with a time scale that depends on the time scale of changes in stimulus statistics. This multiple time scale adaptation is consistent with fractional order differentiation, such that the neuron’s firing rate is a fractional derivative of slowly varying stimulus parameters. Biophysically, even though neuronal fractional differentiation effectively yields adaptation with many time scales, we find that its implementation requires only a few, properly balanced known adaptive mechanisms. Fractional differentiation provides single neurons with a fundamental and general computation that can contribute to efficient information processing, stimulus anticipation, and frequency independent phase shifts of oscillatory neuronal firing. PMID:18931665

  5. Practical stability with respect to initial time difference for Caputo fractional differential equations

    NASA Astrophysics Data System (ADS)

    Agarwal, Ravi; O'Regan, D.; Hristova, S.; Cicek, M.

    2017-01-01

    Practical stability with initial data difference for nonlinear Caputo fractional differential equations is studied. This type of stability generalizes known concepts of stability in the literature. It enables us to compare the behavior of two solutions when both initial values and initial intervals are different. In this paper the concept of practical stability with initial time difference is generalized to Caputo fractional differential equations. A definition of the derivative of Lyapunov like function along the given nonlinear Caputo fractional differential equation is given. Comparison results using this definition and scalar fractional differential equations are proved. Sufficient conditions for several types of practical stability with initial time difference for nonlinear Caputo fractional differential equations are obtained via Lyapunov functions. Some examples are given to illustrate the results.

  6. Fractional Differential and Integral Inequalities with Applications

    DTIC Science & Technology

    2016-02-14

    THE ABOVE ADDRESS. Xavier University of Louisiana 1 Drexel Drive New Orleans, LA 70125 -1098 31-Aug-2014 ABSTRACT Number of Papers published in peer...reviewed journals : Final Report: Fractional Differential and Integral Inequalities with Applications Report Title The monotone method extended to such...differential equations. (a) Papers published in peer-reviewed journals (N/A for none) Enter List of papers submitted or published that acknowledge ARO support

  7. 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.

  8. Laplace transform method for linear sequential Riemann Liouville and Caputo fractional differential equations

    NASA Astrophysics Data System (ADS)

    Vatsala, Aghalaya S.; Sowmya, M.

    2017-01-01

    Study of nonlinear sequential fractional differential equations of Riemann-Lioville type and Caputo type initial value problem are very useful in applications. In order to develop any iterative methods to solve the nonlinear problems, we need to solve the corresponding linear problem. In this work, we develop Laplace transform method to solve the linear sequential Riemann-Liouville fractional differential equations as well as linear sequential Caputo fractional differential equations of order nq which is sequential of order q. Also, nq is chosen such that (n-1) < nq < n. All our results yield the integer results as a special case when q tends to 1.

  9. Efficient modified Chebyshev differentiation matrices for fractional differential equations

    NASA Astrophysics Data System (ADS)

    Dabiri, Arman; Butcher, Eric A.

    2017-09-01

    This paper compares several fractional operational matrices for solving a system of linear fractional differential equations (FDEs) of commensurate or incommensurate order. For this purpose, three fractional collocation differentiation matrices (FCDMs) based on finite differences are first proposed and compared with Podlubny's matrix previously used in the literature, after which two new efficient FCDMs based on Chebyshev collocation are proposed. It is shown via an error analysis that the use of the well-known property of fractional differentiation of polynomial bases applied to these methods results in a limitation in the size of the obtained Chebyshev-based FCDMs. To compensate for this limitation, a new fast spectrally accurate FCDM for fractional differentiation which does not require the use of the gamma function is proposed. Then, the Schur-Pade and Schur decomposition methods are implemented to enhance and improve numerical stability. Therefore, this method overcomes the previous limitation regarding the size limitation. In several illustrative examples, the convergence and computation time of the proposed FCDMs are compared and their advantages and disadvantages are outlined.

  10. 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.

  11. 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.

  12. Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

    PubMed Central

    Song, Junqiang; Leng, Hongze; Lu, Fengshun

    2014-01-01

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

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

    PubMed

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

    2014-01-01

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

  14. Augmented nonlinear differentiator design and application to nonlinear uncertain systems.

    PubMed

    Shao, Xingling; Liu, Jun; Li, Jie; Cao, Huiliang; Shen, Chong; Zhang, Xiaoming

    2017-03-01

    In this paper, an augmented nonlinear differentiator (AND) based on sigmoid function is developed to calculate the noise-less time derivative under noisy measurement condition. The essential philosophy of proposed AND in achieving high attenuation of noise effect is established by expanding the signal dynamics with extra state variable representing the integrated noisy measurement, then with the integral of measurement as input, the augmented differentiator is formulated to improve the estimation quality. The prominent advantages of the present differentiation technique are: (i) better noise suppression ability can be achieved without appreciable delay; (ii) the improved methodology can be readily extended to construct augmented high-order differentiator to obtain multiple derivatives. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, the robust control problems of nonlinear uncertain systems, including a numerical example and a mass spring system, are addressed to demonstrate the effectiveness of AND in precisely estimating the disturbance and providing the unavailable differential estimate to implement output feedback based controller.

  15. Exact solutions of some fractional differential equations by various expansion methods

    NASA Astrophysics Data System (ADS)

    Topsakal, Muammer; Guner, Ozkan; Bekir, Ahmet; Unsal, Omer

    2016-10-01

    In this paper, we construct the exact solutions of some nonlinear spacetime fractional differential equations involving modified Riemann-Liouville derivative in mathematical physics and applied mathematics; namely the fractional modified Benjamin-Bona- Mahony (mBBM) and Kawahara equations by using G'/G and (G'/G, 1/G)-expansion methods.

  16. Numerical study of fractional nonlinear Schrödinger equations.

    PubMed

    Klein, Christian; Sparber, Christof; Markowich, Peter

    2014-12-08

    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.

  17. Modulational instability in fractional nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Zhang, Lifu; He, Zenghui; Conti, Claudio; Wang, Zhiteng; Hu, Yonghua; Lei, Dajun; Li, Ying; Fan, Dianyuan

    2017-07-01

    Fractional calculus is entering the field of nonlinear optics to describe unconventional regimes, as disorder biological media and soft-matter. Here we investigate spatiotemporal modulational instability (MI) in a fractional nonlinear Schrödinger equation. We derive the MI gain spectrum in terms of the Lévy indexes and a varying number of spatial dimensions. We show theoretically and numerically that the Lévy indexes affect fastest growth frequencies and MI bandwidth and gain. Our results unveil a very rich scenario that may occur in the propagation of ultrashort pulses in random media and metamaterials, and may sustain novel kinds of propagation invariant optical bullets.

  18. 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

  19. 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.

  20. On implicit abstract neutral nonlinear differential equations

    SciTech Connect

    Hernández, Eduardo; O’Regan, Donal

    2016-04-15

    In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

  1. New operational matrices for solving fractional differential equations on the half-line.

    PubMed

    Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

    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.

  2. 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

  3. 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.

  4. Amplitude death induced by fractional derivatives in nonlinear coupled oscillators

    NASA Astrophysics Data System (ADS)

    Liu, Q. X.; Liu, J. K.; Chen, Y. M.

    2017-07-01

    This paper presents a study on amplitude death in nonlinear coupled oscillators containing fractional derivatives. Analytical criterion for amplitude death region is obtained by eigenvalue analysis and verified by numerical results. It is found that amplitude death regions can be enlarged to a large extent by fractional derivatives. For this reason, amplitude death can be detected in fractional Stuart-Landau systems with weak coupling strength and low frequency, whereas it never appears in integer-order systems. Interestingly, the widening of amplitude death region induced by fractional derivative is shared by a variety of oscillators with different types of coupling mechanisms. An interpretation for the underlying mechanism of this phenomenon is briefly addressed, based on which we further suggest a coupling organization leading to amplitude death only in fractional oscillators.

  5. An approximation solution of a nonlinear equation with Riemann-Liouville's fractional derivatives by He's variational iteration method

    NASA Astrophysics Data System (ADS)

    Abbasbandy, S.

    2007-10-01

    In this article, an application of He's variational iteration method is proposed to approximate the solution of a nonlinear fractional differential equation with Riemann-Liouville's fractional derivatives. Also, the results are compared with those obtained by Adomian's decomposition method and truncated series method. The results reveal that the method is very effective and simple.

  6. 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.

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

    NASA Astrophysics Data System (ADS)

    Xu, Kaixuan; Wang, Jun

    2017-02-01

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

  8. Homogenizing atomic dynamics by fractional differential equations

    NASA Astrophysics Data System (ADS)

    Tang, Shaoqiang; Ying, Yuping

    2017-10-01

    In this paper, we propose two ways to construct fractional differential equations (FDE) for approximating atomic chain dynamics. Taking harmonic chain as an example, we add a power function of fractional order to Taylor expansion of the dispersion relation, and determine the parameters by matching two selected wave numbers. This approximate function leads to an FDE after considering both directions for wave propagation. As an alternative, we consider the symbol of the force term, and approximate it by a similar function. It also induces an FDE. Both approaches produce excellent agreement with the harmonic chain dynamics. The accuracy may be improved by optimizing the selected wave numbers, or starting with higher order Taylor expansions. When resolved in the lattice constant, the resulting FDE's faithfully reproduce the lattice dynamics. When resolved in a coarse grid instead, they systematically generate homogenized algorithms. Numerical tests are performed to verify the proposed approaches. Moreover, FDE's are also constructed for diatomic chain and anharmonic lattice, to illustrate the generality of the proposed approaches.

  9. Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative

    NASA Astrophysics Data System (ADS)

    Płociniczak, Łukasz; Okrasińska, Hanna

    2013-10-01

    In this paper, we consider a fractional nonlinear problem for anomalous diffusion. The diffusion coefficient we use is of power type, and hence the investigated problem generalizes the porous-medium equation. A generalization is made by introducing a fractional time derivative. We look for self-similar solutions for which the fractional setting introduces other than classical space-time scaling. The resulting similarity equations are of nonlinear integro-differential type. We approximate these equations by an expansion of the integral operator and by looking for solutions in a power function form. Our method can be easily adapted to solve various problems in self-similar diffusion. The approximations obtained give very good results in numerical analysis. Their simplicity allows for easy use in applications, as our fitting with experimental data shows. Moreover, our derivation justifies theoretically some previously used empirical models for anomalous diffusion.

  10. The Generation of a Series of Multiwing Chaotic Attractors Using Integer and Fractional Order Differential Equation Systems

    NASA Astrophysics Data System (ADS)

    Xu, Fei

    In this article, we present a systematic approach to design chaos generators using integer order and fractional order differential equation systems. A series of multiwing chaotic attractors and grid multiwing chaotic attractors are obtained using linear integer order differential equation systems with switching controls. The existence of chaotic attractors in the corresponding fractional order differential equation systems is also investigated. We show that, using the nonlinear fractional order differential equation system, or linear fractional order differential equation systems with switching controls, a series of multiwing chaotic attractors can be obtained.

  11. 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

  12. A new analytical approach to solve some of the fractional-order partial differential equations

    NASA Astrophysics Data System (ADS)

    Manafian, Jalil; Lakestani, Mehrdad

    2017-03-01

    The aim of the present paper is to present an analytical method for the time fractional biological population model, time fractional Burgers, time fractional Cahn-Hilliard, space-time fractional Whitham-Broer-Kaup, space-time fractional Fokas equations by using the generalized tanh-coth method. The fractional derivative is described in the sense of the modified Riemann-Liouville derivatives. The method gives an analytic solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. We have obtained the exact solutions for the aforementioned nonlinear fractional equations. A generalized fractional complex transform is appropriately used to convert these fractional equations to ordinary differential equations which subsequently resulted into number of exact solutions.

  13. Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

    NASA Astrophysics Data System (ADS)

    Li, Lei; Liu, Jian-Guo; Lu, Jianfeng

    2017-09-01

    We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.

  14. Fuzzy fractional order sliding mode controller for nonlinear systems

    NASA Astrophysics Data System (ADS)

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

    2010-04-01

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

  15. Stability of nonlinear Dirichlet BVPs governed by fractional Laplacian.

    PubMed

    Bors, Dorota

    2014-01-01

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

  16. Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian

    PubMed Central

    2014-01-01

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

  17. Transient responses of an axially accelerating viscoelastic string constituted by a fractional differentiation law

    NASA Astrophysics Data System (ADS)

    Chen, Li-Qun; Zhao, Wei-Jia; Zu, Jean W.

    2004-12-01

    This paper deals with the transverse vibration of an initially stressed moving viscoelastic string obeying a fractional differentiation constitutive law. The governing equation is derived from Newtonian second law of motion, and reduced to a set of non-linear differential-integral equations based on Galerkin's truncation. A numerical approach is proposed to solve numerically the differential-integral equation through developing an approximate expression of the fractional derivatives involved. Some numerical examples are presented to highlight the effects of viscoelastic parameters and frequencies of parametric excitations on the transient responses of the axially moving string.

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

    NASA Astrophysics Data System (ADS)

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

    2012-08-01

    In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space-time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics.

  19. A high-speed algorithm for computation of fractional differentiation and fractional integration.

    PubMed

    Fukunaga, Masataka; Shimizu, Nobuyuki

    2013-05-13

    A high-speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm, the stored data are not the function to be differentiated or integrated but the weighted integrals of the function. The intervals of integration for the memory can be increased without loss of accuracy as the computing time-step n increases. The computing cost varies as n log n, as opposed to n(2) of standard algorithms.

  20. Nonlinear vibration of viscoelastic beams described using fractional order derivatives

    NASA Astrophysics Data System (ADS)

    Lewandowski, Roman; Wielentejczyk, Przemysław

    2017-07-01

    The problem of non-linear, steady state vibration of beams, harmonically excited by harmonic forces is investigated in the paper. The viscoelastic material of the beams is described using the Zener rheological model with fractional derivatives. The constitutive equation, which contains derivatives of both stress and strain, significantly complicates the solution to the problem. The von Karman theory is applied to take into account geometric nonlinearities. Amplitude equations are obtained using the finite element method together with the harmonic balance method, and solved using the continuation method. The tangent matrix of the amplitude equations is determined in an explicit form. The stability of the steady-state solution is also examined. A parametric study is carried out to determine the influence of viscoelastic properties of the material on the beam's responses.

  1. Fractional embedding of differential operators and Lagrangian systems

    NASA Astrophysics Data System (ADS)

    Cresson, Jacky

    2007-03-01

    This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the stochastic embedding theory developed with Darses [C. R. Acad. Sci. Ser. I: Math 342, 333 (2006); (preprint IHES 06/27, p. 87, 2006)], we define the fractional embedding of differential operators and ordinary differential equations. We construct an operator combining in a symmetric way the left and right (Riemann-Liouville) fractional derivatives. For Lagrangian systems, our method provides a fractional Euler-Lagrange equation. We prove, developing the corresponding fractional calculus of variations, that such equation can be derived via a fractional least-action principle. We then obtain naturally a fractional Noether theorem and a fractional Hamiltonian formulation of fractional Lagrangian systems. All these constructions are coherents, i.e., the embedding procedure is compatible with the fractional calculus of variations. We then extend our results to cover the Ostrogradski formalism. Using the fractional embedding and following a previous work of Riewe [Phys. Rev. E 53, 1890 (1996); Phys. Rev. E 55, 3581 (1997)], we obtain a fractional Ostrogradski formalism which allows us to derive nonconservative dynamical systems via a fractional generalized least-action principle. We also discuss the Whittaker equations and obtain a fractional Lagrangian formulation. Last, we discuss the fractional embedding of continuous Lagrangian systems. In particular, we obtain a fractional Lagrangian formulation of the classical fractional wave equation introduced by Schneider and Wyss [J. Math. Phys. 30, 134 (1989)] as well as the fractional diffusion equation.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  3. Applications of homogenous balanced principle on investigating exact solutions to a series of time fractional nonlinear PDEs

    NASA Astrophysics Data System (ADS)

    Rui, Weiguo

    2017-06-01

    By using a counterexample, we proved the fractional chain rule appeared in many references does not hold under Riemann-Liouville definition and Caputo definition of fractional derivative. It shows that this chain rule is invalid in investigating exact solutions of nonlinear fractional partial differential equations (PDEs). In this paper, based on the homogenous balanced principle, the function-expansion method of separation variable type are introduced. By using this method, a series of nonlinear time fractional PDEs such as time fractional KdV equation and Burgers equation, time fractional diffusion-convection equations are studied from mathematical viewpoint. The dynamical properties of these exact solutions are discussed and the profiles of several representative exact solutions are illustrated.

  4. Bifurcation and stability for a nonlinear parabolic partial differential equation

    NASA Technical Reports Server (NTRS)

    Chafee, N.

    1973-01-01

    Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.

  5. 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.

  6. 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.

  7. 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.

  8. Existence of a coupled system of fractional differential equations

    NASA Astrophysics Data System (ADS)

    Ibrahim, Rabha W.; Siri, Zailan

    2015-10-01

    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.

  9. Chaos in the fractional order nonlinear Bloch equation with delay

    NASA Astrophysics Data System (ADS)

    Baleanu, Dumitru; Magin, Richard L.; Bhalekar, Sachin; Daftardar-Gejji, Varsha

    2015-08-01

    The Bloch equation describes the dynamics of nuclear magnetization in the presence of static and time-varying magnetic fields. In this paper we extend a nonlinear model of the Bloch equation to include both fractional derivatives and time delays. The Caputo fractional time derivative (α) in the range from 0.85 to 1.00 is introduced on the left side of the Bloch equation in a commensurate manner in increments of 0.01 to provide an adjustable degree of system memory. Time delays for the z component of magnetization are inserted on the right side of the Bloch equation with values of 0, 10 and 100 ms to balance the fractional derivative with delay terms that also express the history of an earlier state. In the absence of delay, τ = 0 , we obtained results consistent with the previously published bifurcation diagram, with two cycles appearing at α = 0.8548 with subsequent period doubling that leads to chaos at α = 0.9436 . A periodic window is observed for the range 0.962 < α < 0.9858 , with chaos arising again as α nears 1.00. The bifurcation diagram for the case with a 10 ms delay is similar: two cycles appear at the value α = 0.8532 , and the transition from two to four cycles at α = 0.9259 . With further increases in the fractional order, period doubling continues until at α = 0.9449 chaos ensues. In the case of a 100 millisecond delay the transitions from one cycle to two cycles and two cycles to four cycles are observed at α = 0.8441 , and α = 0.8635 , respectively. However, the system exhibits chaos at much lower values of α (α = 0.8635). A periodic window is observed in the interval 0.897 < α < 0.9341 , with chaos again appearing for larger values of α . In general, as the value of α decreased the system showed transitions from chaos to transient chaos, and then to stability. Delays naturally appear in many NMR systems, and pulse programming allows the user control over the process. By including both the fractional derivative and time delays in

  10. Jacobi wavelet operational matrix of fractional integration for solving fractional integro-differential equation

    NASA Astrophysics Data System (ADS)

    Rong, Loh Jian; Chang, Phang

    2016-02-01

    In this paper, we first define generalized shifted Jacobi polynomial on interval and then use it to define Jacobi wavelet. Then, the operational matrix of fractional integration for Jacobi wavelet is being derived to solve fractional differential equation and fractional integro-differential equation. This method can be seen as a generalization of other orthogonal wavelet operational methods, e.g. Legendre wavelets, Chebyshev wavelets of 1st kind, Chebyshev wavelets of 2nd kind, etc. which are special cases of the Jacobi wavelets. We apply our method to a special type of fractional integro-differential equation of Fredholm type.

  11. On the solution of system of fractional nonlinear predator-prey population model via homotopy decomposition method

    NASA Astrophysics Data System (ADS)

    Atangana, Abdon

    2013-10-01

    We exploit a relatively new analytical technique, the Homotopy Decomposition Method (HDM), for solving nonlinear fractional partial differential equations arising in prey-predator biological population dynamics system. Numerical solutions are provided and they have certain properties which exhibit biologically significant dependence on the parameter values. The fractional derivatives are described in the Caputo sense. The HDM is reliable and reduces the number of computations. This gives the HDM a wider applicability. In addition, the method is very easy to use.

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

    NASA Astrophysics Data System (ADS)

    Moroney, Timothy; Yang, Qianqian

    2013-08-01

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

  13. Non-Differentiable Exact Solutions for the Nonlinear Odes Defined on Fractal Sets

    NASA Astrophysics Data System (ADS)

    Yang, Xiao-Jun; Gao, Feng; Srivastava, H. M.

    In the present paper, a family of the special functions via the celebrated Mittag-Leffler function defined on the Cantor sets is investigated. The nonlinear local fractional ODEs (NLFODEs) are presented by following the rules of local fractional derivative (LFD). The exact solutions for these problems are also discussed with the aid of the non-differentiable charts on Cantor sets. The obtained results are important for describing the characteristics of the fractal special functions.

  14. On fractional differential inclusions with the Jumarie derivative

    SciTech Connect

    Kamocki, Rafał; Obczyński, Cezary

    2014-02-15

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

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. Fluid limit of nonintegrable continuous-time random walks in terms of fractional differential equations.

    PubMed

    Sánchez, R; Carreras, B A; van Milligen, B Ph

    2005-01-01

    The fluid limit of a recently introduced family of nonintegrable (nonlinear) continuous-time random walks is derived in terms of fractional differential equations. In this limit, it is shown that the formalism allows for the modeling of the interaction between multiple transport mechanisms with not only disparate spatial scales but also different temporal scales. For this reason, the resulting fluid equations may find application in the study of a large number of nonlinear multiscale transport problems, ranging from the study of self-organized criticality to the modeling of turbulent transport in fluids and plasmas.

  20. 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.

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

    PubMed

    Khader, M M

    2013-10-01

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

  2. Analytical schemes for a new class of fractional differential equations

    NASA Astrophysics Data System (ADS)

    Agrawal, O. P.

    2007-05-01

    Fractional differential equations (FDEs) considered so far contain mostly left (or forward) fractional derivatives. In this paper, we present analytical solutions for a class of FDEs which contain both the left and the right (or the forward and the backward) fractional derivatives. The methods presented use properties of fractional integral operators (which, in many cases, lead to Volterra-type integral equations), an operational approach and a successive approximation method to obtain the solutions. The methods are demonstrated using some examples. The FDEs considered may come from fractional variational calculus (FVC) or from other physical principles. In the case of fractional variational problems (FVPs), the transversality conditions are used to identify appropriate boundary conditions and to solve the problems. It is hoped that this study will lead to further investigations in the field and more elegant solutions would be found.

  3. Exact solutions to nonlinear delay differential equations of hyperbolic type

    NASA Astrophysics Data System (ADS)

    Vyazmin, Andrei V.; Sorokin, Vsevolod G.

    2017-01-01

    We consider nonlinear delay differential equations of hyperbolic type, including equations with varying transfer coefficients and varying delays. The equations contain one or two arbitrary functions of a single argument. We present new classes of exact generalized and functional separable solutions. All the solutions involve free parameters and can be suitable for solving certain model problems as well as testing numerical and approximate analytical methods for similar and more complex nonlinear differential-difference equations.

  4. 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.

  5. 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.

  6. GHM method for obtaining rationalsolutions of nonlinear differential equations.

    PubMed

    Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo

    2015-01-01

    In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

  7. An image-enhancement method based on variable-order fractional differential operators.

    PubMed

    Xu, Mengjia; Yang, Jinzhu; Zhao, Dazhe; Zhao, Hong

    2015-01-01

    In this study, we develop a new algorithm based on fractional operators of variable-order in order to enhance image quality. First, three kinds of popular high-order discrete formulas are adopted to obtain the coefficients, and subsequently, a mask optimization method for selecting the fractional order adaptively is applied to construct a variable-order fractional differential mask along with the coefficients generated from the first step. We carry out experiments on OCT thoracic aorta images and some nature images with low contrast and noise, demonstrating that the high-order discrete method leads to significantly better performance in enhancing the edge information nonlinearly compared to the standard first-order discrete method. Moreover, the optimized mask with variable-order of the fractional derivative not only can preserve the edge information of the processed images adequately, but it also effectively suppresses the noise in the smooth area.

