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Sample records for nonlinear fractional differential

  1. 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.

  2. 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

  3. 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.

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

    PubMed

    Güner, Özkan; Cevikel, Adem C

    2014-01-01

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

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

    PubMed Central

    Güner, Özkan; Cevikel, Adem C.

    2014-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

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

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  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. 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.

  8. 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.

  9. 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.

  10. 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.

  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. 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

  13. 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.

  14. 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.

  15. 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

  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. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. Characterizing the Performance of Nonlinear Differential Operators

    DTIC Science & Technology

    2012-09-01

    consist of systems of non-homogenous nonlinear ordinary differential equations together with an output map. Elements Σ in this class of operators map...dissipation properties are equivalent to the existence of a solution to a corresponding Hamilton Jacobi Bellman partial differential equation 4 (HJB... differential Riccati equations . Submitted to SIAM J. Control & Optimization, 29 pages, 2012. [B8] P.M. Dower, C.M. Kellett, and H. Zhang. A weak L2-gain

  6. 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.

  7. Silicon isotope fractionation during magmatic differentiation

    NASA Astrophysics Data System (ADS)

    Savage, Paul S.; Georg, R. Bastian; Williams, Helen M.; Burton, Kevin W.; Halliday, Alex N.

    2011-10-01

    The Si isotopic composition of Earth's mantle is thought to be homogeneous (δ 30Si = -0.29 ± 0.08‰, 2 s.d.) and not greatly affected by partial melting and recycling. Previous analyses of evolved igneous material indicate that such rocks are isotopically heavy relative to the mantle. To understand this variation, it is necessary to investigate the degree of Si isotopic fractionation that takes place during magmatic differentiation. Here we report Si isotopic compositions of lavas from Hekla volcano, Iceland, which has formed in a region devoid of old, geochemically diverse crust. We show that Si isotopic composition varies linearly as a function of silica content, with more differentiated rocks possessing heavier isotopic compositions. Data for samples from the Afar Rift Zone, as well as various igneous USGS standards are collinear with the Hekla trend, providing evidence of a fundamental relationship between magmatic differentiation and Si isotopes. The effect of fractionation has been tested by studying cumulates from the Skaergaard Complex, which show that olivine and pyroxene are isotopically light, and plagioclase heavy, relative to the Si isotopic composition of the Earth's mantle. Therefore, Si isotopes can be utilised to model the competing effects of mafic and felsic mineral fractionation in evolving silicate liquids and cumulates. At an average SiO 2 content of ˜60 wt.%, the predicted δ 30Si value of the continental crust that should result from magmatic fractionation alone is -0.23 ± 0.05‰ (2 s.e.), barely heavier than the mantle. This is, at most, a maximum estimate, as this does not take into account weathered material whose formation drives the products toward lighter δ 30Si values. Mass balance calculations suggest that removal of continental crust of this composition from the upper mantle will not affect the Si isotopic composition of the mantle.

  8. 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.

  9. Algorithms For Integrating Nonlinear Differential Equations

    NASA Technical Reports Server (NTRS)

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

    1994-01-01

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

  10. 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

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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

  7. Fractional Differential and Integral Inequalities with Applications

    DTIC Science & Technology

    2016-02-14

    nanotechnology . Consider the equation (3.1) ( )(t) = f(, () ) + (, () ), (0) = 0, where 0 < < 1, (, () ), (, ...boundary conditions. References [1] D. Baleanu, Z. B. Guvencs̈ , J.A. T. Machado, New Trends in Nanotechnology and Fractional Calculus Applications...Rivero, J. Trujillo and M. Pilar Velasco, “On Deterministic Fractional Models,” New Trends in Nanotechnology and Fractional Calculus Applications, edited

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  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. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. 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.

  2. 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.

  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. 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.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. Synthesis of robust nonlinear autopilots using differential game theory

    NASA Technical Reports Server (NTRS)

    Menon, P. K. A.

    1991-01-01

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

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. Stochastic Computational Approach for Complex Nonlinear Ordinary Differential Equations

    NASA Astrophysics Data System (ADS)

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

    2011-02-01

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

  4. Fractional Trajectories: Decorrelation Versus Friction

    DTIC Science & Technology

    2013-07-27

    from the integration of fractional differential equations in time. In Section 2 we provide a general demonstration of the new perspective on fractional ...section we demonstrate the equivalence between a fractional trajectory that is the solution of a Caputo fractional differential equation , and the... fractional differential equation dα dtα V(t) = OV(t), (1) where 0 < α < 1 and O is an operator, either linear or nonlinear, acting on the vector V(t

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  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. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. An energy conservative difference scheme for the nonlinear fractional Schrödinger equations

    NASA Astrophysics Data System (ADS)

    Wang, Pengde; Huang, Chengming

    2015-07-01

    In this paper, an energy conservative Crank-Nicolson difference scheme for nonlinear Riesz space-fractional Schrödinger equations is studied. We give a rigorous analysis of the conservation properties, including mass conservation and energy conservation in the discrete sense. Based on Brouwer fixed point theorem, the existence of the difference solution is proved. By virtue of the energy method, the difference solution is shown to be unique and convergent at the order of O (τ2 +h2) in the l2-norm with time step τ and mesh size h. Finally a linearized iterative algorithm is presented and numerical experiments are given to confirm the theoretical results.

  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. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2014-07-01

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

  1. 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.

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. 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.

  10. 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

  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. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. 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.

  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. 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.

  4. 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

  5. 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.

  6. 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.

  7. 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…

  8. 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

  9. 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.).

  10. 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

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

    PubMed Central

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

    2016-01-01

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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

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

    SciTech Connect

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

    2014-06-01

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

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

    PubMed

    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.

  6. 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

  7. 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.

  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.

  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 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.

  11. 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

  12. 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.

  13. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  15. 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.

  16. 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.

  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. 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.

  19. 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.

  20. 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.

  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. 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.

  3. 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.

  4. 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

  5. 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.

  6. 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

  7. 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.

  8. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-12-01

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

  10. 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.

  11. 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.

  12. 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

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

    PubMed

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

    2013-06-01

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

  14. 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)

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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

  3. 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

  4. 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.

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

    SciTech Connect

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

    2014-11-15

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

  6. 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.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  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. 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.

  2. 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

  3. 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.

  4. 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.

  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. 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.

  7. 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.

  8. 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

  9. 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.

  10. 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

  11. 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.

  12. 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

  13. 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

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

    PubMed

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

    2015-12-28

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

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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)

  11. 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.

  12. 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.

  13. 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.

  14. 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…

  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. 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.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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…

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

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

    PubMed Central

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

    2016-01-01

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

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. 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…

  10. 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.

  11. 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

  12. 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.

  13. 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.

  14. 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.

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

    SciTech Connect

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

    1993-05-01

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

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

    PubMed

    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.

  18. 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

  19. 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.

  20. 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.

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

    NASA Astrophysics Data System (ADS)

    Khader, M. M.; Adel, M.

    2016-09-01

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

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

    PubMed

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

    2016-11-01

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

  3. 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.

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

    SciTech Connect

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

    2012-01-27

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

  5. Differential branching fraction and angular moments analysis of the decay B 0 → K +π- μ + μ - in the K 0,2 ∗ (1430)0 region

    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.; Archilli, F.; d'Argent, P.; Arnau Romeu, J.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Baalouch, M.; Babuschkin, I.; Bachmann, S.; Back, J. J.; Badalov, A.; Baesso, C.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Baszczyk, M.; Batozskaya, V.; Batsukh, B.; 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.; Betti, F.; Bettler, M.-O.; van Beuzekom, M.; Bezshyiko, I.; 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.; Borgheresi, A.; 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.; Camboni, A.; Campana, P.; Campora Perez, D.; Campora Perez, D. H.; 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.; Costa Sobral, C. 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 Serio, M.; 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.; Ebert, M.; 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.; Fazzini, D.; Ferguson, D.; Fernandez Albor, V.; Fernandez Prieto, A.; Ferrari, F.; Ferreira Rodrigues, F.; Ferro-Luzzi, M.; Filippov, S.; Fini, R. A.; Fiore, M.; Fiorini, M.; Firlej, M.; Fitzpatrick, C.; Fiutowski, T.; Fleuret, F.; Fohl, K.; Fontana, M.; Fontanelli, F.; Forshaw, D. C.; Forty, R.; Franco Lima, V.; Frank, M.; Frei, C.; Fu, J.; Furfaro, E.; Färber, C.; Gallas Torreira, A.; Galli, D.; Gallorini, S.; Gambetta, S.; Gandelman, M.; Gandini, P.; Gao, Y.; Garcia Martin, L. M.; 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.; Gian ı, 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.; Gruberg Cazon, B. R.; 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.; Hatch, M.; 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.; Hopchev, H.; 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.; Kariuki, J. 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.; Koliiev, S.; 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.; Merli, A.; Michielin, E.; Milanes, D. A.; Minard, M.-N.; Mitzel, D. S.; Mogini, A.; 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.; 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.; Pais, P. R.; Palano, A.; Palombo, F.; Palutan, M.; Panman, J.; Papanestis, A.; Pappagallo, M.; Pappalardo, L. L.; Parker, W.; Parkes, C.; Passaleva, G.; Pastore, A.; 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.; Poslavskii, S.; 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.; Rudolph, M. S.; Ruf, T.; Ruiz Valls, P.; Saborido Silva, J. J.; Sadykhov, E.; 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.; Simone, S.; 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.; Stemmle, S.; 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.; Toriello, F.; Tournefier, E.; Tourneur, S.; Trabelsi, K.; Traill, M.; Tran, M. T.; Tresch, M.; Trisovic, A.; Tsaregorodtsev, A.; Tsopelas, P.; Tully, A.; Tuning, N.; Ukleja, A.; Ustyuzhanin, A.; Uwer, U.; Vacca, C.; Vagnoni, V.; Valassi, A.; 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.; Vernet, M.; Vesterinen, M.; Viaud, B.; Vieira, D.; Vieites Diaz, M.; Vilasis-Cardona, X.; Volkov, V.; Vollhardt, A.; Voneki, B.; 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.; Wark, H. M.; 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.; Zhu, X.; Zhukov, V.; Zucchelli, S.

