WorldWideScience

Sample records for higher order nonlinear

  1. Exact solutions to two higher order nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Xu Liping; Zhang Jinliang

    2007-01-01

    Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)

  2. Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation

    International Nuclear Information System (INIS)

    Ren Ji; Ruan Hangyu

    2008-01-01

    We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained

  3. Higher-order modulation instability in nonlinear fiber optics.

    Science.gov (United States)

    Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry

    2011-12-16

    We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. © 2011 American Physical Society

  4. Higher-order techniques for some problems of nonlinear control

    Directory of Open Access Journals (Sweden)

    Sarychev Andrey V.

    2002-01-01

    Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.

  5. Higher-Order Spectrum in Understanding Nonlinearity in EEG Rhythms

    Directory of Open Access Journals (Sweden)

    Cauchy Pradhan

    2012-01-01

    Full Text Available The fundamental nature of the brain's electrical activities recorded as electroencephalogram (EEG remains unknown. Linear stochastic models and spectral estimates are the most common methods for the analysis of EEG because of their robustness, simplicity of interpretation, and apparent association with rhythmic behavioral patterns in nature. In this paper, we extend the use of higher-order spectrum in order to indicate the hidden characteristics of EEG signals that simply do not arise from random processes. The higher-order spectrum is an extension Fourier spectrum that uses higher moments for spectral estimates. This essentially nullifies all Gaussian random effects, therefore, can reveal non-Gaussian and nonlinear characteristics in the complex patterns of EEG time series. The paper demonstrates the distinguishing features of bispectral analysis for chaotic systems, filtered noises, and normal background EEG activity. The bispectrum analysis detects nonlinear interactions; however, it does not quantify the coupling strength. The squared bicoherence in the nonredundant region has been estimated to demonstrate nonlinear coupling. The bicoherence values are minimal for white Gaussian noises (WGNs and filtered noises. Higher bicoherence values in chaotic time series and normal background EEG activities are indicative of nonlinear coupling in these systems. The paper shows utility of bispectral methods as an analytical tool in understanding neural process underlying human EEG patterns.

  6. Exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres

    International Nuclear Information System (INIS)

    Liu Chunping

    2005-01-01

    First, by using the generally projective Riccati equation method, many kinds of exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres are obtained in a unified way. Then, some relations among these solutions are revealed

  7. Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

    Directory of Open Access Journals (Sweden)

    Taher S. Hassan

    2016-01-01

    Full Text Available We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t≔ri(tϕαixi-1Δ(t,  i=1,…,n-1,   with  x0=x,  ϕβ(u≔uβsgn⁡u, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.

  8. On realization of nonlinear systems described by higher-order differential equations

    NARCIS (Netherlands)

    van der Schaft, Arjan

    1987-01-01

    We consider systems of smooth nonlinear differential and algebraic equations in which some of the variables are distinguished as “external variables.” The realization problem is to replace the higher-order implicit differential equations by first-order explicit differential equations and the

  9. Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping

    Directory of Open Access Journals (Sweden)

    Eleni Bisognin

    2007-01-01

    Full Text Available We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.

  10. Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng

    2004-01-01

    Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair

  11. An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

    Directory of Open Access Journals (Sweden)

    Eman S. Alaidarous

    2013-01-01

    Full Text Available In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013. The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.

  12. Compound waves in a higher order nonlinear model of thermoviscous fluids

    DEFF Research Database (Denmark)

    Rønne Rasmussen, Anders; Sørensen, Mads Peter; Gaididei, Yuri B.

    2016-01-01

    A generalized traveling wave ansatz is used to investigate compound shock waves in a higher order nonlinear model of a thermoviscous fluid. The fluid velocity potential is written as a traveling wave plus a linear function of space and time. The latter offers the possibility of predicting...

  13. Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials

    Science.gov (United States)

    Liu, Lei; Tian, Bo; Wu, Xiao-Yu; Sun, Yan

    2018-02-01

    Under investigation in this paper is the higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials which can be applied in the nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation. Based on the Kadomtsev-Petviashvili hierarchy reduction, we construct the Nth order rogue wave-like solutions in terms of the Gramian under the integrable constraint. With the help of the analytic and graphic analysis, we exhibit the first-, second- and third-order rogue wave-like solutions through the different dispersion, nonlinearity and linear potential coefficients. We find that only if the dispersion and nonlinearity coefficients are proportional to each other, heights of the background of those rogue waves maintain unchanged with time increasing. Due to the existence of complex parameters, such nonautonomous rogue waves in the higher-order cases have more complex features than those in the lower.

  14. Maximal intensity higher-order Akhmediev breathers of the nonlinear Schrödinger equation and their systematic generation

    Energy Technology Data Exchange (ETDEWEB)

    Chin, Siu A., E-mail: chin@physics.tamu.edu [Department of Physics and Astronomy, Texas A& M University, College Station, TX 77843 (United States); Ashour, Omar A. [Department of Physics and Astronomy, Texas A& M University, College Station, TX 77843 (United States); Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Nikolić, Stanko N. [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade (Serbia); Belić, Milivoj R. [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar)

    2016-10-23

    It is well known that Akhmediev breathers of the nonlinear cubic Schrödinger equation can be superposed nonlinearly via the Darboux transformation to yield breathers of higher order. Surprisingly, we find that the peak height of each Akhmediev breather only adds linearly to form the peak height of the final breather. Using this peak-height formula, we show that at any given periodicity, there exists a unique high-order breather of maximal intensity. Moreover, these high-order breathers form a continuous hierarchy, growing in intensity with increasing periodicity. For any such higher-order breather, a simple initial wave function can be extracted from the Darboux transformation to dynamically generate that breather from the nonlinear Schrödinger equation. - Highlights: • Proved an analytical formula for the peak-height of an nth-order Akhmediev breather. • Constructed nth-order Akhmediev breathers of maximal peak intensity. • Extracted initial wave functions that can be used experimentally to produce these maximal breathers in optical fibers.

  15. Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

    Science.gov (United States)

    Gao, Peng

    2018-04-01

    This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

  16. Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

    Science.gov (United States)

    Gao, Peng

    2018-06-01

    This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

  17. A higher-order nonlinear Schrödinger equation with variable coefficients

    OpenAIRE

    Carvajal, X.; Linares, F.

    2003-01-01

    We study the initial value problem (IVP) associated to a higher-order nonlinear Schrödinger equation with variable coefficients. Under some regularity on its coefficients we establish local well-posedness for the IVP for data in $H^s(\\mathbb R)$, $s\\ge1/4$, improving previous results [22]. The main ingredient in our proof is an estimate of the maximal function associated to the linear solution similar to the sharp one obtained for linear solutions of the Schrödinger and K...

  18. Multi-soliton and rogue-wave solutions of the higher-order Hirota system for an erbium-doped nonlinear fiber

    Energy Technology Data Exchange (ETDEWEB)

    Zuo, Da-Wei [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics; Shijiazhuang Tiedao University (China). Dept. of Mathematics and Physics; Gao, Yi-Tian; Sun, Yu-Hao; Feng, Yu-Jie; Xue, Long [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics

    2014-10-15

    The nonlinear Schroedinger (NLS) equation appears in fluid mechanics, plasma physics, etc., while the Hirota equation, a higher-order NLS equation, has been introduced. In this paper, a higher-order Hirota system is investigated, which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By virtue of the Darboux transformation and generalized Darboux transformation, multi-soliton solutions and higher-order rogue-wave solutions are derived, beyond the published first-order consideration. Wave propagation and interaction are analyzed: (i) Bell-shape solitons, bright- and dark-rogue waves are found; (ii) the two-soliton interaction is elastic, i.e., the amplitude and velocity of each soliton remain unchanged after the interaction; (iii) the coefficient in the system affects the direction of the soliton propagation, patterns of the soliton interaction, distance, and direction of the first-order rogue-wave propagation, as well as the range and direction of the second-order rogue-wave interaction.

  19. Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains

    CERN Document Server

    Gazzola, Filippo; Sweers, Guido

    2010-01-01

    This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the first part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...

  20. The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Půža, B.

    2015-01-01

    Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

  1. Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Ahmad Bashir

    2010-01-01

    Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.

  2. Nonlinear optics in the LP(02) higher-order mode of a fiber.

    Science.gov (United States)

    Chen, Y; Chen, Z; Wadsworth, W J; Birks, T A

    2013-07-29

    The distinct disperion properties of higher-order modes in optical fibers permit the nonlinear generation of radiation deeper into the ultraviolet than is possible with the fundamental mode. This is exploited using adiabatic, broadband mode convertors to couple light efficiently from an input fundamental mode and also to return the generated light to an output fundamental mode over a broad spectral range. For example, we generate visible and UV supercontinuum light in the LP(02) mode of a photonic crystal fiber from sub-ns pulses with a wavelength of 532 nm.

  3. Nonlinear singular perturbation problems of arbitrary real orders

    International Nuclear Information System (INIS)

    Bijura, Angelina M.

    2003-10-01

    Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)

  4. XY model with higher-order exchange.

    Science.gov (United States)

    Žukovič, Milan; Kalagov, Georgii

    2017-08-01

    An XY model, generalized by inclusion of up to an infinite number of higher-order pairwise interactions with an exponentially decreasing strength, is studied by spin-wave theory and Monte Carlo simulations. At low temperatures the model displays a quasi-long-range-order phase characterized by an algebraically decaying correlation function with the exponent η=T/[2πJ(p,α)], nonlinearly dependent on the parameters p and α that control the number of the higher-order terms and the decay rate of their intensity, respectively. At higher temperatures the system shows a crossover from the continuous Berezinskii-Kosterlitz-Thouless to the first-order transition for the parameter values corresponding to a highly nonlinear shape of the potential well. The role of topological excitations (vortices) in changing the nature of the transition is discussed.

  5. Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications

    Science.gov (United States)

    Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

    2017-12-01

    In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.

  6. A novel algebraic procedure for solving non-linear evolution equations of higher order

    International Nuclear Information System (INIS)

    Huber, Alfred

    2007-01-01

    We report here a systematic approach that can easily be used for solving non-linear partial differential equations (nPDE), especially of higher order. We restrict the analysis to the so called evolution equations describing any wave propagation. The proposed new algebraic approach leads us to traveling wave solutions and moreover, new class of solution can be obtained. The crucial step of our method is the basic assumption that the solutions satisfy an ordinary differential equation (ODE) of first order that can be easily integrated. The validity and reliability of the method is tested by its application to some non-linear evolution equations. The important aspect of this paper however is the fact that we are able to calculate distinctive class of solutions which cannot be found in the current literature. In other words, using this new algebraic method the solution manifold is augmented to new class of solution functions. Simultaneously we would like to stress the necessity of such sophisticated methods since a general theory of nPDE does not exist. Otherwise, for practical use the algebraic construction of new class of solutions is of fundamental interest

  7. Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

    Science.gov (United States)

    Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

    2017-11-01

    In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

  8. PD/PID controller tuning based on model approximations: Model reduction of some unstable and higher order nonlinear models

    Directory of Open Access Journals (Sweden)

    Christer Dalen

    2017-10-01

    Full Text Available A model reduction technique based on optimization theory is presented, where a possible higher order system/model is approximated with an unstable DIPTD model by using only step response data. The DIPTD model is used to tune PD/PID controllers for the underlying possible higher order system. Numerous examples are used to illustrate the theory, i.e. both linear and nonlinear models. The Pareto Optimal controller is used as a reference controller.

  9. Asymptotic Expansions for Higher-Order Scalar Difference Equations

    Directory of Open Access Journals (Sweden)

    Pituk Mihály

    2007-01-01

    Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

  10. Asymptotic Expansions for Higher-Order Scalar Difference Equations

    Directory of Open Access Journals (Sweden)

    Ravi P. Agarwal

    2007-04-01

    Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

  11. A novel condition for stable nonlinear sampled-data models using higher-order discretized approximations with zero dynamics.

    Science.gov (United States)

    Zeng, Cheng; Liang, Shan; Xiang, Shuwen

    2017-05-01

    Continuous-time systems are usually modelled by the form of ordinary differential equations arising from physical laws. However, the use of these models in practice and utilizing, analyzing or transmitting these data from such systems must first invariably be discretized. More importantly, for digital control of a continuous-time nonlinear system, a good sampled-data model is required. This paper investigates the new consistency condition which is weaker than the previous similar results presented. Moreover, given the stability of the high-order approximate model with stable zero dynamics, the novel condition presented stabilizes the exact sampled-data model of the nonlinear system for sufficiently small sampling periods. An insightful interpretation of the obtained results can be made in terms of the stable sampling zero dynamics, and the new consistency condition is surprisingly associated with the relative degree of the nonlinear continuous-time system. Our controller design, based on the higher-order approximate discretized model, extends the existing methods which mainly deal with the Euler approximation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  12. Energy-momentum conserving higher-order time integration of nonlinear dynamics of finite elastic fiber-reinforced continua

    Science.gov (United States)

    Erler, Norbert; Groß, Michael

    2015-05-01

    Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.