  8. Model Predictive Control for Nonlinear Parabolic Partial Differential Equations

    NASA Astrophysics Data System (ADS)

    Hashimoto, Tomoaki; Yoshioka, Yusuke; Ohtsuka, Toshiyuki

    In this study, the optimal control problem of nonlinear parabolic partial differential equations (PDEs) is investigated. Optimal control of nonlinear PDEs is an open problem with applications that include fluid, thermal, biological, and chemically-reacting systems. Model predictive control with a fast numerical solution method has been well established to solve the optimal control problem of nonlinear systems described by ordinary differential equations. In this study, we develop a design method of the model predictive control for nonlinear systems described by parabolic PDEs. Our approach is a direct infinite dimensional extension of the model predictive control method for finite-dimensional systems. The objective of this paper is to develop an efficient algorithm for numerically solving the model predictive control problem of nonlinear parabolic PDEs. The effectiveness of the proposed method is verified by numerical simulations.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. Nonlinear partial differential equations: Integrability, geometry and related topics

    NASA Astrophysics Data System (ADS)

    Krasil'shchik, Joseph; Rubtsov, Volodya

    2017-03-01

    Geometry and Differential Equations became inextricably entwined during the last one hundred fifty years after S. Lie and F. Klein's fundamental insights. The two subjects go hand in hand and they mutually enrich each other, especially after the "Soliton Revolution" and the glorious streak of Symplectic and Poisson Geometry methods in the context of Integrability and Solvability problems for Non-linear Differential Equations.

  14. Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency.

    PubMed

    Chen, W; Holm, S

    2004-04-01

    Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often called the anomalous attenuation. In this study, a linear integro-differential equation wave model was developed for the anomalous attenuation by using the space-fractional Laplacian operation, and the strategy is then extended to the nonlinear Burgers equation. A new definition of the fractional Laplacian is also introduced which naturally includes the boundary conditions and has inherent regularization to ease the hypersingularity in the conventional fractional Laplacian. Under the Szabo's smallness approximation, where attenuation is assumed to be much smaller than the wave number, the linear model is found consistent with arbitrary frequency power-law dependency.

  15. 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.

  16. 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.

  17. 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.

  18. Stability analysis of linear fractional differential system with distributed delays

    NASA Astrophysics Data System (ADS)

    Veselinova, Magdalena; Kiskinov, Hristo; Zahariev, Andrey

    2015-11-01

    In the present work we study the Cauchy problem for linear incommensurate fractional differential system with distributed delays. For the autonomous case with distributed delays with derivatives in Riemann-Liouville or Caputo sense, we establish sufficient conditions under which the zero solution is globally asymptotic stable. The established conditions coincide with the conditions which guaranty the same result in the particular case of system with constant delays and for the case of system without delays in the commensurate case too.

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

    NASA Astrophysics Data System (ADS)

    Baskonus, Haci Mehmet; Bulut, Hasan

    2015-10-01

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

  20. Similarity solution to fractional nonlinear space-time diffusion-wave equation

    NASA Astrophysics Data System (ADS)

    Costa, F. Silva; Marão, J. A. P. F.; Soares, J. C. Alves; de Oliveira, E. Capelas

    2015-03-01

    In this article, the so-called fractional nonlinear space-time wave-diffusion equation is presented and discussed. This equation is solved by the similarity method using fractional derivatives in the Caputo, Riesz-Feller, and Riesz senses. Some particular cases are presented and the corresponding solutions are shown by means of 2-D and 3-D plots.

  1. Characterizing the Performance of Nonlinear Differential Operators

    DTIC Science & Technology

    2012-09-01

    dissipation properties are equivalent to the existence of a solution to a corresponding Hamilton Jacobi Bellman partial differential equation 4 (HJB...that the tightest possible transient bound βγ∗ given γ ∈ K (as defined by (7)) can be represented equivalently by βγ∗ (s) = sup |x|≤s V (x, 0) (23...B9]. 2.7 References [R1] D. Angeli, E.D. Sontag, and Y. Wang. Further equivalences and semiglobal versions of integral input to state stability

  2. A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications

    NASA Astrophysics Data System (ADS)

    Gao, Guang-hua; Sun, Zhi-zhong; Zhang, Hong-wei

    2014-02-01

    In the present work, first, a new fractional numerical differentiation formula (called the L1-2 formula) to approximate the Caputo fractional derivative of order α (0<α<1) is developed. It is established by means of the quadratic interpolation approximation using three points (tj-2,f(tj-2)),(tj-1,f(tj-1)) and (tj,f(tj)) for the integrand f(t) on each small interval [tj-1,tj] (j⩾2), while the linear interpolation approximation is applied on the first small interval [t0,t1]. As a result, the new formula can be formally viewed as a modification of the classical L1 formula, which is obtained by the piecewise linear approximation for f(t). Both the computational efficiency and numerical accuracy of the new formula are superior to that of the L1 formula. The coefficients and truncation errors of this formula are discussed in detail. Two test examples show the numerical accuracy of L1-2 formula. Second, by the new formula, two improved finite difference schemes with high order accuracy in time for solving the time-fractional sub-diffusion equations on a bounded spatial domain and on an unbounded spatial domain are constructed, respectively. In addition, the application of the new formula into solving fractional ordinary differential equations is also presented. Several numerical examples are computed. The comparison with the corresponding results of finite difference methods by the L1 formula demonstrates that the new L1-2 formula is much more effective and more accurate than the L1 formula when solving time-fractional differential equations numerically.

  3. 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.

  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. A fractional differential equation for a MEMS viscometer used in the oil industry

    NASA Astrophysics Data System (ADS)

    Fitt, A. D.; Goodwin, A. R. H.; Ronaldson, K. A.; Wakeham, W. A.

    2009-07-01

    A mathematical model is developed for a micro-electro-mechanical system (MEMS) instrument that has been designed primarily to measure the viscosity of fluids that are encountered during oil well exploration. It is shown that, in one mode of operation, the displacement of the device satisfies a fractional differential equation (FDE). The theory of FDEs is used to solve the governing equation in closed form and numerical solutions are also determined using a simple but efficient central difference scheme. It is shown how knowledge of the exact and numerical solutions enables the design of the device to be optimised. It is also shown that the numerical scheme may be extended to encompass the case of a nonlinear spring, where the resulting FDE is nonlinear.

  6. Stability, boundedness, and lagrange stability of fractional differential equations with initial time difference.

    PubMed

    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.

  7. Renormalization of tracer turbulence leading to fractional differential equations.

    PubMed

    Sánchez, R; Carreras, B A; Newman, D E; Lynch, V E; van Milligen, B Ph

    2006-07-01

    For many years quasilinear renormalization has been applied to numerous problems in turbulent transport. This scheme relies on the localization hypothesis to derive a linear transport equation from a simplified stochastic description of the underlying microscopic dynamics. However, use of the localization hypothesis narrows the range of transport behaviors that can be captured by the renormalized equations. In this paper, we construct a renormalization procedure that manages to avoid the localization hypothesis completely and produces renormalized transport equations, expressed in terms of fractional differential operators, that exhibit much more of the transport phenomenology observed in nature. This technique provides a first step toward establishing a rigorous link between the microscopic physics of turbulence and the fractional transport models proposed phenomenologically for a wide variety of turbulent systems such as neutral fluids or plasmas.

  8. Lithium-ion batteries modeling involving fractional differentiation

    NASA Astrophysics Data System (ADS)

    Sabatier, Jocelyn; Merveillaut, Mathieu; Francisco, Junior Mbala; Guillemard, Franck; Porcelatto, Denis

    2014-09-01

    With hybrid and electric vehicles development, automobile battery monitoring systems (BMS) have to meet the new requirements. These systems have to give information on state of health, state of charge, available power. To get this information, BMS often implement battery models. Accuracy of the information manipulated by the BMS thus depends on the model accuracy. This paper is within this framework and addresses lithium-ion battery modeling. The proposed fractional model is based on simplifications of an electrochemical model and on resolution of some partial differential equations used in its description. Such an approach permits to get a simple model in which electrochemical variables and parameters still appear.

  9. 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.

  10. Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice.

    PubMed

    Huang, Changming; Dong, Liangwei

    2016-12-15

    We predict the existence of gap solitons in the nonlinear fractional Schrödinger equation (NLFSE) with an imprinted optically harmonic lattice. Symmetric/antisymmetric nonlinear localized modes bifurcate from the lower/upper edge of the first/second band in defocusing/focusing Kerr media. A unique feature we revealed is that, in focusing Kerr media, stable solitons appear in the finite bandgaps with the decrease of the Lévy index, which is in sharp contrast to the standard NLSE with a focusing nonlinearity. Nonlinear bound states composed by in-phase and out-of-phase soliton units supported by the NLFSE are also uncovered. Our work may pave the way for the study of spatial lattice solitons in fractional dimensions.

  11. Fractional order of rational Jacobi functions for solving the non-linear singular Thomas-Fermi equation

    NASA Astrophysics Data System (ADS)

    Parand, Kourosh; Mazaheri, Pooria; Yousefi, Hossein; Delkhosh, Mehdi

    2017-02-01

    In this paper, a new method based on Fractional order of Rational Jacobi (FRJ) functions is proposed that utilizes quasilinearization method to solve non-linear singular Thomas-Fermi equation on unbounded interval [0,∞). The equation is solved without domain truncation and variable changing. First, the quasilinearization method is used to convert the equation to the sequence of linear ordinary differential equations. Then, by using the FRJs collocation method the equations are solved. For the evaluation, comparison with some numerical solutions shows that the proposed solution is highly accurate.

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

  13. Reproducibility of Differential Proteomic Technologies in CPTAC Fractionated Xenografts

    SciTech Connect

    Tabb, David L.; Wang, Xia; Carr, Steven A.; Clauser, Karl R.; Mertins, Philipp; Chambers, Matthew C.; Holman, Jerry D.; Wang, Jing; Zhang, Bing; Zimmerman, Lisa J.; Chen, Xian; Gunawardena, Harsha P.; Davies, Sherri R.; Ellis, Matthew J. C.; Li, Shunqiang; Townsend, R. Reid; Boja, Emily S.; Ketchum, Karen A.; Kinsinger, Christopher R.; Mesri, Mehdi; Rodriguez, Henry; Liu, Tao; Kim, Sangtae; McDermott, Jason E.; Payne, Samuel H.; Petyuk, Vladislav A.; Rodland, Karin D.; Smith, Richard D.; Yang, Feng; Chan, Daniel W.; Zhang, Bai; Zhang, Hui; Zhang, Zhen; Zhou, Jian-Ying; Liebler, Daniel C.

    2016-03-04

    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. From these assessments we found that differential genes from a single replicate were confirmed by other replicates on the same instrument from 61-93% of the time. When comparing across different instruments and quantitative technologies, differential genes were reproduced by other data sets from 67-99% of the time. Projecting gene differences to biological pathways and networks increased the similarities. These overlaps send an encouraging message about the maturity of technologies for proteomic differentiation.

  14. 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

  15. Determining the Parameters of Fractional Exponential Hereditary Kernels for Nonlinear Viscoelastic Materials

    NASA Astrophysics Data System (ADS)

    Golub, V. P.; Pavlyuk, Ya. V.; Fernati, P. V.

    2013-03-01

    The parameters of fractional-exponential hereditary kernels for nonlinear viscoelastic materials are determined. Methods for determining the parameters used in the third-order theory of viscoelasticity and in nonlinear theories based on the similarity of primary creep curves and the similarity of isochronous creep curves are analyzed. The parameters of fractional-exponential hereditary kernels are determined and tested against experimental data for microplastic, TC-8/3-250 glass-reinforced plastics, SVAM glass-reinforced plastics. The results (tables and plots) are analyzed

  16. Existence and Uniqueness Theorems for Impulsive Fractional Differential Equations with the Two-Point and Integral Boundary Conditions

    PubMed Central

    Mardanov, M. J.; Mahmudov, N. I.; Sharifov, Y. A.

    2014-01-01

    We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order α (0 < α ≤ 1) involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case α = 1. PMID:24782675

  17. Existence and uniqueness theorems for impulsive fractional differential equations with the two-point and integral boundary conditions.

    PubMed

    Mardanov, M J; Mahmudov, N I; Sharifov, Y A

    2014-01-01

    We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order α (0 < α ≤ 1) involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case α = 1.

  18. Traveling wave solution of fractional KdV-Burger-Kuramoto equation describing nonlinear physical phenomena

    NASA Astrophysics Data System (ADS)

    Gupta, A. K.; Ray, S. Saha

    2014-09-01

    In this paper, KdV-Burger-Kuramoto equation involving instability, dissipation, and dispersion parameters is solved numerically. The numerical solution for the fractional order KdV-Burger-Kuramoto (KBK) equation has been presented using two-dimensional Legendre wavelet method. The approximate solutions of nonlinear fractional KBK equation thus obtained by Legendre wavelet method are compared with the exact solutions. The present scheme is very simple, effective and convenient for obtaining numerical solution of the KBK equation.

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

  20. Evidence for Differentiation by Crystal Fractionation in Theo's Flow, Canada

    NASA Astrophysics Data System (ADS)

    Lentz, R. C.; Collins, L. E.; McCoy, T. J.; Taylor, J.

    2003-12-01

    Theo's Flow, a 120-m thick differentiated lava flow in Munro Twp, Ontario, is an unusual magma body which calls for an unusual formation mechanism. New systematic sampling of the flow for geochemistry and petrography offers additional clues to its post-emplacement differentiation. Evidence for differentiation comes from both petrography and geochemistry. Theo's has four lithologic units: a basal peridotite (3-9 m), a thick pyroxenite (50 m) and gabbro (40 m), and a capping (8-12 m) hyaloclastite. Contacts between lithologic layers are gradual, mostly marked by changes in modal mineralogy, although there is also a distinct change in plagioclase morphology concurrent with its modal increase. From pyroxenite to gabbro, plagioclase shifts from fine, interstitial sprays to large laths in a subophitic intergrowth with pyroxene. Whole rock and pyroxene compositions display typical fractionation trends (e.g. Fe/Mg, Ti, Zr, Nb increase upsection). Furthermore, a weighted sum of 22 whole rock compositions from the internal layers match the hyaloclastite composition well for most non-mobile elements. All these factors suggest formation of the three internal layers by fractional crystallization and evolution of a magma whose composition is represented by the hyaloclastite. Any proposed differentiation process must address some specific observations. Cluster and CSD analysis reveal that pyroxene grains grew in clusters under steady-state conditions of nucleation and growth. Pyroxene grain size is nearly uniform throughout the pyroxenite, suggesting thermal conditions were maintained over a long crystallization interval. Progression of a typical solidification front would produce a fine-grained roof crust beneath the quenched top, but there is no evidence of such a layer in Theo's. Unlike magmas for which solidification fronts are invoked, Theo's parent magma was highly mafic and Al-poor, yielding a low viscosity magma (4 Pa-s) that crystallized only pyroxene over a long

  1. Asymptotic stability for nonlinear damped Kirchhoff systems involving the fractional p-Laplacian operator

    NASA Astrophysics Data System (ADS)

    Pucci, Patrizia; Saldi, Sara

    2017-09-01

    This paper is devoted to the question of global and local asymptotic stability for nonlinear damped Kirchhoff systems, with homogeneous Dirichlet boundary conditions, under fairly natural assumptions on the external force f = f (t , x , u), the distributed damping Q = Q (t , x , u ,ut), the perturbation term μ | u| p - 2 u and the dissipative term ϱ (t) M ([u]sp) |ut| p - 2ut, with ϱ ≥ 0 and in Lloc1 (R0+), when the initial data are in a special region. Here u = (u1 , … ,uN) = u (t , x) represents the vectorial displacement, with N ≥ 1. Particular attention is devoted to the asymptotic behavior of the solutions in the linear case specified in Section 5. Finally, the results are extended to problems where the fractional p-Laplacian is replaced by a more general elliptic nonlocal integro-differential operator. The paper extends in several directions recent theorems and covers also the so-called degenerate case, that is the case in which M is zero at zero.

  2. 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.

  3. Dynamical process of complex systems and fractional differential equations

    NASA Astrophysics Data System (ADS)

    Hara, Hiroaki; Tamura, Yoshiyasu

    2013-10-01

    Behavior of dynamical process of complex systems is investigated. Specifically we analyse two types of ideal complex systems. For analysing the ideal complex systems, we define the response functions describing the internal states to an external force. The internal states are obtained as a relaxation process showing a "power law" distribution, such as scale free behaviors observed in actual measurements. By introducing a hybrid system, the logarithmic time, and double logarithmic time, we show how the "slow relaxation" (SR) process and "super slow relaxation" (SSR) process occur. Regarding the irregular variations of the internal states as an activation process, we calculate the response function to the external force. The behaviors are classified into "power", "exponential", and "stretched exponential" type. Finally we construct a fractional differential equation (FDE) describing the time evolution of these complex systems. In our theory, the exponent of the FDE or that of the power law distribution is expressed in terms of the parameters characterizing the structure of the system.

  4. Cylindrical electron acoustic solitons for modified time-fractional nonlinear equation

    NASA Astrophysics Data System (ADS)

    Abdelwahed, H. G.; El-Shewy, E. K.; Mahmoud, Abeer A.

    2017-08-01

    The modulation of cylindrical electron acoustic characteristics using a time fractal modified nonlinear equation has been investigated in nonisothermal plasmas. The time fractional cylindrical modified-Korteweg-de Vries equation has been obtained by Agrawal's analysis. A cylindrical localized soliton has been obtained via the Adomian decomposition method. The pressure term and cylindrical time fractional effects on the modulated wave properties have been investigated with comparative auroral observations. It is established that the presence of the fractional order factor not only significantly modifies the solitary characteristics but also varies the profile polarity.

  5. Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains

    NASA Astrophysics Data System (ADS)

    Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.

    2017-02-01

    In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.

  6. Function projective synchronization between integer-order and stochastic fractional-order nonlinear systems.

    PubMed

    Geng, Lingling; Yu, Yongguang; Zhang, Shuo

    2016-09-01

    In this paper, the function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is investigated. Firstly, according to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Thus, the stability of the stochastic error system can be analyzed through its equivalent deterministic one. Finally, to demonstrate the effectiveness of the proposed scheme, the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system is studied.

  7. Nonlinear mixing of optical vortices with fractional topological charge in Raman sideband generation

    NASA Astrophysics Data System (ADS)

    Strohaber, J.; Boran, Y.; Sayrac, M.; Johnson, L.; Zhu, F.; Kolomenskii, A. A.; Schuessler, H. A.

    2017-01-01

    We studied the nonlinear parametric interaction of femtosecond fractionally-charged optical vortices in a Raman-active medium. Propagation of such beams was described using the Kirchhoff-Fresnel integrals by embedding a non-integer 2π phase step in a Gaussian beam profile. When using fractionally-charged pump or Stokes beams, we observed the production of new topological charge and phase discontinuities in the Raman field. These newly generated fractionally-charged Raman vortex beams were found to follow the same orbital angular momentum algebra derived by Strohaber et al (2012 Opt. Lett. 37 3411) for integer vortex beams.

  8. 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.

  9. Oscillation of a class of fractional differential equations with damping term.

    PubMed

    Qin, Huizeng; Zheng, Bin

    2013-01-01

    We investigate the oscillation of a class of fractional differential equations with damping term. Based on a certain variable transformation, the fractional differential equations are converted into another differential equations of integer order with respect to the new variable. Then, using Riccati transformation, inequality, and integration average technique, some new oscillatory criteria for the equations are established. As for applications, oscillation for two certain fractional differential equations with damping term is investigated by the use of the presented results.

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

    SciTech Connect

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

    1998-02-01

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

  11. Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods

    NASA Astrophysics Data System (ADS)

    Mao, Zhiping; Karniadakis, George Em

    2017-05-01

    We consider the viscous Burgers equation with a fractional nonlinear term as a model involving non-local nonlinearities in conservation laws, which, surprisingly, has an analytical solution obtained by a fractional extension of the Hopf-Cole transformation. We use this model and its inviscid limit to develop stable spectral and discontinuous Galerkin spectral element methods by employing the concept of spectral vanishing viscosity (SVV). For the global spectral method, SVV is very effective and the computational cost is O (N2), which is essentially the same as for the standard Burgers equation. We also develop a local discontinuous Galerkin (LDG) spectral element method to improve the accuracy around discontinuities, and we again stabilize the LDG method with the SVV operator. Finally, we solve numerically the inviscid fractional Burgers equation both with the spectral and the spectral element LDG methods. We study systematically the stability and convergence of both methods and determine the effectiveness of each method for different parameters.

  12. Control design for one-sided Lipschitz nonlinear differential inclusions.

    PubMed

    Cai, Xiushan; Gao, Hong; Liu, Leipo; Zhang, Wei

    2014-03-01

    This paper considers stabilization and signal tracking control for one-sided Lipschitz nonlinear differential inclusions (NDIs). Sufficient conditions for exponential stabilization for the closed-loop system are given based on linear matrix inequality theory. Further, the design method is extended to signal tracking control for one-sided Lipschitz NDIs. A control law is designed such that the state of the closed-loop system asymptotically tracks the reference signal. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design technique.

  13. 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.

  14. 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.

  15. Numerical Solution of a Nonlinear Integro-Differential Equation

    NASA Astrophysics Data System (ADS)

    Buša, Ján; Hnatič, Michal; Honkonen, Juha; Lučivjanský, Tomáš

    2016-02-01

    A discretization algorithm for the numerical solution of a nonlinear integrodifferential equation modeling the temporal variation of the mean number density a(t) in the single-species annihilation reaction A + A → 0 is discussed. The proposed solution for the two-dimensional case (where the integral entering the equation is divergent) uses regularization and then finite differences for the approximation of the differential operator together with a piecewise linear approximation of a(t) under the integral. The presented numerical results point to basic features of the behavior of the number density function a(t) and suggest further improvement of the proposed algorithm.

  16. Connecting orbits for nonlinear differential equations at resonance

    NASA Astrophysics Data System (ADS)

    Kokocki, Piotr

    We study the existence of orbits connecting stationary points for the first order differential equations being at resonance at infinity, where the right hand side is the perturbations of a sectorial operator. Our aim is to prove an index formula expressing the Conley index of associated semiflow with respect to appropriately large ball, in terms of special geometrical assumptions imposed on the nonlinearity. We also prove that the geometrical assumptions are generalization of the well-known in literature Landesman-Lazer and strong resonance conditions. Obtained index formula will be used to derive the criteria determining the existence of orbits connecting stationary points for the heat equation being at resonance at infinity.

  17. Stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation

    NASA Astrophysics Data System (ADS)

    Yang, Yongge; Xu, Wei; Sun, Yahui; Xiao, Yanwen

    2017-01-01

    This paper aims to investigate the stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation. Firstly, the original stochastic vibroimpact system with fractional derivative is transformed into equivalent stochastic vibroimpact system without fractional derivative. Then, the non-smooth transformation and stochastic averaging method are used to obtain the analytical solutions of the equivalent stochastic system. At last, in order to verify the effectiveness of the above mentioned approach, the van der Pol vibroimpact system with fractional derivative is worked out in detail. A very satisfactory agreement can be found between the analytical results and the numerical results. An interesting phenomenon we found in this paper is that the fractional order and fractional coefficient of the stochastic van der Pol vibroimpact system can induce the occurrence of stochastic P-bifurcation. To the best of authors' knowledge, the stochastic P-bifurcation phenomena induced by fractional order and fractional coefficient have not been found in the present available literature which studies the dynamical behaviors of stochastic system with fractional derivative under Gaussian white noise excitation.

  18. Nonlinear system stochastic response determination via fractional equivalent linearization and Karhunen-Loève expansion

    NASA Astrophysics Data System (ADS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-08-01

    In this paper, a novel fractional equivalent linearization (EL) approach is developed by incorporating a fractional derivative term into the classical linearization equation. Due to the introduction of the fractional derivative term, the accuracy of the new linearization is improved, illustrated by a Duffing oscillator that is subjected to a harmonic excitation. Furthermore, a new method for solving stochastic response of nonlinear SDOF system is developed by combining Karhunen-Loève (K-L) expansion and fractional EL. The method firstly decomposes the stochastic excitation in terms of a set of random variables and deterministic sub-excitations using K-L expansion, and then construct sub-fractional equivalent linear system according to each sub-excitation by fractional EL, the response of the original nonlinear system is finally approximated as the weighed summation of the deterministic response of each sub-system multiplied by the corresponding random variable. The random nature of the final response comes from the set of random variables that is obtained in K-L expansion. In this way, the stochastic response computation is converted to a set of deterministic response analysis problems. The effectiveness of the developed method is demonstrated by a Duffing oscillator that is subjected to stochastic excitation modeled by Winner process. The results are compared with the numerical method and Monte Carlo simulation (MCS).