    2016-12-01

    Measurements of the differential branching fraction and angular moments of the decay B 0 → K +π- μ + μ - in the K +π- invariant mass range 1330 < m( K +π-) < 1530 MeV /c 2 are presented. Proton-proton collision data are used, corresponding to an integrated luminosity of 3 fb-1 collected by the LHCb experiment. Differential branching fraction measurements are reported in five bins of the invariant mass squared of the dimuon system, q 2, between 0 .1 and 8 .0 GeV2 /c 4. For the first time, an angular analysis sensitive to the S-, P- and D-wave contributions of this rare decay is performed. The set of 40 normalised angular moments describing the decay is presented for the q 2 range 1 .1-6 .0 GeV2 /c 4. [Figure not available: see fulltext.

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

    NASA Astrophysics Data System (ADS)

    Hide, Raymond

    1997-02-01

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

  7. Differentiating Wheat Genotypes by Bayesian Hierarchical Nonlinear Mixed Modeling of Wheat Root Density.

    PubMed

    Wasson, Anton P; Chiu, Grace S; Zwart, Alexander B; Binns, Timothy R

    2017-01-01

    Ensuring future food security for a growing population while climate change and urban sprawl put pressure on agricultural land will require sustainable intensification of current farming practices. For the crop breeder this means producing higher crop yields with less resources due to greater environmental stresses. While easy gains in crop yield have been made mostly "above ground," little progress has been made "below ground"; and yet it is these root system traits that can improve productivity and resistance to drought stress. Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a hierarchical nonlinear mixed modeling approach that utilizes the complete field data for wheat genotypes to fit, under the Bayesian paradigm, an "idealized" relative intensity function for the root distribution over depth. Our approach was used to determine heritability: how much of the variation between field samples was purely random vs. being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our approach led

  8. Differentiating Wheat Genotypes by Bayesian Hierarchical Nonlinear Mixed Modeling of Wheat Root Density

    PubMed Central

    Wasson, Anton P.; Chiu, Grace S.; Zwart, Alexander B.; Binns, Timothy R.

    2017-01-01

    Ensuring future food security for a growing population while climate change and urban sprawl put pressure on agricultural land will require sustainable intensification of current farming practices. For the crop breeder this means producing higher crop yields with less resources due to greater environmental stresses. While easy gains in crop yield have been made mostly “above ground,” little progress has been made “below ground”; and yet it is these root system traits that can improve productivity and resistance to drought stress. Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a hierarchical nonlinear mixed modeling approach that utilizes the complete field data for wheat genotypes to fit, under the Bayesian paradigm, an “idealized” relative intensity function for the root distribution over depth. Our approach was used to determine heritability: how much of the variation between field samples was purely random vs. being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our

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

    SciTech Connect

    Muhamadiev, Ergashboy M; Naimov, Alijon N

    2011-09-30

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

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

    PubMed

    Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

    2016-04-01

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

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

    NASA Astrophysics Data System (ADS)

    Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

    2016-04-01

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

  12. Chaos in a Fractional Order Chua System

    NASA Technical Reports Server (NTRS)

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

    1996-01-01

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

  13. 3D non-linear inversion of magnetic anomalies caused by prismatic bodies using differential evolution algorithm

    NASA Astrophysics Data System (ADS)

    Balkaya, Çağlayan; Ekinci, Yunus Levent; Göktürkler, Gökhan; Turan, Seçil

    2017-01-01

    3D non-linear inversion of total field magnetic anomalies caused by vertical-sided prismatic bodies has been achieved by differential evolution (DE), which is one of the population-based evolutionary algorithms. We have demonstrated the efficiency of the algorithm on both synthetic and field magnetic anomalies by estimating horizontal distances from the origin in both north and east directions, depths to the top and bottom of the bodies, inclination and declination angles of the magnetization, and intensity of magnetization of the causative bodies. In the synthetic anomaly case, we have considered both noise-free and noisy data sets due to two vertical-sided prismatic bodies in a non-magnetic medium. For the field case, airborne magnetic anomalies originated from intrusive granitoids at the eastern part of the Biga Peninsula (NW Turkey) which is composed of various kinds of sedimentary, metamorphic and igneous rocks, have been inverted and interpreted. Since the granitoids are the outcropped rocks in the field, the estimations for the top depths of two prisms representing the magnetic bodies were excluded during inversion studies. Estimated bottom depths are in good agreement with the ones obtained by a different approach based on 3D modelling of pseudogravity anomalies. Accuracy of the estimated parameters from both cases has been also investigated via probability density functions. Based on the tests in the present study, it can be concluded that DE is a useful tool for the parameter estimation of source bodies using magnetic anomalies.

  14. A new inertial aid method for high dynamic Compass signal tracking based on a nonlinear tracking differentiator.

    PubMed

    Guo, Yao; Wu, Wenqi; Tang, Kanghua

    2012-01-01

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

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

    PubMed Central

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

    2016-01-01

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

  16. Parameter estimation method for improper fractional models and its application to molecular biological systems.

    PubMed

    Tian, Li-Ping; Liu, Lizhi; Wu, Fang-Xiang

    2010-01-01

    Derived from biochemical principles, molecular biological systems can be described by a group of differential equations. Generally these differential equations contain fractional functions plus polynomials (which we call improper fractional model) as reaction rates. As a result, molecular biological systems are nonlinear in both parameters and states. It is well known that it is challenging to estimate parameters nonlinear in a model. However, in fractional functions both the denominator and numerator are linear in the parameters while polynomials are also linear in parameters. Based on this observation, we develop an iterative linear least squares method for estimating parameters in biological systems modeled by improper fractional functions. The basic idea is to transfer optimizing a nonlinear least squares objective function into iteratively solving a sequence of linear least squares problems. The developed method is applied to the estimation of parameters in a metabolism system. The simulation results show the superior performance of the proposed method for estimating parameters in such molecular biological systems.

  17. Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative

    NASA Astrophysics Data System (ADS)

    He, Shaobo; Sun, Kehui; Mei, Xiaoyong; Yan, Bo; Xu, Siwei

    2017-01-01

    In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method (CADM). We found that CADM is an effective method for numerical solution of conformable fractional-order differential equations. Taking the conformable fractional-order simplified Lorenz system as an example, the numerical solution and chaotic behaviors of the conformable fractional-order simplified Lorenz system are investigated. It is found that rich dynamics exist in the conformable fractional-order simplified Lorenz system, and the minimum order for chaos is even less than 2. The results are validated by means of bifurcation diagram, Lyapunov characteristic exponents and phase portraits.

  18. FITTING NONLINEAR ORDINARY DIFFERENTIAL EQUATION MODELS WITH RANDOM EFFECTS AND UNKNOWN INITIAL CONDITIONS USING THE STOCHASTIC APPROXIMATION EXPECTATION–MAXIMIZATION (SAEM) ALGORITHM

    PubMed Central

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

    2014-01-01

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

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

    PubMed

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

    2016-03-01

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

  20. New non-linear color look-up table for visualization of brain fractional anisotropy based on normative measurements - principals and first clinical use.

    PubMed

    Keller, Jiří; Rulseh, Aaron M; Komárek, Arnošt; Latnerová, Iva; Rusina, Robert; Brožová, Hana; Vymazal, Josef

    2013-01-01

    Fractional anisotropy (FA) is the most commonly used quantitative measure of diffusion in the brain. Changes in FA have been reported in many neurological disorders, but the implementation of diffusion tensor imaging (DTI) in daily clinical practice remains challenging. We propose a novel color look-up table (LUT) based on normative data as a tool for screening FA changes. FA was calculated for 76 healthy volunteers using 12 motion-probing gradient directions (MPG), a subset of 59 subjects was additionally scanned using 30 MPG. Population means and 95% prediction intervals for FA in the corpus callosum, frontal gray matter, thalamus and basal ganglia were used to create the LUT. Unique colors were assigned to inflection points with continuous ramps between them. Clinical use was demonstrated on 17 multiple system atrophy (MSA) patients compared to 13 patients with Parkinson disease (PD) and 17 healthy subjects. Four blinded radiologists classified subjects as MSA/non-MSA. Using only the LUT, high sensitivity (80%) and specificity (84%) were achieved in differentiating MSA subjects from PD subjects and controls. The LUTs generated from 12 and 30 MPG were comparable and accentuate FA abnormalities.

  1. New Non-Linear Color Look-Up Table for Visualization of Brain Fractional Anisotropy Based on Normative Measurements – Principals and First Clinical Use

    PubMed Central

    Keller, Jiří; Rulseh, Aaron M.; Komárek, Arnošt; Latnerová, Iva; Rusina, Robert; Brožová, Hana; Vymazal, Josef

    2013-01-01

    Fractional anisotropy (FA) is the most commonly used quantitative measure of diffusion in the brain. Changes in FA have been reported in many neurological disorders, but the implementation of diffusion tensor imaging (DTI) in daily clinical practice remains challenging. We propose a novel color look-up table (LUT) based on normative data as a tool for screening FA changes. FA was calculated for 76 healthy volunteers using 12 motion-probing gradient directions (MPG), a subset of 59 subjects was additionally scanned using 30 MPG. Population means and 95% prediction intervals for FA in the corpus callosum, frontal gray matter, thalamus and basal ganglia were used to create the LUT. Unique colors were assigned to inflection points with continuous ramps between them. Clinical use was demonstrated on 17 multiple system atrophy (MSA) patients compared to 13 patients with Parkinson disease (PD) and 17 healthy subjects. Four blinded radiologists classified subjects as MSA/non-MSA. Using only the LUT, high sensitivity (80%) and specificity (84%) were achieved in differentiating MSA subjects from PD subjects and controls. The LUTs generated from 12 and 30 MPG were comparable and accentuate FA abnormalities. PMID:23990954

  2. Fractional vector calculus and fractional Maxwell's equations

    SciTech Connect

    Tarasov, Vasily E.

    2008-11-15

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

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

    NASA Technical Reports Server (NTRS)

    Bogdan, V. M.

    1981-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

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

    PubMed

    Kleinert, H; Zatloukal, V

    2013-11-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1995-01-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1995-01-01

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

  8. PBPK modeling to unravel nonlinear pharmacokinetics of verapamil to estimate the fractional clearance for verapamil N-demethylation in the recirculating rat liver preparation.