  13. Perturbative theory of higher-order collision-enhanced wave mixing

    International Nuclear Information System (INIS)

    Trebino, R.; Rahn, L.A.

    1989-01-01

    This paper reports on collision-enhanced resonances which represent an interesting class of nonlinear- optical processes. They occur because collisional dephasing can rephase quantum-mechanical amplitudes that ordinarily cancel out exactly, thereby allowing otherwise unobservable wave-mixing resonances to be seen. This is an especially interesting phenomenon because these resonances are coherent effects that are induced by an incoherent process (collisional dephasing). First predicted in the late 1970s and eventually observed in 1981, these novel effects have now been seen in a wide variety of four-wave-mixing experiments, ranging from self-focusing to coherent anti-Stokes Raman spectroscopy. Recently, the authors have extended these observations to higher order, where the authors have shown both experimentally and theoretically the higher-order, collision-enhanced effects exist in nonlinear optics, appearing as subharmonics of two-photon resonances. Indeed, the authors have found that collision-enhanced processes are ideal systems for studying higher-order, nonlinear-optical effects because very high orders can be made to contribute with little or no saturation braodening. Experiments on sodium in a flame using six- and eight-wave-mixing geometries have revealed still higher-order effects (at least as high- order as χ (13) )

  14. An Algorithm for Higher Order Hopf Normal Forms

    Directory of Open Access Journals (Sweden)

    A.Y.T. Leung

    1995-01-01

    Full Text Available Normal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit. However, the computation of high-order normal forms is usually quite complicated. This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. Illustrative examples include a cubic system, a quadratic system and a Duffing–Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms.

  15. Higher order Lie-Baecklund symmetries of evolution equations

    International Nuclear Information System (INIS)

    Roy Chowdhury, A.; Roy Chowdhury, K.; Paul, S.

    1983-10-01

    We have considered in detail the analysis of higher order Lie-Baecklund symmetries for some representative nonlinear evolution equations. Until now all such symmetry analyses have been restricted only to the first order of the infinitesimal parameter. But the existence of Baecklund transformation (which can be shown to be an overall sum of higher order Lie-Baecklund symmetries) makes it necessary to search for such higher order Lie-Baecklund symmetries directly without taking recourse to the Baecklund transformation or inverse scattering technique. (author)

  16. Stability analysis solutions and optical solitons in extended nonlinear Schrödinger equation with higher-order odd and even terms

    Science.gov (United States)

    Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

    2018-01-01

    In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.

  17. Second-order nonlinearity induced transparency.

    Science.gov (United States)

    Zhou, Y H; Zhang, S S; Shen, H Z; Yi, X X

    2017-04-01

    In analogy to electromagnetically induced transparency, optomechanically induced transparency was proposed recently in [Science330, 1520 (2010)SCIEAS0036-807510.1126/science.1195596]. In this Letter, we demonstrate another form of induced transparency enabled by second-order nonlinearity. A practical application of the second-order nonlinearity induced transparency is to measure the second-order nonlinear coefficient. Our scheme might find applications in quantum optics and quantum information processing.

  18. Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

    KAUST Repository

    El-Beltagy, Mohamed A.

    2014-01-06

    Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

  19. Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

    KAUST Repository

    El-Beltagy, Mohamed A.; Al-Mulla, Noah

    2014-01-01

    Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

  20. Microscopic cascading of second-order molecular nonlinearity: New design principles for enhancing third-order nonlinearity.

    Science.gov (United States)

    Baev, Alexander; Autschbach, Jochen; Boyd, Robert W; Prasad, Paras N

    2010-04-12

    Herein, we develop a phenomenological model for microscopic cascading and substantiate it with ab initio calculations. It is shown that the concept of local microscopic cascading of a second-order nonlinearity can lead to a third-order nonlinearity, without introducing any new loss mechanisms that could limit the usefulness of our approach. This approach provides a new molecular design protocol, in which the current great successes achieved in producing molecules with extremely large second-order nonlinearity can be used in a supra molecular organization in a preferred orientation to generate very large third-order response magnitudes. The results of density functional calculations for a well-known second-order molecule, (para)nitroaniline, show that a head-to-tail dimer configuration exhibits enhanced third-order nonlinearity, in agreement with the phenomenological model which suggests that such an arrangement will produce cascading due to local field effects.

  1. Modulation stability and dispersive optical soliton solutions of higher order nonlinear Schrödinger equation and its applications in mono-mode optical fibers

    Science.gov (United States)

    Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

    2018-01-01

    In mono-mode optical fibers, the higher order non-linear Schrödinger equation (NLSE) describes the propagation of enormously short light pulses. We constructed optical solitons and, solitary wave solutions of higher order NLSE mono-mode optical fibers via employing modified extended mapping method which has important applications in Mathematics and physics. Furthermore, the formation conditions are also given on parameters in which optical bright and dark solitons can exist for this media. The moment of the obtained solutions are also given graphically, that helps to realize the physical phenomena's of this model. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method. The method can also be functional to other sorts of higher order nonlinear problems in contemporary areas of research.

  2. Theoretical analysis of open aperture reflection Z-scan on materials with high-order optical nonlinearities

    International Nuclear Information System (INIS)

    Petris, Adrian I.; Vlad, Valentin I.

    2010-03-01

    We present a theoretical analysis of open aperture reflection Z-scan in nonlinear media with third-, fifth-, and higher-order nonlinearities. A general analytical expression for the normalized reflectance when third-, fifth- and higher-order optical nonlinearities are excited is derived and its consequences on RZ-scan in media with high-order nonlinearities are discussed. We show that by performing RZ-scan experiments at different incident intensities it is possible to put in evidence the excitation of different order nonlinearities in the medium. Their contributions to the overall nonlinear response can be discriminated by using formulas derived by us. A RZ-scan numerical simulation using these formulas and data taken from literature, measured by another method for the third-, fifth-, and seventh-order nonlinear refractive indices of As 2 S 3 chalcogenide glass, is performed. (author)

  3. Neural classifiers for learning higher-order correlations

    International Nuclear Information System (INIS)

    Gueler, M.

    1999-01-01

    Studies by various authors suggest that higher-order networks can be more powerful and biologically more plausible with respect to the more traditional multilayer networks. These architecture make explicit use of nonlinear interactions between input variables in the form of higher-order units or product units. If it is known a priori that the problem to be implemented possesses a given set of invariances like in the translation, rotation, and scale invariant recognition problems, those invariances can be encoded, thus eliminating all higher-order terms which are incompatible with the invariances. In general, however, it is a serious set-back that the complexity of learning increases exponentially with the size of inputs. This paper reviews higher-order networks and introduces an implicit representation in which learning complexity is mainly decided by the number of higher-order terms to be learned and increases only linearly with the input size

  4. Neural Classifiers for Learning Higher-Order Correlations

    Science.gov (United States)

    Güler, Marifi

    1999-01-01

    Studies by various authors suggest that higher-order networks can be more powerful and are biologically more plausible with respect to the more traditional multilayer networks. These architectures make explicit use of nonlinear interactions between input variables in the form of higher-order units or product units. If it is known a priori that the problem to be implemented possesses a given set of invariances like in the translation, rotation, and scale invariant pattern recognition problems, those invariances can be encoded, thus eliminating all higher-order terms which are incompatible with the invariances. In general, however, it is a serious set-back that the complexity of learning increases exponentially with the size of inputs. This paper reviews higher-order networks and introduces an implicit representation in which learning complexity is mainly decided by the number of higher-order terms to be learned and increases only linearly with the input size.

  5. Higher order correlations in computed particle distributions

    International Nuclear Information System (INIS)

    Hanerfeld, H.; Herrmannsfeldt, W.; Miller, R.H.

    1989-03-01

    The rms emittances calculated for beam distributions using computer simulations are frequently dominated by higher order aberrations. Thus there are substantial open areas in the phase space plots. It has long been observed that the rms emittance is not an invariant to beam manipulations. The usual emittance calculation removes the correlation between transverse displacement and transverse momentum. In this paper, we explore the possibility of defining higher order correlations that can be removed from the distribution to result in a lower limit to the realizable emittance. The intent is that by inserting the correct combinations of linear lenses at the proper position, the beam may recombine in a way that cancels the effects of some higher order forces. An example might be the non-linear transverse space charge forces which cause a beam to spread. If the beam is then refocused so that the same non-linear forces reverse the inward velocities, the resulting phase space distribution may reasonably approximate the original distribution. The approach to finding the location and strength of the proper lens to optimize the transported beam is based on work by Bruce Carlsten of Los Alamos National Laboratory. 11 refs., 4 figs

  6. Variable-coefficient higher-order nonlinear Schroedinger model in optical fibers: Variable-coefficient bilinear form, Baecklund transformation, brightons and symbolic computation

    International Nuclear Information System (INIS)

    Tian Bo; Gao Yitian; Zhu Hongwu

    2007-01-01

    Symbolically investigated in this Letter is a variable-coefficient higher-order nonlinear Schroedinger (vcHNLS) model for ultrafast signal-routing, fiber laser systems and optical communication systems with distributed dispersion and nonlinearity management. Of physical and optical interests, with bilinear method extend, the vcHNLS model is transformed into a variable-coefficient bilinear form, and then an auto-Baecklund transformation is constructed. Constraints on coefficient functions are analyzed. Potentially observable with future optical-fiber experiments, variable-coefficient brightons are illustrated. Relevant properties and features are discussed as well. Baecklund transformation and other results of this Letter will be of certain value to the studies on inhomogeneous fiber media, core of dispersion-managed brightons, fiber amplifiers, laser systems and optical communication links with distributed dispersion and nonlinearity management

  7. Higher-order chaotic oscillator using active bessel filter

    DEFF Research Database (Denmark)

    Lindberg, Erik; Mykolaitis, Gytis; Bumelien, Skaidra

    2010-01-01

    A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending...

  8. Electromagnetic cloaking in higher order spherical cloaks

    Science.gov (United States)

    Sidhwa, H. H.; Aiyar, R. P. R. C.; Kulkarni, S. V.

    2017-06-01

    The inception of transformation optics has led to the realisation of the invisibility devices for various applications, one of which is spherical cloaking. In this paper, a formulation for a higher-order spherical cloak has been proposed to reduce its physical thickness significantly by introducing a nonlinear relation between the original and transformed coordinate systems and it has been verified using the ray tracing approach. Analysis has been carried out to observe the anomalies in the variation of refractive index for higher order cloaks indicating the presence of poles in the relevant equations. Furthermore, a higher-order spherical cloak with predefined values of the material characteristics on its inner and outer surfaces has been designed for practical application.

  9. Partially integrable nonlinear equations with one higher symmetry

    International Nuclear Information System (INIS)

    Mikhailov, A V; Novikov, V S; Wang, J P

    2005-01-01

    In this letter, we present a family of second order in time nonlinear partial differential equations, which have only one higher symmetry. These equations are not integrable, but have a solution depending on one arbitrary function. (letter to the editor)

  10. The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow

    Energy Technology Data Exchange (ETDEWEB)

    Mohammadimehr, M., E-mail: mmohammadimehr@kashanu.ac.ir [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of); Mohammadi-Dehabadi, A.A. [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of); Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Maraghi, Z. Khoddami [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of)

    2017-04-01

    In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.

  11. The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow

    International Nuclear Information System (INIS)

    Mohammadimehr, M.; Mohammadi-Dehabadi, A.A.; Maraghi, Z. Khoddami

    2017-01-01

    In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.

  12. On the Painleve integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Xu Guiqiong; Li Zhibin

    2005-01-01

    It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests

  13. Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

    KAUST Repository

    Gottlieb, Sigal

    2015-04-10

    High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.

  14. Contribution of higher order terms in the reductive perturbation theory, 2

    International Nuclear Information System (INIS)

    Ichikawa, Y.H.; Mitsuhashi, Teruo; Konno, Kimiaki.

    1977-01-01

    Contribution of higher order terms in the reductive perturbation theory has been investigated for nonlinear propagation of strongly dispersive ion plasma wave. The basic set of fluid equation is reduced to a coupled set of the nonlinear Schroedinger equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential. A steady state solution of the coupled set of equations has been solved analytically in the asymptotic limit of small wave number. (auth.)

  15. Higher-Order Approximations of Motion of a Nonlinear Oscillator Using the Parameter Expansion Technique

    Science.gov (United States)

    Ganji, S. S.; Domairry, G.; Davodi, A. G.; Babazadeh, H.; Seyedalizadeh Ganji, S. H.