  19. 1/f noise from nonlinear stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Ruseckas, J.; Kaulakys, B.

    2010-03-01

    We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/fβ noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/fβ noise, and provides further insights into the origin of 1/fβ noise.

  20. A model to determine the petroleum pressure in a well using fractional differential equations

    NASA Astrophysics Data System (ADS)

    Brito Martinez, Beatriz; Brambila Paz, Fernando; Fuentes Ruiz, Carlos

    2016-11-01

    A noninvasive method was used to determine the pressure of petroleum leaving a well. The mathematical model is based on nonlinear fractional differential equations. This model comes from the fractal dimension of the porous medium. The problem is solved in three stages. In the first stage the fractal dimension of the porous medium is determined. We show that microwaves reflected and transmitted through soil have a fractal dimension which is correlated with the fractal dimension of the porous medium. The fractal signature of microwave scattering correlates with certain physical and mechanical properties of soils (porosity, permeability, conductivity, etc.). In the second stage we use three partial fractional equations as a mathematical model to study the diffusion inside the porous medium. In this model sub-diffusive phenomenon occurs if fractal derivative is between zero and one and supra-diffusive occurs if the derivative is greater than 1 and less than 2. Finally in the third stage the mathematical model is used to determinate the petroleum pressure output in a Mexican oil field, which contains three partial fractional equations with triple porosity and permeability.

  1. Nonlinear analysis and analog simulation of a piezoelectric buckled beam with fractional derivative

    NASA Astrophysics Data System (ADS)

    Mokem Fokou, I. S.; Buckjohn, C. Nono Dueyou; Siewe Siewe, M.; Tchawoua, C.

    2017-08-01

    In this article, an analog circuit for implementing fractional-order derivative and a harmonic balance method for a vibration energy harvesting system under pure sinusoidal vibration source is proposed in order to predict the system response. The objective of this paper is to discuss the performance of the system with fractional derivative and nonlinear damping (μb). Bifurcation diagram, phase portrait and power spectral density (PSD) are provided to deeply characterize the dynamics of the system. These results are corroborated by the 0-1 test. The appearance of the chaotic vibrations reduces the instantaneous voltage. The pre-experimental investigation is carried out through appropriate software electronic circuit (Multisim). The corresponding electronic circuit is designed, exhibiting periodic and chaotic behavior, in accord with numerical simulations. The impact of fractional derivative and nonlinear damping is presented with detail on the output voltage and power of the system. The agreement between numerical and analytical results justifies the efficiency of the analytical technique used. In addition, by combining the harmonic excitation with the random force, the stochastic resonance phenomenon occurs and improves the harvested energy. It emerges from these results that the order of fractional derivative μ and nonlinear damping μb play an important role in the response of the system.

  2. 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}}.

  3. A conservative difference scheme for solving the strongly coupled nonlinear fractional Schrödinger equations

    NASA Astrophysics Data System (ADS)

    Ran, Maohua; Zhang, Chengjian

    2016-12-01

    This paper focuses on numerically solving the strongly coupled nonlinear space fractional Schrödinger equations. First, the laws of conservation of mass and energy are given. Then, an implicit difference scheme is proposed, under the assumption that the analytical solution decays to zero when the space variable x tends to infinity. We show that the scheme conserves the mass and energy and is unconditionally stable with respect to the initial values. Moreover, the solvability, boundedness and convergence in the maximum norm are established. To avoid solving nonlinear systems, a linear difference scheme with two identities is proposed. Several numerical experiments are provided to confirm the theoretical results.

  4. An algorithm for solving the fractional convection diffusion equation with nonlinear source term

    NASA Astrophysics Data System (ADS)

    Momani, Shaher

    2007-10-01

    In this paper an algorithm based on Adomian's decomposition method is developed to approximate the solution of the nonlinear fractional convection-diffusion equation {∂αu}/{∂tα}={∂2u}/{∂x2}-c{∂u}/{∂x}+Ψ(u)+f(x,t),00. The fractional derivative is considered in the Caputo sense. The approximate solutions are calculated in the form of a convergent series with easily computable components. The analysis is accompanied by numerical examples and the obtained results are found to be in good agreement with the exact solutions known for some special cases.

  5. A new class of traveling solitons for cubic fractional nonlinear Schrödinger equations

    NASA Astrophysics Data System (ADS)

    Hong, Younghun; Sire, Yannick

    2017-04-01

    We consider the one-dimensional cubic fractional nonlinear Schrödinger equation i∂tu‑(‑Δ)σu + |u|2u=0, where σ \\in ≤ft(\\frac{1}{2},1\\right) and the operator {{(- Δ )}σ} is the fractional Laplacian of symbol |ξ {{|}2σ} . Despite the lack of any Galilean-type invariance, we construct a new class of traveling soliton solutions of the form u(t,x)=e‑it(|k|2σ‑ω2σ)Qω,k(x‑2tσ|k|2σ‑2k),k∈R, ω>0 by a rather involved variational argument.

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

    NASA Astrophysics Data System (ADS)

    Lukashchuk, S. Yu.

    2015-08-01

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

  7. Leader-following exponential consensus of fractional order nonlinear multi-agents system with hybrid time-varying delay: A heterogeneous impulsive method

    NASA Astrophysics Data System (ADS)

    Wang, Fei; Yang, Yongqing

    2017-09-01

    In this paper, we study the leader-following exponential consensus of multi-agent system. Each agent in the system is described by nonlinear fractional order differential equation. Both the internal delay and coupling delay are taken into consideration. The heterogeneous impulsive control is used for ensuring the consensus of all agents. Based on Lyapunov function method and matrix analysis, some sufficient conditions for exponential consensus are obtained. Finally, some illustrative examples are given to show the effectiveness of the obtained results.

  8. Numerical simulations to the nonlinear model of interpersonal relationships with time fractional derivative

    NASA Astrophysics Data System (ADS)

    Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan

    2017-01-01

    The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.

  9. Estimation of Delays and Other Parameters in Nonlinear Functional Differential Equations.

    DTIC Science & Technology

    1981-12-01

    FSTIMATION OF DELAYS AND OTHER PARAMETERS IN NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS by K. T. Banks and P. L. Daniel December 1981 LCDS Report #82...ESTIMATION OF DELAYS AND OTHER PARAMETERS IN NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS H. T. Banks and P. L. Daniel ABSTRACT We discuss a spline...based approximation scheme for nonlinear nonautonomous delay differential equations . Convergence results (using dissipative type estimates on the

  10. 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.

  11. Incomplete data based parameter identification of nonlinear and time-variant oscillators with fractional derivative elements

    NASA Astrophysics Data System (ADS)

    Kougioumtzoglou, Ioannis A.; dos Santos, Ketson R. M.; Comerford, Liam

    2017-09-01

    Various system identification techniques exist in the literature that can handle non-stationary measured time-histories, or cases of incomplete data, or address systems following a fractional calculus modeling. However, there are not many (if any) techniques that can address all three aforementioned challenges simultaneously in a consistent manner. In this paper, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. In this regard, the oscillator is transformed into an equivalent MISO system in the wavelet domain. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Finally, these wavelet coefficients are utilized to determine appropriately defined time- and frequency-dependent wavelet based frequency response functions and related oscillator parameters. Several linear and nonlinear time-variant systems with fractional derivative elements are used as numerical examples to demonstrate the reliability of the technique even in cases of noise corrupted and incomplete data.

  12. Relation between observability and differential embeddings for nonlinear dynamics

    NASA Astrophysics Data System (ADS)

    Letellier, Christophe; Aguirre, Luis A.; Maquet, Jean

    2005-06-01

    In the analysis of a scalar time series, which lies on an m -dimensional object, a great number of techniques will start by embedding such a time series in a d -dimensional space, with d>m . Therefore there is a coordinate transformation Φs from the original phase space to the embedded one. The embedding space depends on the observable s(t) . In theory, the main results reached are valid regardless of s(t) . In a number of practical situations, however, the choice of the observable does influence our ability to extract dynamical information from the embedded attractor. This may arise in problems in nonlinear dynamics such as model building, control and synchronization. To some degree, ease of success will depend on the choice of the observable simply because it is related to the observability of the dynamics. In this paper the observability matrix for nonlinear systems, which uses Lie derivatives, is revisited. It is shown that such a matrix can be interpreted as the Jacobian matrix of Φs —the map between the original phase space and the differential embedding induced by the observable—thus establishing a link between observability and embedding theory.

  13. 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.

  14. Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: A new iterative algorithm

    NASA Astrophysics Data System (ADS)

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

    2015-07-01

    In this paper, explicit and approximate solutions of the nonlinear fractional KdV-Burgers equation with time-space-fractional derivatives are presented and discussed. The solutions of our equation are calculated in the form of rabidly convergent series with easily computable components. The utilized method is a numerical technique based on the generalized Taylor series formula which constructs an analytical solution in the form of a convergent series. Five illustrative applications are given to demonstrate the effectiveness and the leverage of the present method. Graphical results and series formulas are utilized and discussed quantitatively to illustrate the solution. The results reveal that the method is very effective and simple in determination of solution of the fractional KdV-Burgers equation.

  15. A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains

    NASA Astrophysics Data System (ADS)

    Bonforte, Matteo; Vázquez, Juan Luis

    2015-10-01

    We investigate quantitative properties of the nonnegative solutions to the nonlinear fractional diffusion equation, , posed in a bounded domain, , with m > 1 for t > 0. As we use one of the most common definitions of the fractional Laplacian , 0 < s < 1, in a bounded domain with zero Dirichlet boundary conditions. We consider a general class of very weak solutions of the equation, and obtain a priori estimates in the form of smoothing effects, absolute upper bounds, lower bounds, and Harnack inequalities. We also investigate the boundary behaviour and we obtain sharp estimates from above and below. In addition, we obtain similar estimates for fractional semilinear elliptic equations. Either the standard Laplacian case s = 1 or the linear case m = 1 are recovered as limits. The method is quite general, suitable to be applied to a number of similar problems.

  16. Solving linear fractional-order differential equations via the enhanced homotopy perturbation method

    NASA Astrophysics Data System (ADS)

    Naseri, E.; Ghaderi, R.; Ranjbar N, A.; Sadati, J.; Mahmoudian, M.; Hosseinnia, S. H.; Momani, S.

    2009-10-01

    The linear fractional differential equation is solved using the enhanced homotopy perturbation method (EHPM). In this method, the convergence has been provided by selecting a stabilizing linear part. The most significant features of this method are its simplicity and its excellent accuracy and convergence for the whole range of fractional-order differential equations.

  17. Lump-type solutions to nonlinear differential equations derived from generalized bilinear equations

    NASA Astrophysics Data System (ADS)

    Ma, Wen-Xiu; Zhou, Yuan; Dougherty, Rachael

    2016-08-01

    Lump-type solutions, rationally localized in many directions in the space, are analyzed for nonlinear differential equations derived from generalized bilinear differential equations. By symbolic computations with Maple, positive quadratic and quartic polynomial solutions to two classes of generalized bilinear differential equations on f are computed, and thus, lump-type solutions are presented to the corresponding nonlinear differential equations on u, generated from taking a transformation of dependent variables u = 2(ln f)x.

  18. Mechanical energy and equivalent differential equations of motion for single-degree-of-freedom fractional oscillators

    NASA Astrophysics Data System (ADS)

    Yuan, Jian; Zhang, Youan; Liu, Jingmao; Shi, Bao; Gai, Mingjiu; Yang, Shujie

    2017-06-01

    This paper addresses the total mechanical energy and equivalent differential equation of motion for single degree of freedom fractional oscillators. Based on the energy storage and dissipation properties of the Caputo fractional derivatives, the expression for total mechanical energy in the single degree of freedom fractional oscillators is firstly presented. The energy regeneration due to the external exciting force and the energy loss due to the fractional damping force during the vibratory motion are analyzed. Furthermore, based on the mean energy dissipation and storage in the fractional damping element in steady-state vibration, two new concepts, namely mean equivalent viscous damping and mean equivalent stiffness are suggested and the above coefficient values are evaluated. By this way, the fractional differential equations of motion for single-degree-of-freedom fractional oscillators are equivalently transformed into integer-order ordinary differential equations.

  19. Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method

    NASA Astrophysics Data System (ADS)

    Cigeroglu, Ender; Samandari, Hamed

    2014-11-01

    Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.

  20. 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.

  1. 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.

  2. Tunable fractional-order photonic differentiator using a distributed feedback semiconductor optical amplifier

    NASA Astrophysics Data System (ADS)

    Sun, Shuqian; Deng, Ye; Zhu, Ninghua; Li, Ming

    2016-03-01

    We propose a tunable fractional-order photonic differentiator based on a distributed feedback semiconductor optical amplifier (SOA) working in reflection mode. The phase shift at the resonant wavelength can be adjusted by controlling the current injected into the DFB-SOA, which can implement the fractional-order differentiation. A 60 ps Gaussian pulse is temporally differentiated with a tunable order range from 0.7 to 1.3.

  3. 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.

  4. 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.

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

    SciTech Connect

    Baskonus, Haci Mehmet; Bulut, Hasan

    2016-06-08

    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.

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

    PubMed

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

    2015-07-01

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

  7. 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.

  8. An approximation method for fractional integro-differential equations

    NASA Astrophysics Data System (ADS)

    Emiroglu, Ibrahim

    2015-12-01

    In this work, an approximation method is proposed for fractional order linear Fredholm type integrodifferential equations with boundary conditions. The Sinc collocation method is applied to the examples and its efficiency and strength is also discussed by some special examples. The results of the proposed method are compared to the available analytic solutions.

  9. Fractional differential equations based modeling of microbial survival and growth curves: model development and experimental validation.

    PubMed

    Kaur, A; Takhar, P S; Smith, D M; Mann, J E; Brashears, M M

    2008-10-01

    A fractional differential equations (FDEs)-based theory involving 1- and 2-term equations was developed to predict the nonlinear survival and growth curves of foodborne pathogens. It is interesting to note that the solution of 1-term FDE leads to the Weibull model. Nonlinear regression (Gauss-Newton method) was performed to calculate the parameters of the 1-term and 2-term FDEs. The experimental inactivation data of Salmonella cocktail in ground turkey breast, ground turkey thigh, and pork shoulder; and cocktail of Salmonella, E. coli, and Listeria monocytogenes in ground beef exposed at isothermal cooking conditions of 50 to 66 degrees C were used for validation. To evaluate the performance of 2-term FDE in predicting the growth curves-growth of Salmonella typhimurium, Salmonella Enteritidis, and background flora in ground pork and boneless pork chops; and E. coli O157:H7 in ground beef in the temperature range of 22.2 to 4.4 degrees C were chosen. A program was written in Matlab to predict the model parameters and survival and growth curves. Two-term FDE was more successful in describing the complex shapes of microbial survival and growth curves as compared to the linear and Weibull models. Predicted curves of 2-term FDE had higher magnitudes of R(2) (0.89 to 0.99) and lower magnitudes of root mean square error (0.0182 to 0.5461) for all experimental cases in comparison to the linear and Weibull models. This model was capable of predicting the tails in survival curves, which was not possible using Weibull and linear models. The developed model can be used for other foodborne pathogens in a variety of food products to study the destruction and growth behavior.

  10. 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.

  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 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.

  13. 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.

  14. A hybrid algorithm for Caputo fractional differential equations

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  15. On the convergence of difference schemes for fractional differential equations with Robin boundary conditions

    NASA Astrophysics Data System (ADS)

    Bazzaev, A. K.; Shkhanukov-Lafishev, M. Kh.

    2017-01-01

    Locally one-dimensional difference schemes for partial differential equations with fractional order derivatives with respect to time and space in multidimensional domains are considered. Stability and convergence of locally one-dimensional schemes for this equation are proved.

  16. Analytic study on a state observer synchronizing a class of linear fractional differential systems

    NASA Astrophysics Data System (ADS)

    Zhou, Xian-Feng; Huang, Qun; Jiang, Wei; Liu, Song

    2014-10-01

    This paper is concerned with Theorem 2 in Matignon and d’André-Novel (1997) [1], which was sufficient and necessary criterion on a state observer for a class of linear fractional differential systems. Based on the stability theory, the dual principle and the pole assignment theory of the fractional differential system, we have proved the validity of sufficiency of Theorem 2 in details. A counterexample is provided to show that the condition of Theorem 2 is not necessary.

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

    PubMed

    Lorenzo, C F; Hartley, T T; Malti, R

    2013-05-13

    A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

  18. High-order fractional partial differential equation transform for molecular surface construction

    PubMed Central

    Hu, Langhua; Chen, Duan; Wei, Guo-Wei

    2013-01-01

    Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model

  19. High-order fractional partial differential equation transform for molecular surface construction.

    PubMed

    Hu, Langhua; Chen, Duan; Wei, Guo-Wei

    2013-01-01

    Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model

  20. 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.

  1. 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.

  2. On the local fractional derivative of everywhere non-differentiable continuous functions on intervals

    NASA Astrophysics Data System (ADS)

    Liu, Cheng-shi

    2017-01-01

    We first prove that for a continuous function f(x) defined on an open interval, the Kolvankar-Gangal's (or equivalently Chen-Yan-Zhang's) local fractional derivative f(α)(x) is not continuous, and then prove that it is impossible that the KG derivative f(α)(x) exists everywhere on the interval and satisfies f(α)(x) ≠ 0 in the same time. In addition, we give a criterion of the nonexistence of the local fractional derivative of everywhere non-differentiable continuous functions. Furthermore, we construct two simple nowhere differentiable continuous functions on (0, 1) and prove that they have no the local fractional derivatives everywhere.

  3. Solving nonlinear or stiff differential equations by Laplace homotopy analysis method(LHAM)

    NASA Astrophysics Data System (ADS)

    Chong, Fook Seng; Lem, Kong Hoong; Wong, Hui Lin

    2015-10-01

    The initial value problems of nonlinear or stiff ordinary differential equation appear in many fields of engineering science, particularly in the studies of electrical circuits, chemical reactions, wave vibration and so on. In this research, the standard homotopy analysis method hybrids with Laplace transform method to solve nonlinear and stiff differential equations. Using this modification, the problems solved by LHAM successfully yield good solutions. Some examples are examined to highlight the convenience and effectiveness of LHAM.

  4. On the bound of the Lyapunov exponents for the fractional differential systems.

    PubMed

    Li, Changpin; Gong, Ziqing; Qian, Deliang; Chen, YangQuan

    2010-03-01

    In recent years, fractional(-order) differential equations have attracted increasing interests due to their applications in modeling anomalous diffusion, time dependent materials and processes with long range dependence, allometric scaling laws, and complex networks. Although an autonomous system cannot define a dynamical system in the sense of semigroup because of the memory property determined by the fractional derivative, we can still use the Lyapunov exponents to discuss its dynamical evolution. In this paper, we first define the Lyapunov exponents for fractional differential systems then estimate the bound of the corresponding Lyapunov exponents. For linear fractional differential system, the bounds of its Lyapunov exponents are conveniently derived which can be regarded as an example for the theoretical results established in this paper. Numerical example is also included which supports the theoretical analysis.

  5. On the bound of the Lyapunov exponents for the fractional differential systems

    NASA Astrophysics Data System (ADS)

    Li, Changpin; Gong, Ziqing; Qian, Deliang; Chen, YangQuan

    2010-03-01

    In recent years, fractional(-order) differential equations have attracted increasing interests due to their applications in modeling anomalous diffusion, time dependent materials and processes with long range dependence, allometric scaling laws, and complex networks. Although an autonomous system cannot define a dynamical system in the sense of semigroup because of the memory property determined by the fractional derivative, we can still use the Lyapunov exponents to discuss its dynamical evolution. In this paper, we first define the Lyapunov exponents for fractional differential systems then estimate the bound of the corresponding Lyapunov exponents. For linear fractional differential system, the bounds of its Lyapunov exponents are conveniently derived which can be regarded as an example for the theoretical results established in this paper. Numerical example is also included which supports the theoretical analysis.

  6. 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.

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

    NASA Astrophysics Data System (ADS)

    Sayevand, K.; Pichaghchi, K.

    2017-09-01

    In this paper, we were concerned with the description of the singularly perturbed differential equations within the scope of fractional calculus. However, we shall note that one of the main methods used to solve these problems is the so-called \\mathsf {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 \\mathsf {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 \\mathsf {WKB} method in the scope of the fractional differential equation. By means of this extension, the \\mathsf {WKB} analysis based on the Borel resummation, for fractional differential operators of \\mathsf {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 \\mathsf {WKB}.

  8. Differentiability at lateral boundary for fully nonlinear parabolic equations

    NASA Astrophysics Data System (ADS)

    Ma, Feiyao; Moreira, Diego R.; Wang, Lihe

    2017-09-01

    For fully nonlinear uniformly parabolic equations, the first derivatives regularity of viscosity solutions at lateral boundary is studied under new Dini type conditions for the boundary, which is called Reifenberg Dini conditions and is weaker than usual Dini conditions.

  9. 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.

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

    PubMed

    Teng, Fang-Zhen; Dauphas, Nicolas; Helz, Rosalind T

    2008-06-20

    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-stagemeltveins are 0.2 permil (per thousand) greater than values for olivine cumulates. Olivine phenocrysts are up to 1.2 per thousand 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.

  11. Nonlinear sprint performance differentiates professional from young soccer players.

    PubMed

    Cardoso de Araújo, Maithe; Baumgart, Christian; Freiwald, Jürgen; Hoppe, Matthias W

    2017-02-22

    Linear and nonlinear sprinting activities are relevant physical capacities in soccer. This study aimed (1) to compare linear and nonlinear sprint performance between professional and young soccer players and (2) to investigate relationships between both sprint types. Sixty-eight German male elite field soccer players were grouped based on age as professional (PRO, n = 20), under-23 (U23, n = 16), under-19 (U19, n = 18), and under-17 (U17, n = 14). All players were tested for 30 m linear (split-times at 5, 10, and 20 m) and 22 m nonlinear sprint performance. In linear sprint, PRO players were moderately to very largely faster than U17 players at all distances and also than U19 players at 20 m (effect size [ES] = 0.90-2.06, p ≤ 0.04). U23 players were moderately to largely faster than U17 players at 5 and 10 m (ES = 0.93-1.74, p ≤ 0.04). In nonlinear sprint, PRO players were moderately to largely faster than all other groups (ES = 1.04-1.84, p ≤ 0.02). Moderate to large correlations were found between linear and nonlinear sprint performance for all players (r = 0.48-0.50, p < 0.01). Within groups, moderate to large correlations were evident only for PRO at 5-20 m (r = 0.45-0.61, p ≤ 0.05) and U23 at 30 m (r = 0.55, p = 0.03). The findings indicate that nonlinear sprint performance is a key physical capacity in professional soccer. Therefore, training programs should focus to increase this capacity in younger players. Furthermore, linear and nonlinear sprint performance should be independently tested and trained in elite players.

  12. The influence of fractionation on cell survival and premature differentiation after carbon ion irradiation.

    PubMed

    Wang, Jufang; Li, Renming; Guo, Chuanling; Fournier, Claudia; K-Weyrather, Wilma

    2008-07-01

    To investigate the influence of fractionation on cell survival and radiation induced premature differentiation as markers for early and late effects after X-rays and carbon irradiation. Normal human fibroblasts NHDF, AG1522B and WI-38 were irradiated with 250 kV X-rays, or 266 MeV/u, 195 MeV/u and 11 MeV/u carbon ions. Cytotoxicity was measured by a clonogenic survival assay or by determination of the differentiation pattern. Experiments with high-energy carbon ions show that fractionation induced repair effects are similar to photon irradiation. The RBE(10) values for clonogenic survival are 1.3 and 1.6 for irradiation in one or two fractions for NHDF cells and around 1.2 for AG1522B cells regardless of the fractionation scheme. The RBE for a doubling of post mitotic fibroblasts (PMF) in the population is 1 for both single and two fractionated irradiation of NHDF cells. Using 11 MeV/u carbon ions, no repair effect can be seen in WI-38 cells. The RBE(10) for clonogenic survival is 3.2 for single irradiation and 4.9 for two fractionated irradiations. The RBE for a doubling of PMF is 3.1 and 5.0 for single and two fractionated irradiations, respectively. For both cell lines the effects of high-energy carbon ions representing the irradiation of the skin and the normal tissue in the entrance channel are similar to the effects of X-rays. The fractionation effects are maintained. For the lower energy, which is representative for the irradiation of the tumor region, RBE is enhanced for clonogenic survival as well as for premature terminal differentiation. Fractionation effects are not detectable. Consequently, the therapeutic ratio is significantly enhanced by fractionated irradiation with carbon ions.