    PubMed

    Yang, Qi Joy; Si, Luqin; Tang, Hui; Sveigaard, Helle H; Chow, Edwin C Y; Pang, K Sandy

    2015-04-01

    We applied physiologically based pharmacokinetic (PBPK) modeling to study the dose-dependent metabolism and excretion of verapamil and its preformed metabolite, norverapamil, to unravel the kinetics of norverapamil formation via N-demethylation. Various initial verapamil (1, 50, and 100 μM) and preformed norverapamil (1.5 and 5 μM) concentrations, perfused at 12 ml/min, were investigated in the perfused rat liver preparation. Perfusate and bile were collected over 90 minutes, and livers were harvested at the end of perfusion for high-performance liquid chromatography analysis. After correction for the adsorption of 10%-25% dose verapamil and norverapamil onto Tygon tubing and binding to albumin and red blood cell, fitting of verapamil and formed and preformed norverapamil data with ADAPT5 revealed nonlinearity for protein binding, N-demethylation (V(max,met1)(VER --> NOR) = 96.6 ± 33.4 nmol/min; K(m,met1)(VER --> NOR) = 10.4 ± 4.1 μM), formation of other metabolites (V(max,met2(VER -->others) 288 ± 51 nmol/min; K(m.met2)(VER -->others )= 14.1 ± 4.9 μM), as well as biliary excretion (V(max,sec)(VER)= 0.911 ± 0.505 nmol/min; K(m,sec)(VER) = 4.75 ± 2.29 μM). The hepatic clearance of verapamil (CL(L)(VER) decreased with the dose (8.16-10.2 ml/min), with values remaining high relative to perfusate blood flow rate among the doses. The hepatic clearance of preformed norverapamil (11 ml/min) remained unchanged for the concentrations studied and approximated perfusate blood flow rate, suggesting a high norverapamil extraction ratio. The fractional formation of norverapamil and biliary excretion of verapamil based on fitted constants were 31.1% and 0.64% of CL(L)(VER), respectively. Enantiomeric disposition and auto-inhibition of verapamil failed to perturb these estimaties according to PBPK modeling, due to the low values of the Michaelis-Menten constant, Km, and inhibition parameter, kI.

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

    NASA Astrophysics Data System (ADS)

    Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

    2015-12-01

    In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

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

    PubMed

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

    2013-01-01

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

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

    SciTech Connect

    Charles R. Tolle; Mark Pengitore

    2009-08-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Kogarko, Liya

    2016-04-01

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

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

    PubMed

    Pitkänen, Leena; Striegel, André M

    2015-02-06

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

  15. Significance of iron isotope mineral fractionation in pallasites and iron meteorites for the core-mantle differentiation of terrestrial planets [rapid communication

    NASA Astrophysics Data System (ADS)

    Poitrasson, Franck; Levasseur, Sylvain; Teutsch, Nadya

    2005-05-01

    Seven bulk chondrites, with δ57Fe/ 54Fe values between -0.1‰ and 0‰ relative to IRMM-14, tend to be slightly lighter than 11 bulk iron meteorites, which have δ57Fe/ 54Fe values ranging from 0.04‰ to 0.2‰. At the mineral scale, taenite from two iron meteorites, Cranbourne and Toluca, shows δ57Fe/ 54Fe values heavier by up to 0.3‰ than their kamacite counterpart, thus calling into question the significance of bulk iron meteorite data. On three pallasites (Esquel, Marjalahti and Springwater) we measured a heavier iron isotope composition for the metal fractions compared to the coexisting olivines as previously observed on two other pallasites (Eagle Station and Imilac), but the range of δ57Fe/ 54Fe differences (from 0.32‰ to 0.07‰) is larger than that originally found. Troilite from two pallasites appears to be even heavier than the metal fraction, whereas schreibersite is lighter than its olivine counterpart. There is thus a general tendency for minerals within a given rock to show a heavier Fe isotope composition as the coordination number of Fe increases, although troilite is an exception to this rule. Iron meteorites are classically considered as remnants of asteroid cores and pallasites as core-mantle interfaces. The simultaneous finding that the metal fractions of pallasites have a higher δ57Fe/ 54Fe signature than the coexisting olivines, and that the iron meteorites are slightly heavier than chondrites could be taken as an indication that planetary core-mantle differentiation is accompanied by sizeable iron isotope fractionation. In this hypothesis, mass balance constraints imply that resultant planetary mantles should be isotopically lighter than the chondritic starting material. That is not observed, however, since all planetary mantles analyzed so far have δ57Fe/ 54Fe values equivalent to or heavier than those of chondrites. It thus appears that the moderate temperature and pressure metal-silicate fractionation that occurred in pallasite

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

    NASA Astrophysics Data System (ADS)

    Fuchssteiner, Benno; Oevel, Walter

    1982-03-01

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

  17. An efficient method for systems of variable coefficient coupled Burgers' equation with time-fractional derivative.

    PubMed

    Aminikhah, Hossein; Malekzadeh, Nasrin

    2013-01-01

    A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered as a power series expansion that converges rapidly to the nonlinear problem. The new approximate analytical procedure depends on two iteratives. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. Results indicate that the introduced method is promising for solving other types of systems of nonlinear fractional-order partial differential equations.

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

    PubMed

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

    2014-01-15

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

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

    PubMed

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

    2015-04-01

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

  20. Differentiation of Low- and High-Grade Pediatric Brain Tumors with High b-Value Diffusion-weighted MR Imaging and a Fractional Order Calculus Model

    PubMed Central

    Sui, Yi; Wang, He; Liu, Guanzhong; Damen, Frederick W.; Wanamaker, Christian; Li, Yuhua

    2015-01-01

    Purpose To demonstrate that a new set of parameters (D, β, and μ) from a fractional order calculus (FROC) diffusion model can be used to improve the accuracy of MR imaging for differentiating among low- and high-grade pediatric brain tumors. Materials and Methods The institutional review board of the performing hospital approved this study, and written informed consent was obtained from the legal guardians of pediatric patients. Multi-b-value diffusion-weighted magnetic resonance (MR) imaging was performed in 67 pediatric patients with brain tumors. Diffusion coefficient D, fractional order parameter β (which correlates with tissue heterogeneity), and a microstructural quantity μ were calculated by fitting the multi-b-value diffusion-weighted images to an FROC model. D, β, and μ values were measured in solid tumor regions, as well as in normal-appearing gray matter as a control. These values were compared between the low- and high-grade tumor groups by using the Mann-Whitney U test. The performance of FROC parameters for differentiating among patient groups was evaluated with receiver operating characteristic (ROC) analysis. Results None of the FROC parameters exhibited significant differences in normal-appearing gray matter (P ≥ .24), but all showed a significant difference (P < .002) between low- (D, 1.53 μm2/msec ± 0.47; β, 0.87 ± 0.06; μ, 8.67 μm ± 0.95) and high-grade (D, 0.86 μm2/msec ± 0.23; β, 0.73 ± 0.06; μ, 7.8 μm ± 0.70) brain tumor groups. The combination of D and β produced the largest area under the ROC curve (0.962) in the ROC analysis compared with individual parameters (β, 0.943; D,0.910; and μ, 0.763), indicating an improved performance for tumor differentiation. Conclusion The FROC parameters can be used to differentiate between low- and high-grade pediatric brain tumor groups. The combination of FROC parameters or individual parameters may serve as in vivo, noninvasive, and quantitative imaging markers for classifying

  1. 'Fractional heating' differential scanning calorimetry: a tool to study energetics and kinetics of solid-state reactions in photoactive systems with distributed parameters

    NASA Astrophysics Data System (ADS)

    Sworakowski, Juliusz; Nešpůrek, Stanislav

    1998-11-01

    The technique of differential scanning calorimetry (DSC), used in measurements of thermal effects accompanying solid-state chemical reactions, can be regarded as a thermally stimulated method. Model calculations demonstrate the applicability of the DSC technique in determining parameters controlling the kinetics of solid-state reactions. In particular, it has been shown that the fractional heating technique can be successfully used to analyse DSC curves in case of distributions of kinetic parameters. The method was employed to obtain information about the parameters controlling a thermally driven reaction following UV illumination of photoactive 1-methyl-2,4,4,6-tetraphenyl-1,4-dihydropyridine. Two peaks on DSC curves were distinguished, probably corresponding to different processes associated with reactions responsible for the bleaching of the coloured material. The activation energy and the pre-exponential factor of at least one of them were determined.

  2. Near-Optimal Control for Nonzero-Sum Differential Games of Continuous-Time Nonlinear Systems Using Single-Network ADP.

    PubMed

    Zhang, Huaguang; Cui, Lili; Luo, Yanhong

    2013-02-01

    In this paper, a near-optimal control scheme is proposed to solve the nonzero-sum differential games of continuous-time nonlinear systems. The single-network adaptive dynamic programming (ADP) is utilized to obtain the optimal control policies which make the cost functions reach the Nash equilibrium of nonzero-sum differential games, where only one critic network is used for each player instead of the action-critic dual network used in a typical ADP architecture. Furthermore, the novel weight tuning laws for critic neural networks are proposed, which not only ensure the Nash equilibrium to be reached but also guarantee the system to be stable. No initial stabilizing control policy is required for each player. Moreover, Lyapunov theory is utilized to demonstrate the uniform ultimate boundedness of the closed-loop system. Finally, a simulation example is given to verify the effectiveness of the proposed near-optimal control scheme.

  3. Comment on "Nonlinear differential algorithm to compute all the zeros of a generic polynomial" [J. Math. Phys. 57, 083508 (2016)

    NASA Astrophysics Data System (ADS)

    Calogero, Francesco

    2016-10-01

    Recently a simple differential algorithm to compute all the zeros of a generic polynomial was introduced. In this paper an analogous, but finite-difference, algorithm is introduced and discussed. At the end of the paper a minor generalization of the differential algorithm is also mentioned.

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

    NASA Astrophysics Data System (ADS)

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

    2009-02-01

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

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

    SciTech Connect

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

    2015-07-15

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

  6. On fractional Langevin equation involving two fractional orders

    NASA Astrophysics Data System (ADS)

    Baghani, Omid

    2017-01-01

    In numerical analysis, it is frequently needed to examine how far a numerical solution is from the exact one. To investigate this issue quantitatively, we need a tool to measure the difference between them and obviously this task is accomplished by the aid of an appropriate norm on a certain space of functions. For example, Sobolev spaces are indispensable part of theoretical analysis of partial differential equations and boundary integral equations, as well as are necessary for the analysis of some numerical methods for the solving of such equations. But most of articles that appear in this field usually use ‖.‖∞ in the space of C[a, b] which is very restrictive. In this paper, we introduce a new norm that is convenient for the fractional and singular differential equations. Using this norm, the existence and uniqueness of initial value problems for nonlinear Langevin equation with two different fractional orders are studied. In fact, the obtained results could be used for the classical cases. Finally, by two examples we show that we cannot always speak about the existence and uniqueness of solutions just by using the previous methods.