    The main objective of this paper is to apply the parameter expansion technique (a modified Lindstedt-Poincaré method) to calculate the first, second, and third-order approximations of motion of a nonlinear oscillator arising in rigid rod rocking back. The dynamics and frequency of motion of this nonlinear mechanical system are analyzed. A meticulous attention is carried out to the study of the introduced nonlinearity effects on the amplitudes of the oscillatory states and on the bifurcation structures. We examine the synchronization and the frequency of systems using both the strong and special method. Numerical simulations and computer's answers confirm and complement the results obtained by the analytical approach. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. The solutions of this method are compared with the exact ones in order to validate the approach, and assess the accuracy of the solutions. In particular, APL-PM works well for the whole range of oscillation amplitudes and excellent agreement of the approximate frequency with the exact one has been demonstrated. The approximate period derived here is accurate and close to the exact solution. This method has a distinguished feature which makes it simple to use, and also it agrees with the exact solutions for various parameters.

  16. Stochastic Parameter Estimation of Non-Linear Systems Using Only Higher Order Spectra of the Measured Response

    Science.gov (United States)

    Vasta, M.; Roberts, J. B.

    1998-06-01

    Methods for using fourth order spectral quantities to estimate the unknown parameters in non-linear, randomly excited dynamic systems are developed. Attention is focused on the case where only the response is measurable and the excitation is unmeasurable and known only in terms of a stochastic process model. The approach is illustrated through application to a non-linear oscillator with both non-linear damping and stiffness and with excitation modelled as a stationary Gaussian white noise process. The methods have applications in studies of the response of structures to random environmental loads, such as wind and ocean wave forces.

  17. Giant fifth-order nonlinearity via tunneling induced quantum interference in triple quantum dots

    Directory of Open Access Journals (Sweden)

    Si-Cong Tian

    2015-02-01

    Full Text Available Schemes for giant fifth-order nonlinearity via tunneling in both linear and triangular triple quantum dots are proposed. In both configurations, the real part of the fifth-order nonlinearity can be greatly enhanced, and simultaneously the absorption is suppressed. The analytical expression and the dressed states of the system show that the two tunnelings between the neighboring quantum dots can induce quantum interference, resulting in the giant higher-order nonlinearity. The scheme proposed here may have important applications in quantum information processing at low light level.

  18. Dark solitons for a variable-coefficient higher-order nonlinear Schrödinger equation in the inhomogeneous optical fiber

    Science.gov (United States)

    Sun, Yan; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Yuan, Yu-Qiang

    2017-04-01

    Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with d1(z), d2(z) and d3(z), which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficients, we obtain the parabolic, periodic and V-shaped dark solitons. Head-on and overtaking collisions are depicted via the dark two soliton solutions. Velocities of the dark solitons are linearly related to d1(z), d2(z) and d3(z), respectively, while the amplitudes of the dark solitons are not related to such variable coefficients.

  19. Nonlinearity management in higher dimensions

    International Nuclear Information System (INIS)

    Kevrekidis, P G; Pelinovsky, D E; Stefanov, A

    2006-01-01

    In the present paper, we revisit nonlinearity management of the time-periodic nonlinear Schroedinger equation and the related averaging procedure. By means of rigorous estimates, we show that the averaged nonlinear Schroedinger equation does not blow up in the higher dimensional case so long as the corresponding solution remains smooth. In particular, we show that the H 1 norm remains bounded, in contrast with the usual blow-up mechanism for the focusing Schroedinger equation. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management

  20. Dark-dark solitons for a coupled variable-coefficient higher-order nonlinear Schrödinger system in an inhomogeneous optical fiber

    Science.gov (United States)

    Li, Ming-Zhen; Tian, Bo; Qu, Qi-Xing; Chai, Han-Peng; Liu, Lei; Du, Zhong

    2017-12-01

    In this paper, under investigation is a coupled variable-coefficient higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the Lax pair and binary Darboux transformation, we present the nondegenerate N-dark-dark soliton solutions. With the graphical simulation, soliton propagation and interaction are discussed with the group velocity dispersion and fourth-order dispersion effects, which affect the velocity but have no effect on the amplitude. Linear, parabolic and periodic one dark-dark solitons are displayed. Interactions between the two solitons are presented as well, which are all elastic.

  1. Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities

    DEFF Research Database (Denmark)

    Khare, A.; Rasmussen, Kim Ø; Salerno, M.

    2006-01-01

    -Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.......A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz...

  2. Charges in nonlinear higher-spin theory

    Energy Technology Data Exchange (ETDEWEB)

    Didenko, V.E. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Misuna, N.G. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Moscow Institute of Physics and Technology,Institutsky lane 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation)

    2017-03-30

    Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS{sub 4} Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.

  3. Charges in nonlinear higher-spin theory

    International Nuclear Information System (INIS)

    Didenko, V.E.; Misuna, N.G.; Vasiliev, M.A.

    2017-01-01

    Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS 4 Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.

  4. Integrability and solitons for the higher-order nonlinear Schrödinger equation with space-dependent coefficients in an optical fiber

    Science.gov (United States)

    Su, Jing-Jing; Gao, Yi-Tian

    2018-03-01

    Under investigation in this paper is a higher-order nonlinear Schrödinger equation with space-dependent coefficients, related to an optical fiber. Based on the self-similarity transformation and Hirota method, related to the integrability, the N-th-order bright and dark soliton solutions are derived under certain constraints. It is revealed that the velocities and trajectories of the solitons are both affected by the coefficient of the sixth-order dispersion term while the amplitudes of the solitons are determined by the gain function. Amplitudes increase when the gain function is positive and decrease when the gain function is negative. Furthermore, we find that the intensities of dark solitons are presented as a superposition of the solitons and stationary waves.

  5. A mixed-order nonlinear diffusion compressed sensing MR image reconstruction.

    Science.gov (United States)

    Joy, Ajin; Paul, Joseph Suresh

    2018-03-07

    Avoid formation of staircase artifacts in nonlinear diffusion-based MR image reconstruction without compromising computational speed. Whereas second-order diffusion encourages the evolution of pixel neighborhood with uniform intensities, fourth-order diffusion considers smooth region to be not necessarily a uniform intensity region but also a planar region. Therefore, a controlled application of fourth-order diffusivity function is used to encourage second-order diffusion to reconstruct the smooth regions of the image as a plane rather than a group of blocks, while not being strong enough to introduce the undesirable speckle effect. Proposed method is compared with second- and fourth-order nonlinear diffusion reconstruction, total variation (TV), total generalized variation, and higher degree TV using in vivo data sets for different undersampling levels with application to dictionary learning-based reconstruction. It is observed that the proposed technique preserves sharp boundaries in the image while preventing the formation of staircase artifacts in the regions of smoothly varying pixel intensities. It also shows reduced error measures compared with second-order nonlinear diffusion reconstruction or TV and converges faster than TV-based methods. Because nonlinear diffusion is known to be an effective alternative to TV for edge-preserving reconstruction, the crucial aspect of staircase artifact removal is addressed. Reconstruction is found to be stable for the experimentally determined range of fourth-order regularization parameter, and therefore not does not introduce a parameter search. Hence, the computational simplicity of second-order diffusion is retained. © 2018 International Society for Magnetic Resonance in Medicine.

  6. Higher order terms of the nonlinear forces in plasmas with collisions at laser interaction

    International Nuclear Information System (INIS)

    Kentwell, G.W.; Hora, H.

    1980-01-01

    The evaluation of the general expression of the nonlinear force of laser-plasma interaction showed discrepancies depending on the assumptions of the phase and collisions in the expressions used for E and H. While the first order terms of the derivations are remaining unchanged, new third order terms are found for the case of perpendicular incidence without collisions. With collisions, the additional non-pondermotive terms are derived to be more general than known before. It is then possible to evaluate the forces for oblique incidence with collisions and find an absorption caused force in the plane of the plasma surface. (author)

  7. Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

    International Nuclear Information System (INIS)

    Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A

    2009-01-01

    A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.

  8. Tunnelling effects of solitons in optical fibers with higher-order effects

    Energy Technology Data Exchange (ETDEWEB)

    Dai, Chao-Qing [Zhejiang A and F Univ., Lin' an (China). School of Sciences; Suzhou Univ., Jiangsu (China). School of Physical Science and Technology; Zhu, Hai-Ping [Zhejiang Lishui Univ., Zhejiang (China). School of Science; Zheng, Chun-Long [Shaoguan Univ., Guangdong (China). College of Physics and Electromechanical Engineering

    2012-06-15

    We construct four types of analytical soliton solutions for the higher-order nonlinear Schroedinger equation with distributed coefficients. These solutions include bright solitons, dark solitons, combined solitons, and M-shaped solitons. Moreover, the explicit functions which describe the evolution of the width, peak, and phase are discussed exactly. We finally discuss the nonlinear soliton tunnelling effect for four types of femtosecond solitons. (orig.)

  9. Retrieval of high-order susceptibilities of nonlinear metamaterials

    International Nuclear Information System (INIS)

    Wang Zhi-Yu; Qiu Jin-Peng; Chen Hua; Mo Jiong-Jiong; Yu Fa-Xin

    2017-01-01

    Active metamaterials embedded with nonlinear elements are able to exhibit strong nonlinearity in microwave regime. However, existing S -parameter based parameter retrieval approaches developed for linear metamaterials do not apply in nonlinear cases. In this paper, a retrieval algorithm of high-order susceptibilities for nonlinear metamaterials is derived. Experimental demonstration shows that, by measuring the power level of each harmonic while sweeping the incident power, high-order susceptibilities of a thin-layer nonlinear metamaterial can be effectively retrieved. The proposedapproach can be widely used in the research of active metamaterials. (paper)

  10. Second-order nonlinear optical metamaterials: ABC-type nanolaminates

    International Nuclear Information System (INIS)

    Alloatti, L.; Kieninger, C.; Lauermann, M.; Köhnle, K.; Froelich, A.; Wegener, M.; Frenzel, T.; Freude, W.; Leuthold, J.; Koos, C.

    2015-01-01

    We demonstrate a concept for second-order nonlinear metamaterials that can be obtained from non-metallic centrosymmetric constituents with inherently low optical absorption. The concept is based on iterative atomic-layer deposition of three different materials, A = Al 2 O 3 , B = TiO 2 , and C = HfO 2 . The centrosymmetry of the resulting ABC stack is broken since the ABC and the inverted CBA sequences are not equivalent—a necessary condition for non-zero second-order nonlinearity. In our experiments, we find that the bulk second-order nonlinear susceptibility depends on the density of interfaces, leading to a nonlinear susceptibility of 0.26 pm/V at a wavelength of 800 nm. ABC-type nanolaminates can be deposited on virtually any substrate and offer a promising route towards engineering of second-order optical nonlinearities at both infrared and visible wavelengths

  11. Solitons and rogue waves for a higher-order nonlinear Schroedinger-Maxwell-Bloch system in an erbium-doped fiber

    International Nuclear Information System (INIS)

    Su, Chuan-Qi; Gao, Yi-Tian; Yu, Xin; Xue, Long; Aviation Univ. of Air Force, Liaoning

    2015-01-01

    Under investigation in this article is a higher-order nonlinear Schroedinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.

  12. Soliton-like solutions of a generalized variable-coefficient higher order nonlinear Schroedinger equation from inhomogeneous optical fibers with symbolic computation

    International Nuclear Information System (INIS)

    Li Juan; Zhang Haiqiang; Xu Tao; Zhang, Ya-Xing; Tian Bo

    2007-01-01

    For the long-distance communication and manufacturing problems in optical fibers, the propagation of subpicosecond or femtosecond optical pulses can be governed by the variable-coefficient nonlinear Schroedinger equation with higher order effects, such as the third-order dispersion, self-steepening and self-frequency shift. In this paper, we firstly determine the general conditions for this equation to be integrable by employing the Painleve analysis. Based on the obtained 3 x 3 Lax pair, we construct the Darboux transformation for such a model under the corresponding constraints, and then derive the nth-iterated potential transformation formula by the iterative process of Darboux transformation. Through the one- and two-soliton-like solutions, we graphically discuss the features of femtosecond solitons in inhomogeneous optical fibers

  13. Third-order nonlinearity of Er3+-doped lead phosphate glass

    Energy Technology Data Exchange (ETDEWEB)

    Santos, C. C. [Universidade Federal do Ceara, Ceara, Brazil; Guedes Da Silva, Ilde [ORNL; Siqueira, J. P. [Instituto de Física de São Carlos, Universidade de São Paulo, Brazil; Misoguti, L. [Instituto de Física de São Carlos, Universidade de São Paulo, Brazil; Zilio, S. C. [Instituto de Física de São Carlos, Universidade de São Paulo, Brazil; Boatner, Lynn A [ORNL

    2010-01-01

    The third-order optical susceptibility and dispersion of the linear refractive index of Er3+-doped lead phosphate glass were measured in the wavelength range between 400 and 1940 nm by using the spectrally resolved femtosecond Maker fringes technique. The nonlinear refractive index obtained from the third-order susceptibility was found to be five times higher than that of silica, indicating that Er3+-doped lead phosphate glass is a potential candidate to be used as the base component for the fabrication of photonic devices. For comparison purposes, the Z-scan technique was also employed to obtain the values of the nonlinear refractive index of E-doped lead phosphate glass at several wavelengths, and the values obtained using the two techniques agree to within 15%.