  13. Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

    PubMed

    Shah, A A; Xing, W W; Triantafyllidis, V

    2017-04-01

    In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

  14. Analytical approach to linear fractional partial differential equations arising in fluid mechanics

    NASA Astrophysics Data System (ADS)

    Momani, Shaher; Odibat, Zaid

    2006-07-01

    In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods.

  15. 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.

  16. Design and Analysis of Electrical Circuits that Produce Fractional-Order Differentiation

    DTIC Science & Technology

    1992-03-01

    INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio THESIS AFIT/GE/ENG/92M-05 DESIGN AND ANALYSIS OF ELECTRICAL CIRCUITS THAT PRODUCE FRACTIONAL...blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED March 1992 Master’s Thesis 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS DESIGN AND ANALYSIS OF...ENG/92M-05 DESIGN AND ANALYSIS OF ELECTRICAL CIRCUITS THAT PRODUCE FRACTIONAL-ORDER DIFFERENTIATION THESIS Presented to the Faculty of the School of

  17. The numerical solution of linear multi-term fractional differential equations: systems of equations

    NASA Astrophysics Data System (ADS)

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  18. Differential rotation of the unstable nonlinear r-mode

    NASA Astrophysics Data System (ADS)

    Friedman, John; Lindblom, Lee; Lockitch, Keith

    2014-03-01

    To second order in perturbation theory, the r-modes of uniformly rotating stars include an axisymmetric part that can be identified with a growing 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 a choice of equilibrium configuration: Adding to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders: δΩ = δΩ (ϖ) . For the radiation-reaction driven r-mode, however, the differential rotation includes an exponentially growing part that is unique, gauge-independent, and vorticity-conserving. We compute this differential rotation for slowly rotating Newtonian models, acted on by the radiation-reaction force of the unstable mode. Work supported in part by NSF grants PHY 1001515 and DMS1065438 and by a grant from the Sherman Fairchild Foundation.

  19. On Differences between Fractional and Integer Order Differential Equations for Dynamical Games

    NASA Astrophysics Data System (ADS)

    Ahmed, Elsayed M. E.; Elgazzar, Ahmed S.; Shehata, Mohamed I.

    2008-04-01

    We argue that fractional order differential equations are more suitable to model complex adaptive systems. Hence they are applied in replicator equations for non-cooperative games. Rock-scissors-paper game is discussed. It is known that its integer order model does not have a stable equilibrium. Its fractional order model is shown to have a locally asymptotically stable internal solution. A fractional order asymmetric game is shown to have a locally asymptotically stable internal solution. This is not the case for its integer order counterpart.

  20. 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.

  1. Calf Thymus Composition. A Comparison of Differential Centrifugation and Chemical Fractionation Procedures

    PubMed Central

    Hess, Eugene L.; Lagg, Saima E.

    1958-01-01

    The extraction behavior of thymus and the composition of fractions prepared from this organ has been studied. Sequential extraction methods using 0.15 M NaCl followed by water gave information with respect to the weight fraction of cytoplasmic and nuclear constituents. Lipide, nucleic acid, and electrophoretic analysis of the extracts provided additional information. A less complex electrophoretic pattern was obtained from subsequent extracts in the sequence. Sucrose and saline dispersates obtained from tissue fragmented with either the Potter-Elvehjem homogenizer or in a Waring blendor were fractionated, using standard differential sedimentation methods. The fractions obtained by means of four different dispersion procedures were compared in terms of yield, chemical analysis, and electrophoretic composition. The quantity of material in thymus having the sedimentation characteristics of liver mitochondrial and microsomal fractions was remarkably small. Both the suspension medium employed and the method used to bring about a disruption of the cells in the tissue affected the yield of "particulate" material. The components present in the later extracts in the sequence, E4 to E7, in the case of sequential extraction study resembled with respect to chemical composition and electrophoretic characteristics, the microsome fraction prepared by differential sedimentation methods. About 76 per cent of the PNA in the tissue appeared to be in the cytoplasm. The remaining 24 per cent PNA was found in the nucleus and accounted for 1.7 per cent of nucleus on a dry weight basis. From 75 to 88 per cent of cytoplasmic PNA was extracted from the tissue and 76 to 94 per cent of the PNA in the extract was found in the final supernatant solutions, depending upon the dispersion methods and suspension medium used in the extraction procedure. The composition of the final supernatant fractions using differential sedimentation methods were comparable in terms of electrophoretic properties

  2. The Painlevé test for nonlinear system of differential equations with complex chaotic behavior

    NASA Astrophysics Data System (ADS)

    Tsegel’nik, V.

    2017-01-01

    The Painlevé-analysis was performed for solutions of nonlinear third-order autonomous system of differential equations with quadratic nonlinearities on their right-hand sides. At certain values of two constant parameters incorporated into the system, the latter exhibits complex chaotic behavior. When the parameters attain the values corresponding to complex chaotic behavior, the system was found not to possess the Painlevé property.

  3. Nonlinear interaction in differential mode delay managed mode-division multiplexed transmission systems.

    PubMed

    Rademacher, Georg; Warm, Stefan; Petermann, Klaus

    2015-01-12

    We analyze the impact of Differential Mode Delay (DMD) Management on the nonlinear impairments in mode-division multiplexed transmission systems. It is found out that DMD Management can lead to a degraded performance, due to enhanced intermodal nonlinear interaction. This can be attributed to an increased correlation of co-propagating channels, similar to the effects that show up in dispersion managed single-mode systems.

  4. Algorithmic Approximation of Optimal Value Differential Stability Bounds in Nonlinear Programming,

    DTIC Science & Technology

    1981-08-01

    NCLASSIFIED RANO/PA6659 N IN *~4 112.0.0 ~11111,.. I32 111 IIIII 111111.25 MICROCOPY RESOLUTION TESI CHART NATIOt AL BJRLAU Of SIANDARD 1964 A * LEVEL 00 o pm...Sensitivity Analysis in Parametric Nonlinear Programming, Doctoral Dissertation, School of Engineering and Applied Science, The George Washington University...Differential Stability of the Optimal Value Function in Constrained Nonlinear Programing, Doctoral Disser- tation, School of Engineering and Applied

  5. 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

  6. Analytical lie group approach for solving fractional integro-differential equations

    NASA Astrophysics Data System (ADS)

    Pashayi, S.; Hashemi, M. S.; Shahmorad, S.

    2017-10-01

    This study is concerned with the Lie symmetry group analysis of Fractional Integro-Differential Equations (FIDEs) with nonlocal structures based on a new development of prolongation formula. A new prolongation for FIDEs is extracted and invariant solutions are finally presented for some illustrative examples.

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

    PubMed

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

    2014-01-01

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

  8. Nonlinear grid error effects on numerical solution of partial differential equations

    NASA Technical Reports Server (NTRS)

    Dey, S. K.

    1980-01-01

    Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

  9. Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type

    NASA Astrophysics Data System (ADS)

    Parand, K.; Shahini, M.; Dehghan, Mehdi

    2009-12-01

    Lane-Emden equation is a nonlinear singular equation in the astrophysics that corresponds to the polytropic models. In this paper, a pseudospectral technique is proposed to solve the Lane-Emden type equations on a semi-infinite domain. The method is based on rational Legendre functions and Gauss-Radau integration. The method reduces solving the nonlinear ordinary differential equation to solve a system of nonlinear algebraic equations. The comparison of the results with the other numerical methods shows the efficiency and accuracy of this method.

  10. Existence of Forced Oscillations for Some Nonlinear Differential Equations.

    DTIC Science & Technology

    1982-11-01

    groups of level sets of the functional associated with the system are ", -t4 . I not trivial. Some more general results concerning systems of the type, f... general non autonomous systems of the type (1.3) 9 + v;(t,x) - 0 There is a vast literature devoted to the subject of nonlinear oscillations in systems...g(t,x) - 0 (x(t) .3) quite general results on the existence of periodic solutions have been obtained by Hartman 114] and Jacobovitz (151 (by using

  11. 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.

  12. The generalized fractional order of the Chebyshev functions on nonlinear boundary value problems in the semi-infinite domain

    NASA Astrophysics Data System (ADS)

    Parand, Kourosh; Delkhosh, Mehdi

    2017-09-01

    A new collocation method, namely the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) collocation method, is given for solving some nonlinear boundary value problems in the semi-infinite domain, such as equations of the unsteady isothermal flow of a gas, the third grade fluid, the Blasius, and the field equation determining the vortex profile. The method reduces the solution of the problem to the solution of a nonlinear system of algebraic equations. To illustrate the reliability of the method, the numerical results of the present method are compared with several numerical results.

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

    NASA Astrophysics Data System (ADS)

    Birk, Carolin; Song, Chongmin

    2010-10-01

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

  14. Numerical study of the process of nonlinear supratransmission in Riesz space-fractional sine-Gordon equations

    NASA Astrophysics Data System (ADS)

    Macías-Díaz, J. E.

    2017-05-01

    In this work, we consider a (1 + 1) -dimensional Riesz space-fractional damped sine-Gordon equation defined on a bounded spatial interval. Sinusoidal Dirichlet boundary data are imposed at one end of the interval and homogeneous Neumann conditions at the other. The system is initially at rest in the equilibrium position, and is discretized to simulate its complex dynamics. The method employed in this work is a finite-difference discretization of the mathematical model of interest. Our scheme is throughly validated against simulations on the dynamics of the classical and the space-fractional sine-Gordon equations, which are available in the literature. As the main result of this manuscript, we have found numerical evidence on the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional sine-Gordon systems. Simulations have been conducted in order to predict its occurrence for some values of the fractional order of the spatial derivative, and a wide range of values of the frequency of the sinusoidal perturbation at the boundary. As far as the author knows, this may be one of the first numerical reports on the existence of nonlinear supratransmission in sine-Gordon systems of Riesz space-fractional order.

  15. Nonlinear Hadley circulation driven by asymmetric differential heating

    NASA Technical Reports Server (NTRS)

    Dunkerton, Timothy J.

    1989-01-01

    The dynamical state of the stratosphere influenced by radiative heating, with no internal sources or sinks of angular momentum, is examined. It is shown that there exists a nonlinear Hadley regime driven by antisymmetric (or more generally, asymmetric) thermal equilibria typical of the middle atmosphere at the solstices. This regime consists of a single mean meridional cell, equatorial easterlies, and strong winter westerlies. Outside of the circulation region the flow is in thermal equilibrium. The effect of one-sided friction, acting as a drag on midlatitude westerlies only, is to expand the Hadley cell into the winter hemisphere and increase the magnitude of cross-equatorial flow. This result is possible even in the steady state when the advection of angular momentum in the tropics is made small by reducing the gradient of angular momentum in this region instead of the advecting velocity.

  16. 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.

  17. Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions

    NASA Astrophysics Data System (ADS)

    Dehghan, Mehdi; Manafian, Jalil; Saadatmandi, Abbas

    2010-11-01

    In this paper, the homotopy analysis method is applied to solve linear fractional problems. Based on this method, a scheme is developed to obtain approximation solution of fractional wave, Burgers, Korteweg-de Vries (KdV), KdV-Burgers, and Klein-Gordon equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for partial differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.

  18. Existence and concentration of positive solutions for fractional nonlinear Schrödinger equation with critical growth

    NASA Astrophysics Data System (ADS)

    Shang, Xudong; Zhang, Jihui

    2017-08-01

    In this paper, we study the existence and concentration behavior of positive solutions for the following critical fractional nonlinear Schrödinger equation ℏ2 s(-Δ) su +V (x ) u =u2s*-1+f (u ) with u (x ) >0 , u ∈Hs(RN ) , where ℏ is a positive parameter, s ∈(0 ,1 ) , N >2 s and 2s*=2/N N -2 s are the fractional critical exponent, and f is a continuous subcritical nonlinearity. Suppose the potential V(x) satisfying infRNV (x ) >0 and there exists an open bounded domain Ω of RN such that infx ∈∂ ΩV (x ) >infx ∈ΩV (x ) =m0. By using variational methods, we show that the problem has a positive bound state solution which concentrates around a local minimum point of V as ℏ tends to zero. Moreover, we investigate regularity and decay properties of the solution.

  19. Double-image encryption using chaotic maps and nonlinear non-DC joint fractional Fourier transform correlator

    NASA Astrophysics Data System (ADS)

    Zhao, Hongjie; Zhong, Zhi; Fang, Weiwei; Xie, Hong; Zhang, Yabin; Shan, Mingguang

    2016-09-01

    A double-image encryption method is reported using chaotic maps, nonlinear non-DC joint transform correlator (JTC), and fractional Fourier transform (FrFT). The double images are converted into the amplitude and phase of a synthesized function through the application of chaotic pixel scrambling. The synthesized function bonded with a chaotic random phase mask (CRPM) and another different CRPM serve as the input signal of the JTC architecture in the fractional Fourier domain to obtain a real-valued encrypted image. The nonlinear and non-DC operation is also done to improve the security and decrypted image quality. The parameters in joint FrFT correlator and chaotic map serve as the encrypted keys. Numerical simulations have been done to demonstrate the feasibility and validity of this algorithm.

  20. On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations

    NASA Astrophysics Data System (ADS)

    Glatt-Holtz, Nathan; Mattingly, Jonathan C.; Richards, Geordie

    2017-02-01

    We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart possesses a finite number of determining modes. Examples exhibiting parabolic and hyperbolic structure are studied in detail. In the later situation we also present a simple framework for establishing the existence of invariant measures when the usual approach relying on the Krylov-Bogolyubov procedure and compactness fails.

  1. Spline Approximation for Autonomous Nonlinear Functional Differential Equations.

    DTIC Science & Technology

    1980-06-18

    Af(e / a e(-T)/ P(T)dT) + q. An easy calculation using (H2) shows that h has the Lipschitz constant XL(m+l+r1 /2) on In. This proves b) with X0 = i/L...84A(1979), 71-91. [13] R.D. Nussbaum, Uniqueness and nonuniqueness for periodic solutions of x’(t) - -g(x(t-1)), J. Differential Eqs. 34(1979), 25-54

  2. 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.

  3. 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.

  4. The Non-Linear Relationship between BMI and Health Care Costs and the Resulting Cost Fraction Attributable to Obesity.

    PubMed

    Laxy, Michael; Stark, Renée; Peters, Annette; Hauner, Hans; Holle, Rolf; Teuner, Christina M

    2017-08-30

    This study aims to analyse the non-linear relationship between Body Mass Index (BMI) and direct health care costs, and to quantify the resulting cost fraction attributable to obesity in Germany. Five cross-sectional surveys of cohort studies in southern Germany were pooled, resulting in data of 6757 individuals (31-96 years old). Self-reported information on health care utilisation was used to estimate direct health care costs for the year 2011. The relationship between measured BMI and annual costs was analysed using generalised additive models, and the cost fraction attributable to obesity was calculated. We found a non-linear association of BMI and health care costs with a continuously increasing slope for increasing BMI without any clear threshold. Under the consideration of the non-linear BMI-cost relationship, a shift in the BMI distribution so that the BMI of each individual is lowered by one point is associated with a 2.1% reduction of mean direct costs in the population. If obesity was eliminated, and the BMI of all obese individuals were lowered to 29.9 kg/m², this would reduce the mean direct costs by 4.0% in the population. Results show a non-linear relationship between BMI and health care costs, with very high costs for a few individuals with high BMI. This indicates that population-based interventions in combination with selective measures for very obese individuals might be the preferred strategy.

  5. Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems

    NASA Astrophysics Data System (ADS)

    Pourmahmood Aghababa, Mohammad

    2013-10-01

    This paper investigates the problem of robust control of nonlinear fractional-order dynamical systems in the presence of uncertainties. First, a novel switching surface is proposed and its finite-time stability to the origin is proved. Subsequently, using the sliding mode theory, a robust fractional control law is proposed to ensure the existence of the sliding motion in finite time. We use a fractional Lyapunov stability theory to prove the stability of the system in a given finite time. In order to avoid the chattering, which is inherent in conventional sliding mode controllers, we transfer the sign function of the control input into the fractional derivative of the control signal. The proposed chattering-free sliding mode technique is then applied for stabilisation of a broad class of three-dimensional fractional-order chaotic systems via a single variable driving control input. Simulation results reveal that the proposed fractional sliding mode controller works well for chaos control of fractional-order hyperchaotic Chen, chaotic Lorenz and chaotic Arneodo systems with no-chatter control inputs.

  6. 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

  7. A new mixed element method for a class of time-fractional partial differential equations.

    PubMed

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

    2014-01-01

    A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω) space. Some a priori error estimates in L (2)-norm for the scalar unknown u and in (L (2))(2)-norm for its gradient σ. Moreover, we also discuss a priori error estimates in H (1)-norm for the scalar unknown u.

  8. 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. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

  9. Direct application of Padé approximant for solving nonlinear differential equations.

    PubMed

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

    2014-01-01

    This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

  10. 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…

  11. 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.

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

    PubMed Central

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

    2013-01-01

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

  13. Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations.

    PubMed

    Tornøe, Christoffer W; Agersø, Henrik; Jonsson, E Niclas; Madsen, Henrik; Nielsen, Henrik A

    2004-10-01

    The standard software for non-linear mixed-effect analysis of pharmacokinetic/pharmacodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as long as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential equation (ODE) solver package odesolve and the non-linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlmeODE package for population PK/PD analysis using the available data analysis tools in R for model inspection and validation. The nlmeODE package is numerically stable and provides accurate parameter estimates which are consistent with NONMEM estimates.

  14. 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.

  15. Discontinuous Galerkin Methods for NonLinear Differential Systems

    NASA Technical Reports Server (NTRS)

    Barth, Timothy; Mansour, Nagi (Technical Monitor)

    2001-01-01

    This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

  16. On the existence of positive solutions for fractional differential inclusions at resonance.

    PubMed

    Hu, Lei

    2016-01-01

    In this paper, we discuss the existence of positive solutions for a boundary value problem of fractional differential inclusions with resonant boundary conditions. By using the Leggett-Williams theorem for coincidences of multi-valued operators due to O'Regan and Zima, results on the existence of positive solutions are established. An example is given to illustrate the efficiency of the main theorems.

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

    PubMed

    Pashaei, Shabnam; Badamchizadeh, Mohammadali

    2016-07-01

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

  18. 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.

  19. 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

  20. A Cosmology Governed by a Fractional Differential Equation and the Generalized Kilbas-Saigo-Mittag-Leffler Function

    NASA Astrophysics Data System (ADS)

    El-Nabulsi, Rami Ahmad

    2016-02-01

    In this paper we discussed the FRW cosmology characterized by a scale factor obeying different independent types of fractional differential equations with solutions givens in terms of Mittag-Leffler and generalized Kilbas-Saigo-Mittag-Leffler functions. Both types of fractional operators: the Riemann-Liouville fractional integral and the Caputo fractional derivative were considered independently. Some new cosmological features were observed and discussed accordingly.

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

    NASA Astrophysics Data System (ADS)

    Rigatos, Gerasimos; Raffo, Guilerme

    2015-12-01

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

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

    PubMed Central

    Calderhead, Ben; Girolami, Mark

    2011-01-01

    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

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

    PubMed

    Calderhead, Ben; Girolami, Mark

    2011-12-06

    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.

  4. Analytical approximations for a population growth model with fractional order

    NASA Astrophysics Data System (ADS)

    Xu, Hang

    2009-05-01

    In this paper, we apply the homotopy analysis method (HAM) to solve the fractional Volterra's model for population growth of a species in a closed system. This technique is extended to give solutions for nonlinear fractional integro-differential equations. The whole HAM solution procedure for nonlinear fractional differential equations is established. Further, the accurate analytical approximations are obtained for the first time, which are valid and convergent for all time t. This indicates the validity and great potential of the homotopy analysis method for solving nonlinear fractional integro-differential equations.

  5. 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.).

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

  7. 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.

  8. Modification of perturbation-iteration method to solve different types of nonlinear differential equations

    NASA Astrophysics Data System (ADS)

    Bildik, Necdet; Deniz, Sinan

    2017-01-01

    Perturbation iteration method has been recently constructed by Pakdemirli and co-workers. It has been also proven that this technique is very effective and applicable for solving some nonlinear differential equations. In this study we suggest a modification to expedite the solution process of perturbation-iteration algorithms. This work might greatly improve the computational efficiency of the perturbation iteration method and also its Mathematica package to solve nonlinear equations. Numerical illustrations are also given to show how modified method eliminates cumbersome computational work needed by perturbation iteration method.

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

    PubMed Central

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

    2016-01-01

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

  10. A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

    PubMed

    Benhammouda, Brahim; Vazquez-Leal, Hector

    2016-01-01

    This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

  11. Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

    PubMed

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

    2014-01-01

    In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

  12. 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.

  13. The asymptotic solutions for a class of nonlinear singular perturbed differential systems with time delays.

    PubMed

    Xu, Han; Jin, Yinlai

    2014-01-01

    We study a kind of vector singular perturbed delay-differential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer at t = σ. Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved.

  14. 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.

  15. 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.

  16. On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

    NASA Astrophysics Data System (ADS)

    Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

    2017-01-01

    In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

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

    PubMed

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

    2015-07-01

    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.

  18. A nonlinear ordinary differential equation associated with the quantum sojourn time

    NASA Astrophysics Data System (ADS)

    Benguria, Rafael D.; Duclos, Pierre; Fernández, Claudio; Sing-Long, Carlos

    2010-11-01

    We study a nonlinear ordinary differential equation on the half-line, with the Dirichlet boundary condition at the origin. This equation arises when studying the local maxima of the sojourn time for a free quantum particle whose states belong to an adequate subspace of the unit sphere of the corresponding Hilbert space. We establish several results concerning the existence and asymptotic behavior of the solutions.

  19. 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

  20. The uncertainty principle and a semiclassical nonlinear differential equation formulation for bound states

    NASA Astrophysics Data System (ADS)

    Mukhopadhyay, S.; Bhattacharyya, K.

    2000-10-01

    The kinship of a simple variational scheme involving the uncertainty product with a prevalent semiclassical nonlinear differential equation approach for finding energies of stationary states is established. This leads to a transparent physical interpretation of the embedded parameters in the latter approach, providing additionally a lower bound to the integration constant. The domain of applicability of this strategy is also extended to encompass neighbouring states. Other advantages of the simpler alternative route are stressed. Pilot calculations demonstrate nicely the efficacy of the endeavour.

  1. 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)

  2. Differential diagnosis of breast lesions by use of biomagnetic activity and non-linear analysis.

    PubMed

    Anninos, P A; Kotini, A; Koutlaki, N; Adamopoulos, A; Galazios, G; Anastasiadis, P

    2000-01-01

    Breast cancer mortality rates have not changed during the past 60 years despite significant advances in screening methods. It is tempting therefore to use novel technology in order to better understand breast oncology. In this study we investigated the biomagnetic activity obtained in benign and malignant breast lesions using a single channel biomagnetometer SQUID (Superconducting Quantum Interference Device) in order to assess the method's efficacy in the differential diagnosis of these two types of lesions and its establishment as a screening technique. Magnetic recordings were obtained from 21 patients with palpable breast lumps. Of these 11 were invasive carcinomas and 10 were benign breast lesions. We used non-linear analysis to investigate whether there is any biological differentiation in the dynamics in these two types of lesions. High amplitudes characterized the waveform of a malignant breast lesion whereas in benign breast lesions the corresponding amplitudes were low. Using the application of non-linear analysis we observed a clear saturation value for the dimension of malignant breast lesions and no saturation for benign ones. Biomagnetic measurements with the SQUID and the application of non-linear analysis are promising procedures in assessing and differentiating breast tumors.