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

    NASA Astrophysics Data System (ADS)

    Puķīte, Jānis; Wagner, Thomas

    2016-05-01

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

  8. Cubication of Conservative Nonlinear Oscillators

    ERIC Educational Resources Information Center

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

    2009-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-07-01

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

  11. Trigonometric Integrals via Partial Fractions

    ERIC Educational Resources Information Center

    Chen, H.; Fulford, M.

    2005-01-01

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

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

    EPA Science Inventory

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

  13. Quantitative Proteomics Analysis of the Nuclear Fraction of Human CD4+ Cells in the Early Phases of IL-4-induced Th2 Differentiation*

    PubMed Central

    Moulder, Robert; Lönnberg, Tapio; Elo, Laura L.; Filén, Jan-Jonas; Rainio, Eeva; Corthals, Garry; Oresic, Matej; Nyman, Tuula A.; Aittokallio, Tero; Lahesmaa, Riitta

    2010-01-01

    We used stable isotope labeling with 4-plex iTRAQ (isobaric tags for relative and absolute quantification) reagents and LC-MS/MS to investigate proteomic changes in the nucleus of activated human CD4+ cells during the early stages of Th2 cell differentiation. The effects of IL-4 stimulation upon activated naïve CD4+ cells were measured in the nuclear fractions from 6 and 24 h in three biological replicates, each using pooled cord blood samples derived from seven or more individuals. In these analyses, in the order of 800 proteins were detected with two or more peptides and quantified in three biological replicates. In addition to consistent differences observed with the nuclear localization/expression of established human Th2 and Th1 markers, there were changes that suggested the involvement of several proteins either only recently reported or otherwise not known in this context. These included SATB1 and among the novel changes detected and validated an IL-4-induced increase in the level of YB1. This unique data set from human cord blood CD4+ T cells details an extensive list of protein determinations that compares with and complements previous data determined from the Jurkat cell nucleus. PMID:20467038

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

    PubMed Central

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

    2015-01-01

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

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

    PubMed Central

    El-Qulity, Said Ali; Mohamed, Ali Wagdy

    2016-01-01

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

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

    PubMed

    El-Qulity, Said Ali; Mohamed, Ali Wagdy

    2016-01-01

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

  17. Unmodeled dynamics and nonlinear control: Wrapup

    NASA Technical Reports Server (NTRS)

    Hunt, L. R.

    1988-01-01

    Theoretical and applicable results concerning systems of nonlinear ordinary differential equations and control of partial differential equations are examined. Titles and abstracts of recent papers are presented.

  18. On Fractional Model Reference Adaptive Control

    PubMed Central

    Shi, Bao; Dong, Chao

    2014-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Wang, Lijian

    2015-12-01

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

  20. Nonlinear Ship Dynamics

    DTIC Science & Technology

    1992-07-07

    mrtegrating the original governing differential equation. 2. A. H. Nayfeh, " Parametric Identification of Nonlinear Dynamic Systems," Computers...Structures, Vol. 20. No. 1-3. 1985, pp. 487-493. A parametric identification technique that exploits nonlinear resonances and comparisons of the behavior of...617-631. Presentations 1. A. H. Vn’.yfeh, " Parametric Identification of Nonlinear Dynamic Systems," Symposium on Advances and Trends in Structures

  1. On nonlinear conservation laws with a nonlocal diffusion term

    NASA Astrophysics Data System (ADS)

    Achleitner, F.; Hittmeir, S.; Schmeiser, C.

    Scalar one-dimensional conservation laws with a nonlocal diffusion term corresponding to a Riesz-Feller differential operator are considered. Solvability results for the Cauchy problem in L are adapted from the case of a fractional derivative with homogeneous symbol. The main interest of this work is the investigation of smooth shock profiles. In the case of a genuinely nonlinear smooth flux function we prove the existence of such travelling waves, which are monotone and satisfy the standard entropy condition. Moreover, the dynamic nonlinear stability of the travelling waves under small perturbations is proven, similarly to the case of the standard diffusive regularisation, by constructing a Lyapunov functional.

  2. Accessible solitons of fractional dimension

    SciTech Connect

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

    2016-05-15

    We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.

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

    PubMed

    Xue, Hongqi; Miao, Hongyu; Wu, Hulin

    2010-01-01

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

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

    PubMed Central

    Xue, Hongqi; Miao, Hongyu; Wu, Hulin

    2010-01-01

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

  5. Fractional diffusion on bounded domains

    DOE PAGES

    Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

    2015-03-13

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

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

    NASA Astrophysics Data System (ADS)

    Ding, J. Y.

    2013-12-01

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

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

    NASA Astrophysics Data System (ADS)

    S Saha, Ray

    2016-04-01

    In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

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

    PubMed

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

    2012-01-01

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

  9. Investigations of a compartmental model for leucine kinetics using non-linear mixed effects models with ordinary and stochastic differential equations.

    PubMed

    Berglund, Martin; Sunnåker, Mikael; Adiels, Martin; Jirstrand, Mats; Wennberg, Bernt

    2012-12-01

    Non-linear mixed effects (NLME) models represent a powerful tool to simultaneously analyse data from several individuals. In this study, a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady-state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analysed. We find that the interindividual variation of the model parameters is much smaller for the NLME models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual, the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion, NLME models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies.

  10. Fractional randomness

    NASA Astrophysics Data System (ADS)

    Tapiero, Charles S.; Vallois, Pierre

    2016-11-01

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

  11. Fractional dissipative standard map.

    PubMed

    Tarasov, Vasily E; Edelman, M

    2010-06-01

    Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term memory. The memory effect in the fractional maps means that their present state of evolution depends on all past states with special forms of weights. Already a small deviation of the order of derivative from the integer value corresponding to the regular dissipative standard map (small memory effects) leads to the qualitatively new behavior of the corresponding attractors. The fractional dissipative standard maps are used to demonstrate a new type of fractional attractors in the wide range of the fractional orders of derivatives.

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

    PubMed Central

    2012-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Xu, Fei

    2016-06-01

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

  14. A general fractional-order dynamical network: synchronization behavior and state tuning.

    PubMed

    Wang, Junwei; Xiong, Xiaohua

    2012-06-01

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

  15. Fractional-time quantum dynamics.

    PubMed

    Iomin, Alexander

    2009-08-01

    Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional time Schrödinger equation (SE), which differs from the standard SE by the fractional time derivative: partial differential/partial differentialt --> partial differential(alpha)/partial differentialt(alpha). It is shown that for alpha=1/2 the fractional SE is isospectral to a comb model. An analytical expression for the Green's functions of the systems are obtained. The semiclassical limit is discussed.

  16. Variational solutions and random dynamical systems to SPDEs perturbed by fractional Gaussian noise.

    PubMed

    Zeng, Caibin; Yang, Qigui; Cao, Junfei

    2014-01-01

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

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

    PubMed Central

    Zeng, Caibin; Yang, Qigui; Cao, Junfei

    2014-01-01

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

  18. Fractional calculus in bioengineering.

    PubMed

    Magin, Richard L

    2004-01-01

    Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub

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

    PubMed Central

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

    2016-01-01

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

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

    PubMed

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

    2016-04-19

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

  1. Fractional market dynamics

    NASA Astrophysics Data System (ADS)

    Laskin, Nick

    2000-12-01

    A new extension of a fractality concept in financial mathematics has been developed. We have introduced a new fractional Langevin-type stochastic differential equation that differs from the standard Langevin equation: (i) by replacing the first-order derivative with respect to time by the fractional derivative of order μ; and (ii) by replacing “white noise” Gaussian stochastic force by the generalized “shot noise”, each pulse of which has a random amplitude with the α-stable Lévy distribution. As an application of the developed fractional non-Gaussian dynamical approach the expression for the probability distribution function (pdf) of the returns has been established. It is shown that the obtained fractional pdf fits well the central part and the tails of the empirical distribution of S&P 500 returns.

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

    PubMed

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

    2012-01-01

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

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

    PubMed Central

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

    2012-01-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1991-01-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1990-01-01

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

  6. Automatic differentiation bibliography

    SciTech Connect

    Corliss, G.F.

    1992-07-01

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

  7. Understanding Multiplication of Fractions.

    ERIC Educational Resources Information Center

    Sweetland, Robert D.

    1984-01-01

    Discussed the use of Cuisenaire rods in teaching the multiplication of fractions. Considers whole number times proper fraction, proper fraction multiplied by proper fraction, mixed number times proper fraction, and mixed fraction multiplied by mixed fractions. (JN)

  8. Numerical solution of the one-dimensional fractional convection diffusion equations based on Chebyshev operational matrix.

    PubMed

    Xie, Jiaquan; Huang, Qingxue; Yang, Xia

    2016-01-01

    In this paper, we are concerned with nonlinear one-dimensional fractional convection diffusion equations. An effective approach based on Chebyshev operational matrix is constructed to obtain the numerical solution of fractional convection diffusion equations with variable coefficients. The principal characteristic of the approach is the new orthogonal functions based on Chebyshev polynomials to the fractional calculus. The corresponding fractional differential operational matrix is derived. Then the matrix with the Tau method is utilized to transform the solution of this problem into the solution of a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via examples. It is shown that the proposed algorithm yields better results. Finally, error analysis shows that the algorithm is convergent.

  9. Quantitative proteomics of fractionated membrane and lumen exosome proteins from isogenic metastatic and nonmetastatic bladder cancer cells reveal differential expression of EMT factors.

    PubMed

    Jeppesen, Dennis Kjølhede; Nawrocki, Arkadiusz; Jensen, Steffen Grann; Thorsen, Kasper; Whitehead, Bradley; Howard, Kenneth A; Dyrskjøt, Lars; Ørntoft, Torben Falck; Larsen, Martin R; Ostenfeld, Marie Stampe

    2014-03-01

    Cancer cells secrete soluble factors and various extracellular vesicles, including exosomes, into their tissue microenvironment. The secretion of exosomes is speculated to facilitate local invasion and metastatic spread. Here, we used an in vivo metastasis model of human bladder carcinoma cell line T24 without metastatic capacity and its two isogenic derivate cell lines SLT4 and FL3, which form metastases in the lungs and liver of mice, respectively. Cultivation in CLAD1000 bioreactors rather than conventional culture flasks resulted in a 13- to 16-fold increased exosome yield and facilitated quantitative proteomics of fractionated exosomes. Exosomes from T24, SLT4, and FL3 cells were partitioned into membrane and luminal fractions and changes in protein abundance related to the gain of metastatic capacity were identified by quantitative iTRAQ proteomics. We identified several proteins linked to epithelial-mesenchymal transition, including increased abundance of vimentin and hepatoma-derived growth factor in the membrane, and casein kinase II α and annexin A2 in the lumen of exosomes, respectively, from metastatic cells. The change in exosome protein abundance correlated little, although significant for FL3 versus T24, with changes in cellular mRNA expression. Our proteomic approach may help identification of proteins in the membrane and lumen of exosomes potentially involved in the metastatic process.