  14. Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order

    International Nuclear Information System (INIS)

    Pradeep, R Gladwin; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M

    2011-01-01

    In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs. (paper)

  15. Interactions, strings and isotopies in higher order anisotropic superspaces

    CERN Document Server

    Vacaru, Sergiu Ion

    2001-01-01

    The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions, published in J. Math. Phys., Nucl. Phys. B, Ann. Phys. (NY), JHEP, Rep. Math. Phys., Int. J. Theor. Phys. and in some former Soviet Union and Romanian scientific journals. The main subjects are in the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces with higher order anisotropy and inhomogeneity. The approach proceeds by developing the concept of higher order anisotropic (super)space which unifies the logical and manthematical aspects of modern Kaluza--Klein theories and generalized Lagrange and Finsler geometry and leads to modeling of physical processes on higher order fiber (super)bundles provided with nonlinear and distinguished connections and metric structures. This book can be also considered as a pedagogical survey on the mentioned subjects.

  16. Higher Order Continuous SI Engine Observers

    DEFF Research Database (Denmark)

    Vesterholm, Thomas; Hendricks, Elbert; Houbak, Niels

    1992-01-01

    A nonlinear compensator for the fuel film dynamics and a second order nonlinear observer for a spark ignition engine are presented in this paper. The compensator and observer are realized as continuous differential equations and an especially designed integration algorithm is used to integrate them...

  17. Physical uniqueness of higher-order Korteweg-de Vries theory for continuously stratified fluids without background shear

    Science.gov (United States)

    Shimizu, Kenji

    2017-10-01

    The 2nd-order Korteweg-de Vries (KdV) equation and the Gardner (or extended KdV) equation are often used to investigate internal solitary waves, commonly observed in oceans and lakes. However, application of these KdV-type equations for continuously stratified fluids to geophysical problems is hindered by nonuniqueness of the higher-order coefficients and the associated correction functions to the wave fields. This study proposes to reduce arbitrariness of the higher-order KdV theory by considering its uniqueness in the following three physical senses: (i) consistency of the nonlinear higher-order coefficients and correction functions with the corresponding phase speeds, (ii) wavenumber-independence of the vertically integrated available potential energy, and (iii) its positive definiteness. The spectral (or generalized Fourier) approach based on vertical modes in the isopycnal coordinate is shown to enable an alternative derivation of the 2nd-order KdV equation, without encountering nonuniqueness. Comparison with previous theories shows that Parseval's theorem naturally yields a unique set of special conditions for (ii) and (iii). Hydrostatic fully nonlinear solutions, derived by combining the spectral approach and simple-wave analysis, reveal that both proposed and previous 2nd-order theories satisfy (i), provided that consistent definitions are used for the wave amplitude and the nonlinear correction. This condition reduces the arbitrariness when higher-order KdV-type theories are compared with observations or numerical simulations. The coefficients and correction functions that satisfy (i)-(iii) are given by explicit formulae to 2nd order and by algebraic recurrence relationships to arbitrary order for hydrostatic fully nonlinear and linear fully nonhydrostatic effects.

  18. Conservation laws and rogue waves for a higher-order nonlinear Schrödinger equation with variable coefficients in the inhomogeneous fiber

    Science.gov (United States)

    Du, Zhong; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Sun, Yan

    2017-07-01

    Subpicosecond or femtosecond optical pulse propagation in the inhomogeneous fiber can be described by a higher-order nonlinear Schrödinger equation with variable coefficients, which is investigated in the paper. Via the Ablowitz-Kaup-Newell-Segur system and symbolic computation, the Lax pair and infinitely-many conservation laws are deduced. Based on the Lax pair and a modified Darboux transformation technique, the first- and second-order rogue wave solutions are constructed. Effects of the groupvelocity dispersion and third-order dispersion on the properties of the first- and second-order rouge waves are graphically presented and analyzed: The groupvelocity dispersion and third-order dispersion both affect the ranges and shapes of the first- and second-order rogue waves: The third-order dispersion can produce a skew angle of the first-order rogue wave and the skew angle rotates counterclockwise with the increase of the groupvelocity dispersion, when the groupvelocity dispersion and third-order dispersion are chosen as the constants; When the groupvelocity dispersion and third-order dispersion are taken as the functions of the propagation distance, the linear, X-shaped and parabolic trajectories of the rogue waves are obtained.

  19. Holographic conductivity of holographic superconductors with higher-order corrections

    Energy Technology Data Exchange (ETDEWEB)

    Sheykhi, Ahmad [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Ghazanfari, Afsoon; Dehyadegari, Amin [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)

    2018-02-15

    We analytically and numerically disclose the effects of the higher-order correction terms in the gravity and in the gauge field on the properties of s-wave holographic superconductors. On the gravity side, we consider the higher curvature Gauss-Bonnet corrections and on the gauge field side, we add a quadratic correction term to the Maxwell Lagrangian. We show that, for this system, one can still obtain an analytical relation between the critical temperature and the charge density. We also calculate the critical exponent and the condensation value both analytically and numerically. We use a variational method, based on the Sturm-Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. For a fixed value of the Gauss-Bonnet parameter, we observe that the critical temperature decreases with increasing the nonlinearity of the gauge field. This implies that the nonlinear correction term to the Maxwell electrodynamics makes the condensation harder. We also study the holographic conductivity of the system and disclose the effects of the Gauss-Bonnet and nonlinear parameters α and b on the superconducting gap. We observe that, for various values of α and b, the real part of the conductivity is proportional to the frequency per temperature, ω/T, as the frequency is large enough. Besides, the conductivity has a minimum in the imaginary part which is shifted toward greater frequency with decreasing temperature. (orig.)

  20. Nonlinear dynamics of fractional order Duffing system

    International Nuclear Information System (INIS)

    Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian

    2015-01-01

    In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

  1. Analysis of wheezes using wavelet higher order spectral features.

    Science.gov (United States)

    Taplidou, Styliani A; Hadjileontiadis, Leontios J

    2010-07-01

    Wheezes are musical breath sounds, which usually imply an existing pulmonary obstruction, such as asthma and chronic obstructive pulmonary disease (COPD). Although many studies have addressed the problem of wheeze detection, a limited number of scientific works has focused in the analysis of wheeze characteristics, and in particular, their time-varying nonlinear characteristics. In this study, an effort is made to reveal and statistically analyze the nonlinear characteristics of wheezes and their evolution over time, as they are reflected in the quadratic phase coupling of their harmonics. To this end, the continuous wavelet transform (CWT) is used in combination with third-order spectra to define the analysis domain, where the nonlinear interactions of the harmonics of wheezes and their time variations are revealed by incorporating instantaneous wavelet bispectrum and bicoherence, which provide with the instantaneous biamplitude and biphase curves. Based on this nonlinear information pool, a set of 23 features is proposed for the nonlinear analysis of wheezes. Two complementary perspectives, i.e., general and detailed, related to average performance and to localities, respectively, were used in the construction of the feature set, in order to embed trends and local behaviors, respectively, seen in the nonlinear interaction of the harmonic elements of wheezes over time. The proposed feature set was evaluated on a dataset of wheezes, acquired from adult patients with diagnosed asthma and COPD from a lung sound database. The statistical evaluation of the feature set revealed discrimination ability between the two pathologies for all data subgroupings. In particular, when the total breathing cycle was examined, all 23 features, but one, showed statistically significant difference between the COPD and asthma pathologies, whereas for the subgroupings of inspiratory and expiratory phases, 18 out of 23 and 22 out of 23 features exhibited discrimination power, respectively

  2. Higher-order Multivariable Polynomial Regression to Estimate Human Affective States

    Science.gov (United States)

    Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin

    2016-03-01

    From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.

  3. Higher-order harmonics of limited diffraction Bessel beams

    Science.gov (United States)

    Ding; Lu

    2000-03-01

    We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.

  4. Stabilization of the higher order nonlinear Schrödinger equation with ...

    Indian Academy of Sciences (India)

    18

    self-steepening and delayed nonlinear response effect arising from stimulated Raman s- cattering ... The method is a power series expansion of the solution along this direction. ..... The proof of Theorem 1.1 is motivated by [12, 13]. Proof.

  5. Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

    International Nuclear Information System (INIS)

    Jia Li-Xin; Dai Hao; Hui Meng

    2010-01-01

    This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method

  6. Fractional equivalent Lagrangian densities for a fractional higher-order equation

    International Nuclear Information System (INIS)

    Fujioka, J

    2014-01-01

    In this communication we show that the equivalent Lagrangian densities (ELDs) of a fractional higher-order nonlinear Schrödinger equation with stable soliton-like solutions can be related in a hitherto unknown way. This new relationship is described in terms of a new fractional operator that includes both left- and right-sided fractional derivatives. Using this operator it is possible to generate new ELDs that contain different fractional parts, in addition to the already known ELDs, which only differ by a sum of first-order partial derivatives of two arbitrary functions. (fast track communications)

  7. Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

    Directory of Open Access Journals (Sweden)

    Tieshan He

    2011-01-01

    Full Text Available This paper is concerned with the existence of nontrivial periodic solutions and positive periodic solutions to a nonlinear second-order difference equation. Under some conditions concerning the first positive eigenvalue of the linear equation corresponding to the nonlinear second-order equation, we establish the existence results by using the topological degree and fixed point index theories.

  8. Z-scan: A simple technique for determination of third-order optical nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Vijender, E-mail: chahal-gju@rediffmail.com [Department of Applied Science, N.C. College of Engineering, Israna, Panipat-132107, Haryana (India); Aghamkar, Praveen, E-mail: p-aghamkar@yahoo.co.in [Department of Physics, Chaudhary Devi Lal University, Sirsa-125055, Haryana (India)

    2015-08-28

    Z-scan is a simple experimental technique to measure intensity dependent nonlinear susceptibilities of third-order nonlinear optical materials. This technique is used to measure the sign and magnitude of both real and imaginary part of the third order nonlinear susceptibility (χ{sup (3)}) of nonlinear optical materials. In this paper, we investigate third-order nonlinear optical properties of Ag-polymer composite film by using single beam z-scan technique with Q-switched, frequency doubled Nd: YAG laser (λ=532 nm) at 5 ns pulse. The values of nonlinear absorption coefficient (β), nonlinear refractive index (n{sub 2}) and third-order nonlinear optical susceptibility (χ{sup (3)}) of permethylazine were found to be 9.64 × 10{sup −7} cm/W, 8.55 × 10{sup −12} cm{sup 2}/W and 5.48 × 10{sup −10} esu, respectively.

  9. Discrete second order trajectory generator with nonlinear constraints

    NARCIS (Netherlands)

    Morselli, R.; Zanasi, R.; Stramigioli, Stefano

    2005-01-01

    A discrete second order trajectory generator for motion control systems is presented. The considered generator is a nonlinear system which receives as input a raw reference signal and provides as output a smooth reference signal satisfying nonlinear constraints on the output derivatives as UM-(x) ≤

  10. Evaluation of third order nonlinear optical parameters of CdS/PVA nanocomposite

    International Nuclear Information System (INIS)

    Sharma, Mamta; Tripathi, S. K.

    2015-01-01

    CdS nanoparticles dispersed in PVA are prepared by Chemical method at room temperature. The nonlinear optical parameters such as nonlinear absorption (β), nonlinear refractive index (n 2 ) and nonlinear susceptibility (χ 3 ) are calculated for this sample by using Z-scan technique. CdS/PVA samples show the two photon absorption mechanism. The third order nonlinear susceptibility is calculated from n 2 and β and is found to be of the order of 10 −7 – 10 −8 m 2 /V 2 . The larger value of third order nonlinear susceptibility is due to dielectric and quantum confinement effect

  11. High-order nonlinear susceptibilities of He

    International Nuclear Information System (INIS)

    Liu, W.C.; Clark, C.W.

    1996-01-01

    High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. The authors have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s, within the framework of Rayleigh=Schroedinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Ponte and Shakeshaft, and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used; the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals

  12. Controllable excitation of higher-order rogue waves in nonautonomous systems with both varying linear and harmonic external potentials

    Science.gov (United States)

    Jia, Heping; Yang, Rongcao; Tian, Jinping; Zhang, Wenmei

    2018-05-01

    The nonautonomous nonlinear Schrödinger (NLS) equation with both varying linear and harmonic external potentials is investigated and the semirational rogue wave (RW) solution is presented by similarity transformation. Based on the solution, the interactions between Peregrine soliton and breathers, and the controllability of the semirational RWs in periodic distribution and exponential decreasing nonautonomous systems with both linear and harmonic potentials are studied. It is found that the harmonic potential only influences the constraint condition of the semirational solution, the linear potential is related to the trajectory of the semirational RWs, while dispersion and nonlinearity determine the excitation position of the higher-order RWs. The higher-order RWs can be partly, completely and biperiodically excited in periodic distribution system and the diverse excited patterns can be generated for different parameter relations in exponential decreasing system. The results reveal that the excitation of the higher-order RWs can be controlled in the nonautonomous system by choosing dispersion, nonlinearity and external potentials.