  3. On some fractional equations with convex-concave and logistic-type nonlinearities

    NASA Astrophysics Data System (ADS)

    Carboni, Giulia; Mugnai, Dimitri

    2017-02-01

    We consider existence and multiplicity results for a semilinear problem driven by the square root of the negative Laplacian in presence of a nonlinear term which is the difference of two powers. In the case of convex-concave powers, a precise description of the problem at the threshold value of a given parameter is established through variational methods and truncation techniques.

  4. Nonlinear Fractional Sliding Mode Controller Based on Reduced Order FNPK Model for Output Power Control of Nuclear Research Reactors

    NASA Astrophysics Data System (ADS)

    Davijani, Nafiseh Zare; Jahanfarnia, Gholamreza; Abharian, Amir Esmaeili

    2017-01-01

    One of the most important issues with respect to nuclear reactors is power control. In this study, we designed a fractional-order sliding mode controller based on a nonlinear fractional-order model of the reactor system in order to track the reference power trajectory and overcome uncertainties and external disturbances. Since not all of the variables in an operating reactor are measurable or specified in the control law, we propose a reduced-order fractional neutron point kinetic (ROFNPK) model based on measurable variables. In the design, we assume the differences between the approximated model and the real system is limited. We use the obtained model in the controller design process and use the Lyapunov method to perform a stability analysis of the closed-loop system. We simulate the proposed reduced-order fractional-order sliding mode controller (ROFOSMC) using Matlab/Simulink, and its performance is compared with that of a reduced order integer-order sliding mode controller (ROIOSMC). Our simulation results indicate an acceptable performance of the proposed approach in tracking the reference power trajectory with respect to ROIOSMC because of faster response of control effort signal and the smaller tracking error. Moreover, the results illustrate the capability of the controller in rejection of the disturbance and the noise signals and the robustness of controller against uncertainty.

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

    NASA Astrophysics Data System (ADS)

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

    2015-08-01

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

  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. Existence and uniqueness of solutions for nonlinear impulsive differential equations with two-point and integral boundary conditions

    NASA Astrophysics Data System (ADS)

    Ashyralyev, Allaberen; Sharifov, Y. A.

    2012-08-01

    The system of nonlinear impulsive differential equations with two-point and integral boundary conditions are investigated. Theorems on existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.

  8. Design of minimum multiplier fractional order differentiator based on lattice wave digital filter.

    PubMed

    Barsainya, Richa; Rawat, Tarun Kumar; Kumar, Manjeet

    2017-01-01

    In this paper, a novel design of fractional order differentiator (FOD) based on lattice wave digital filter (LWDF) is proposed which requires minimum number of multiplier for its structural realization. Firstly, the FOD design problem is formulated as an optimization problem using the transfer function of lattice wave digital filter. Then, three optimization algorithms, namely, genetic algorithm (GA), particle swarm optimization (PSO) and cuckoo search algorithm (CSA) are applied to determine the optimal LWDF coefficients. The realization of FOD using LWD structure increases the design accuracy, as only N number of coefficients are to be optimized for Nth order FOD. Finally, two design examples of 3rd and 5th order lattice wave digital fractional order differentiator (LWDFOD) are demonstrated to justify the design accuracy. The performance analysis of the proposed design is carried out based on magnitude response, absolute magnitude error (dB), root mean square (RMS) magnitude error, arithmetic complexity, convergence profile and computation time. Simulation results are attained to show the comparison of the proposed LWDFOD with the published works and it is observed that an improvement of 29% is obtained in the proposed design. The proposed LWDFOD approximates the ideal FOD and surpasses the existing ones reasonably well in mid and high frequency range, thereby making the proposed LWDFOD a promising technique for the design of digital FODs. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

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

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

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

  10. 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.

  11. 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.

  12. 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.

  13. Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm.

    PubMed

    Overgaard, Rune V; Jonsson, Niclas; Tornøe, Christoffer W; Madsen, Henrik

    2005-02-01

    Pharmacokinetic/pharmacodynamic modelling is most often performed using non-linear mixed-effects models based on ordinary differential equations with uncorrelated intra-individual residuals. More sophisticated residual error models as e.g. stochastic differential equations (SDEs) with measurement noise can in many cases provide a better description of the variations, which could be useful in various aspects of modelling. This general approach enables a decomposition of the intra-individual residual variation epsilon into system noise w and measurement noise e. The present work describes implementation of SDEs in a non-linear mixed-effects model, where parameter estimation was performed by a novel approximation of the likelihood function. This approximation is constructed by combining the First-Order Conditional Estimation (FOCE) method used in non-linear mixed-effects modelling with the Extended Kalman Filter used in models with SDEs. Fundamental issues concerning the proposed model and estimation algorithm are addressed by simulation studies, concluding that system noise can successfully be separated from measurement noise and inter-individual variability.

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

    NASA Technical Reports Server (NTRS)

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

    2014-01-01

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

  15. 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

  16. Non-linear classification for on-the-fly fractional mass filtering and targeted precursor fragmentation in mass spectrometry experiments.

    PubMed

    Kirchner, Marc; Timm, Wiebke; Fong, Peying; Wangemann, Philine; Steen, Hanno

    2010-03-15

    Mass spectrometry (MS) has become the method of choice for protein/peptide sequence and modification analysis. The technology employs a two-step approach: ionized peptide precursor masses are detected, selected for fragmentation, and the fragment mass spectra are collected for computational analysis. Current precursor selection schemes are based on data- or information-dependent acquisition (DDA/IDA), where fragmentation mass candidates are selected by intensity and are subsequently included in a dynamic exclusion list to avoid constant refragmentation of highly abundant species. DDA/IDA methods do not exploit valuable information that is contained in the fractional mass of high-accuracy precursor mass measurements delivered by current instrumentation. We extend previous contributions that suggest that fractional mass information allows targeted fragmentation of analytes of interest. We introduce a non-linear Random Forest classification and a discrete mapping approach, which can be trained to discriminate among arbitrary fractional mass patterns for an arbitrary number of classes of analytes. These methods can be used to increase fragmentation efficiency for specific subsets of analytes or to select suitable fragmentation technologies on-the-fly. We show that theoretical generalization error estimates transfer into practical application, and that their quality depends on the accuracy of prior distribution estimate of the analyte classes. The methods are applied to two real-world proteomics datasets. All software used in this study is available from http://software.steenlab.org/fmf hanno.steen@childrens.harvard.edu Supplementary data are available at Bioinformatics online.

  17. 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.

  18. Modelling groundwater fractal flow with fractional differentiation via Mittag-Leffler law

    NASA Astrophysics Data System (ADS)

    Ahokposi, D. P.; Atangana, Abdon; Vermeulen, D. P.

    2017-04-01

    Modelling the flow of groundwater within a network of fractures is perhaps one of the most difficult exercises within the field of geohydrology. This physical problem has attracted the attention of several scientists across the globe. Already two different types of differentiations have been used to attempt modelling this problem including the classical and the fractional differentiation. In this paper, we employed the most recent concept of differentiation based on the non-local and non-singular kernel called the generalized Mittag-Leffler function, to reshape the model of groundwater fractal flow. We presented the existence of positive solution of the new model. Using the fixed-point approach, we established the uniqueness of the positive solution. We solve the new model with three different numerical schemes including implicit, explicit and Crank-Nicholson numerical methods. Experimental data collected from four constant discharge tests conducted in a typical fractured crystalline rock aquifer of the Northern Limb (Bushveld Complex) in the Limpopo Province (South Africa) are compared with the numerical solutions. It is worth noting that the four boreholes (BPAC1, BPAC2, BPAC3, and BPAC4) are located on Faults.

  19. Analysis of fractional anisotropy facilitates differentiation of glioblastoma and brain metastases in a clinical setting.

    PubMed

    Bette, Stefanie; Huber, Thomas; Wiestler, Benedikt; Boeckh-Behrens, Tobias; Gempt, Jens; Ringel, Florian; Meyer, Bernhard; Zimmer, Claus; Kirschke, Jan S

    2016-12-01

    Differentiating glioblastoma from brain metastases is important for therapy planning. Diffusion tensor imaging (DTI) was described as a promising tool, however with conflicting results. of this study was to analyze the clinical utility of DTI for the differentiation of brain metastases and glioblastoma. 294 patients (165 glioblastoma, 129 brain metastases) with preoperative DTI were included in this retrospective study. Fractional anisotropy (FA) was measured via regions of interest (ROIs) in the contrast-enhancing tumor, the necrosis and the FLAIR-hyperintense non-enhancing peritumoral region (NEPTR). Two neuroradiologists classified patient cases as glioblastoma or brain metastases without and with knowledge of FA values. Glioblastoma showed significantly higher FAcontrast (median glioblastoma=0.33, metastases=0.23; P<0.001) whereas no significant difference was observed for FANEPTR (0.21 vs. 0.22; P=0.28) and for FAnecrosis (0.17 vs. 0.18, P=0.37). FA improved diagnostic accuracy of the neuroradiologists significantly from an AUC of 0.84/0.85 (Reader1/Reader2) to 0.89/0.92. Glioblastoma show significantly higher FA values in the contrast enhancing tumor part than brain metastases. Implementation of a ROI-based measurement of FA values and FA color maps in clinical routine helps to differentiate between glioblastoma and brain metastases. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

  20. Evidence for Mo isotope fractionation in the solar nebula and during planetary differentiation

    NASA Astrophysics Data System (ADS)

    Burkhardt, Christoph; Hin, Remco C.; Kleine, Thorsten; Bourdon, Bernard

    2014-04-01

    Mass-dependent Mo isotope fractionation has been investigated for a wide range of meteorites including chondrites (enstatite, ordinary and carbonaceous chondrites), iron meteorites, and achondrites (eucrites, angrites and martian meteorites), as well as for lunar and terrestrial samples. Magmatic iron meteorites together with enstatite, ordinary and most carbonaceous chondrites define a common δMo value of -0.16±0.02‰ (relative to the NIST SRM 3134 Mo standard), which is interpreted to reflect the Mo isotope composition of bulk planetary bodies in the inner solar system. Heavy Mo isotope compositions for IAB iron meteorites most likely reflect impact-induced evaporative losses of Mo from these meteorites. Carbonaceous chondrites define an inverse correlation between δMo and metal content, and a positive correlation between δMo and matrix abundance. These correlations are mainly defined by CM and CK chondrites, and may reflect the heterogeneous distribution of an isotopically light metal and/or an isotopically heavy matrix component in the formation region of carbonaceous chondrites. Alternatively, the elevated δMo of the CM and CK chondrites could result from the loss of volatile, isotopically light Mo oxides, that formed under oxidized conditions typical for the formation of these chondrites. The Mo isotope compositions of samples derived from the silicate portion of differentiated planetary bodies are heavy compared to the mean composition of chondrites and iron meteorites. This difference is qualitatively consistent with experimental evidence for Mo isotope fractionation between metal and silicate. The common δMo values of -0.05±0.03‰ of lunar samples derived from different geochemical reservoirs indicate the absence of significant Mo isotope fractionation by silicate differentiation or impact metamorphism/volatilization on the Moon. The most straightforward interpretation of the Mo isotope composition of the lunar mantle corresponds to the formation

  1. 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.

  2. 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.

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

    DOE PAGES

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

    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

  4. Density-based Monte Carlo filter and its applications in nonlinear stochastic differential equation models.

    PubMed

    Huang, Guanghui; Wan, Jianping; Chen, Hui

    2013-02-01

    Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error. Copyright © 2012 Elsevier Ltd. All rights reserved.

  5. A HAM-based wavelet approach for nonlinear ordinary differential equations

    NASA Astrophysics Data System (ADS)

    Yang, Zhaochen; Liao, Shijun

    2017-07-01

    Based on the homotopy analysis method (HAM) and the generalized Coiflet-type orthogonal wavelet, a new analytic approximation approach for solving nonlinear boundary value problems (governed by nonlinear ordinary differential equations), namely the wavelet homotopy analysis method (wHAM), is proposed. The basic ideas of the wHAM are described using the one-dimensional Bratu's equation as an example. This method not only keeps the main advantages of the normal HAM, but also possesses some new properties and advantages. First of all, the wHAM possesses high computational efficiency. Besides, based on multi-resolution analysis, it provides us a convenient way to balance the accuracy and efficiency by simply adjusting the resolution level. Furthermore, different from the normal HAM, the wHAM provides us much larger freedom to choose the auxiliary linear operator. In addition, just like the normal HAM, iteration can greatly accelerate the computational efficiency of the wHAM without loss of accuracy.

  6. Integrable nonlinear evolution partial differential equations in 4 + 2 and 3 + 1 dimensions.

    PubMed

    Fokas, A S

    2006-05-19

    The derivation and solution of integrable nonlinear evolution partial differential equations in three spatial dimensions has been the holy grail in the field of integrability since the late 1970s. The celebrated Korteweg-de Vries and nonlinear Schrödinger equations, as well as the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. Do there exist integrable analogs of these equations in three spatial dimensions? In what follows, I present a positive answer to this question. In particular, I first present integrable generalizations of the KP and DS equations, which are formulated in four spatial dimensions and which have the novelty that they involve complex time. I then impose the requirement of real time, which implies a reduction to three spatial dimensions. I also present a method of solution.

  7. Existence results for differential inclusions with nonlinear growth conditions in Banach spaces.

    PubMed

    Bounkhel, Messaoud

    2013-01-01

    In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, x(·)(t) ∈ a.e. on I, x(t) ∈ S, ∀t ∈ I, x(0) = x₀ ∈ S, (∗), where S is a closed subset in a Banach space X, I = [0, T], (T > 0), F : I × S → X, is an upper semicontinuous set-valued mapping with convex values satisfying F(t, x) ⊂ c(t)(||x|| + ||x|| (p)K, ∀(t, x) ∈ I × S, where p ∈ ℝ, with p ≠ 1, and c ∈ C([0, T], ℝ(+)). The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.

  8. 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.

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

    SciTech Connect

    Angstmann, C.N.; Donnelly, I.C.; Henry, B.I.; Jacobs, B.A.; Langlands, T.A.M.; Nichols, J.A.

    2016-02-15

    We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

  10. Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

    PubMed

    Hasegawa, Chihiro; Duffull, Stephen B

    2017-05-26

    Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

  11. 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.

  12. 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

  13. The Construction of Implicit and Explicit Solitary Wave Solutions of Nonlinear Partial Differential Equations.

    DTIC Science & Technology

    1987-08-01

    solution of the Korteweg-de Vries equation ( KdV ), working our way up to the derivation of the multi-soliton solution of the sine-Gordon equation (sG...SOLITARY WAVE SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS j DiS~~Uj~l. _’UDistribution/Willy Hereman AvaiiLi -itY Codes Technical Summary Report...Key Words: soliton theory, solitary waves, coupled KdV , evolution equations , direct methods, Harry Dym, sine-Gordon Mathematics Department, University

  14. 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.

  15. 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.

  16. Tsallis distributions and 1/f noise from nonlinear stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Ruseckas, J.; Kaulakys, B.

    2011-11-01

    Probability distributions that emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this article we unite modeling of such distributions with the model of widespread 1/f noise. We propose a class of nonlinear stochastic differential equations giving both the q-exponential or q-Gaussian distributions of signal intensity, revealing long-range correlations and 1/fβ behavior of the power spectral density. The superstatistical framework to get 1/fβ noise with q-exponential and q-Gaussian distributions of the signal intensity is proposed, as well.

  17. Non-differentiable minimax fractional programming with generalized [alpha]-univexity

    NASA Astrophysics Data System (ADS)

    Jayswal, Anurag

    2008-04-01

    In this paper, we study a non-differentiable minimax fractional programming problem under the assumption of generalized [alpha]-univex function. In this paper we extend the concept of [alpha]-invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1-9] and pseudo [alpha]-invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69-75] to [alpha]-univexity and pseudo [alpha]-univexity from a view point of generalized convexity. We also introduce the concept of strict pseudo [alpha]-univex and quasi [alpha]-univex functions. We derive Karush-Kuhn-Tucker-type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different form of dual problems. The results in this paper extend a few known results in the literature.

  18. 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.

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

    USGS Publications Warehouse

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

    2000-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

    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.

  1. 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)

  2. 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)

  3. Multiplicity of solutions for a class of fractional Choquard-Kirchhoff equations involving critical nonlinearity

    NASA Astrophysics Data System (ADS)

    Wang, Fuliang; Xiang, Mingqi

    2017-05-01

    The aim of this paper is to investigate the multiplicity of solutions to the following nonlocal fractional Choquard-Kirchhoff type equation involving critical exponent, ( a+b[u]_{s,p}^p) (-Δ )_p^su=\\int _{R^N}|u(y)|^{p_{μ ,s}^*}/|x-y|^{μ }dy|u|^{p_{μ ,s}^*-2}u +λ h(x)|u|^{q-2}u\\quad { in } {R}^N, [u]_{s,p}=( \\int _{RN}\\int _{R^N}|u(x)- u(y)|^p/|x-y|^{N+sp}dxdy) ^{1/p} where a≥0, b>0 , 0fractional p-Laplace operator, λ >0 is a parameter, p_{μ ,s}^*=(N-{μ/2)p}/{N-sp} is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality, 1

  4. Unified fractional differential approach for transient interporosity flow in naturally fractured media

    NASA Astrophysics Data System (ADS)

    Babak, Petro; Azaiez, Jalel

    2014-12-01

    A unified approach to modeling flows of slightly compressible fluids through naturally fractured media is presented. The unified fractional differential model is derived by combining the flow at micro scale for matrix blocks and macro scale for fractures, using the transient interporosity flow behavior at the interface between matrix blocks and fractures. The derived model is able to unify existing transient interporosity flow models formulated for different shapes of matrix blocks in any medium dimensions. The model is formulated in the form of a fractional order partial differential equation that involves Caputo derivative of order 1/2 with respect to time. Explicit solutions for the unified model are derived for different axisymmetrical spatial domains using Hankel or Hankel-Weber finite or infinite transforms. Comparisons between the predictions of the unified model and those obtained from existing transient interporosity flow models for matrix blocks in the form of slabs, spheres and cylinders are presented. It is shown that the unified fractional derivative model leads to solutions that are very close to those of transient interporosity flow models for fracture-dominant and transitional fracture-to-matrix dominant flow regimes. An analysis of the results of the unified model reveals that the pressure varies linearly with the logarithm of time for different flow regimes, with half slope for the transitional fracture-to-matrix dominant flow regime vs. the fracture and matrix dominant flow regimes. In addition, a new re-scaling that involves the characteristic length in the form of matrix block volume to surface area ratio is derived for the transient interporosity flow models for matrix blocks of different shapes. It is shown that the re-scaled transient interporosity flow models are governed by two dimensionless parameters Θ and Λ compared to only one dimensionless parameter Θ for the unified model. It is shown that the solutions of the transient

  5. FACS Fractionation and Differentiation of Skeletal-Muscle Resident Multipotent Tie2+ Progenitors.

    PubMed

    Biswas, Arpita A; Goldhamer, David J

    2016-01-01

    The skeletal muscle niche is complex and heterogeneous. Over the past few decades, various groups have reported the existence of multiple adult stem cell populations within this environment. Techniques commonly used to identify and assess the differentiation capacities of these cellular fractions, oftentimes rare populations, include the use of lineage tracers, immunofluorescence and histochemistry, flow cytometry, gene expression assays, and phenotypic analysis in culture or in vivo. In 2012, our lab identified and characterized a skeletal-muscle resident Tie2+ progenitor that exhibits adipogenic, chondrogenic, and osteogenic differentiation potentials (Wosczyna et al., J Bone Miner Res 27:1004-1017, 2012). This Tie2+ progenitor also expresses the markers PDGFRα and Sca-1 which in turn label a population of muscle-resident fibro/adipogenic progenitors (FAPs) (Joe et al., Nat Cell Biol 12:153-163, 2010; Uezumi et al., Nat Cell Biol 12:143-152, 2010), suggesting similar identities or overlap in the two mesenchymal progenitor populations. Our study demonstrated that these Tie2-expressing mesenchymal progenitors contribute robustly to BMP-induced heterotopic ossification (HO) in mice, and therefore could represent a key cellular target for therapeutic intervention in HO treatment (Wosczyna et al., J Bone Miner Res 27:1004-1017, 2012). In this chapter, we provide a detailed description of our updated fluorescence-activated cell sorting (FACS) strategy and describe cell culture methods for differentiation of Tie2+ progenitors to adipogenic and osteogenic fates. This strategy is easily adaptable for the prospective isolation of other rare subpopulations resident in skeletal muscle.

  6. 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.

  7. 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.

  8. Non-linear classification for on-the-fly fractional mass filtering and targeted precursor fragmentation in mass spectrometry experiments

    PubMed Central

    Kirchner, Marc; Timm, Wiebke; Fong, Peying; Wangemann, Philine; Steen, Hanno

    2010-01-01

    Motivation: Mass spectrometry (MS) has become the method of choice for protein/peptide sequence and modification analysis. The technology employs a two-step approach: ionized peptide precursor masses are detected, selected for fragmentation, and the fragment mass spectra are collected for computational analysis. Current precursor selection schemes are based on data- or information-dependent acquisition (DDA/IDA), where fragmentation mass candidates are selected by intensity and are subsequently included in a dynamic exclusion list to avoid constant refragmentation of highly abundant species. DDA/IDA methods do not exploit valuable information that is contained in the fractional mass of high-accuracy precursor mass measurements delivered by current instrumentation. Results: We extend previous contributions that suggest that fractional mass information allows targeted fragmentation of analytes of interest. We introduce a non-linear Random Forest classification and a discrete mapping approach, which can be trained to discriminate among arbitrary fractional mass patterns for an arbitrary number of classes of analytes. These methods can be used to increase fragmentation efficiency for specific subsets of analytes or to select suitable fragmentation technologies on-the-fly. We show that theoretical generalization error estimates transfer into practical application, and that their quality depends on the accuracy of prior distribution estimate of the analyte classes. The methods are applied to two real-world proteomics datasets. Availability: All software used in this study is available from http://software.steenlab.org/fmf Contact: hanno.steen@childrens.harvard.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:20134030

  9. 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). Copyright © 2013 Elsevier Inc. All rights reserved.

  10. Comparative Evaluation of Two Methods for Preparative Fractionation of Proteinaceous Subvisible Particles--Differential Centrifugation and FACS.

    PubMed

    Boll, Björn; Folzer, Emilien; Finkler, Christof; Huwyler, Jörg; Mahler, Hanns-Christian; Schmidt, Roland; Koulov, Atanas V

    2015-12-01

    The goal of this study was to compare and evaluate two preparative techniques for fractionation of proteinaceous subvisible particles. This work enables future studies to address the potential biological consequences of proteinaceous subvisible particles in protein therapeutic products. Particles were generated by heat stress and separated by size using differential centrifugation and FACS (Fluorescence-activated cell sorter). Resulting fractions were characterized by size-exclusion chromatography, light obscuration, flow imaging microscopy and resonant mass measurement. Here we report the optimization and comprehensive evaluation of two methods for preparative fractionation of subvisible proteinaceous particles into distinct size fractions in the range between 0.25 and 100 μm: differential centrifugation and FACS. Using these methods, well-defined size fractions were prepared and characterized in detail. Critical assessment and comparison of the two techniques demonstrated their complementarity and for the first time-their relative advantages and drawbacks. FACS and differential centrifugation are valuable tools to prepare well-defined size-fractions of subvisible proteinaceous particles. Both techniques possess unique and advantageous attributes and will likely find complementary application in future research on the biological consequences of proteinaceous subvisible particles.

  11. Local and global existence of mild solution to impulsive fractional semilinear integro-differential equation with noncompact semigroup

    NASA Astrophysics Data System (ADS)

    Gou, Haide; Li, Baolin

    2017-01-01

    In this paper, we study local and global existence of mild solution for an impulsive fractional functional integro differential equation with non-compact semi-group in Banach spaces. We establish a general framework to find the mild solutions for impulsive fractional integro-differential equations, which will provide an effective way to deal with such problems. The theorems proved in this paper improve and extend some related conclusions on this topic. Finally, two applications are given to illustrate that our results are valuable.

  12. 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.