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

    PubMed

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

    2015-02-01

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

  11. Radiating subdispersive fractional optical solitons

    NASA Astrophysics Data System (ADS)

    Fujioka, J.; Espinosa, A.; Rodríguez, R. F.; Malomed, B. A.

    2014-09-01

    It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.

  12. Radiating subdispersive fractional optical solitons

    SciTech Connect

    Fujioka, J. Espinosa, A.; Rodríguez, R. F.; Malomed, B. A.

    2014-09-01

    It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.

  13. Parametrically defined differential equations

    NASA Astrophysics Data System (ADS)

    Polyanin, A. D.; Zhurov, A. I.

    2017-01-01

    The paper deals with nonlinear ordinary differential equations defined parametrically by two relations. It proposes techniques to reduce such equations, of the first or second order, to standard systems of ordinary differential equations. It obtains the general solution to some classes of nonlinear parametrically defined ODEs dependent on arbitrary functions. It outlines procedures for the numerical solution of the Cauchy problem for parametrically defined differential equations.

  14. Fractional Galilean symmetries

    NASA Astrophysics Data System (ADS)

    Hosseiny, Ali; Rouhani, Shahin

    2016-09-01

    We generalize the differential representation of the operators of the Galilean algebras to include fractional derivatives. As a result a whole new class of scale invariant Galilean algebras are obtained. The first member of this class has dynamical index z = 2 similar to the Schrödinger algebra. The second member of the class has dynamical index z = 3 / 2, which happens to be the dynamical index Kardar-Parisi-Zhang equation.

  15. Generalized Nonlinear Yule Models

    NASA Astrophysics Data System (ADS)

    Lansky, Petr; Polito, Federico; Sacerdote, Laura

    2016-11-01

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

  16. Linearization of Conservative Nonlinear Oscillators

    ERIC Educational Resources Information Center

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

    2009-01-01

    A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

  17. Mystery Fractions

    ERIC Educational Resources Information Center

    Bhattacharyya, Sonalee; Namakshi, Nama; Zunker, Christina; Warshauer, Hiroko K.; Warshauer, Max

    2016-01-01

    Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

  18. Pitch Fractionation.

    DTIC Science & Technology

    1981-12-15

    13 3. Solvent Fractionation Experiments .................................... 15 4. Fourier Transform Infrared Spectra for A240 Petrolem Pitch AG 12...34 and Mesophase Pitch AG 164B ............................... 21 5. Fourier Transform Infrared Spectra ................................... 23 6...compared by Fourier transform infrared (FTIR) analysis using a Digilab Model FTS 14 spectrophotometer (Rockwell International, Anaheim, California

  19. Fractional variational calculus and the transversality conditions

    NASA Astrophysics Data System (ADS)

    Agrawal, O. P.

    2006-08-01

    This paper presents the Euler-Lagrange equations and the transversality conditions for fractional variational problems. The fractional derivatives are defined in the sense of Riemann-Liouville and Caputo. The connection between the transversality conditions and the natural boundary conditions necessary to solve a fractional differential equation is examined. It is demonstrated that fractional boundary conditions may be necessary even when the problem is defined in terms of the Caputo derivative. Furthermore, both fractional derivatives (the Riemann-Liouville and the Caputo) arise in the formulations, even when the fractional variational problem is defined in terms of one fractional derivative only. Examples are presented to demonstrate the applications of the formulations.

  20. Fraction Reduction through Continued Fractions

    ERIC Educational Resources Information Center

    Carley, Holly

    2011-01-01

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

  1. Nonlinear Waves

    DTIC Science & Technology

    1989-06-15

    following surprising situation. Namely associated with the integrable nonlinear Schrodinger equations are standard numerical schemes which exhibit at...36. An Initial Boundary Value Problem for the Nonlinear Schrodinger Equations , A.S. Fokas, Physica D March 1989. 37. Evolution Theory, Periodic... gravity waves and wave excitation phenomena related to moving pressure distributions; numerical approximation and computation; nonlinear optics; and

  2. Isotope fractionation

    NASA Astrophysics Data System (ADS)

    Bell, Peter M.

    A rash of new controversy has emerged around the subject of mass-independent isotope fractionation effects, particularly in the case of the oxygen isotopes. To be sure, the controversy has been around for awhile, but it has been given new impetus by the results of a recent study by Mark H. Thiemens and John E. Heidenreich III of the University of California, San Diego (Science, March 4, 1983).Gustav Arrhenius has been trying to convince the planetary science community that chemical effects in isotope fractionation processes could explain observations in meteorites that appear to be outside of the traditionally understood mass-dependent fractionations (G. Arrhenius, J . L. McCrumb, and N. F. Friedman, Astrophys. Space Sci, 65, 297, 1974). Robert Clayton had made the basic observations of oxygen in carbonaceous chondrites that the slope of the δ17 versus δ18 line was 1 instead of the slope of ½ characteristic of terrestrial rocks and lunar samples (Ann. Rev. Nucl. Part. Sci., 28, 501, 1978). The mass-independent effects were ascribed to the apparent contribution of an ancient presolar system component of O16.

  3. One input-class and two input-class classifications for differentiating olive oil from other edible vegetable oils by use of the normal-phase liquid chromatography fingerprint of the methyl-transesterified fraction.

    PubMed

    Jiménez-Carvelo, Ana M; Pérez-Castaño, Estefanía; González-Casado, Antonio; Cuadros-Rodríguez, Luis

    2017-04-15

    A new method for differentiation of olive oil (independently of the quality category) from other vegetable oils (canola, safflower, corn, peanut, seeds, grapeseed, palm, linseed, sesame and soybean) has been developed. The analytical procedure for chromatographic fingerprinting of the methyl-transesterified fraction of each vegetable oil, using normal-phase liquid chromatography, is described and the chemometric strategies applied and discussed. Some chemometric methods, such as k-nearest neighbours (kNN), partial least squared-discriminant analysis (PLS-DA), support vector machine classification analysis (SVM-C), and soft independent modelling of class analogies (SIMCA), were applied to build classification models. Performance of the classification was evaluated and ranked using several classification quality metrics. The discriminant analysis, based on the use of one input-class, (plus a dummy class) was applied for the first time in this study.

  4. Control problems for semilinear neutral differential equations in Hilbert spaces.

    PubMed

    Jeong, Jin-Mun; Cho, Seong Ho

    2014-01-01

    We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the local Lipschitz continuity of nonlinear term. Our purpose is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. Finally we give a simple example to which our main result can be applied.

  5. Control Problems for Semilinear Neutral Differential Equations in Hilbert Spaces

    PubMed Central

    Jeong, Jin-Mun; Cho, Seong Ho

    2014-01-01

    We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the local Lipschitz continuity of nonlinear term. Our purpose is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. Finally we give a simple example to which our main result can be applied. PMID:24772022

  6. A fractional model of a dynamical Brusselator reaction-diffusion system arising in triple collision and enzymatic reactions

    NASA Astrophysics Data System (ADS)

    Singh, Jagdev; Rashidi, M. M.; Kumar, Devendra; Swroop, Ram

    2016-12-01

    In this paper, we study a dynamical Brusselator reaction-diffusion system arising in triple collision and enzymatic reactions with time fractional Caputo derivative. The present article involves a more generalized effective approach, proposed for the Brusselator system say q-homotopy analysis transform method (q-HATM), providing the family of series solutions with nonlocal generalized effects. The convergence of the q-HATM series solution is adjusted and controlled by auxiliary parameter ℏ and asymptotic parameter n. The numerical results are demonstrated graphically. The outcomes of the study show that the q-HATM is computationally very effective and accurate to analyze nonlinear fractional differential equations.

  7. Nonlinear supratransmission

    NASA Astrophysics Data System (ADS)

    Geniet, F.; Leon, J.

    2003-05-01

    A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.

  8. Spline approximations for nonlinear hereditary control systems

    NASA Technical Reports Server (NTRS)

    Daniel, P. L.

    1982-01-01

    A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

  9. Nonlinear systems in medicine.

    PubMed Central

    Higgins, John P.

    2002-01-01

    Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107

  10. Finite elements of nonlinear continua.

    NASA Technical Reports Server (NTRS)

    Oden, J. T.

    1972-01-01

    The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

  11. Nonlinear Conservation Laws and Finite Volume Methods

    NASA Astrophysics Data System (ADS)

    Leveque, Randall J.

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

  12. Numerical study for multi-strain tuberculosis (TB) model of variable-order fractional derivatives.

    PubMed

    Sweilam, Nasser H; Al-Mekhlafi, Seham M

    2016-03-01

    In this paper, we presented a novel multi-strain TB model of variable-order fractional derivatives, which incorporates three strains: drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), as an extension for multi-strain TB model of nonlinear ordinary differential equations which developed in 2014 by Arino and Soliman [1]. Numerical simulations for this variable-order fractional model are the main aim of this work, where the variable-order fractional derivative is defined in the sense of Grünwald-Letnikov definition. Two numerical methods are presented for this model, the standard finite difference method (SFDM) and nonstandard finite difference method (NSFDM). Numerical comparison between SFDM and NSFDM is presented. It is concluded that, NSFDM preserves the positivity of the solutions and numerically stable in large regions than SFDM.

  13. Numerical study for multi-strain tuberculosis (TB) model of variable-order fractional derivatives

    PubMed Central

    Sweilam, Nasser H.; AL-Mekhlafi, Seham M.

    2015-01-01

    In this paper, we presented a novel multi-strain TB model of variable-order fractional derivatives, which incorporates three strains: drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), as an extension for multi-strain TB model of nonlinear ordinary differential equations which developed in 2014 by Arino and Soliman [1]. Numerical simulations for this variable-order fractional model are the main aim of this work, where the variable-order fractional derivative is defined in the sense of Grünwald–Letnikov definition. Two numerical methods are presented for this model, the standard finite difference method (SFDM) and nonstandard finite difference method (NSFDM). Numerical comparison between SFDM and NSFDM is presented. It is concluded that, NSFDM preserves the positivity of the solutions and numerically stable in large regions than SFDM. PMID:26966568

  14. Howard University Symposium on Nonlinear Semigroups, Partial Differential Equations and Attractors (2nd) Held in Washington, D. C. on 3-7 August 1987.