  13. Fourth Order Nonlinear Intensity and the corresponding Refractive ...

    African Journals Online (AJOL)

    Nonlinear effects occur whenever the optical fields associated with one or more intense light such as from laser beams propagating in a crystal are large enough to produce polarization fields. This paper describes how the fourth order nonlinear intensity and the corresponding effective refractive index that is intensity ...

  14. Solution of continuous nonlinear PDEs through order completion

    CERN Document Server

    Oberguggenberger, MB

    1994-01-01

    This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.

  15. The multi-order envelope periodic solutions to the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Xiao Yafeng; Xue Haili; Zhang Hongqing

    2011-01-01

    Based on Jacobi elliptic function and the Lame equation, the perturbation method is applied to get the multi-order envelope periodic solutions of the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation. These multi-order envelope periodic solutions can degenerate into the different envelope solitary solutions. (authors)

  16. Propagation of high power electromagnetic beam in relativistic magnetoplasma: Higher order paraxial ray theory

    Science.gov (United States)

    Gill, Tarsem Singh; Kaur, Ravinder; Mahajan, Ranju

    2010-09-01

    This paper presents an analysis of self-consistent, steady-state, theoretical model, which explains the ring formation in a Gaussian electromagnetic beam propagating in a magnetoplasma, characterized by relativistic nonlinearity. Higher order terms (up to r4) in the expansion of the dielectric function and the eikonal have been taken into account. The condition for the formation of a dark and bright ring derived earlier by Misra and Mishra [J. Plasma Phys. 75, 769 (2009)] has been used to study focusing/defocusing of the beam. It is seen that inclusion of higher order terms does significantly affect the dependence of the beam width on the distance of propagation. Further, the effect of the magnetic field and the nature of nonlinearity on the ring formation and self-focusing of the beam have been explored.

  17. Propagation of high power electromagnetic beam in relativistic magnetoplasma: Higher order paraxial ray theory

    International Nuclear Information System (INIS)

    Gill, Tarsem Singh; Kaur, Ravinder; Mahajan, Ranju

    2010-01-01

    This paper presents an analysis of self-consistent, steady-state, theoretical model, which explains the ring formation in a Gaussian electromagnetic beam propagating in a magnetoplasma, characterized by relativistic nonlinearity. Higher order terms (up to r 4 ) in the expansion of the dielectric function and the eikonal have been taken into account. The condition for the formation of a dark and bright ring derived earlier by Misra and Mishra [J. Plasma Phys. 75, 769 (2009)] has been used to study focusing/defocusing of the beam. It is seen that inclusion of higher order terms does significantly affect the dependence of the beam width on the distance of propagation. Further, the effect of the magnetic field and the nature of nonlinearity on the ring formation and self-focusing of the beam have been explored.

  18. Analysis of an Nth-order nonlinear differential-delay equation

    Science.gov (United States)

    Vallée, Réal; Marriott, Christopher

    1989-01-01

    The problem of a nonlinear dynamical system with delay and an overall response time which is distributed among N individual components is analyzed. Such a system can generally be modeled by an Nth-order nonlinear differential delay equation. A linear-stability analysis as well as a numerical simulation of that equation are performed and a comparison is made with the experimental results. Finally, a parallel is established between the first-order differential equation with delay and the Nth-order differential equation without delay.

  19. Evaluation of third order nonlinear optical parameters of CdS/PVA nanocomposite

    Energy Technology Data Exchange (ETDEWEB)

    Sharma, Mamta [Department of Physics, Center of Advanced Study in Physics, Panjab University, Chandigarh-160014 (India); Department of Applied Sciences (Physics), UIET, Panjab University, Chandigarh-160014 (India); Tripathi, S. K., E-mail: surya@pu.ac.in, E-mail: surya-tr@yahoo.com [Department of Physics, Center of Advanced Study in Physics, Panjab University, Chandigarh-160014 (India)

    2015-06-24

    CdS nanoparticles dispersed in PVA are prepared by Chemical method at room temperature. The nonlinear optical parameters such as nonlinear absorption (β), nonlinear refractive index (n{sub 2}) and nonlinear susceptibility (χ{sup 3}) are calculated for this sample by using Z-scan technique. CdS/PVA samples show the two photon absorption mechanism. The third order nonlinear susceptibility is calculated from n{sub 2} and β and is found to be of the order of 10{sup −7} – 10{sup −8} m{sup 2}/V{sup 2}. The larger value of third order nonlinear susceptibility is due to dielectric and quantum confinement effect.

  20. Stability Analysis of Fractional-Order Nonlinear Systems with Delay

    Directory of Open Access Journals (Sweden)

    Yu Wang

    2014-01-01

    Full Text Available Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.

  1. Investigation of odd-order nonlinear susceptibilities in atomic vapors

    Energy Technology Data Exchange (ETDEWEB)

    Yan, Yaqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Teaching and Research Section of Maths and Physics, Guangzhou Commanding Academy of Chinese People’s Armed Police Force, Guangzhou, 510440 (China); Wu, Zhenkun; Si, Jinhai; Yan, Lihe; Zhang, Yiqi; Yuan, Chenzhi; Sun, Jia [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

    2013-06-15

    We theoretically deduce the macroscopic symmetry constraints for arbitrary odd-order nonlinear susceptibilities in homogeneous media including atomic vapors for the first time. After theoretically calculating the expressions using a semiclassical method, we demonstrate that the expressions for third- and fifth-order nonlinear susceptibilities for undressed and dressed four- and six-wave mixing (FWM and SWM) in atomic vapors satisfy the macroscopic symmetry constraints. We experimentally demonstrate consistence between the macroscopic symmetry constraints and the semiclassical expressions for atomic vapors by observing polarization control of FWM and SWM processes. The experimental results are in reasonable agreement with our theoretical calculations. -- Highlights: •The macroscopic symmetry constraints are deduced for homogeneous media including atomic vapors. •We demonstrate that odd-order nonlinear susceptibilities satisfy the constraints. •We experimentally demonstrate the deduction in part.

  2. Dynamics of Nonlinear Excitation of the High-Order Mode in a Single-Mode Step-Index Optical Fiber

    Science.gov (United States)

    Burdin, V.; Bourdine, A.

    2018-04-01

    This work is concerned with approximate model of higher-order mode nonlinear excitation in a singlemode silica optical fiber. We present some results of simulation for step-index optical fiber under femtosecond optical pulse launching, which confirm ability of relatively stable higher-order mode excitation in such singlemode optical fiber over sufficiently narrow range of launched optical power variation.

  3. The third order nonlinear susceptibility of InAs at infrared region

    International Nuclear Information System (INIS)

    Musayev, M.A.

    2008-01-01

    Nonlinear susceptibilities of the third order and coefficient of nonlinear absorption in InAs n-type with a different degree of a doping have been measured. The values of the third order nonlinear susceptibilities have derived from these measurements essentially exceed the values calculated on the basis of model featuring nonlinear susceptibility of electrons, being in conduction-band nonparabolicity. It has been shown that the observable discrepancy has been eliminated, if in calculation a dissipation of energy of electrons has been considered. Growth of efficiency at four-wave mixingin narrow-gap semiconductors has been restricted to nonlinear absorption of interacting waves

  4. Cascading second-order nonlinear processes in a lithium niobate-on-insulator microdisk.

    Science.gov (United States)

    Liu, Shijie; Zheng, Yuanlin; Chen, Xianfeng

    2017-09-15

    Whispering-gallery-mode (WGM) microcavities are very important in both fundamental science and practical applications, among which on-chip second-order nonlinear microresonators play an important role in integrated photonic functionalities. Here we demonstrate resonant second-harmonic generation (SHG) and cascaded third-harmonic generation (THG) in a lithium niobate-on-insulator (LNOI) microdisk resonator. Efficient SHG in the visible range was obtained with only several mW input powers at telecom wavelengths. THG was also observed through a cascading process, which reveals simultaneous phase matching and strong mode coupling in the resonator. Cascading of second-order nonlinear processes gives rise to an effectively large third-order nonlinearity, which makes on-chip second-order nonlinear microresonators a promising frequency converter for integrated nonlinear photonics.

  5. Current interactions from the one-form sector of nonlinear higher-spin equations

    Science.gov (United States)

    Gelfond, O. A.; Vasiliev, M. A.

    2018-06-01

    The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in AdS4. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter η = exp ⁡ iφ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant η η bar . Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at (η = 0) η bar = 0.

  6. An efficient flexible-order model for 3D nonlinear water waves

    DEFF Research Database (Denmark)

    Engsig-Karup, Allan Peter; Bingham, Harry B.; Lindberg, Ole

    2009-01-01

    The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal......, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental...

  7. Synthesis, characterization and third-order nonlinear optical ...

    Indian Academy of Sciences (India)

    2016-09-20

    Sep 20, 2016 ... the past, several strategies have been evolved to enhance the third-order nonlinear ..... retical fit using the formulation given in ref. [22]. Fit param- ..... Acknowledgement. The corresponding author acknowledges the financial.

  8. Institutional Traps of Russia’s Higher Education Nonlinear Development

    Directory of Open Access Journals (Sweden)

    Maria V.

    2018-03-01

    Full Text Available Introduction: the article deals with the problems arising in the Russian higher education system during its transformation. The topicality of this study lies in posing a problem of higher education development within the boundaries of a Russian macroregion. The objective of this article is to reveal barriers to the implementation of nonlinear processes in Russian higher education, which trigger the emergence of institutional traps and to determine the ways to avoid them. The purpose of this article is to identify barriers to the implementation of nonlinear processes in Russian higher education, which cause the emergence of institutional traps and determine the ways out of them. Materials and Methods: an institutional approach and the concept of non-linear models of higher education are the methodological basis of this research. The methods were developed by the research group of the Ural Federal University for sociological estimation of higher education transformation in the region. The procedure for selecting experts was realized according to the sociological methodology of I. E. Shteinberg (eight-window selection. Results: a summary analysis is made; inter-institutional interaction in terms of the “higher education – stakeholders” dyad is presented; the principal problematic areas are highlighted; and institutional traps preventing potential nonlinear development in Russian higher education are described. In the first problem zone, motivation traps, traps of formalisation/individualisation of the educational process, traps of intensification of the introduction of new information technologies in education and traps of unification of management were revealed. In the second problem area, traps of network interactions, traps of network interactions of higher education and employers, as well as traps of global/local orientation of universities were identified and analysed. Discussion and Conclusions: the authors outlined the most significant

  9. Modulational instability and nano-scale energy localization in ferromagnetic spin chain with higher order dispersive interactions

    International Nuclear Information System (INIS)

    Kavitha, L.; Mohamadou, A.; Parasuraman, E.; Gopi, D.; Akila, N.; Prabhu, A.

    2016-01-01

    The nonlinear localization phenomena in ferromagnetic spin lattices have attracted a steadily growing interest and their existence has been predicted in a wide range of physical settings. We investigate the onset of modulational instability of a plane wave in a discrete ferromagnetic spin chain with physically significant higher order dispersive octupole–dipole and dipole–dipole interactions. We derive the discrete nonlinear equation of motion with the aid of Holstein–Primakoff (H–P) transformation combined with Glauber's coherent state representation. We show that the discrete ferromagnetic spin dynamics is governed by an entirely new discrete NLS model with complex coefficients not reported so far. We report the study of modulational instability (MI) of the ferromagnetic chain with long range dispersive interactions both analytically in the frame work of linear stability analysis and numerically by means of molecular dynamics (MD) simulations. Our numerical simulations explore that the analytical predictions correctly describe the onset of instability. It is found that the presence of the various exchange and dispersive higher order interactions systematically favors the local gathering of excitations and thus supports the growth of high amplitude, long-lived discrete breather (DB) excitations. We analytically compute the strongly localized odd and even modes. Further, we employ the Jacobi elliptic function method to solve the nonlinear evolution equation and an exact propagating bubble-soliton solution is explored. - Highlights: • Higher order dispersive interactions plays significant role in ferromagnetic spin chain. • The energy localization is studied both analytically and numerically. • The existence of DBs are studied under the effect of higher order dispersive interaction.

  10. Experimental investigations of higher-order springing and whipping-WILS project

    Directory of Open Access Journals (Sweden)

    Hong Sa Young

    2014-12-01

    Full Text Available Springing and whipping are becoming increasingly important considerations in ship design as container ships increase in size. In this study, the springing and whipping characteristics of a large container ship were investigated through a series of systematic model tests in waves. A multi-segmented hull model with a backbone was adopted for measurement of springing and whipping signals. A conversion method for extracting torsion springing and whipping is described in this paper for the case of an open-section backbone. Higher-order springing, higher-mode torsion responses, and the effects of linear and nonlinear springing in irregular waves are highlighted in the discussion.