  13. Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem

    NASA Astrophysics Data System (ADS)

    Marinca, Vasile; Ene, Remus-Daniel

    2017-01-01

    In this paper, the Optimal Homotopy Perturbation Method (OHPM) is employed to determine an analytic approximate solution for the nonlinear MHD Jeffery-Hamel flow and heat transfer problem. The Navier-Stokes equations, taking into account Maxwell's electromagnetism and heat transfer, lead to two nonlinear ordinary differential equations. The results obtained by means of OHPM show very good agreement with numerical results and with Homotopy Perturbation Method (HPM) results.

  14. 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

  15. Nonlinear Neural Networks, Motion Sensing and Fractional Charge Detection with Silicon P-I Structures at 4.2 K.

    NASA Astrophysics Data System (ADS)

    Betarbet, Sandeep Raghunandan

    A model has been constructed to predict interpulse time intervals (IPTI) of current spikes of spontaneous pulsing Si p-i-n diodes at 4.2K. The model yields an iterative formula of the form T_{n+1} = f(T_{n}, beta, gamma), where f is the transfer function, T_{n } is the n^{th} IPTI and beta and gamma are the feedback and noise factors respectively. The transfer function has been shown to be similar to a sigmoid neural transfer function under small signal conditions, with gamma/beta equivalent to the voltage bias. A diode produces a nonlinear 2-D return map of the IPTI's when driven by a second diode through a filter circuit. Increasing the bias on the first diode produces a Hopf bifurcation from a fixed point to a limit cycle both in the experimental output and the model. Circuits which can both detect transient light signals and also show lateral inhibition and integration of temporal signals, have been constructed with spontaneously pulsing Si p-i-n diodes. The experimental output of these circuits agree with a model based on simple circuit equations. The circuits have been shown to have equivalent units in the lamina and medulla of the fly eye. A search has been conducted for unconfined primordial fractional charges (FCP) and FCP's created during high energy collisions. The search is based on fractional charge impurity energy level predictions of Chaudhuri et al., (P. R. L. 1374, 45 1980) in Si p-i-n diodes and (for the created FCP's) those properties described by A. De Rujula et al. (Phys. Rev. D, 285, 17 (1978)). An upper limit (95% C.L.) of 2.3 times 10 ^{-20} fractional charges per atom is obtained for primordial FCP's. The diode readout technique uses a combination of an IR photoionization and a field ionization technique. This optoelectronic approach has the advantage of giving an estimate for the concentration of fractional charges. The production experiment had Al as a target, where the FCP's would be created. A stack of 20 diodes contiguous to the target

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

    NASA Astrophysics Data System (ADS)

    Zia, Haider

    2017-06-01

    This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

  17. A modified cubic B-spline differential quadrature method for three-dimensional non-linear diffusion equations

    NASA Astrophysics Data System (ADS)

    Dahiya, Sumita; Mittal, Ramesh Chandra

    2017-07-01

    This paper employs a differential quadrature scheme for solving non-linear partial differential equations. Differential quadrature method (DQM), along with modified cubic B-spline basis, has been adopted to deal with three-dimensional non-linear Brusselator system, enzyme kinetics of Michaelis-Menten type problem and Burgers' equation. The method has been tested efficiently to three-dimensional equations. Simple algorithm and minimal computational efforts are two of the major achievements of the scheme. Moreover, this methodology produces numerical solutions not only at the knot points but also at every point in the domain under consideration. Stability analysis has been done. The scheme provides convergent approximate solutions and handles different cases and is particularly beneficial to higher dimensional non-linear PDEs with irregularities in initial data or initial-boundary conditions that are discontinuous in nature, because of its capability of damping specious oscillations induced by high frequency components of solutions.

  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.

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

    NASA Technical Reports Server (NTRS)

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

    1975-01-01

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

  20. 3D early embryogenesis image filtering by nonlinear partial differential equations.

    PubMed

    Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O

    2010-08-01

    We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which

  1. 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.

  2. A nonlinear mathematical model of cell turnover, differentiation and tumorigenesis in the intestinal crypt.

    PubMed

    d'Onofrio, Alberto; Tomlinson, Ian P M

    2007-02-07

    We present a development of a model [Tomlinson, I.P.M., Bodmer, W.F., 1995. Failure of programmed cell death and differentiation as causes of tumors: Some simple mathematical models. Proc. Natl. Acad. Sci. USA 92, 11130-11134.] of the relationship between cells in three compartments of the intestinal crypt: stem cells, semi-differentiated cells and fully differentiated cells. Stem and semi-differentiated cells may divide to self-renew, undergo programmed death or progress to semi-differentiated and fully differentiated cells, respectively. The probabilities of each of these events provide the most important parameters of the model. Fully differentiated cells do not divide, but a proportion undergoes programmed death in each generation. Our previous models showed that failure of programmed death--for example, in tumorigenesis--could lead either to exponential growth in cell numbers or to growth to some plateau. Our new models incorporate plausible fluctuation in the parameters of the model and introduce nonlinearity by assuming that the parameters depend on the numbers of cells in each state of differentiation. We present detailed analysis of the equilibrium conditions for various forms of these models and, where appropriate, simulate the changes in cell numbers. We find that the model is characterized by bifurcation between increase in cell numbers to stable equilibrium or explosive exponential growth; in a restricted number of cases, there may be multiple stable equilibria. Fluctuation in cell numbers undergoing programmed death, for example caused by tissue damage, generally makes exponential growth more likely, as long as the size of the fluctuation exceeds a certain critical value for a sufficiently long period of time. In most cases, once exponential growth has started, this process is irreversible. In some circumstances, exponential growth is preceded by a long plateau phase, of variable duration, mimicking equilibrium: thus apparently self-limiting lesions

  3. Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method.

    PubMed

    Benhammouda, Brahim

    2015-01-01

    The solution of higher-index Hessenberg differential-algebraic equations (DAEs) is of great importance since this type of DAEs often arises in applications. Higher-index DAEs are known to be numerically and analytically difficult to solve. In this paper, we present a new analytical method for the solution of two classes of higher-index Hessenberg DAEs. The method is based on Adomian polynomials and the differential transform method (DTM). First, the DTM is applied to the DAE where the differential transforms of nonlinear terms are calculated using Adomian polynomials. Then, based on the index condition, the resulting recursion system is transformed into a nonsingular linear algebraic system. This system is then solved to obtain the coefficients of the power series solution. The main advantage of the proposed technique is that it does not require an index reduction nor a linearization. Two test problems are solved to demonstrate the effectiveness of the method. In addition, to extend the domain of convergence of the approximate series solution, we propose a post-treatment with Laplace-Padé resummation method.

  4. 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

  5. Variable-coefficient discrete (GG)-expansion method for nonlinear differential-difference equations

    NASA Astrophysics Data System (ADS)

    Tang, Bo; He, Yinnian; Wei, Leilei; Wang, Shaoli

    2011-09-01

    In this Letter, a variable-coefficient discrete (GG)-expansion method is proposed to seek new and more general exact solutions of nonlinear differential-difference equations. Being concise and straightforward, this method is applied to the (2+1)-dimension Toda equation. As a result, many new and more general exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the proposed method provides a very effective and powerful mathematical tool for solving a great many nonlinear differential-difference equations in mathematical physics.

  6. Learning automata-based solutions to the nonlinear fractional knapsack problem with applications to optimal resource allocation.

    PubMed

    Granmo, Ole-Christoffer; Oommen, B John; Myrer, Svein Arild; Olsen, Morten Goodwin

    2007-02-01

    This paper considers the nonlinear fractional knapsack problem and demonstrates how its solution can be effectively applied to two resource allocation problems dealing with the World Wide Web. The novel solution involves a "team" of deterministic learning automata (LA). The first real-life problem relates to resource allocation in web monitoring so as to "optimize" information discovery when the polling capacity is constrained. The disadvantages of the currently reported solutions are explained in this paper. The second problem concerns allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. This is the scenario encountered when the user has to evaluate multiple web sites by accessing a limited number of web pages, and the proportions of interest are the fraction of each web site that is successfully validated by an HTML validator. Using the general LA paradigm to tackle both of the real-life problems, the proposed scheme improves a current solution in an online manner through a series of informed guesses that move toward the optimal solution. At the heart of the scheme, a team of deterministic LA performs a controlled random walk on a discretized solution space. Comprehensive experimental results demonstrate that the discretization resolution determines the precision of the scheme, and that for a given precision, the current solution (to both problems) is consistently improved until a nearly optimal solution is found--even for switching environments. Thus, the scheme, while being novel to the entire field of LA, also efficiently handles a class of resource allocation problems previously not addressed in the literature.

  7. Nonlinear Response of Inertial Tracers in Steady Laminar Flows: Differential and Absolute Negative Mobility

    NASA Astrophysics Data System (ADS)

    Sarracino, A.; Cecconi, F.; Puglisi, A.; Vulpiani, A.

    2016-10-01

    We study the mobility and the diffusion coefficient of an inertial tracer advected by a two-dimensional incompressible laminar flow, in the presence of thermal noise and under the action of an external force. We show, with extensive numerical simulations, that the force-velocity relation for the tracer, in the nonlinear regime, displays complex and rich behaviors, including negative differential and absolute mobility. These effects rely upon a subtle coupling between inertia and applied force that induces the tracer to persist in particular regions of phase space with a velocity opposite to the force. The relevance of this coupling is revisited in the framework of nonequilibrium response theory, applying a generalized Einstein relation to our system. The possibility of experimental observation of these results is also discussed.

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

    PubMed

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

    2011-07-01

    Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

    NASA Astrophysics Data System (ADS)

    Rigatos, Gerasimos; Siano, Pierluigi

    2013-10-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1974-01-01

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

  11. Modeling scaled processes and 1/fβ noise using nonlinear stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Kaulakys, B; Alaburda, M

    2009-02-01

    We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/fβ noise, power-law autocorrelations and second-order structural (height-height correlation) functions. Analytical expressions for such characteristics are derived and a comparison with numerical calculations is presented. The numerical calculations reveal links between the proposed model and models where signals consist of bursts characterized by power-law distributions of burst size, burst duration and interburst time, as in the case of avalanches in self-organized critical models and the extreme event return times in long-term memory processes. The approach presented may be useful for modeling long-range scaled processes exhibiting 1/f noise and power-law distributions.

  12. 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.

  13. A differentiable reformulation for E-optimal design of experiments in nonlinear dynamic biosystems.

    PubMed

    Telen, Dries; Van Riet, Nick; Logist, Flip; Van Impe, Jan

    2015-06-01

    Informative experiments are highly valuable for estimating parameters in nonlinear dynamic bioprocesses. Techniques for optimal experiment design ensure the systematic design of such informative experiments. The E-criterion which can be used as objective function in optimal experiment design requires the maximization of the smallest eigenvalue of the Fisher information matrix. However, one problem with the minimal eigenvalue function is that it can be nondifferentiable. In addition, no closed form expression exists for the computation of eigenvalues of a matrix larger than a 4 by 4 one. As eigenvalues are normally computed with iterative methods, state-of-the-art optimal control solvers are not able to exploit automatic differentiation to compute the derivatives with respect to the decision variables. In the current paper a reformulation strategy from the field of convex optimization is suggested to circumvent these difficulties. This reformulation requires the inclusion of a matrix inequality constraint involving positive semidefiniteness. In this paper, this positive semidefiniteness constraint is imposed via Sylverster's criterion. As a result the maximization of the minimum eigenvalue function can be formulated in standard optimal control solvers through the addition of nonlinear constraints. The presented methodology is successfully illustrated with a case study from the field of predictive microbiology.

  14. Single shot, double differential spectral measurements of inverse Compton scattering in the nonlinear regime

    NASA Astrophysics Data System (ADS)

    Sakai, Y.; Gadjev, I.; Hoang, P.; Majernik, N.; Nause, A.; Fukasawa, A.; Williams, O.; Fedurin, M.; Malone, B.; Swinson, C.; Kusche, K.; Polyanskiy, M.; Babzien, M.; Montemagno, M.; Zhong, Z.; Siddons, P.; Pogorelsky, I.; Yakimenko, V.; Kumita, T.; Kamiya, Y.; Rosenzweig, J. B.

    2017-06-01

    Inverse Compton scattering (ICS) is a unique mechanism for producing fast pulses—picosecond and below—of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by this source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K -edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.

  15. Single shot, double differential spectral measurements of inverse Compton scattering in the nonlinear regime

    DOE PAGES

    Sakai, Y.; Gadjev, I.; Hoang, P.; ...

    2017-06-05

    Inverse Compton scattering (ICS) is a unique mechanism for producing fast pulses$-$picosecond and below$-$of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by thismore » source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K -edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.« less

  16. 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

  17. A marginal fractional moments based strategy for points selection in seismic response analysis of nonlinear structures with uncertain parameters

    NASA Astrophysics Data System (ADS)

    Xu, Jun; Wang, Ding; Dang, Chao

    2017-01-01

    The present paper proposes a new strategy for selecting representative points in the probability density evolution method (PDEM) to conduct stochastic seismic response analysis of nonlinear structures with uncertain parameters. In PDEM, the strategy for selecting representative points in random-variate space is of critical importance to the efficiency and accuracy. The proposed strategy is established based on the marginal fractional moments of input random variables, which can be evaluated both analytically and numerically without difficulty before performing stochastic analysis. In this strategy, an optimization problem is actually involved. First, the initial points are generated by a low discrepancy sequence and the corresponding assigned probabilities can be computed accordingly. Then, the initial points are rearranged to minimize the index, which is adopted as the maximum relative error between the estimated marginal moments and the exact ones. The rearranged points are accepted as the representative points in PDEM when the index reaches the prescribed tolerance. Numerical example is investigated, showing that the proposed strategy can achieve the good tradeoff of efficiency and accuracy in PDEM for seismic response analysis of structures with uncertain parameters.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-01-01

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

  4. New insight in fractional differentiation: power, exponential decay and Mittag-Leffler laws and applications

    NASA Astrophysics Data System (ADS)

    Gómez-Aguilar, J. F.; Atangana, Abdon

    2017-01-01

    Some physical problems found in nature can follow the power law; others can follow the Mittag-Leffler law and others the exponential decay law. On the other hand, one can observe in nature a physical problem that combines the three laws, it is therefore important to provide a new fractional operator that could possibly be used to model such physical problem. In this paper, we suggest a fractional operator power-law-exponential-Mittag-Leffler kernel with three fractional orders. Some very useful properties are obtained. Numerical solutions were obtained for three examples proposed. The results show that the new fractional operators are powerful mathematical tools to model complex problems.

  5. Symmetry classification of time-fractional diffusion equation

    NASA Astrophysics Data System (ADS)

    Naeem, I.; Khan, M. D.

    2017-01-01

    In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

  6. 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.

  7. Robust non-linear differential equation models of gene expression evolution across Drosophila development.

    PubMed

    Haye, Alexandre; Albert, Jaroslav; Rooman, Marianne

    2012-01-19

    This paper lies in the context of modeling the evolution of gene expression away from stationary states, for example in systems subject to external perturbations or during the development of an organism. We base our analysis on experimental data and proceed in a top-down approach, where we start from data on a system's transcriptome, and deduce rules and models from it without a priori knowledge. We focus here on a publicly available DNA microarray time series, representing the transcriptome of Drosophila across evolution from the embryonic to the adult stage. In the first step, genes were clustered on the basis of similarity of their expression profiles, measured by a translation-invariant and scale-invariant distance that proved appropriate for detecting transitions between development stages. Average profiles representing each cluster were computed and their time evolution was analyzed using coupled differential equations. A linear and several non-linear model structures involving a transcription and a degradation term were tested. The parameters were identified in three steps: determination of the strongest connections between genes, optimization of the parameters defining these connections, and elimination of the unnecessary parameters using various reduction schemes. Different solutions were compared on the basis of their abilities to reproduce the data, to keep realistic gene expression levels when extrapolated in time, to show the biologically expected robustness with respect to parameter variations, and to contain as few parameters as possible. We showed that the linear model did very well in reproducing the data with few parameters, but was not sufficiently robust and yielded unrealistic values upon extrapolation in time. In contrast, the non-linear models all reached the latter two objectives, but some were unable to reproduce the data. A family of non-linear models, constructed from the exponential of linear combinations of expression levels, reached

  8. Robust non-linear differential equation models of gene expression evolution across Drosophila development

    PubMed Central

    2012-01-01

    Background This paper lies in the context of modeling the evolution of gene expression away from stationary states, for example in systems subject to external perturbations or during the development of an organism. We base our analysis on experimental data and proceed in a top-down approach, where we start from data on a system's transcriptome, and deduce rules and models from it without a priori knowledge. We focus here on a publicly available DNA microarray time series, representing the transcriptome of Drosophila across evolution from the embryonic to the adult stage. Results In the first step, genes were clustered on the basis of similarity of their expression profiles, measured by a translation-invariant and scale-invariant distance that proved appropriate for detecting transitions between development stages. Average profiles representing each cluster were computed and their time evolution was analyzed using coupled differential equations. A linear and several non-linear model structures involving a transcription and a degradation term were tested. The parameters were identified in three steps: determination of the strongest connections between genes, optimization of the parameters defining these connections, and elimination of the unnecessary parameters using various reduction schemes. Different solutions were compared on the basis of their abilities to reproduce the data, to keep realistic gene expression levels when extrapolated in time, to show the biologically expected robustness with respect to parameter variations, and to contain as few parameters as possible. Conclusions We showed that the linear model did very well in reproducing the data with few parameters, but was not sufficiently robust and yielded unrealistic values upon extrapolation in time. In contrast, the non-linear models all reached the latter two objectives, but some were unable to reproduce the data. A family of non-linear models, constructed from the exponential of linear combinations

  9. 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.

  10. 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

  11. Fractional approximations for linear first-order differential equations with polynomial coefficients—application to E1(x)

    NASA Astrophysics Data System (ADS)

    Martin, Pablo; Zamudio-Cristi, Jorge

    1982-12-01

    A method is described to obtain fractional approximations for linear first-order differential equations with polynomial coefficients. This approximation can give good accuracy in a large region of the complex variable plane that may include all of the real axis. The parameters of the approximation are solutions of algebraic equations obtained through the coefficients of the higher and lower powers of the variable after the substitution of the fractional approximation in the differential equation. The method is more general than the asymptotical Padé method, and it is not required to determine the power series or asymptotical expansion. A simple approximation for the exponential integral is found, which gives three exact digits for most of the real values of the variable. Approximations of higher accuracy than those of other authors are also obtained.

  12. Haar based numerical solution of Fredholm-Volterra fractional integro-differential equation with nonlocal boundary conditions

    NASA Astrophysics Data System (ADS)

    Setia, Amit; Prakash, Bijil; Vatsala, Aghalaya S.

    2017-01-01

    In this paper, a numerical method is proposed to solve the Fredholm-Volterra fractional integro-differential equation with nonlocal boundary conditions by using Haar wavelets. A collocation based Galerkin's method is applied by using Haar wavelets as basis functions over the interval [0, 1). It converts the Fredholm-Volterra fractional integro-differential equation into a system of m linear equations. On incorporating q nonlocal boundary conditions, it leads to further q equations. All together it will give a system of (m + q) linear equations in (m + q) variables which can be solved. A variety of test examples are considered to illustrate the proposed method. The actual error is also measured with respect to a norm and the results are validated through error bounds.

  13. 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.

  14. 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.

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

    NASA Astrophysics Data System (ADS)

    Zolfaghari, M.; Ghaderi, R.; Sheikhol Eslami, A.; Ranjbar, A.; Hosseinnia, S. H.; Momani, S.; Sadati, J.

    2009-10-01

    The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

  16. Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives

    NASA Astrophysics Data System (ADS)

    Maraaba (Abdeljawad), Thabet; Baleanu, Dumitru; Jarad, Fahd

    2008-08-01

    The existence and uniqueness theorems for functional right-left delay and left-right advanced fractional functional differential equations with bounded delay and advance, respectively, are proved. The continuity with respect to the initial function for these equations is also proved under some Lipschitz kind conditions. The Q-operator is used to transform the delay-type equation to an advanced one and vice versa. An example is given to clarify the results.

  17. ESTIMATION OF CONSTANT AND TIME-VARYING DYNAMIC PARAMETERS OF HIV INFECTION IN A NONLINEAR DIFFERENTIAL EQUATION MODEL.

    PubMed

    Liang, Hua; Miao, Hongyu; Wu, Hulin

    2010-03-01

    Modeling viral dynamics in HIV/AIDS studies has resulted in deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper, we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies. We applied the proposed techniques to estimate the key HIV viral dynamic parameters for two individual AIDS patients treated with antiretroviral therapies. We demonstrate that HIV viral dynamics can be well characterized and

  18. 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.

  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. 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.

  1. On the limits of probabilistic forecasting in nonlinear time series analysis II: Differential entropy

    NASA Astrophysics Data System (ADS)

    Amigó, José M.; Hirata, Yoshito; Aihara, Kazuyuki

    2017-08-01

    In a previous paper, the authors studied the limits of probabilistic prediction in nonlinear time series analysis in a perfect model scenario, i.e., in the ideal case that the uncertainty of an otherwise deterministic model is due to only the finite precision of the observations. The model consisted of the symbolic dynamics of a measure-preserving transformation with respect to a finite partition of the state space, and the quality of the predictions was measured by the so-called ignorance score, which is a conditional entropy. In practice, though, partitions are dispensed with by considering numerical and experimental data to be continuous, which prompts us to trade off in this paper the Shannon entropy for the differential entropy. Despite technical differences, we show that the core of the previous results also hold in this extended scenario for sufficiently high precision. The corresponding imperfect model scenario will be revisited too because it is relevant for the applications. The theoretical part and its application to probabilistic forecasting are illustrated with numerical simulations and a new prediction algorithm.

  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. On the limits of probabilistic forecasting in nonlinear time series analysis II: Differential entropy.

    PubMed

    Amigó, José M; Hirata, Yoshito; Aihara, Kazuyuki

    2017-08-01

    In a previous paper, the authors studied the limits of probabilistic prediction in nonlinear time series analysis in a perfect model scenario, i.e., in the ideal case that the uncertainty of an otherwise deterministic model is due to only the finite precision of the observations. The model consisted of the symbolic dynamics of a measure-preserving transformation with respect to a finite partition of the state space, and the quality of the predictions was measured by the so-called ignorance score, which is a conditional entropy. In practice, though, partitions are dispensed with by considering numerical and experimental data to be continuous, which prompts us to trade off in this paper the Shannon entropy for the differential entropy. Despite technical differences, we show that the core of the previous results also hold in this extended scenario for sufficiently high precision. The corresponding imperfect model scenario will be revisited too because it is relevant for the applications. The theoretical part and its application to probabilistic forecasting are illustrated with numerical simulations and a new prediction algorithm.

  4. 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

  5. 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

  6. 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

  7. 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.

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

    PubMed

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

    2015-12-28

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

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

    PubMed

    Lu, Tao

    2016-01-01

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

  10. 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.

  11. Identification and correction of analog-to-digital-converter nonlinearities and their implications for differential absorption lidar measurements.

    PubMed

    Langford, A O

    1995-12-20

    Differential absorption lidar (DIAL) is a powerful remote-sensing technique widely used to probe the spatial and temporal distribution of ozone and other gaseous atmospheric trace constituents. Although conceptually simple, the DIAL technique presents many challenging and often subtle technical difficulties that can limit its useful range and accuracy. One potentially serious source of error for many DIAL experiments is nonlinearity in the analog-to-digital converters used to capture lidar return signals. The impact of digitizer nonlinearity on DIAL measurements is examined, and a simple and inexpensive low-frequency dithering technique that significantly reduces the effects of ADC nonlinearity in DIAL and other applications in which the signal is repetitively averaged is described.

  12. The Riccati equation with variable coefficients expansion algorithm to find more exact solutions of nonlinear differential equations

    NASA Astrophysics Data System (ADS)

    Yan, Zhenya

    2003-04-01

    In this paper based on a system of Riccati equations with variable coefficients, we present a new Riccati equation with variable coefficients expansion method and its algorithm, which are direct and more powerful than the tanh-function method, sine-cosine method, the generalized hyperbolic-function method and the generalized Riccati equation with constant coefficient expansion method to construct more new exact solutions of nonlinear differential equations in mathematical physics. A pair of generalized Hamiltonian equations is chosen to illustrate our algorithm such that more families of new exact solutions are obtained which contain soliton-like solution and periodic solutions. This algorithm can also be applied to other nonlinear differential equations.

  13. 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.

  14. 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

  15. Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries

    NASA Astrophysics Data System (ADS)

    Startsev, Sergey Ya.