    DTIC Science & Technology

    1987-09-30

    Building GENERAL INTEREST Chairman: Luis Vazquez, Universidad Complutense , Madrid 8:30 - 9:15 a.m. Robert Sternberg, ONR, Boston "Symmetry in Geometrical...Universite de Paris VI "Some Remarks on Nonlinear Schrodinger Equations" 10:45 - 11:15 a.m. Coffee Break 11:15 - 12:00 noon Luis Vazquez, Universidad ... Complutense , MTadrid "The Finite Difference Method in the Quantum Theory" 12:00 - 12:45 p.m. Walter Miller, Howard University "Dynamics of Periodically

  15. Approximate solution of two-term fractional-order diffusion, wave-diffusion, and telegraph models arising in mathematical physics using optimal homotopy asymptotic method

    NASA Astrophysics Data System (ADS)

    Sarwar, S.; Rashidi, M. M.

    2016-07-01

    This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.

  16. Fractional Adams-Bashforth/Moulton methods: An application to the fractional Keller-Segel chemotaxis system

    NASA Astrophysics Data System (ADS)

    Zayernouri, Mohsen; Matzavinos, Anastasios

    2016-07-01

    We first formulate a fractional class of explicit Adams-Bashforth (A-B) and implicit Adams-Moulton (A-M) methods of first- and second-order accuracy for the time-integration of τ 0 CDt u (x , t) = g (t ; u), τ ∈ (0 , 1 ], where τ 0 CDt denotes the fractional derivative in the Caputo sense. In this fractional setting and in contrast to the standard Adams methods, an extra history load term emerges and the associated weight coefficients are τ-dependent. However when τ = 1, the developed schemes reduce to the well-known A-B and A-M methods with standard coefficients. Hence, in terms of scientific computing, our approach constitutes a minimal modification of the existing Adams libraries. Next, we develop an implicit-explicit (IMEX) splitting scheme for linear and nonlinear fractional PDEs of a general advection-reaction-diffusion type, and we apply our scheme to the time-space fractional Keller-Segel chemotaxis system. In this context, we evaluate the nonlinear advection term explicitly, employing the fractional A-B method in the prediction step, and we treat the corresponding diffusion term implicitly in the correction step using the fractional A-M scheme. Moreover, we perform the corresponding spatial discretization by employing an efficient and spectrally-accurate fractional spectral collocation method. Our numerical experiments exhibit the efficiency of the proposed IMEX scheme in solving nonlinear fractional PDEs.

  17. Nonlinear vibrations of functionally graded doubly curved shallow shells

    NASA Astrophysics Data System (ADS)

    Alijani, F.; Amabili, M.; Karagiozis, K.; Bakhtiari-Nejad, F.

    2011-03-01

    Nonlinear forced vibrations of FGM doubly curved shallow shells with a rectangular base are investigated. Donnell's nonlinear shallow-shell theory is used and the shell is assumed to be simply supported with movable edges. The equations of motion are reduced using the Galerkin method to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities. Using the multiple scales method, primary and subharmonic resonance responses of FGM shells are fully discussed and the effect of volume fraction exponent on the internal resonance conditions, softening/hardening behavior and bifurcations of the shallow shell when the excitation frequency is (i) near the fundamental frequency and (ii) near two times the fundamental frequency is shown. Moreover, using a code based on arclength continuation method, a bifurcation analysis is carried out for a special case with two-to-one internal resonance between the first and second doubly symmetric modes with respect to the panel's center ( ω13≈2 ω11). Bifurcation diagrams and Poincaré maps are obtained through direct time integration of the equations of motion and chaotic regions are shown by calculating Lyapunov exponents and Lyapunov dimension.

  18. Dark and singular optical solitons perturbation with fractional temporal evolution

    NASA Astrophysics Data System (ADS)

    Younis, Muhammad; ur Rehman, Hamood; Rizvi, Syed Tahir Raza; Mahmood, Syed Amer

    2017-04-01

    The article studies the dynamics of dark, singular, combined optical solitons and many other periodic solutions to fractional temporal perturbed nonlinear Schrödinger equation in nonlinear optics. The fractional extended Fan sub-equation method is first time used for any fractional temporal nonlinear Schrödinger equation. The solutions are of qualitatively different nature, depending on the five parameters. The constraint conditions, for the existence of the solitons, are also listed. Moreover a couple of other solutions known as combined soliton and combined periodic solution, fall out as a by product in limiting cases.

  19. Unilateral Global Bifurcation, Half-Linear Eigenvalues and Constant Sign Solutions for a Fractional Laplace Problem

    NASA Astrophysics Data System (ADS)

    Yang, Bian-Xia; Sun, Hong-Rui; Feng, Zhaosheng

    In this paper, we are concerned with the unilateral global bifurcation structure of fractional differential equation (‑Δ)αu(x) = λa(x)u(x) + F(x,u,λ),x ∈ Ω,u = 0,inℝN\\Ω with nondifferentiable nonlinearity F. It shows that there are two distinct unbounded subcontinua 𝒞+ and 𝒞‑ consisting of the continuum 𝒞 emanating from [λ1 ‑ d,λ1 + d] ×{0}, and two unbounded subcontinua 𝒟+ and 𝒟‑ consisting of the continuum 𝒟 emanating from [λ1 ‑d¯,λ1 + d¯] ×{∞}. As an application of this unilateral global bifurcation results, we present the existence of the principal half-eigenvalues of the half-linear fractional eigenvalue problem. Finally, we deal with the existence of constant sign solutions for a class of fractional nonlinear problems. Main results of this paper generalize the known results on classical Laplace operators to fractional Laplace operators.

  20. Optimal q-homotopy analysis method for time-space fractional gas dynamics equation

    NASA Astrophysics Data System (ADS)

    Saad, K. M.; AL-Shareef, E. H.; Mohamed, Mohamed S.; Yang, Xiao-Jun

    2017-01-01

    It is well known that the homotopy analysis method is one of the most efficient methods for obtaining analytical or approximate semi-analytical solutions of both linear and non-linear partial differential equations. A more general form of HAM is introduced in this paper, which is called Optimal q-Homotopy Analysis Method (Oq-HAM). It has better convergence properties as compared with the usual HAM, due to the presence of fraction factor associated with the solution. The convergence of q-HAM is studied in details elsewhere (M.A. El-Tawil, Int. J. Contemp. Math. Sci. 8, 481 (2013)). Oq-HAM is applied to the non-linear homogeneous and non-homogeneous time and space fractional gas dynamics equations with initial condition. An optimal convergence region is determined through the residual error. By minimizing the square residual error, the optimal convergence control parameters can be obtained. The accuracy and efficiency of the proposed method are verified by comparison with the exact solution of the fractional gas dynamics equation. Also, it is shown that the Oq-HAM for the fractional gas dynamics equation is equivalent to the exact solution. We obtain graphical representations of the solutions using MATHEMATICA.

  1. Automatic Differentiation Package

    SciTech Connect

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

    2007-03-01

    Sacado is an automatic differentiation package for C++ codes using operator overloading and C++ templating. Sacado provide forward, reverse, and Taylor polynomial automatic differentiation classes and utilities for incorporating these classes into C++ codes. Users can compute derivatives of computations arising in engineering and scientific applications, including nonlinear equation solving, time integration, sensitivity analysis, stability analysis, optimization and uncertainity quantification.

  2. A functional realization of 𝔰𝔩(3, ℝ) providing minimal Vessiot-Guldberg-Lie algebras of nonlinear second-order ordinary differential equations as proper subalgebras

    NASA Astrophysics Data System (ADS)

    Campoamor-Stursberg, R.

    2016-06-01

    A functional realization of the Lie algebra s l (" separators=" 3 , R) as a Vessiot-Guldberg-Lie algebra of second order differential equation (SODE) Lie systems is proposed. It is shown that a minimal Vessiot-Guldberg-Lie algebra L V G is obtained from proper subalgebras of s l (" separators=" 3 , R) for each of the SODE Lie systems of this type by particularization of one functional and two scalar parameters of the s l (" separators=" 3 , R) -realization. The relation between the various Vessiot-Guldberg-Lie algebras by means of a limiting process in the scalar parameters further allows to define a notion of contraction of SODE Lie systems.

  3. Possible isotopic fractionation effects in sputtered minerals

    NASA Technical Reports Server (NTRS)

    Haff, P. K.; Watson, C. C.; Tombrello, T. A.

    1980-01-01

    A model which makes definite predictions for the fractionation of isotopes in sputtered material is discussed. The fractionation patterns are nonlinear, and the pattern for a particular set of isotopes depends on the chemical matrix within which those isotopes are contained. Calculations are presented for all nonmonoisotopic elements contained in the minerals perovskite, anorthite, ackermanite, enstatite, and troilite. All isotopes are fractionated at the level of approximately 4-6 deg/o per atomic mass unit. Oxygen is always positively fractionated (heavier isotopes sputtered preferentially), and heavier elements are generally negatively fractioned (light isotopes sputtered preferentially). The value of Delta (O-18:O-16) is always less by about 1.8 deg/o than a linear extrapolation based upon the calculated delta (O-17:O-16) value would suggest. The phenomenon of both negative and positive fractionation patterns from a single target mineral are used to make an experimental test of the proposed model.

  4. Caputo standard α-family of maps: fractional difference vs. fractional.

    PubMed

    Edelman, M

    2014-06-01

    In this paper, the author compares behaviors of systems which can be described by fractional differential and fractional difference equations using the fractional and fractional difference Caputo standard α-Families of maps as examples. The author shows that properties of fractional difference maps (systems with falling factorial-law memory) are similar to the properties of fractional maps (systems with power-law memory). The similarities (types of attractors, power-law convergence of trajectories, existence of cascade of bifurcations and intermittent cascade of bifurcations type trajectories, and dependence of properties on the memory parameter α) and differences in properties of falling factorial- and power-law memory maps are investigated.

  5. A Fractional Variational Approach to the Fractional Basset-Type Equation

    NASA Astrophysics Data System (ADS)

    Baleanu, Dumitru; Garra, Roberto; Petras, Ivo

    2013-08-01

    In this paper we discuss an application of fractional variational calculus to the Basset-type fractional equations. It is well known that the unsteady motion of a sphere immersed in a Stokes fluid is described by an integro-differential equation involving derivative of real order. Here we study the inverse problem, i.e. we consider the problem from a Lagrangian point of view in the framework of fractional variational calculus. In this way we find an application of fractional variational methods to a classical physical model, finding a Basset-type fractional equation starting from a Lagrangian depending on derivatives of fractional order.