  11. Linear and nonlinear Stability analysis for finite difference discretizations of higher order Boussinesq equations

    DEFF Research Database (Denmark)

    Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.

    2004-01-01

    of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water nonlinearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into into the numerical behavior of this rather complicated system of nonlinear PDEs....

  12. Riccati-parameter solutions of nonlinear second-order ODEs

    International Nuclear Information System (INIS)

    Reyes, M A; Rosu, H C

    2008-01-01

    It has been proven by Rosu and Cornejo-Perez (Rosu and Cornejo-Perez 2005 Phys. Rev. E 71 046607, Cornejo-Perez and Rosu 2005 Prog. Theor. Phys. 114 533) that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a 'growth' parameter from the trivial null solution up to the particular solution found through the factorization procedure

  13. Higher-order ice-sheet modelling accelerated by multigrid on graphics cards

    Science.gov (United States)

    Brædstrup, Christian; Egholm, David

    2013-04-01

    Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.

  14. Large optical second-order nonlinearity of poled WO3-TeO2 glass.

    Science.gov (United States)

    Tanaka, K; Narazaki, A; Hirao, K

    2000-02-15

    Second-harmonic generation, one of the second-order nonlinear optical properties of thermally and electrically poled WO>(3)-TeO>(2) glasses, has been examined. We poled glass samples with two thicknesses (0.60 and 0.86 mm) at various temperatures to explore the effects of external electric field strength and poling temperature on second-order nonlinearity. The dependence of second-harmonic intensity on the poling temperature is maximum at a specific poling temperature. A second-order nonlinear susceptibility of 2.1 pm/V was attained for the 0.60-mm-thick glass poled at 250 degrees C. This value is fairly large compared with those for poled silica and tellurite glasses reported thus far. We speculate that the large third-order nonlinear susceptibility of WO>(3)- TeO>(2) glasses gives rise to the large second-order nonlinearity by means of a X((2)) = 3X((3)) E(dc) process.

  15. Analysis of warping deformation modes using higher order ANCF beam element

    Science.gov (United States)

    Orzechowski, Grzegorz; Shabana, Ahmed A.

    2016-02-01

    Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition. However, in the absolute nodal coordinate formulation (ANCF) continuum-based beams, this assumption can be relaxed allowing for capturing deformation modes that couple the cross-section deformation and beam bending, torsion, and/or elongation. The deformation modes captured by ANCF finite elements depend on the interpolating polynomials used. The most widely used spatial ANCF beam element employs linear approximation in the transverse direction, thereby restricting the cross section deformation and leading to locking problems. The objective of this investigation is to examine the behavior of a higher order ANCF beam element that includes quadratic interpolation in the transverse directions. This higher order element allows capturing warping and non-uniform stretching distribution. Furthermore, this higher order element allows for increasing the degree of continuity at the element interface. It is shown in this paper that the higher order ANCF beam element can be used effectively to capture warping and eliminate Poisson locking that characterizes lower order ANCF finite elements. It is also shown that increasing the degree of continuity requires a special attention in order to have acceptable results. Because higher order elements can be more computationally expensive than the lower order elements, the use of reduced integration for evaluating the stress forces and the use of explicit and implicit numerical integrations to solve the nonlinear dynamic equations of motion are investigated in this paper. It is shown that the use of some of these integration methods can be very effective in reducing the CPU time without adversely affecting the solution accuracy.

  16. Surface plasmon enhanced third-order optical nonlinearity of Ag nanocomposite film

    International Nuclear Information System (INIS)

    Singh, Vijender; Aghamkar, Praveen

    2014-01-01

    We obtain a large third-order optical nonlinearity (χ (3)  ≈ 10 −10 esu) of silver nanoparticles dispersed in polyvinyl alcohol/tetraethyl orthosilicate matrix using single beam z-scan technique at 532 nm by Q-switched Nd:YAG laser. We have shown that mechanisms responsible for third-order optical nonlinearity of Ag nanocomposite film are reverse saturable absorption (RSA) and self-defocusing in the purlieu of surface plasmon resonance (SPR). Optical band-gap and width of SPR band of Ag nanocomposite film decrease with increasing silver concentration, which leads to enhancement of local electric field and hence third-order optical nonlinearity. Optical limiting, due to RSA has also been demonstrated at 532 nm

  17. On nonlinear differential equation with exact solutions having various pole orders

    International Nuclear Information System (INIS)

    Kudryashov, N.A.

    2015-01-01

    We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed

  18. Higher-order (non-)modularity

    DEFF Research Database (Denmark)

    Appel, Claus; van Oostrom, Vincent; Simonsen, Jakob Grue

    2010-01-01

    We show that, contrary to the situation in first-order term rewriting, almost none of the usual properties of rewriting are modular for higher-order rewriting, irrespective of the higher-order rewriting format. We show that for the particular format of simply typed applicative term rewriting...... systems modularity of confluence, normalization, and termination can be recovered by imposing suitable linearity constraints....

  19. Nonlinear noninteger order circuits and systems an introduction

    CERN Document Server

    Arena, P; Fortuna, L; Porto, D

    2001-01-01

    In this book, the reader will find a theoretical introduction to noninteger order systems, as well as several applications showing their features and peculiarities. The main definitions and results of research on noninteger order systems and modelling of physical noninteger phenomena are reported together with problems of their approximation. Control applications, noninteger order CNNs and circuit realizations of noninteger order systems are also presented.The book is intended for students and researchers involved in the simulation and control of nonlinear noninteger order systems, with partic

  20. Higher order branching of periodic orbits from polynomial isochrones

    Directory of Open Access Journals (Sweden)

    B. Toni

    1999-09-01

    Full Text Available We discuss the higher order local bifurcations of limit cycles from polynomial isochrones (linearizable centers when the linearizing transformation is explicitly known and yields a polynomial perturbation one-form. Using a method based on the relative cohomology decomposition of polynomial one-forms complemented with a step reduction process, we give an explicit formula for the overall upper bound of branch points of limit cycles in an arbitrary $n$ degree polynomial perturbation of the linear isochrone, and provide an algorithmic procedure to compute the upper bound at successive orders. We derive a complete analysis of the nonlinear cubic Hamiltonian isochrone and show that at most nine branch points of limit cycles can bifurcate in a cubic polynomial perturbation. Moreover, perturbations with exactly two, three, four, six, and nine local families of limit cycles may be constructed.

  1. Analysis of higher order harmonics with holographic reflection gratings

    Science.gov (United States)

    Mas-Abellan, P.; Madrigal, R.; Fimia, A.

    2017-05-01

    Silver halide emulsions have been considered one of the most energetic sensitive materials for holographic applications. Nonlinear recording effects on holographic reflection gratings recorded on silver halide emulsions have been studied by different authors obtaining excellent experimental results. In this communication specifically we focused our investigation on the effects of refractive index modulation, trying to get high levels of overmodulation that will produce high order harmonics. We studied the influence of the overmodulation and its effects on the transmission spectra for a wide exposure range by use of 9 μm thickness films of ultrafine grain emulsion BB640, exposed to single collimated beams using a red He-Ne laser (wavelength 632.8 nm) with Denisyuk configuration obtaining a spatial frequency of 4990 l/mm recorded on the emulsion. The experimental results show that high overmodulation levels of refractive index produce second order harmonics with high diffraction efficiency (higher than 75%) and a narrow grating bandwidth (12.5 nm). Results also show that overmodulation produce diffraction spectra deformation of the second order harmonic, transforming the spectrum from sinusoidal to approximation of square shape due to very high overmodulation. Increasing the levels of overmodulation of refractive index, we have obtained higher order harmonics, obtaining third order harmonic with diffraction efficiency (up to 23%) and narrowing grating bandwidth (5 nm). This study is the first step to develop a new easy technique to obtain narrow spectral filters based on the use of high index modulation reflection gratings.

  2. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

    KAUST Repository

    N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

  3. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

    KAUST Repository

    N'Doye, Ibrahima

    2015-07-01

    This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

  4. Surface plasmon enhanced third-order optical nonlinearity of Ag nanocomposite film

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Vijender [Department of Applied Science, N.C. College of Engineering, Israna, Panipat 132107, Haryana (India); Aghamkar, Praveen, E-mail: p-aghamkar@yahoo.in [Department of Physics, Chaudhary Devi Lal University, Sirsa 125055, Haryana (India)

    2014-03-17

    We obtain a large third-order optical nonlinearity (χ{sup (3)} ≈ 10{sup −10}esu) of silver nanoparticles dispersed in polyvinyl alcohol/tetraethyl orthosilicate matrix using single beam z-scan technique at 532 nm by Q-switched Nd:YAG laser. We have shown that mechanisms responsible for third-order optical nonlinearity of Ag nanocomposite film are reverse saturable absorption (RSA) and self-defocusing in the purlieu of surface plasmon resonance (SPR). Optical band-gap and width of SPR band of Ag nanocomposite film decrease with increasing silver concentration, which leads to enhancement of local electric field and hence third-order optical nonlinearity. Optical limiting, due to RSA has also been demonstrated at 532 nm.

  5. The nonlocal boundary value problems for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

    -, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf

  6. Nonlinear elliptic equations of the second order

    CERN Document Server

    Han, Qing

    2016-01-01

    Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...

  7. An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

    Science.gov (United States)

    Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

    2018-06-01

    This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

  8. Certified higher-order recursive path ordering

    NARCIS (Netherlands)

    Koprowski, A.; Pfenning, F.

    2006-01-01

    The paper reports on a formalization of a proof of wellfoundedness of the higher-order recursive path ordering (HORPO) in the proof checker Coq. The development is axiom-free and fully constructive. Three substantive parts that could be used also in other developments are the formalizations of the

  9. A new hybrid nonlinear congruential number generator based on higher functional power of logistic maps

    International Nuclear Information System (INIS)

    Cecen, Songul; Demirer, R. Murat; Bayrak, Coskun

    2009-01-01

    We propose a nonlinear congruential pseudorandom number generator consisting of summation of higher order composition of random logistic maps under certain congruential mappings. We change both bifurcation parameters of logistic maps in the interval of U=[3.5599,4) and coefficients of the polynomials in each higher order composition of terms up to degree d. This helped us to obtain a perfect random decorrelated generator which is infinite and aperiodic. It is observed from the simulation results that our new PRNG has good uniformity and power spectrum properties with very flat white noise characteristics. The results are interesting, new and may have applications in cryptography and in Monte Carlo simulations.

  10. Lattice Boltzmann model for high-order nonlinear partial differential equations.

    Science.gov (United States)

    Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

    2018-01-01

    In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

  11. Lattice Boltzmann model for high-order nonlinear partial differential equations

    Science.gov (United States)

    Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

    2018-01-01

    In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

  12. A Higher-Order Neural Network Design for Improving Segmentation Performance in Medical Image Series

    International Nuclear Information System (INIS)

    Selvi, Eşref; Selver, M Alper; Güzeliş, Cüneyt; Dicle, Oǧuz

    2014-01-01

    Segmentation of anatomical structures from medical image series is an ongoing field of research. Although, organs of interest are three-dimensional in nature, slice-by-slice approaches are widely used in clinical applications because of their ease of integration with the current manual segmentation scheme. To be able to use slice-by-slice techniques effectively, adjacent slice information, which represents likelihood of a region to be the structure of interest, plays critical role. Recent studies focus on using distance transform directly as a feature or to increase the feature values at the vicinity of the search area. This study presents a novel approach by constructing a higher order neural network, the input layer of which receives features together with their multiplications with the distance transform. This allows higher-order interactions between features through the non-linearity introduced by the multiplication. The application of the proposed method to 9 CT datasets for segmentation of the liver shows higher performance than well-known higher order classification neural networks

  13. Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders

    KAUST Repository

    El Beltagy, Mohamed

    2016-01-01

    In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.

  14. Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders

    KAUST Repository

    El Beltagy, Mohamed

    2016-01-06

    In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.

  15. Ultrafast third-order nonlinearity of silver nanospheres and nanodiscs

    International Nuclear Information System (INIS)

    Jayabalan, J; Singh, Asha; Chari, Rama; Oak, Shrikant M

    2007-01-01

    We have measured and compared the absolute values of nonlinear susceptibility of colloidal solutions containing silver nanospheres and nanodiscs at their respective plasmon peaks using a femtosecond laser. The nonlinear process responsible for the laser-induced grating formation in the sample is determined to be of third order. The ratio between the third-order susceptibility (|χ (3) |) and the linear absorption coefficient (α) of the nanodiscs at 590 nm is three times than that of the similar ratio for nanospheres at 398 nm. Using a randomly oriented ellipsoidal model, we have shown that the increase in |χ (3) |/α for a nanodisc at 590 nm can be attributed to the change in the field enhancement factor with shape

  16. Nonsingular Terminal Sliding Mode Control of Uncertain Second-Order Nonlinear Systems

    Directory of Open Access Journals (Sweden)

    Minh-Duc Tran

    2015-01-01

    Full Text Available This paper presents a high-performance nonsingular terminal sliding mode control method for uncertain second-order nonlinear systems. First, a nonsingular terminal sliding mode surface is introduced to eliminate the singularity problem that exists in conventional terminal sliding mode control. By using this method, the system not only can guarantee that the tracking errors reach the reference value in a finite time with high-precision tracking performance but also can overcome the complex-value and the restrictions of the exponent (the exponent should be fractional number with an odd numerator and an odd denominator in traditional terminal sliding mode. Then, in order to eliminate the chattering phenomenon, a super-twisting higher-order nonsingular terminal sliding mode control method is proposed. The stability of the closed-loop system is established using the Lyapunov theory. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.