    2017-05-01

    The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above property if and only if this system admits a full set of formal integrals (i.e., differential operators which map symmetries into integrals of the system). As a consequence, such systems possess both direct and inverse Noether operators (in the terminology of a work by B. Fuchssteiner and A.S. Fokas who have used these terms for operators that map cosymmetries into symmetries and perform transformations in the opposite direction). Systems admitting Noether operators are not exhausted by Euler-Lagrange systems and the systems with formal integrals. In particular, a hyperbolic system admits an inverse Noether operator if a differential substitution maps this system into a system possessing an inverse Noether operator.

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

    PubMed

    Kramer, Sean; Bollt, Erik M

    2013-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Kramer, Sean; Bollt, Erik M.

    2013-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Rui, Wenjuan; Zhang, Xiangzhi

    2016-05-01

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

  19. 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. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  20. Multimodal non-linear optical imaging for label-free differentiation of lung cancerous lesions from normal and desmoplastic tissues

    PubMed Central

    Xu, Xiaoyun; Cheng, Jie; Thrall, Michael J.; Liu, Zhengfan; Wang, Xi; Wong, Stephen T.C.

    2013-01-01

    Lung carcinoma is the leading cause of cancer-related death in the United States, and non-small cell carcinoma accounts for 85% of all lung cancer cases. One major characteristic of non-small cell carcinoma is the appearance of desmoplasia and deposition of dense extracellular collagen around the tumor. The desmoplastic response provides a radiologic target but may impair sampling during traditional image-guided needle biopsy and is difficult to differentiate from normal tissues using single label free imaging modality; for translational purposes, label-free techniques provide a more promising route to clinics. We thus investigated the potential of using multimodal, label free optical microscopy that incorporates Coherent Anti-Stokes Raman Scattering (CARS), Two-Photon Excited AutoFluorescence (TPEAF), and Second Harmonic Generation (SHG) techniques for differentiating lung cancer from normal and desmoplastic tissues. Lung tissue samples from patients were imaged using CARS, TPEAF, and SHG for comparison and showed that the combination of the three non-linear optics techniques is essential for attaining reliable differentiation. These images also illustrated good pathological correlation with hematoxylin and eosin (H&E) stained sections from the same tissue samples. Automated image analysis algorithms were developed for quantitative segmentation and feature extraction to enable lung tissue differentiation. Our results indicate that coupled with automated morphology analysis, the proposed tri-modal nonlinear optical imaging technique potentially offers a powerful translational strategy to differentiate cancer lesions reliably from surrounding non-tumor and desmoplastic tissues. PMID:24409386

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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.

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

    PubMed

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

    2014-11-07

    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.

  7. Practical stability analysis of fractional-order impulsive control systems.

    PubMed

    Stamova, Ivanka; Henderson, Johnny

    2016-09-01

    In this paper we obtain sufficient conditions for practical stability of a nonlinear system of differential equations of fractional order subject to impulse effects. Our results provide a design method of impulsive control law which practically stabilizes the impulse free fractional-order system.

  8. Monotonicity, concavity, and convexity of fractional derivative of functions.

    PubMed

    Zhou, Xian-Feng; Liu, Song; Zhang, Zhixin; Jiang, Wei

    2013-01-01

    The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. Then we discuss monotonicity, concavity, and convexity of fractional derivative of some functions and derive corresponding criteria. Several examples are provided to illustrate the applications of our results.

  9. Type-2 fuzzy fractional derivatives

    NASA Astrophysics Data System (ADS)

    Mazandarani, Mehran; Najariyan, Marzieh

    2014-07-01

    In this paper, we introduce two definitions of the differentiability of type-2 fuzzy number-valued functions of fractional order. The definitions are in the sense of Riemann-Liouville and Caputo derivative of order β ɛ (0, 1), and based on type-2 Hukuhara difference and H2-differentiability. The existence and uniqueness of the solutions of type-2 fuzzy fractional differential equations (T2FFDEs) under Caputo type-2 fuzzy fractional derivative and the definition of Laplace transform of type-2 fuzzy number-valued functions are also given. Moreover, the approximate solution to T2FFDE by a Predictor-Evaluate-Corrector-Evaluate (PECE) method is presented. Finally, the approximate solutions of two examples of linear and nonlinear T2FFDEs are obtained using the PECE method, and some cases of T2FFDEs applications in some sciences are presented.

  10. Two generalized Lyapunov-type inequalities for a fractional p-Laplacian equation with fractional boundary conditions.

    PubMed

    Liu, Yang; Xie, Dapeng; Yang, Dandan; Bai, Chuanzhi

    2017-01-01

    In this paper, we investigate the existence of positive solutions for the boundary value problem of nonlinear fractional differential equation with mixed fractional derivatives and p-Laplacian operator. Then we establish two smart generalizations of Lyapunov-type inequalities. Some applications are given to demonstrate the effectiveness of the new results.

  11. 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

    2012-05-04

    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.

  12. Applicability of non-linear versus linear fractional abundance calibration plots for the quantitative determination of triacylglycerol regioisomers by tandem mass spectrometry.

    PubMed

    Ramaley, Louis; Herrera, Lisandra Cubero; Melanson, Jeremy E

    2013-06-15

    Regioisomeric analysis of triacylglycerols is important in understanding lipid biochemistry and the involvement of lipids in disease and nutrition. The use of calibration plots employing fractional abundances provides a simple and rapid method for such analyses. These plots are believed to be linear, but evidence exists for non-linearity. The behavior of such plots needs to be understood to allow for proper interpretation of regioisomeric data. Solutions of five regioisomer pairs were prepared from pure standards and used to construct calibration plots using triple-stage tandem mass spectrometry (MS(3) ) with electrospray ionization (ESIMS(3) ) and cationization by lithium ions. The data were taken by direct infusion with an AB SCIEX QTRAP 2000 QqLIT mass spectrometer. Non-linear calibration plots were observed for the four isomer pairs containing the polyunsaturated eicosapentaenoic (20:5) and docosahexaenoic (22:6) acids paired with palmitic acid (16:0) or myristic acid (14:0), while the pair including palmitic and stearic (18:0) acids provided a linear plot. A non-linear model was developed for these plots and then verified experimentally. The fractional abundance calibration plots used in regioisomeric analysis of triacylglycerols are intrinsically non-linear, but may appear linear if the scatter in data points obscures the curvature, if the curvature is slight, or if the response factors for the two isomers in the regioisomer pair are similar. Therefore, linearity should not be assumed for these types of measurements until confirmed experimentally. Copyright © 2013 John Wiley & Sons, Ltd.

  13. Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique

    NASA Astrophysics Data System (ADS)

    Cortés, J.-C.; Romero, J.-V.; Roselló, M.-D.; Villanueva, R.-J.

    2017-09-01

    Generalized polynomial chaos (gPC) is a spectral technique in random space to represent random variables and stochastic processes in terms of orthogonal polynomials of the Askey scheme. One of its most fruitful applications consists of solving random differential equations. With gPC, stochastic solutions are expressed as orthogonal polynomials of the input random parameters. Different types of orthogonal polynomials can be chosen to achieve better convergence. This choice is dictated by the key correspondence between the weight function associated to orthogonal polynomials in the Askey scheme and the probability density functions of standard random variables. Otherwise, adaptive gPC constitutes a complementary spectral method to deal with arbitrary random variables in random differential equations. In its original formulation, adaptive gPC requires that both the unknowns and input random parameters enter polynomially in random differential equations. Regarding the inputs, if they appear as non-polynomial mappings of themselves, polynomial approximations are required and, as a consequence, loss of accuracy will be carried out in computations. In this paper an extended version of adaptive gPC is developed to circumvent these limitations of adaptive gPC by taking advantage of the random variable transformation method. A number of illustrative examples show the superiority of the extended adaptive gPC for solving nonlinear random differential equations. In addition, for the sake of completeness, in all examples randomness is tackled by nonlinear expressions.

  14. Some experiences in the estimation of parameters in non-linear differential equations.

    PubMed

    Barnes, J G.P.

    1969-03-01

    The author describes a procedure developed by himself and his colleagues for obtaining estimates of the parameters of rate equations, together with information about confidence regions for the estimates. The program has been used successfully for processing results from the chemical engineering industry, with highly non-linear model systems, particularly since temperature was a variable, and the "rate constants" were non-linear combinations of other constants. In biochemical situations, in which investigations are almost always at constant temperature, the non-linearity should not be so extreme, and the procedure may well be capable of dealing with more than 5 to 7 parameters for which it is recommended.

  15. 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.

  16. Fractional active disturbance rejection control.

    PubMed

    Li, Dazi; Ding, Pan; Gao, Zhiqiang

    2016-05-01

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

  17. Corridengum: Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables (2017 Nonlinearity 30 1204)

    NASA Astrophysics Data System (ADS)

    Baladi, Viviane; Kuna, Tobias; Lucarini, Valerio

    2017-08-01

    The first main result of Baladi et al (2017 Nonlinearity 30 1204-20) is modified as follows: For any θ in the Sobolev space H^r_p(M) , with 1 and 0, the map t\\mapsto \\int θ dρt is α-Hölder continuous for all \

  18. Copper isotope fractionation during sulfide-magma differentiation in the Tulaergen magmatic Ni-Cu deposit, NW China

    NASA Astrophysics Data System (ADS)

    Zhao, Yun; Xue, Chunji; Liu, Sheng-Ao; Symons, David T. A.; Zhao, Xiaobo; Yang, Yongqiang; Ke, Junjun

    2017-08-01

    Although it has been recently demonstrated that Cu isotope fractionation during mantle melting and basaltic magma differentiation is limited, the behavior of Cu isotopes during magmatic differentiation involving significant sulfide segregation remains unclear. Magmatic Ni-Cu deposits, which formed via sulfide segregation from basaltic or picritic magmas, are appropriate targets to address this issue. Here we report Cu isotope data for sulfides (chalcopyrite) from the Tulaergen Ni-Cu sulfide deposit in Xinjiang, NW China. Sulfides, including sparsely disseminated (hosted by hornblende gabbro), moderately disseminated (hosted by hornblende olivine websterite), densely disseminated (hosted by hornblende lherzolite) and massive sulfides (sandwiched between country rocks and mafic-ultramafic rocks), were collected from adits at 1050 m, 1100 m and 1150 m levels. The sparsely and moderately disseminated sulfides on 1150 m and 1050 m levels have a restricted range of δ65Cu values from - 0.38‰ to 0.15‰, whereas disseminated and massive sulfides on 1100 m level have δ65Cu values ranging widely from - 1.98‰ to - 0.04‰ and from - 1.08‰ to - 0.52‰, respectively. The δ65Cu values of disseminated sulfides are negatively correlated with whole-rock S and Cu concentrations, and sulfides formed at later stages have heavier δ65Cu values. These observations suggest significant Cu isotope fractionation during sulfide-magma differentiation above 600 °C. During the formation of the Tulaergen magmatic Ni-Cu deposit, sulfide segregation and crystallization of olivine and pyroxene caused the increase of Fe3 + contents in the residual magmas, which would move the redox reaction Cu+ + Fe3 + = Fe2 + + Cu2 + toward larger amounts of Cu2 + in the melt. The presence of Cu2 + in melt allowed redox transformation to happen during sulfide segregation. The residual magmas are enriched in heavy Cu isotopes due to the removal of 65Cu-depleted sulfides, and sulfides formed at later

  19. A New Analytical Procedure for Solving the Non-Linear Differential Equation Arising in the Stretching Sheet Problem

    NASA Astrophysics Data System (ADS)

    Siddheshwar, P. G.; Mahabaleswar, U. S.; Andersson, H. I.

    2013-08-01

    The paper discusses a new analytical procedure for solving the non-linear boundary layer equation arising in a linear stretching sheet problem involving a Newtonian/non-Newtonian liquid. On using a technique akin to perturbation the problem gives rise to a system of non-linear governing differential equations that are solved exactly. An analytical expression is obtained for the stream function and velocity as a function of the stretching parameters. The Clairaut equation is obtained on consideration of consistency and its solution is shown to be that of the stretching sheet boundary layer equation. The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem

  20. Equilibrium Tin Isotope Fractionation during Metal-Sulfide-Silicate Differentiation: A Nuclear Resonant Inelastic X-ray Scattering Approach

    NASA Astrophysics Data System (ADS)

    Roskosz, M.; Amet, Q.; Fitoussi, C.; Laporte, D.; Hu, M. Y.; Alp, E. E.

    2016-12-01

    Metal-silicate differentiation was recently addressed through the insight of the isotopic composition of siderophile elements (mainly Fe, Si and Cr isotopes) of planetary and extraterrestrial bodies. A key limitation of this approach is however the knowledge of equilibrium fractionation factors between coexisting phases (metal alloys, silicates and sulfides) used to interpret data on natural samples. These properties are difficult to determine experimentally. In this context, tin is generally classified as a chalcophile element but it is also siderophile and volatile. We applied a synchrotron-based method to circumvent difficulties related to determination of equilibrium isotope fractionation. The nuclear resonant inelastic x-ray scattering (NRIXS) was used to measure the phonon excitation spectrum and then to derive the force constant and finally the fractionation factors of Sn-bearing geomaterials. Spectroscopic measurements were carried out at room pressure at Sector 30-ID (APS, USA). A range of Fe-Ni alloys, rhyolitic and basaltic glasses and iron sulfides containing isotopically enriched 119Sn were synthesized. The tin content and the redox conditions prevailing during the synthesis were varied. The data evaluation was carried out using PHOENIX and SciPhon programs. A strong effect of both the redox state and the tin content was measured. In addition, the composition of the silicate glasses was found to be another important factor determining the tin isotope metal-silicate-sulfide fractionation factors. Our results are consistent with trends previously observed in the case of iron isotopes [1,2]. We will discuss the implications of our experimental results in terms of tin isotope planetary signatures. References: [1] Dauphas et al. (2014), EPSL, 398, 127-140; [2] Roskosz et al. (2015), GCA, 169, 184-199.

  1. Non-linear patterns in age-related DNA methylation may reflect CD4(+) T cell differentiation.

    PubMed

    Johnson, Nicholas D; Wiener, Howard W; Smith, Alicia K; Nishitani, Shota; Absher, Devin M; Arnett, Donna K; Aslibekyan, Stella; Conneely, Karen N

    2017-04-07

    DNA methylation (DNAm) is an important epigenetic process involved in the regulation of gene expression. While many studies have identified thousands of loci associated with age, few have differentiated between linear and non-linear DNAm trends with age. Non-linear trends could indicate early- or late-life gene regulatory processes. Using data from the Illumina 450K array on 336 human peripheral blood samples, we identified 21 CpG sites that associated with age (P<1.03E-7) and exhibited changing rates of DNAm change with age (P<1.94E-6). For two of these CpG sites (cg07955995 and cg22285878), DNAm increased with age at an increasing rate, indicating that differential DNAm was greatest among elderly individuals. We observed significant replication for both CpG sites (P<5.0E-8) in a second set of peripheral blood samples. In 8 of 9 additional datasets comprising samples of monocytes, T cell subtypes, and brain tissue, we observed a pattern directionally consistent with DNAm increasing with age at an increasing rate, which was nominally significant in the three largest datasets (4.3E-15differentiation via the repression of FOXP3. These findings may suggest a possible role for cg07955995 and cg22285878 in immunosenescence.

  2. 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.

  3. Nitrogen and carbon fractionation during core-mantle differentiation at shallow depth

    NASA Astrophysics Data System (ADS)

    Dalou, Celia; Hirschmann, Marc M.; von der Handt, Anette; Mosenfelder, Jed; Armstrong, Lora S.

    2017-01-01

    One of the most remarkable observations regarding volatile elements in the solar system is the depletion of N in the bulk silicate Earth (BSE) relative to chondrites, leading to a particularly high and non-chondritic C:N ratio. The N depletion may reflect large-scale differentiation events such as sequestration in Earth's core or massive blow off of Earth's early atmosphere, or alternatively the characteristics of a late-added volatile-rich veneer. As the behavior of N during early planetary differentiation processes is poorly constrained, we determined together the partitioning of N and C between Fe-N-C metal alloy and two different silicate melts (a terrestrial and a martian basalt). Conditions spanned a range of fO2 from ΔIW-0.4 to ΔIW-3.5 at 1.2 to 3 GPa, and 1400 °C or 1600 °C, where ΔIW is the logarithmic difference between experimental fO2 and that imposed by the coexistence of crystalline Fe and wüstite.

  4. 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.

  5. 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)

  6. The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations

    NASA Astrophysics Data System (ADS)

    Jensen, Robert

    1988-03-01

    We prove that viscosity solutions in W 1,∞ of the second order, fully nonlinear, equation F( D 2 u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) F is uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions, respectively. This method is completely different from that used in Lions [8, 9] for second order problems with F convex in D 2 u and from that used by Crandall & Lions [3] and Crandall, Evans & Lions [2] for fully nonlinear first order problems.

  7. 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. Copyright © 2015 Elsevier Ltd. All rights reserved.

  8. 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.

  9. 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.

  10. Differential effects of lipid fractions from silver carp brain on human cervical carcinoma cells in vitro.

    PubMed

    Wang, Caixia; Xia, Wenshui; Jiang, Qixing; Xu, Yanshun; Yu, Peipei

    2014-09-01

    Previous research has revealed that n3 polyunsaturated fatty acids (PUFAs) exhibit anticancer activities. Lipids from a fish brain contain substantial n3 PUFAs. However, no research has been conducted on the action and mechanism of their potent anticancer activities. In this study, total lipids (TLs) from silver carp brain were isolated into polar lipids (PLs) and neutral lipids (NLs), and the anticancer potential of the lipid fractions (LFs) was investigated using the human cervical carcinoma HeLa cell line. LFs effectively inhibited the cell proliferation of HeLa cells in a time- and dose-dependent manner by cell cycle arrest at the S stage and by inducing apoptosis. Further analyses indicated that the loss of mitochondrial membrane potential could be one of mechanisms of apoptosis induced by LFs. Among the TLs, PLs have proven to be more effective in inducing cervical carcinoma cell death than NLs. This work will play a role in promoting lipids from silver carp brain as a potential preventive and therapeutic agent against human cervical carcinoma.

  11. Adipose stromal vascular fraction improves cardiac function in chronic myocardial infarction through differentiation and paracrine activity.

    PubMed

    Mazo, Manuel; Cemborain, Arantxa; Gavira, Juan José; Abizanda, Gloria; Araña, Miriam; Casado, Mayte; Soriano, Mario; Hernández, Salomón; Moreno, Cristina; Ecay, Margarita; Albiasu, Edurne; Belzunce, Miriam; Orbe, Josune; Páramo, José Antonio; Merino, Juana; Peñuelas, Iván; Verdugo, José Manuel García; Pelacho, Beatriz; Prosper, Felipe

    2012-01-01

    Fresh adipose-derived cells have been shown to be effective in the treatment of acute myocardial infarction (MI), but their role in the chronic setting is unknown. We sought to determine the long-term effect of the adipose derived-stromal vascular fraction (SVF) cell transplantation in a rat model of chronic MI. MI was induced in 82 rats by permanent coronary artery ligation and 5 weeks later rats were allocated to receive an intramyocardial injection of 10(7) GFP-expressing fresh SVF cells or culture media as control. Heart function and tissue metabolism were determined by echocardiography and (18)F-FDG-microPET, respectively, and histological studies were performed for up to 3 months after transplantation. SVF induced a statistically significant long-lasting (3 months) improvement in cardiac function and tissue metabolism that was associated with increased revascularization and positive heart remodeling, with a significantly smaller infarct size, thicker infarct wall, lower scar fibrosis, and lower cardiac hypertrophy. Importantly, injected cells engrafted and were detected in the treated hearts for at least 3 months, directly contributing to the vasculature and myofibroblasts and at negligible levels to cardiomyocytes. Furthermore, SVF release of angiogenic (VEGF and HGF) and proinflammatory (MCP-1) cytokines, as well as TIMP1 and TIMP4, was demonstrated in vitro and in vivo, strongly suggesting that they have a trophic effect. These results show the potential of SVF to contribute to the regeneration of ischemic tissue and to provide a long-term functional benefit in a rat model of chronic MI, by both direct and indirect mechanisms.

  12. Does the differential photodissociation and chemical fractionation reaction of 13CO affect the column density estimates?

    NASA Astrophysics Data System (ADS)

    Szücs, László; Glover, Simon

    2013-07-01

    Carbon monoxide (CO) and its isotopes are frequently used as a tracer of column density in studies of the dense interstellar medium. The most abundant CO isotope, 12CO, is usually optically thick in intermediate and high density regions and so provides only a lower limit for the column density. In these regions, less abundant isotopes are used, such as 13CO. To relate observations of 13CO to the 12CO column density, a constant 12CO/13CO isotopic ratio is often adopted. In this work, we examine the impact of two effects -- selective photodissociation of 13CO and chemical fractionation -- on the 12CO/13CO isotopic ratio, with the aid of numerical simulations. Our simulations follow the coupled chemical, thermal and dynamical evolution of isolated molecular clouds in several different environments. We post-process our simulation results with line radiative transfer and produce maps of the emergent 13CO emission. We compare emission maps produced assuming a constant isotopic ratio with ones produced using the results from a more self-consistent calculation, and also compare the column density maps derived from the emission maps. We find that at low and high column densities, the column density estimates that we obtain with the approximation of constant isotopic ratio agree well with those derived from the self-consistent model. At intermediate column densities, 10^12 cm^-2 < N(13CO)< 10^15 cm^-2, the approximate model under-predicts the column density by a factor of a few, but we show that we can correct for this, and hence obtain accurate column density estimates, via application of a simple correction factor.

  13. Ultrasound tissue characterization does not differentiate genotype, but indexes ejection fraction deterioration in becker muscular dystrophy.

    PubMed

    Giglio, Vincenzo; Puddu, Paolo Emilio; Holland, Mark R; Camastra, Giovanni; Ansalone, Gerardo; Ricci, Enzo; Mela, Julia; Sciarra, Federico; Di Gennaro, Marco

    2014-12-01

    The aims of the study were, first, to assess whether myocardial ultrasound tissue characterization (UTC) in Becker muscular dystrophy (BMD) can be used to differentiate between patients with deletions and those without deletions; and second, to determine whether UTC is helpful in diagnosing the evolution of left ventricular dysfunction, a precursor of dilated cardiomyopathy. Both cyclic variation of integrated backscatter and calibrated integrated backscatter (cIBS) were assessed in 87 patients with BMD and 70 controls. The average follow-up in BMD patients was 48 ± 12 mo. UTC analysis was repeated only in a subgroup of 40 BMD patients randomly selected from the larger overall group (15 with and 25 without left ventricular dysfunction). Discrimination between BMD patients with and without dystrophin gene deletion was not possible on the basis of UTC data: average cvIBS was 5.2 ± 1.2 and 5.5 ± 1.4 dB, and average cIBS was 29.9 ± 4.7 and 29.6 ± 5.8, respectively, significantly different (p < 0.001) only from controls (8.6 ± 0.5 and 24.6 ± 1.2 dB). In patients developing left ventricular dysfunction during follow-up, cIBS increased to 31.3 ± 5.4 dB, but not significantly (p = 0.08). The highest cIBS values (34.6 ± 5.3 dB, p < 0.09 vs. baseline, p < 0.01 vs BMD patients without left ventricular dysfunction) were seen in the presence of severe left ventricular dysfunction. Multivariate statistics indicated that an absolute change of 6 dB in cIBS is associated with a high probability of left ventricular dysfunction. UTC analysis does not differentiate BMD patients with or without dystrophin gene deletion, but may be useful in indexing left ventricular dysfunction during follow-up. Copyright © 2014 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

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

  15. 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.

  16. Non-Linear EMG Parameters for Differential and Early Diagnostics of Parkinson's Disease.

    PubMed

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

    2013-01-01

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

  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. Differential proteomic analysis of virus-enriched fractions obtained from plasma pools of patients with dengue fever or severe dengue.