  6. The Vertical Linear Fractional Initialization Problem

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.

    1999-01-01

    This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.

  7. Fractional dynamics pharmacokinetics-pharmacodynamic models.

    PubMed

    Verotta, Davide

    2010-06-01

    While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics-pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics.

  8. Fractional dynamics pharmacokinetics–pharmacodynamic models

    PubMed Central

    2010-01-01

    While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics. PMID:20455076

  9. Fractional chemotaxis diffusion equations.

    PubMed

    Langlands, T A M; Henry, B I

    2010-05-01

    We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.

  10. Nonlinear channelizer.

    PubMed

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

    2012-12-01

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

  11. Investigation of a Nonlinear Control System

    NASA Technical Reports Server (NTRS)

    Flugge-Lotz, I; Taylor, C F; Lindberg, H E

    1958-01-01

    A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

  12. Nonlinear Dynamics: Maps, Integrators and Solitons

    SciTech Connect

    Parsa, Z.

    1998-10-01

    For many physical systems of interest in various disciplines, the solution to nonlinear differential equations describing the physical systems can be generated using maps, symplectic integrators and solitons. We discuss these methods and apply them for various examples.

  13. Approximating a nonlinear MTFDE from physiology

    NASA Astrophysics Data System (ADS)

    Teodoro, M. Filomena

    2016-12-01

    This paper describes a numerical scheme which approximates the solution of a nonlinear mixed type functional differential equation from nerve conduction theory. The solution of such equation is defined in all the entire real axis and tends to known values at ±∞. A numerical method extended from linear case is developed and applied to solve a nonlinear equation.

  14. Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control

    NASA Astrophysics Data System (ADS)

    Yu, Zhiyong; Jiang, Haijun; Hu, Cheng; Yu, Juan

    2015-09-01

    In this paper, the leader-following consensus problem of fractional-order multi-agent systems is considered via adaptive pinning control. The dynamics of leader and all followers with linear and nonlinear functions are investigated, respectively. We assume that the node should be pinned if its in-degree is less than its out-degree in the paper. Under this assumption and based on the stability theory of fractional-order differential systems, some leader-following consensus criteria are derived, which are easily obtained by matrix inequalities. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and the Riccati inequality. Several simulation examples are presented to demonstrate the effectiveness of the proposed method.

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

    NASA Technical Reports Server (NTRS)

    Doohovskoy, A.

    1977-01-01

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

  16. SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

    DOEpatents

    Collier, D.M.; Meeks, L.A.; Palmer, J.P.

    1960-05-10

    A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

  17. 10 ps resolution, 160 ns full scale range and less than 1.5% differential non-linearity time-to-digital converter module for high performance timing measurements

    NASA Astrophysics Data System (ADS)

    Markovic, B.; Tamborini, D.; Villa, F.; Tisa, S.; Tosi, A.; Zappa, F.

    2012-07-01

    We present a compact high performance time-to-digital converter (TDC) module that provides 10 ps timing resolution, 160 ns dynamic range and a differential non-linearity better than 1.5% LSBrms. The TDC can be operated either as a general-purpose time-interval measurement device, when receiving external START and STOP pulses, or in photon-timing mode, when employing the on-chip SPAD (single photon avalanche diode) detector for detecting photons and time-tagging them. The instrument precision is 15 psrms (i.e., 36 psFWHM) and in photon timing mode it is still better than 70 psFWHM. The USB link to the remote PC allows the easy setting of measurement parameters, the fast download of acquired data, and their visualization and storing via an user-friendly software interface. The module proves to be the best candidate for a wide variety of applications such as: fluorescence lifetime imaging, time-of-flight ranging measurements, time-resolved positron emission tomography, single-molecule spectroscopy, fluorescence correlation spectroscopy, diffuse optical tomography, optical time-domain reflectometry, quantum optics, etc.

  18. 10 ps resolution, 160 ns full scale range and less than 1.5% differential non-linearity time-to-digital converter module for high performance timing measurements

    SciTech Connect

    Markovic, B.; Tamborini, D.; Villa, F.; Tisa, S.; Tosi, A.; Zappa, F.

    2012-07-15

    We present a compact high performance time-to-digital converter (TDC) module that provides 10 ps timing resolution, 160 ns dynamic range and a differential non-linearity better than 1.5% LSB{sub rms}. The TDC can be operated either as a general-purpose time-interval measurement device, when receiving external START and STOP pulses, or in photon-timing mode, when employing the on-chip SPAD (single photon avalanche diode) detector for detecting photons and time-tagging them. The instrument precision is 15 ps{sub rms} (i.e., 36 ps{sub FWHM}) and in photon timing mode it is still better than 70 ps{sub FWHM}. The USB link to the remote PC allows the easy setting of measurement parameters, the fast download of acquired data, and their visualization and storing via an user-friendly software interface. The module proves to be the best candidate for a wide variety of applications such as: fluorescence lifetime imaging, time-of-flight ranging measurements, time-resolved positron emission tomography, single-molecule spectroscopy, fluorescence correlation spectroscopy, diffuse optical tomography, optical time-domain reflectometry, quantum optics, etc.

  19. 10 ps resolution, 160 ns full scale range and less than 1.5% differential non-linearity time-to-digital converter module for high performance timing measurements.

    PubMed

    Markovic, B; Tamborini, D; Villa, F; Tisa, S; Tosi, A; Zappa, F

    2012-07-01

    We present a compact high performance time-to-digital converter (TDC) module that provides 10 ps timing resolution, 160 ns dynamic range and a differential non-linearity better than 1.5% LSB(rms). The TDC can be operated either as a general-purpose time-interval measurement device, when receiving external START and STOP pulses, or in photon-timing mode, when employing the on-chip SPAD (single photon avalanche diode) detector for detecting photons and time-tagging them. The instrument precision is 15 ps(rms) (i.e., 36 ps(FWHM)) and in photon timing mode it is still better than 70 ps(FWHM). The USB link to the remote PC allows the easy setting of measurement parameters, the fast download of acquired data, and their visualization and storing via an user-friendly software interface. The module proves to be the best candidate for a wide variety of applications such as: fluorescence lifetime imaging, time-of-flight ranging measurements, time-resolved positron emission tomography, single-molecule spectroscopy, fluorescence correlation spectroscopy, diffuse optical tomography, optical time-domain reflectometry, quantum optics, etc.

  20. Nonlinear Systems.

    ERIC Educational Resources Information Center

    Seider, Warren D.; Ungar, Lyle H.

    1987-01-01

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

  1. Nonlinear Acoustics

    DTIC Science & Technology

    1974-02-14

    Wester- velt. [60] Streaming. In 1831, Michael Faraday [61] noted that currents of air were set up in the neighborhood of vibrating plates-the first... ducei in the case of a paramettc amy (from Berktay an Leahy 141). C’ "". k•, SEC 10.1 NONLINEAR ACOUSTICS 345 The principal results of their analysis

  2. Nonlinear resonance

    NASA Astrophysics Data System (ADS)

    Kevorkian, J.

    This report discusses research in the area of slowly varying nonlinear oscillatory systems. Some of the topics discussed are as follows: adiabatic invariants and transient resonance in very slowly varying Hamiltonian systems; sustained resonance in very slowly varying Hamiltonian systems; free-electron lasers with very slow wiggler taper; and bursting oscillators.

  3. Robust H ∞ control of a nonlinear uncertain system via a stable nonlinear output feedback controller

    NASA Astrophysics Data System (ADS)

    Harno, Hendra G.; Petersen, Ian R.

    2011-04-01

    A new approach to solving a nonlinear robust H ∞ control problem using a stable nonlinear output feedback controller is presented in this article. The class of nonlinear uncertain systems being considered is characterised in terms of integral quadratic constraints and global Lipschitz conditions describing the admissible uncertainties and nonlinearities, respectively. The nonlinear controller is able to exploit the plant nonlinearities through the inclusion of a copy of the known plant nonlinearities in the controller. The H ∞ control objective is to obtain an absolutely stable closed-loop system with a specified disturbance attenuation level. The solution to this control problem involves stabilising solutions to parametrised algebraic Riccati equations. We apply a differential evolution algorithm to solve a non-convex nonlinear optimisation problem arising in the controller synthesis.

  4. Fractional characteristic times and dissipated energy in fractional linear viscoelasticity

    NASA Astrophysics Data System (ADS)

    Colinas-Armijo, Natalia; Di Paola, Mario; Pinnola, Francesco P.

    2016-08-01

    In fractional viscoelasticity the stress-strain relation is a differential equation with non-integer operators (derivative or integral). Such constitutive law is able to describe the mechanical behavior of several materials, but when fractional operators appear, the elastic and the viscous contribution are inseparable and the characteristic times (relaxation and retardation time) cannot be defined. This paper aims to provide an approach to separate the elastic and the viscous phase in the fractional stress-strain relation with the aid of an equivalent classical model (Kelvin-Voigt or Maxwell). For such equivalent model the parameters are selected by an optimization procedure. Once the parameters of the equivalent model are defined, characteristic times of fractional viscoelasticity are readily defined as ratio between viscosity and stiffness. In the numerical applications, three kinds of different excitations are considered, that is, harmonic, periodic, and pseudo-stochastic. It is shown that, for any periodic excitation, the equivalent models have some important features: (i) the dissipated energy per cycle at steady-state coincides with the Staverman-Schwarzl formulation of the fractional model, (ii) the elastic and the viscous coefficients of the equivalent model are strictly related to the storage and the loss modulus, respectively.

  5. Control methods for localization of nonlinear waves.

    PubMed

    Porubov, Alexey; Andrievsky, Boris

    2017-03-06

    A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.This article is part of the themed issue 'Horizons of cybernetical physics'.

  6. Control methods for localization of nonlinear waves

    NASA Astrophysics Data System (ADS)

    Porubov, Alexey; Andrievsky, Boris

    2017-03-01

    A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions. This article is part of the themed issue 'Horizons of cybernetical physics'.

  7. Quantum disorder, duality, and fractional statistics in 2 + 1 dimensions

    NASA Technical Reports Server (NTRS)

    Wen, X. G.; Zee, A.