  17. Third-order nonlinear optical properties of the poly(methyl methacrylate)-phenothiazinium dye hybrid thin films

    International Nuclear Information System (INIS)

    Sun, Ru; Lu, Yue-Ting; Yan, Bao-Long; Lu, Jian-Mei; Wu, Xing-Zhi; Song, Ying-Lin; Ge, Jian-Feng

    2014-01-01

    The third-order nonlinear optical properties of poly(methyl methacrylate) films doped with charge flowable 3,7-di(piperidinyl)phenothiazin-5-ium chloride, which tested by Z-scan method with nanosecond laser beam at 532 nm, are reported. Large third-order nonlinear optical susceptibilities (up to 10 −7 esu) and high second hyperpolarizabilities (up to 10 −27 esu) are found. The third-order nonlinear absorptions change from reverse saturated absorptions to saturated absorptions with different percentage of the phenothiazinium dye in the poly(methyl methacrylate) films, which can be explained by the accumulation phenomenon of the phenothiazinium. The results suggest that the phenothiazinium salt is a promising material for third order non-linear applications. - Highlights: • Phenothiazinium containing optical films • Strong third-order nonlinear optical (NLO) absorption • Large third-order NLO susceptibilities

  18. Ultrafast third-order nonlinearity of silver nanospheres and nanodiscs

    Energy Technology Data Exchange (ETDEWEB)

    Jayabalan, J; Singh, Asha; Chari, Rama; Oak, Shrikant M [Ultrafast Studies Section, Laser Physics Application Division, Raja Ramanna Centre for Advanced Technology, Indore-452013 (India)

    2007-08-08

    We have measured and compared the absolute values of nonlinear susceptibility of colloidal solutions containing silver nanospheres and nanodiscs at their respective plasmon peaks using a femtosecond laser. The nonlinear process responsible for the laser-induced grating formation in the sample is determined to be of third order. The ratio between the third-order susceptibility (|{chi}{sup (3)}|) and the linear absorption coefficient ({alpha}) of the nanodiscs at 590 nm is three times than that of the similar ratio for nanospheres at 398 nm. Using a randomly oriented ellipsoidal model, we have shown that the increase in |{chi}{sup (3)}|/{alpha} for a nanodisc at 590 nm can be attributed to the change in the field enhancement factor with shape.

  19. Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

    Energy Technology Data Exchange (ETDEWEB)

    Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)

    2013-09-02

    We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.

  20. Higher order criterion for the nonexistence of formal first integral for nonlinear systems

    Directory of Open Access Journals (Sweden)

    Zhiguo Xu

    2017-11-01

    Full Text Available The main purpose of this article is to find a criterion for the nonexistence of formal first integrals for nonlinear systems under general resonance. An algorithm illustrates an application to a class of generalized Lokta-Volterra systems. Our result generalize the classical Poincare's nonintegrability theorem and the existing results in the literature.

  1. European Workshop on High Order Nonlinear Numerical Schemes for Evolutionary PDEs

    CERN Document Server

    Beaugendre, Héloïse; Congedo, Pietro; Dobrzynski, Cécile; Perrier, Vincent; Ricchiuto, Mario

    2014-01-01

    This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.

  2. A Study of Enhanced, Higher Order Boussinesq-Type Equations and Their Numerical Modelling

    DEFF Research Database (Denmark)

    Banijamali, Babak

    model is designated for the solution of higher-order Boussinesq-type equations, formulated in terms of the horizontal velocity at an arbitrary depth vector. Various discretisation techniques and grid definitions have been considered in this endeavour, undertaking a detailed analysis of the selected......This project has encompassed efforts in two separate veins: on the one hand, the acquiring of highly accurate model equations of the Boussinesq-type, and on the other hand, the theoretical and practical work in implementing such equations in the form of conventional numerical models, with obvious...... potential for applications to the realm of numerical modelling in coastal engineering. The derivation and analysis of several forms of higher-order in dispersion and non-linearity Boussinesq-type equations have been undertaken, obtaining and investigating the properties of a new and generalised class...

  3. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

    KAUST Repository

    Calatroni, Luca

    2013-08-01

    We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

  4. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

    KAUST Repository

    Calatroni, Luca; Dü ring, Bertram; Schö nlieb, Carola-Bibiane

    2013-01-01

    We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

  5. Second order optical nonlinearity in silicon by symmetry breaking

    Energy Technology Data Exchange (ETDEWEB)

    Cazzanelli, Massimo, E-mail: massimo.cazzanelli@unitn.it [Laboratorio IdEA, Dipartimento di Fisica, Università di Trento, via Sommarive, 14 Povo (Trento) (Italy); Schilling, Joerg, E-mail: joerg.schilling@physik.uni-halle.de [Centre for Innovation Competence SiLi-nano, Martin-Luther-University Halle-Wittenberg, Karl-Freiherr-von-Fritsch Str. 3, 06120 Halle (Germany)

    2016-03-15

    Although silicon does not possess a dipolar bulk second order nonlinear susceptibility due to its centro-symmetric crystal structure, in recent years several attempts were undertaken to create such a property in silicon. This review presents the different sources of a second order susceptibility (χ{sup (2)}) in silicon and the connected second order nonlinear effects which were investigated up to now. After an introduction, a theoretical overview discusses the second order nonlinearity in general and distinguishes between the dipolar contribution—which is usually dominating in non-centrosymmetric structures—and the quadrupolar contribution, which even exists in centro-symmetric materials. Afterwards, the classic work on second harmonic generation from silicon surfaces in reflection measurements is reviewed. Due to the abrupt symmetry breaking at surfaces and interfaces locally a dipolar second order susceptibility appears, resulting in, e.g., second harmonic generation. Since the bulk contribution is usually small, the study of this second harmonic signal allows a sensitive observation of the surface/interface conditions. The impact of covering films, strain, electric fields, and defect states at the interfaces was already investigated in this way. With the advent of silicon photonics and the search for ever faster electrooptic modulators, the interest turned to the creation of a dipolar bulk χ{sup (2)} in silicon. These efforts have been focussing on several experiments applying an inhomogeneous strain to the silicon lattice to break its centro-symmetry. Recent results suggesting the impact of electric fields which are exerted from fixed charges in adjacent covering layers are also included. After a subsequent summary on “competing” concepts using not Si but Si-related materials, the paper will end with some final conclusions, suggesting possible future research direction in this dynamically developing field.

  6. Oscillation criteria for fourth-order nonlinear delay dynamic equations

    Directory of Open Access Journals (Sweden)

    Yunsong Qi

    2013-03-01

    Full Text Available We obtain criteria for the oscillation of all solutions to a fourth-order nonlinear delay dynamic equation on a time scale that is unbounded from above. The results obtained are illustrated with examples

  7. Contribution of Higher-Order Dispersion to Nonlinear Electron-Acoustic Solitary Waves in a Relativistic Electron Beam Plasma System

    International Nuclear Information System (INIS)

    Zahran, M.A.; El-Shewy, E.K.

    2008-01-01

    The nonlinear properties of solitary wave structures are reported in an unmagnetized collisionless plasma comprising of cold relativistic electron fluid, Maxwellian hot electrons, relativistic electron beam, and stationary ions. The Korteweg--de Vries (KdV) equation has been derived using a reductive perturbation theory. As the wave amplitude increases, the width and velocity of the soliton deviate from the prediction of the KdV equation i.e. the breakdown of the KdV approximation. On the other hand, to overcome this weakness we extend our analysis to obtain the KdV equation with fifth-order dispersion term. The solution of the resulting equation has been obtained

  8. Higher Order Expectations in Asset Pricing

    OpenAIRE

    Philippe BACCHETTA; Eric VAN WINCOOP

    2004-01-01

    We examine formally Keynes' idea that higher order beliefs can drive a wedge between an asset price and its fundamental value based on expected future payoffs. Higher order expectations add an additional term to a standard asset pricing equation. We call this the higher order wedge, which depends on the difference between higher and first order expectations of future payoffs. We analyze the determinants of this wedge and its impact on the equilibrium price. In the context of a dynamic noisy r...

  9. Oscillation criteria for third order delay nonlinear differential equations

    Directory of Open Access Journals (Sweden)

    E. M. Elabbasy

    2012-01-01

    via comparison with some first differential equations whose oscillatory characters are known. Our results generalize and improve some known results for oscillation of third order nonlinear differential equations. Some examples are given to illustrate the main results.

  10. Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

    Science.gov (United States)

    Gholami, Raheb; Ansari, Reza

    2018-02-01

    This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton's principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy's third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.

  11. State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation

    Directory of Open Access Journals (Sweden)

    Junhai Luo

    2014-01-01

    Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.

  12. The third-order nonlinear optical susceptibility of C{sub 60}-derived nanotubes

    Energy Technology Data Exchange (ETDEWEB)

    Xiangang, Wan [Nanjing Univ. (China). National Lab. of Solid State Microstructures; [Center for Advanced Studies in Science and Technology of Microstructures, Nanjing (China); Jinming, Dong [Nanjing Univ. (China). National Lab. of Solid State Microstructures; [Center for Advanced Studies in Science and Technology of Microstructures, Nanjing (China); Jie, Jiang [Nanjing Univ., JS (China). Dept. of Physics; Xing, D Y [Nanjing Univ., JS (China). Dept. of Physics

    1997-02-01

    Using the extended Su-Schrieffer-Heeger (SSH) model and the sum-over-state (SOS) method, we have calculated the third-order nonlinear polarizability {gamma} and its dispersion spectra for C{sub 60}-derived nanotubes, which is one of the narrowest tubes. Our numerical calculations indicate that both symmetry and size of the nanotubes have great effect on the third-order nonlinear polarizability {gamma} spectra. We find that with increasing size, both static {gamma} values and dynamical response peak values increase. When the atom number of the C{sub 60}-derived nanotubes is 140, the static {gamma} value is about 65 times larger than that of C{sub 60}, and the highest peak value of {gamma} (at 3{omega} = 3.52 eV) is about three orders larger than that of C{sub 60}. So, C{sub 60}-derived nanotubes may become a kind of good nonlinear optical materials. (orig.)

  13. Spectral dependence of third-order nonlinear optical properties in InN

    International Nuclear Information System (INIS)

    Ahn, H.; Lee, M.-T.; Chang, Y.-M.

    2014-01-01

    We report on the nonlinear optical properties of InN measured in a wide near-infrared spectral range with the femtosecond Z-scan technique. The above-bandgap nonlinear absorption in InN is found to originate from the saturation of absorption by the band-state-filling and its cross-section increases drastically near the bandgap energy. With below-bandgap excitation, the nonlinear absorption undergoes a transition from saturation absorption (SA) to reverse-SA (RSA), attributed to the competition between SA of band-tail states and two-photon-related RSA. The measured large nonlinear refractive index of the order of 10 −10 cm 2 /W indicates InN as a potential material for all-optical switching and related applications

  14. Order-sorted Algebraic Specifications with Higher-order Functions

    DEFF Research Database (Denmark)

    Haxthausen, Anne Elisabeth

    1995-01-01

    This paper gives a proposal for how order-sorted algebraic specification languages can be extended with higher-order functions. The approach taken is a generalisation to the order-sorted case of an approach given by Mller, Tarlecki and Wirsing for the many-sorted case. The main idea in the proposal...

  15. Oscillation criteria for third order nonlinear delay differential equations with damping

    Directory of Open Access Journals (Sweden)

    Said R. Grace

    2015-01-01

    Full Text Available This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \\[\\label{*} \\left( r_{2}(t\\left( r_{1}(ty^{\\prime}(t\\right^{\\prime}\\right^{\\prime}+p(ty^{\\prime}(t+q(tf(y(g(t=0.\\tag{\\(\\ast\\}\\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007, 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010, 756-762], the authors established some sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates or converges to zero, provided that the second order equation \\[\\left( r_{2}(tz^{\\prime }(t\\right^{\\prime}+\\left(p(t/r_{1}(t\\right z(t=0\\tag{\\(\\ast\\ast\\}\\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates if equation (\\(\\ast\\ast\\ is nonoscillatory. We also establish results for the oscillation of equation (\\(\\ast\\ when equation (\\(\\ast\\ast\\ is oscillatory.