    PubMed

    Fragnoud, Romain; Flamand, Marie; Reynier, Frederic; Buchy, Philippe; Duong, Vasna; Pachot, Alexandre; Paranhos-Baccala, Glaucia; Bedin, Frederic

    2015-11-14

    Dengue is the most widespread mosquito-borne viral disease of public health concern. In some patients, endothelial cell and platelet dysfunction lead to life-threatening hemorrhagic dengue fever or dengue shock syndrome. Prognostication of disease severity is urgently required to improve patient management. The pathogenesis of severe dengue has not been fully elucidated, and the role of host proteins associated with viral particles has received little exploration. The proteomes of virion-enriched fractions purified from plasma pools of patients with dengue fever or severe dengue were compared. Virions were purified by ultracentrifugation combined with a water-insoluble polyelectrolyte-based technique. Following in-gel hydrolysis, peptides were analyzed by nano-liquid chromatography coupled to ion trap mass spectrometry and identified using data libraries. Both dengue fever and severe dengue viral-enriched fractions contained identifiable viral envelope proteins and host cellular proteins. Canonical pathway analysis revealed the identified host proteins are mainly involved in the coagulation cascade, complement pathway or acute phase response signaling pathway. Some host proteins were over- or under-represented in plasma from patients with severe dengue compared to patients with dengue fever. ELISAs were used to validate differential expression of a selection of identified host proteins in individual plasma samples of patients with dengue fever compared to patients with severe dengue. Among 22 host proteins tested, two could differentiate between dengue fever and severe dengue in two independent cohorts (olfactomedin-4: area under the curve (AUC), 0.958; and platelet factor-4: AUC, 0.836). A novel technique of virion-enrichment from plasma has allowed to identify two host proteins that have prognostic value for classifying patients with acute dengue who are more likely to develop a severe dengue. The impact of these host proteins on pathogenicity and disease outcome

  19. Oscillator with fraction order restoring force

    NASA Astrophysics Data System (ADS)

    Cveticanin, L.

    2009-03-01

    In this paper a new analytical method for solving the differential equations which describe the motion of the oscillator with fraction order elastic force is introduced. Using the first integral of motion the exact period of vibration in the form of the Euler beta function is obtained. Based on that value the approximate solution of the strong nonlinear fraction order differential equation is formed. The suggested procedure is applied for various fraction values, but also for the pure quadratic, cubic and quintic oscillators. The advantage of the suggested method is that is valid for all fraction values α⩾1, the accuracy of the approximate solution is very high as the period of vibration is exactly analytically determined and is independent on the time. In the paper the fraction order differential equation with small linear and nonlinear terms is also considered. The Krylov-Bogolubov method is extended due to the fact that frequency of vibration depends on the amplitude of vibration. The approximate solution is with time variable amplitude, phase and frequency. The linear damped fraction order oscillator is widely discussed. The approximate solution of the differential equation which describes the vibrations of such oscillator is compared with exact numerical one and shows a good agreement.

  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. 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.

  2. 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.

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

    PubMed Central

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

    2016-01-01

    Several approaches currently exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA), generalized local linear approximation (GLLA), and generalized orthogonal local derivative approximation (GOLD). 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 study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children’s self-regulation. PMID:27391255

  4. Measurements of the S-wave fraction in B 0 → K + π - μ + μ - decays and the B 0 → K ∗(892)0 μ + μ - differential branching fraction

    NASA Astrophysics Data System (ADS)

    Aaij, R.; Adeva, B.; Adinolfi, M.; 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.; 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.; Belous, K.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Benton, J.; Berezhnoy, A.; Bernet, R.; Bertolin, A.; Bettler, M.-O.; van Beuzekom, M.; Bifani, S.; Billoir, P.; Bird, T.; Birnkraut, A.; Bitadze, A.; Bizzeti, A.; Blake, T.; Blanc, F.; Blouw, J.; Blusk, S.; Bocci, V.; Boettcher, T.; Bondar, A.; Bondar, N.; Bonivento, W.; Borghi, S.; Borisyak, M.; Borsato, M.; Bossu, F.; Boubdir, M.; Bowcock, T. J. V.; Bowen, E.; Bozzi, C.; Braun, S.; Britsch, M.; Britton, T.; Brodzicka, J.; Buchanan, E.; Burr, C.; 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.; Chatzikonstantinidis, G.; Chefdeville, M.; Chen, S.; Cheung, S.-F.; Chobanova, V.; 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.; 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 Aguiar Francisco, O.; 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.; Demmer, M.; Derkach, D.; Deschamps, O.; Dettori, F.; Dey, B.; Di Canto, A.; Dijkstra, H.; Dordei, F.; Dorigo, M.; Dosil Suárez, A.; Dovbnya, A.; Dreimanis, K.; Dufour, L.; Dujany, G.; Dungs, K.; Durante, P.; Dzhelyadin, R.; Dziurda, A.; Dzyuba, A.; Déléage, N.; Easo, S.; Egede, U.; Egorychev, V.; Eidelman, S.; Eisenhardt, S.; Eitschberger, U.; Ekelhof, R.; Eklund, L.; Elsasser, Ch.; Ely, S.; Esen, S.; Evans, H. M.; Evans, T.; Falabella, A.; 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.; Fleuret, F.; Fohl, K.; Fontana, M.; Fontanelli, F.; Forshaw, D. C.; Forty, R.; Frank, M.; Frei, C.; Frosini, M.; Fu, J.; Furfaro, E.; Färber, C.; Gallas Torreira, A.; Galli, D.; Gallorini, S.; Gambetta, S.; Gandelman, M.; Gandini, P.; Gao, Y.; García Pardiñas, J.; Garra Tico, J.; Garrido, L.; Garsed, P. J.; Gascon, D.; Gaspar, C.; Gavardi, L.; Gazzoni, G.; Gerick, D.; Gersabeck, E.; Gersabeck, M.; Gershon, T.; Ghez, Ph.; Gianì, S.; Gibson, V.; Girard, O. G.; Giubega, L.; Gizdov, K.; Gligorov, V. V.; Golubkov, D.; Golutvin, A.; Gomes, A.; Gorelov, I. V.; Gotti, C.; Grabalosa Gándara, M.; Graciani Diaz, R.; Granado Cardoso, L. A.; Graugés, E.; Graverini, E.; Graziani, G.; Grecu, A.; Griffith, P.; Grillo, L.; Grünberg, O.; Gushchin, E.; Guz, Yu.; Gys, T.; Göbel, C.; 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.; Heister, A.; Hennessy, K.; Henrard, P.; Henry, L.; Hernando Morata, J. A.; van Herwijnen, E.; Heß, M.; Hicheur, A.; Hill, D.; Hombach, C.; Hulsbergen, W.; Humair, T.; Hushchyn, M.; Hussain, N.; Hutchcroft, D.; Idzik, M.; Ilten, P.; Jacobsson, R.; Jaeger, A.; Jalocha, J.; Jans, E.; Jawahery, A.; 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.; Khairullin, E.; Khanji, B.; Khurewathanakul, C.; Kirn, T.; Klaver, S.; Klimaszewski, K.; Kolpin, M.; Komarov, I.; Koopman, R. F.; Koppenburg, P.; Kozachuk, A.; Kozeiha, M.; Kravchuk, L.; Kreplin, K.; Kreps, M.; 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.; Leflat, A.; Lefrançois, J.; Lefèvre, R.; Lemaitre, F.; Lemos Cid, E.; Leroy, O.; Lesiak, T.; Leverington, B.; Li, Y.; Likhomanenko, T.; 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.; Lyu, X.; Machefert, F.; Maciuc, F.; Maev, O.; Maguire, K.; Malde, S.; Malinin, A.; Maltsev, T.; Manca, G.; Mancinelli, G.; Manning, P.; 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.; Massacrier, L. M.; 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.; Mulder, M.; Mussini, M.; Müller, D.; Müller, J.; Müller, K.; Müller, V.; Naik, P.; Nakada, T.; Nandakumar, R.; Nandi, A.; Nasteva, I.; Needham, M.; Neri, N.; Neubert, S.; Neufeld, N.; Neuner, M.; Nguyen, A. D.; Nguyen-Mau, C.; Niess, V.; Nieswand, S.; Niet, R.; Nikitin, N.; Nikodem, T.; Novoselov, A.; O'Hanlon, D. P.; Oblakowska-Mucha, A.; Obraztsov, V.; Ogilvy, S.; Oldeman, R.; Onderwater, C. J. G.; 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.; Parker, W.; 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.; Petrov, A.; Petruzzo, M.; Picatoste Olloqui, E.; Pietrzyk, B.; Pikies, M.; Pinci, D.; Pistone, A.; Piucci, A.; Playfer, S.; Plo Casasus, M.; Poikela, T.; Polci, F.; Poluektov, A.; Polyakov, I.; Polycarpo, E.; Pomery, G. J.; 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.; Ramos Pernas, M.; Rangel, M. S.; Raniuk, I.; Raven, G.; Redi, F.; Reichert, S.; dos Reis, A. C.; Remon Alepuz, C.; Renaudin, V.; 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.; Rogozhnikov, A.; Roiser, S.; Romanovskiy, V.; Romero Vidal, A.; Ronayne, J. W.; Rotondo, M.; Ruf, T.; Ruiz Valls, P.; Saborido Silva, J. J.; Sagidova, N.; 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.; Schael, S.; Schellenberg, M.; Schiller, M.; Schindler, H.; Schlupp, M.; Schmelling, M.; Schmelzer, T.; Schmidt, B.; Schneider, O.; Schopper, A.; Schubert, K.; Schubiger, M.; Schune, M.-H.; Schwemmer, R.; Sciascia, B.; Sciubba, A.; Semennikov, A.; Sergi, 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.; Skwarnicki, T.; Smith, E.; Smith, I. T.; Smith, J.; Smith, M.; Snoek, H.; Sokoloff, M. D.; Soler, F. J. P.; Souza, D.; Souza De Paula, B.; Spaan, B.; Spradlin, P.; Sridharan, S.; Stagni, F.; Stahl, M.; Stahl, S.; Stefko, P.; 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.; Syropoulos, V.; Szczekowski, M.; Szumlak, T.; T'Jampens, S.; Tayduganov, A.; Tekampe, T.; Tellarini, G.; Teubert, F.; Thomas, C.; Thomas, E.; van Tilburg, J.; Tisserand, V.; Tobin, M.; Tolk, S.; Tomassetti, L.; Tonelli, D.; Topp-Joergensen, S.; Tournefier, E.; Tourneur, S.; Trabelsi, K.; Traill, M.; Tran, M. T.; Tresch, M.; Trisovic, A.; Tsaregorodtsev, A.; Tsopelas, P.; Tuning, N.; Ukleja, A.; Ustyuzhanin, A.; Uwer, U.; Vacca, C.; Vagnoni, V.; Valat, S.; Valenti, G.; Vallier, A.; Vazquez Gomez, R.; Vazquez Regueiro, P.; Vecchi, S.; van Veghel, M.; Velthuis, J. J.; Veltri, M.; Veneziano, G.; Venkateswaran, A.; Vesterinen, M.; Viaud, B.; Vieira, D.; Vieites Diaz, M.; Vilasis-Cardona, X.; Volkov, V.; Vollhardt, A.; Voneki, B.; Voong, D.; Vorobyev, A.; Vorobyev, V.; Voß, C.; de Vries, J. A.; Vázquez Sierra, C.; Waldi, R.; Wallace, C.; Wallace, R.; Walsh, J.; Wang, J.; Ward, D. R.; Watson, N. K.; Websdale, D.; Weiden, A.; Whitehead, M.; Wicht, J.; 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.; Wraight, K.; Wright, S.; Wyllie, K.; Xie, Y.; Xing, Z.; Xu, Z.; Yang, Z.; Yin, H.; Yu, J.; Yuan, X.; Yushchenko, O.; Zangoli, M.; Zarebski, K. A.; Zavertyaev, M.; Zhang, L.; Zhang, Y.; Zhang, Y.; Zhelezov, A.; Zheng, Y.; Zhokhov, A.; Zhukov, V.; Zucchelli, S.

    2016-11-01

    A measurement of the differential branching fraction of the decay B 0 → K ∗(892)0 μ + μ - is presented together with a determination of the S-wave fraction of the K + π - system in the decay B 0 → K +π- μ + μ -. The analysis is based on pp-collision data corresponding to an integrated luminosity of 3 fb-1 collected with the LHCb experiment. The measurements are made in bins of the invariant mass squared of the dimuon system, q 2. Precise theoretical predictions for the differential branching fraction of B 0 → K ∗(892)0 μ + μ - decays are available for the q 2 region 1 .1 < q 2 < 6 .0 GeV2 /c 4. In this q 2 region, for the K +π- invariant mass range 796 < m Kπ < 996 MeV /c 2, the S-wave fraction of the K +π- system in B 0 → K +π- μ + μ - decays is found to be {F}S=0.101± 0.017(stat)± 0.009(syst), and the differential branching fraction of B 0 → K ∗(892)0 μ + μ - decays is determined to be dB/d{q}^2=(0.{392}_{-0.019}^{+0.020}(stat)± 0.010(syst)± 0.027(norm))× 1{0}^{-7}{c}^4/{GeV}^2.

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

    PubMed

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

    2015-04-08

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

  6. 3-D zebrafish embryo image filtering by nonlinear partial differential equations.

    PubMed

    Rizzi, Barbara; Campana, Matteo; Zanella, Cecilia; Melani, Camilo; Cunderlik, Robert; Krivá, Zuzana; Bourgine, Paul; Mikula, Karol; Peyriéras, Nadine; Sarti, Alessandro

    2007-01-01

    We discuss application of nonlinear PDE based methods to filtering of 3-D confocal images of embryogenesis. We focus on the mean curvature driven and the regularized Perona-Malik equations, where standard as well as newly suggested edge detectors are used. After presenting the related mathematical models, the practical results are given and discussed by visual inspection and quantitatively using the mean Hausdorff distance.

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

    ERIC Educational Resources Information Center

    Fay, Temple H.; Lott, P. Aaron

    2002-01-01

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

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

    ERIC Educational Resources Information Center

    Fay, Temple H.; Lott, P. Aaron

    2002-01-01

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

  9. On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations.

    PubMed

    Edelman, Mark

    2015-07-01

    In this paper, we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is a total (a convolution) of the generating functions of all previous values of the variable with weights, which are powers of the time passed. In discrete cases, these systems can be described by difference equations in which a fractional difference on the left hand side is equal to a total (also a convolution) of the generating functions of all previous values of the system's variable with the fractional Eulerian number weights on the right hand side. In the continuous limit, the considered systems can be described by the Grünvald-Letnikov fractional differential equations, which are equivalent to the Volterra integral equations of the second kind. New properties of the fractional Eulerian numbers and possible applications of the results are discussed.

  10. Exp-Function Method and Fractional Complex Transform for Space-Time Fractional KP-BBM Equation

    NASA Astrophysics Data System (ADS)

    Guner, Ozkan

    2017-08-01

    In the present article, He’s fractional derivative, the ansatz method, the (G‧/G)-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM). As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations (FDEs) and it can be applied to other nonlinear FDEs.

  11. 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.

    2016-01-01

    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.

  12. Delayed singularity formation for solutions of nonlinear partial differential equations in higher dimensions

    PubMed Central

    John, Fritz

    1976-01-01

    Strict solutions u of genuinely nonlinear homogeneous hyperbolic equations in two independent variables with initial data f(x) of compact support become singular after a time interval of order ∥f∥-1. In higher dimensions solutions initially of compact support are likely to have life expectancies of orders ∥f∥-2+ε at least. This is proved for the special case of solutions u(x1,..., xn, t) of a second order equation utt = Σi,jaijuxixj, where n ≥ 3 and where the coefficients aij are C∞-functions in the first derivatives of u, forming a symmetric positive definite matrix. PMID:16578737

  13. An efficient algorithm for computation of solitary wave solutions to nonlinear differential equations

    NASA Astrophysics Data System (ADS)

    Ayub, Kamran; Khan, M. Yaqub; Mahmood-Ul-Hassan, Qazi; Ahmad, Jamshad

    2017-09-01

    Nonlinear mathematical problems and their solutions attain much attention in solitary waves. In soliton theory, an efficient tool to attain various types of soliton solutions is the \\exp (-φ (ζ ))-expansion technique. This article is devoted to find exact travelling wave solutions of Drinfeld-Sokolov equation via a reliable mathematical technique. By using the proposed technique, we attain soliton wave solution of various types. It is observed that the technique under discussion is user friendly with minimum computational work, and can be extended for physical problems of different nature in mathematical physics.

  14. Parallel Numerical Solution Process of a Two Dimensional Time Dependent Nonlinear Partial Differential Equation

    NASA Astrophysics Data System (ADS)

    Martin, I.; Tirado, F.; Vazquez, L.

    We present a process to achieve the solution of the two dimensional nonlinear Schrödinger equation using a multigrid technique on a distributed memory machine. Some features about the multigrid technique as its good convergence and parallel properties are explained in this paper. This makes multigrid method the optimal one to solve the systems of equations arising at each time step from an implicit numerical scheme. We give some experimental results about the parallel numerical simulation of this equation on a message passing parallel machine.

  15. 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.

  16. 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

  17. 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.

  18. 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

  19. Existence of entire solutions of some non-linear differential-difference equations.

    PubMed

    Chen, Minfeng; Gao, Zongsheng; Du, Yunfei

    2017-01-01

    In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation [Formula: see text], where [Formula: see text], [Formula: see text] are two non-constant polynomials, [Formula: see text], m, n are positive integers and satisfy [Formula: see text] except for [Formula: see text], [Formula: see text].

  20. A Numerical and Analytic Analysis of Nonlinear Implicit Differential Equations Arising in Control and Circuit Problems

    DTIC Science & Technology

    1991-01-15

    This research project was to develop methods for the numerical and analytic analysis of implicit systems of differential equations, (DAE)- F(x’, z ,t...0 (1) which are not equivalent to an explicit ordinary differential equation (ODE), (ODE) z ’ = G( z , t) (2) That is, the Jacobian Fe of (1) is...structure theorems and a general numerical procedure for the linear time varying DAE E(t)w’(t) + F(t) z (t) = f(t) (3) This numerical algorithm was the

  1. 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.

  2. Non-linear regularized phase retrieval for unidirectional X-ray differential phase contrast radiography.

    PubMed

    Thüring, Thomas; Modregger, Peter; Pinzer, Bernd R; Wang, Zhentian; Stampanoni, Marco

    2011-12-05

    Phase retrieval from unidirectional radiographic differential phase contrast images requires integration of noisy data. A method is presented, which aims to suppress stripe artifacts arising from direct image integration. It is purely algorithmic and therefore, compared to alternative approaches, neither additional alignment nor an increased scan time is required. We report on the theory of this method and present results using numerical as well as experimental data. The method shows significant improvements on the phase retrieval accuracy and enhances contrast in the phase image. Due to its general applicability, the proposed method provides a valuable tool for various 2D imaging applications using differential data.

  3. Convergence of step-by-step methods for non-linear integro-differential equations.

    NASA Technical Reports Server (NTRS)

    Mocarsky, W. L.

    1971-01-01

    The theory of consistent step-by-step methods for solving Volterra integral equations is extended to nonsingular Volterra integro-differential equations. It is shown that standard step-by-step algorithms for these more general equations are convergent. Several numerical examples are included.

  4. Convergence of step-by-step methods for non-linear integro-differential equations.

    NASA Technical Reports Server (NTRS)

    Mocarsky, W. L.

    1971-01-01

    The theory of consistent step-by-step methods for solving Volterra integral equations is extended to nonsingular Volterra integro-differential equations. It is shown that standard step-by-step algorithms for these more general equations are convergent. Several numerical examples are included.

  5. On the Resonance Concept in Systems of Linear and Nonlinear Ordinary Differential Equations

    DTIC Science & Technology

    1965-11-01

    Determinanten und Matrizen mit Anwen- dungen in Physik und Technik). Berlin: Akademie-Verlag 1949. The author wishes to express his thanks to Prof.Dr.R.Iglisch...Case in the System of Ordinary Linear Differential Equations, Part III ( Studium des Resonanzfalles bei Systemen linearer gew6hnlicher

  6. Modelling autonomous oscillations in the human pupil light reflex using non-linear delay-differential equations.

    PubMed

    Longtin, A; Milton, J G

    1989-01-01

    Neurophysiological and anatomical observations are used to derive a non-linear delay-differential equation for the pupil light reflex with negative feedback. As the gain or the time delay in the reflex is increased, a supercritical Hopf bifurcation occurs from a stable fixed point to a stable limit cycle oscillation in pupil area. A Hopf bifurcation analysis is used to determine the conditions for instability and the period and amplitude of these oscillations. The more complex waveforms typical of the occurrence of higher order bifurcations were not seen in numerical simulations of the model. This model provides a general framework to study the different types of dynamical behaviors which can be produced by the pupil light reflex, e.g. edge-light pupil cycling.

  7. 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.

  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. Fully Implicit Temporal Integration of Index One Differential-Algebraic Equations from Nonlinear Porous Media Flow

    NASA Astrophysics Data System (ADS)

    Miller, C. T.; Kees, C. E.

    2002-12-01

    Time integration methods that adapt in both the order of approximation and time step have been shown to provide efficient solutions for Richards' equation. In this work, we extend the same method of lines approach to solve a set of two-phase flow formulations and address some mass conservation issues from the previous work. We analyze these formulations and the nonlinear systems that result from applying the integration methods, placing particular emphasis on their index, range of applicability, and mass conservation characteristics. We conduct numerical experiments to study the behavior of the numerical models for three test problems. We demonstrate that higher order integration in time is more efficient than standard low-order methods for a variety of practical grids and integration tolerances, that the adaptive scheme successfully varies the step size in response to changing conditions, and that mass balance can be maintained efficiently using variable-order integration and an appropriately chosen numerical model formulation.

  10. An inverse approach to the center-focus problem for polynomial differential system with homogenous nonlinearities

    NASA Astrophysics Data System (ADS)

    Llibre, Jaume; Ramírez, Rafael; Ramírez, Valentín

    2017-09-01

    We consider polynomial vector fields X with a linear type and with homogenous nonlinearities. It is well-known that X has a center at the origin if and only if X has an analytic first integral of the form H =1/2 (x2 +y2) + ∑ j = 3 ∞Hj, where Hj =Hj (x , y) is a homogenous polynomial of degree j. The classical center-focus problem already studied by H. Poincaré consists in distinguishing when the origin of X is either a center or a focus. In this paper we study the inverse center-focus problem. In particular for a given analytic function H defined in a neighborhood of the origin we want to determine the homogenous polynomials in such a way that H is a first integral of X and consequently the origin of X will be a center. We study the particular case of centers which have a local analytic first integral of the form H =1/2 (x2 +y2) (1 + ∑ j = 1 ∞ϒj) , in a neighborhood of the origin, where ϒj is a convenient homogenous polynomial of degree j, for j ≥ 1. These centers are called weak centers, they contain the class of center studied by Alwash and Lloyd, the uniform isochronous centers and the isochronous holomorphic centers, but they do not coincide with the class of isochronous centers. We give a classification of the weak centers for quadratic and cubic vector fields with homogenous nonlinearities.

  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. 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.

  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. 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

  15. 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.

  16. Complete group classification of systems of two nonlinear second-Order ordinary differential equations of the form y‧‧ = F(y)

    NASA Astrophysics Data System (ADS)

    Oguis, G. F.; Moyo, S.; Meleshko, S. V.

    2017-03-01

    Extensive work has been done on the group classification of systems of equations in the literature. This paper identifies the gap in the literature which concerns the group classification of systems of two nonlinear second-order ordinary differential equations. We provide a complete group classification of systems of two ordinary differential equations of the form, y‧‧ = F(y) , which occur in many physical applications using two approaches which form the essence of this paper.

  17. 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…

  18. 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…

  19. Differential quadrature solution of nonlinear Klein-Gordon and sine-Gordon equations

    NASA Astrophysics Data System (ADS)

    Pekmen, B.; Tezer-Sezgin, M.

    2012-08-01

    Differential quadrature method (DQM) is proposed to solve the one-dimensional quadratic and cubic Klein-Gordon equations, and two-dimensional sine-Gordon equation. We apply DQM in space direction and also blockwise in time direction. Initial and derivative boundary conditions are also approximated by DQM. DQM provides one to obtain numerical results with very good accuracy using considerably small number of grid points. Numerical solutions are obtained by using Gauss-Chebyshev-Lobatto (GCL) grid points in space intervals, and GCL grid points in each equally divided time blocks.

  20. 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.