    1989-01-01

    A low-energy equivalence between two apparently unrelated Lagrangians with fractional statistics is reported. Exploiting this equivalence, it is possible to study the quantum disordered phase of the nonlinear sigma model with Hopf term. It is found that the quasi-particles in the disordered phase also have fractional statistics. There appears to be a dual relationship between the ordered and disordered phases.

  8. A class of finite dimensional optimal nonlinear estimators

    NASA Technical Reports Server (NTRS)

    Marcus, S. I.; Willsky, A. S.

    1974-01-01

    Finite dimensional optimal nonlinear state estimators are derived for bilinear systems evolving on nilpotent and solvable Lie groups. These results are extended to other classes of systems involving polynomial nonlinearities. The concepts of exact differentials and path-independent integrals are used to derive optimal finite dimensional estimators for a further class of nonlinear systems.

  9. Coupled nonlinear dynamical systems

    NASA Astrophysics Data System (ADS)

    Sun, Hongyan

    In this dissertation, we study coupled nonlinear dynamical systems that exhibit new types of complex behavior. We numerically and analytically examine a variety of dynamical models, ranging from systems of ordinary differential equations (ODE) with novel elements of feedback to systems of partial differential equations (PDE) that model chemical pattern formation. Chaos, dynamical uncertainty, synchronization, and spatiotemporal pattern formation constitute the primary topics of the dissertation. Following the introduction in Chapter 1, we study chaos and dynamical uncertainty in Chapter 2 with coupled Lorenz systems and demonstrate the existence of extreme complexity in high-dimensional ODE systems. In Chapter 3, we demonstrate that chaos synchronization can be achieved by mutual and multiplicative coupling of dynamical systems. Chapter 4 and 5 focus on pattern formation in reaction-diffusion systems, and we investigate segregation and integration behavior of populations in competitive and cooperative environments, respectively.

  10. Initialized Fractional Calculus

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.

    2000-01-01

    This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

  11. Tempered fractional calculus

    SciTech Connect

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

    2015-07-15

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

  12. Fermentation and dry fractionation increase bioactivity of cloudberry (Rubus chamaemorus).

    PubMed

    Puupponen-Pimiä, Riitta; Nohynek, Liisa; Juvonen, Riikka; Kössö, Tuija; Truchado, Pilar; Westerlund-Wikström, Benita; Leppänen, Tiina; Moilanen, Eeva; Oksman-Caldentey, Kirsi-Marja

    2016-04-15

    Phenolic composition and bioactivity of cloudberry was modified by bioprocessing, and highly bioactive fractions were produced by dry fractionation of the press cake. During fermentation polymeric ellagitannins were partly degraded into ellagic acid derivatives. Phenolic compounds were differentially distributed in seed coarse and fine fractions after dry fractionation process. Tannins concentrated in fine fraction, and flavonol derivatives were mainly found in coarse fraction. Ellagic acid derivatives were equally distributed between the dry fractions. Fermentation and dry fractionation increased statistically significantly anti-adhesion and anti-inflammatory activity of cloudberry. The seed fine fraction showed significant inhibition of P fimbria-mediated haemagglutination assay of uropathogenic Escherichia coli. The seed coarse fraction significantly reduced NO and IL-6 production and iNOS expression in activated macrophages. Fermentation did not affect antimicrobial activity, but slight increase in activity was detected in dry fractions. The results indicate the potential of cloudberry in pharma or health food applications.

  13. Functional fractionation of platelets.

    PubMed

    Haver, V M; Gear, A R

    1981-02-01

    Studies of platelet populations suggest that they are heterogeneous in size, age, and metabolic parameters. In an attempt to correlate these parameters with efficiency of aggregation, a new technique, functional fractionation, was developed. Platelet populations are separated by their differential reactivity to aggregating agents. For example, low doses of ADP (0.1 to 0.7 microM) are added to stirred PRP, after which gentle centrifugation is used to remove aggregates from single unreacted platelets. The loose aggregates can be readily dispersed for comparison of the physical or biochemical properties of the reacted versus unreacted platelets. It was found that reactive platelets were larger (6.5 micrometer3) than unreacted platelets (5.51 micrometer3). No significant difference in density existed between the two populations, and no release of [14C]serotonin from prelabeled platelets occurred during functional fractionation. Scanning and transmission electron microscopy confirmed the size difference and revealed that in both populations platelets were structurally intact with a normal discoid shape and no significant difference in organelle content. Human platelets most reactive to ADP were also enriched in glycogen (3.6-fold), ATP (1.6-fold), and ADP (twofold), compared with less reactive cells. These "reactive" cells took up more 51[Cr] and contained 1.9 times more surface sialic acid. In an in vivo aging experiment, rats were injected with 75[Se]methionine. Shortly after labeling (1 day), the most reactive platelets possessed the highest amount of 75[Se]. These results reveal that functionally active platelets, which are also larger, are more active metabolically than less reactive platelets, possess a higher negative surface charge, and may be a younger population.

  14. Constructing general partial differential equations using polynomial and neural networks.

    PubMed

    Zjavka, Ladislav; Pedrycz, Witold

    2016-01-01

    Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems.

  15. Fraction Sense: Foundational Understandings.

    PubMed

    Fennell, Francis Skip; Karp, Karen

    2016-08-09

    The intent of this commentary is to identify elements of fraction sense and note how the research studies provided in this special issue, in related but somewhat different ways, validate the importance of such understandings. Proficiency with fractions serves as a prerequisite for student success in higher level mathematics, as well as serving as a gateway to many occupations and varied contexts beyond the mathematics classroom. Fraction sense is developed through instructional opportunities involving fraction equivalence and magnitude, comparing and ordering fractions, using fraction benchmarks, and computational estimation. Such foundations are then extended to operations involving fractions and decimals and applications involving proportional reasoning. These components of fraction sense are all addressed in the studies provided in this issue, with particular consideration devoted to the significant importance of the use of the number line as a central representational tool for conceptually understanding fraction magnitude.

  16. TEMPERED FRACTIONAL CALCULUS

    PubMed Central

    MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; CHEN, JINGHUA

    2014-01-01

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series. PMID:26085690

  17. On the origins of generalized fractional calculus

    NASA Astrophysics Data System (ADS)

    Kiryakova, Virginia

    2015-11-01

    In Fractional Calculus (FC), as in the (classical) Calculus, the notions of derivatives and integrals (of first, second, etc. or arbitrary, incl. non-integer order) are basic and co-related. One of the most frequent approach in FC is to define first the Riemann-Liouville (R-L) integral of fractional order, and then by means of suitable integer-order differentiation operation applied over it (or under its sign) a fractional derivative is defined - in the R-L sense (or in Caputo sense). The first mentioned (R-L type) is closer to the theoretical studies in analysis, but has some shortages - from the point of view of interpretation of the initial conditions for Cauchy problems for fractional differential equations (stated also by means of fractional order derivatives/ integrals), and also for the analysts' confusion that such a derivative of a constant is not zero in general. The Caputo (C-) derivative, arising first in geophysical studies, helps to overcome these problems and to describe models of applied problems with physically consistent initial conditions. The operators of the Generalized Fractional Calculus - GFC (integrals and derivatives) are based on commuting m-tuple (m = 1, 2, 3, …) compositions of operators of the classical FC with power weights (the so-called Erdélyi-Kober operators), but represented in compact and explicit form by means of integral, integro-differential (R-L type) or differential-integral (C-type) operators, where the kernels are special functions of most general hypergeometric kind. The foundations of this theory are given in Kiryakova 18. In this survey we present the genesis of the definitions of the GFC - the generalized fractional integrals and derivatives (of fractional multi-order) of R-L type and Caputo type, analyze their properties and applications. Their special cases are all the known operators of classical FC, their generalizations introduced by other authors, the hyper-Bessel differential operators of higher integer

  18. Discrete Surface Modelling Using Partial Differential Equations.

    PubMed

    Xu, Guoliang; Pan, Qing; Bajaj, Chandrajit L

    2006-02-01

    We use various nonlinear partial differential equations to efficiently solve several surface modelling problems, including surface blending, N-sided hole filling and free-form surface fitting. The nonlinear equations used include two second order flows, two fourth order flows and two sixth order flows. These nonlinear equations are discretized based on discrete differential geometry operators. The proposed approach is simple, efficient and gives very desirable results, for a range of surface models, possibly having sharp creases and corners.

  19. Highly nonlinear stress-relaxation response of articular cartilage in indentation: Importance of collagen nonlinearity.

    PubMed

    Mäkelä, J T A; Korhonen, R K

    2016-06-14

    Modern fibril-reinforced computational models of articular cartilage can include inhomogeneous tissue composition and structure, and nonlinear mechanical behavior of collagen, proteoglycans and fluid. These models can capture well experimental single step creep and stress-relaxation tests or measurements under small strains in unconfined and confined compression. Yet, it is known that in indentation, especially at high strain velocities, cartilage can express highly nonlinear response. Different fibril reinforced poroelastic and poroviscoelastic models were used to assess measured highly nonlinear stress-relaxation response of rabbit articular cartilage in indentation. Experimentally measured depth-dependent volume fractions of different tissue constituents and their mechanical nonlinearities were taken into account in the models. In particular, the collagen fibril network was modeled using eight separate models that implemented five different constitutive equations to describe the nonlinearity. These consisted of linear elastic, nonlinear viscoelastic and multiple nonlinear elastic representations. The model incorporating the most nonlinearly increasing Young׳s modulus of collagen fibrils as a function of strain captured best the experimental data. Relative difference between the model and experiment was ~3%. Surprisingly, the difference in the peak forces between the experiment and the model with viscoelastic collagen fibrils was almost 20%. Implementation of the measured volume fractions did not improve the ability of the model to capture the measured mechanical data. These results suggest that a highly nonlinear formulation for collagen fibrils is needed to replicate multi-step stress-relaxation response of rabbit articular cartilage in indentation with high strain rates.

  20. A fractional-order infectivity SIR model

    NASA Astrophysics Data System (ADS)

    Angstmann, C. N.; Henry, B. I.; McGann, A. V.

    2016-06-01

    Fractional-order SIR models have become increasingly popular in the literature in recent years, however unlike the standard SIR model, they often lack a derivation from an underlying stochastic process. Here we derive a fractional-order infectivity SIR model from a stochastic process that incorporates a time-since-infection dependence on the infectivity of individuals. The fractional derivative appears in the generalised master equations of a continuous time random walk through SIR compartments, with a power-law function in the infectivity. We show that this model can also be formulated as an infection-age structured Kermack-McKendrick integro-differential SIR model. Under the appropriate limit the fractional infectivity model reduces to the standard ordinary differential equation SIR model.