  16. Linear and nonlinear stability analysis in BWRs applying a reduced order model

    Energy Technology Data Exchange (ETDEWEB)

    Olvera G, O. A.; Espinosa P, G.; Prieto G, A., E-mail: omar_olverag@hotmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico)

    2016-09-15

    Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

  17. Linear and nonlinear stability analysis in BWRs applying a reduced order model

    International Nuclear Information System (INIS)

    Olvera G, O. A.; Espinosa P, G.; Prieto G, A.

    2016-09-01

    Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

  18. Higher-Order Hierarchies

    DEFF Research Database (Denmark)

    Ernst, Erik

    2003-01-01

    This paper introduces the notion of higher-order inheritance hierarchies. They are useful because they provide well-known benefits of object-orientation at the level of entire hierarchies-benefits which are not available with current approaches. Three facets must be adressed: First, it must be po...

  19. Nonlinear second order evolution inclusions with noncoercive viscosity term

    Science.gov (United States)

    Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D.

    2018-04-01

    In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and a priori bounds that permit passing to the limit, we prove that the problem has a solution.

  20. An efficient flexible-order model for 3D nonlinear water waves

    Science.gov (United States)

    Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

    2009-04-01

    The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

  1. An efficient flexible-order model for 3D nonlinear water waves

    International Nuclear Information System (INIS)

    Engsig-Karup, A.P.; Bingham, H.B.; Lindberg, O.

    2009-01-01

    The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature

  2. Embedded solitons in the third-order nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Pal, Debabrata; Ali, Sk Golam; Talukdar, B

    2008-01-01

    We work with a sech trial function with space-dependent soliton parameters and envisage a variational study for the nonlinear Schoedinger (NLS) equation in the presence of third-order dispersion. We demonstrate that the variational equations for pulse evolution in this NLS equation provide a natural basis to derive a potential model which can account for the existence of a continuous family of embedded solitons supported by the third-order NLS equation. Each member of the family is parameterized by the propagation velocity and co-efficient of the third-order dispersion

  3. New Efficient Fourth Order Method for Solving Nonlinear Equations

    Directory of Open Access Journals (Sweden)

    Farooq Ahmad

    2013-12-01

    Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.

  4. Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation

    International Nuclear Information System (INIS)

    Bouard, Anne de; Debussche, Arnaud

    2006-01-01

    In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1

  5. Third order nonlinear optical properties and optical limiting behavior of alkali metal complexes of p-nitrophenol

    Science.gov (United States)

    Thangaraj, M.; Vinitha, G.; Sabari Girisun, T. C.; Anandan, P.; Ravi, G.

    2015-10-01

    Optical nonlinearity of metal complexes of p-nitrophenolate (M=Li, Na and K) in ethanol is studied by using a continuous wave (cw) diode pumped Nd:YAG laser (532 nm, 50 mW). The predominant mechanism of observed nonlinearity is thermal in origin. The nonlinear refractive index and the nonlinear absorption coefficient of the samples were found to be in the order of 10-8 cm2/W and 10-3 cm/W respectively. Magnitude of third-order optical parameters varies according to the choice of alkali metal chosen for metal complex formation of p-nitrophenolate. The third-order nonlinear susceptibility was found to be in the order of 10-6 esu. The observed saturable absorption and the self-defocusing effect were used to demonstrate the optical limiting action at 532 nm by using the same cw laser beam.

  6. Alkali-Responsive Absorption Spectra and Third-Order Optical Nonlinearities of Imino Squaramides

    International Nuclear Information System (INIS)

    Li Zhong-Yu; Xu Song; Zhou Xin-Yu; Zhang Fu-Shi

    2012-01-01

    Third-order optical nonlinearities and dynamic responses of two imino squaramides under neutral and base conditions were studied using the femtosecond degenerate four-wave mixing technique at 800 nm. Ultrafast optical responses have been observed and the magnitude of the second-order hyperpolarizabilities of the squaramides has been measured to be as large as 10 −31 esu. The absorption spectra, color of solution, and third-order optical nonlinearities of two imino squaramides change with the addition of sodium hydroxide. The γ value under the base condition for each dye is approximately 1.25 times larger than that under neutral conditions. (fundamental areas of phenomenology(including applications))

  7. Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

    International Nuclear Information System (INIS)

    Hwang, Jai-chan; Noh, Hyerim

    2005-01-01

    We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of φ v order higher than the second-order terms where φ v is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have δΦ∼(3/5)φ v to the linear order. Therefore, the pure general relativistic effects are of φ v order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have (δT/T)∼(1/3)δΦ∼(1/5)φ v ∼10 -5 . Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon

  8. Further results on global state feedback stabilization of nonlinear high-order feedforward systems.

    Science.gov (United States)

    Xie, Xue-Jun; Zhang, Xing-Hui

    2014-03-01

    In this paper, by introducing a combined method of sign function, homogeneous domination and adding a power integrator, and overcoming several troublesome obstacles in the design and analysis, the problem of state feedback control for a class of nonlinear high-order feedforward systems with the nonlinearity's order being relaxed to an interval rather than a fixed point is solved. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

  9. Output Feedback Distributed Containment Control for High-Order Nonlinear Multiagent Systems.

    Science.gov (United States)

    Li, Yafeng; Hua, Changchun; Wu, Shuangshuang; Guan, Xinping

    2017-01-31

    In this paper, we study the problem of output feedback distributed containment control for a class of high-order nonlinear multiagent systems under a fixed undirected graph and a fixed directed graph, respectively. Only the output signals of the systems can be measured. The novel reduced order dynamic gain observer is constructed to estimate the unmeasured state variables of the system with the less conservative condition on nonlinear terms than traditional Lipschitz one. Via the backstepping method, output feedback distributed nonlinear controllers for the followers are designed. By means of the novel first virtual controllers, we separate the estimated state variables of different agents from each other. Consequently, the designed controllers show independence on the estimated state variables of neighbors except outputs information, and the dynamics of each agent can be greatly different, which make the design method have a wider class of applications. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed method.

  10. Nonlinear absorption and receptivity of the third order in InAs infrared region

    International Nuclear Information System (INIS)

    Musayev, M.A.

    2005-01-01

    Nonlinear absorption and receptivity of the third order and coefficient nonlinear absorption in InAs n-type with different degree of alloying was measured. Obtained score considerably exceed sense, calculated on the basis of the models describing nonlinear receptivity of electrons, situated in the nonparabolic area of conductivity. It was shown that, observable deviations withdraw; if in the calculation apply energy dissipation of electrons. Growth of the efficiency under four-wave interaction in low-energy-gap semiconductors confines nonlinear absorption of interacting waves

  11. Non-linear realizations and higher curvature supergravity

    Energy Technology Data Exchange (ETDEWEB)

    Farakos, F. [Dipartimento di Fisica e Astronomia ' ' Galileo Galilei' ' , Universita di Padova (Italy); INFN, Sezione di Padova (Italy); Ferrara, S. [Department of Theoretical Physics, Geneva (Switzerland); INFN - Laboratori Nazionali di Frascati, Frascati (Italy); Department of Physics and Astronomy, Mani L. Bhaumik Institute for Theoretical Physics, U.C.L.A., Los Angeles, CA (United States); Kehagias, A. [Physics Division, National Technical University of Athens (Greece); Luest, D. [Arnold Sommerfeld Center for Theoretical Physics, Muenchen (Germany); Max-Planck-Institut fuer Physik, Muenchen (Germany)

    2017-12-15

    We focus on non-linear realizations of local supersymmetry as obtained by using constrained superfields in supergravity. New constraints, beyond those of rigid supersymmetry, are obtained whenever curvature multiplets are affected as well as higher derivative interactions are introduced. In particular, a new constraint, which removes a very massive gravitino is introduced, and in the rigid limit it merely reduces to an explicit supersymmetry breaking. Higher curvature supergravities free of ghosts and instabilities are also obtained in this way. Finally, we consider direct coupling of the goldstino multiplet to the super Gauss-Bonnet multiplet and discuss the emergence of a new scalar degree of freedom. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  12. ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.

  13. Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

    International Nuclear Information System (INIS)

    Qu Gai-Zhu; Zhang Shun-Li; Li Yao-Long

    2014-01-01

    In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators. (general)

  14. Challenges in higher order mode Raman amplifiers

    DEFF Research Database (Denmark)

    Rottwitt, Karsten; Nielsen, Kristian; Friis, Søren Michael Mørk

    2015-01-01

    A higher order Raman amplifier model that take random mode coupling into account ispresented. Mode dependent gain and signal power fluctuations at the output of the higher order modeRaman amplifier are discussed......A higher order Raman amplifier model that take random mode coupling into account ispresented. Mode dependent gain and signal power fluctuations at the output of the higher order modeRaman amplifier are discussed...

  15. HIGHER ORDER THINKING IN TEACHING GRAMMAR

    Directory of Open Access Journals (Sweden)

    Citra Dewi

    2017-04-01

    Full Text Available The aim of this paper discussed about how to enhance students’ higher order thinking that should be done by teacher in teaching grammar. Usually teaching grammar was boring and has the same way to learn like change the pattern of sentence into positive, negative and introgative while the students’ need more various way to develop their thinking. The outcome of students’ competence in grammar sometimes not sufficient enough when the students’ occured some test international standart like Test of English Foreign Language, International English Language Testing. Whereas in TOEFL test it needed higher order thinking answer, so teacher should develop students’ higher order thingking in daily teaching grammar in order to make the students’ enhance their thinking are higher. The method was used in this paper by using field study based on the experience of teaching grammar. It can be shown by students’ toefl score was less in stucture and written expression. The result of this paper was after teacher gave some treatments to enhance students’ higher order thinking in teaching grammar, the students’ toefl scores are sufficient enough as a part of stucture and written expression. It can concluded that it needed some strategies to enhancce students higher order thinking by teaching grammar it can make students’ higher toefl score. Teachers should be creative and inovative to teach the students’ started from giving the students’ question or test in teaching grammar.

  16. On higher-order corrections in M theory

    International Nuclear Information System (INIS)

    Howe, P.S.; Tsimpis, D.

    2003-01-01

    A theoretical analysis of higher-order corrections to D=11 supergravity is given in a superspace framework. It is shown that any deformation of D=11 supergravity for which the lowest-dimensional component of the four-form G 4 vanishes is trivial. This implies that the equations of motion of D=11 supergravity are specified by an element of a certain spinorial cohomology group and generalises previous results obtained using spinorial or pure spinor cohomology to the fully non-linear theory. The first deformation of the theory is given by an element of a different spinorial cohomology group with coefficients which are local tensorial functions of the massless supergravity fields. The four-form Bianchi Identities are solved, to first order and at dimension -{1/2}, in the case that the lowest-dimensional component of G 4 is non-zero. Moreover, it is shown how one can calculate the first-order correction to the dimension-zero torsion and thus to the supergravity equations of motion given an explicit expression for this object in terms of the supergravity fields. The version of the theory with both a four-form and a seven-form is discussed in the presence of the five-brane anomaly-cancelling term. It is shown that the supersymmetric completion of this term exists and it is argued that it is the unique anomaly-cancelling invariant at this dimension which is at least quartic in the fields. This implies that the first deformation of the theory is completely determined by the anomaly term from which one can, in principle, read off the corrections to all of the superspace field strength tensors. (author)

  17. Transparent Higher Order Sliding Mode Control for Nonlinear Master-Slave Systems without Velocity Measurement

    Directory of Open Access Journals (Sweden)

    Luis G. Garcia-Valdovinos

    2015-04-01

    Full Text Available Transparency has been a major objective in bilateral teleoperation systems, even in the absence of time delay induced by the communication channel, since a high degree of transparency would allow humans to drive the remote teleoperator as if he or she were directly interacting with the remote environment, with the remote teleoperator as a physical and sensorial extension of the operator. When fast convergence of position and force tracking errors are ensured by the control system, then complete transparency is obtained, which would ideally guarantee humans to be tightly kinaesthetically coupled. In this paper a model-free Cartesian second order sliding mode (SOSM PD control scheme for nonlinear master-slave systems is presented. The proposed scheme does not rely on velocity measurements and attains very fast convergence of position trajectories, with bounded tracking of force trajectories, rendering a high degree of transparency with lesser knowledge of the system. The degree of transparency can easily be improved by tuning a feedback gain in the force loop. A unique energy storage function is introduced; such that a similar Cartesian-based controller is implemented in the master and slave sides. The resulting properties of the Cartesian control structure allows the human operator to input directly Cartesian variables, which makes clearer the kinaesthetic coupling, thus the proposed controller becomes a suitable candidate for practical implementation. The performance of the proposed scheme is evaluated in a semi-experimental setup.

  18. Existence of solutions to second-order nonlinear coupled systems with nonlinear coupled boundary conditions

    Directory of Open Access Journals (Sweden)

    Imran Talib

    2015-12-01

    Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.

  19. Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation

    CERN Document Server

    Petráš, Ivo

    2011-01-01

    "Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...

  20. Computation of Nonlinear Backscattering Using a High-Order Numerical Method

    Science.gov (United States)

    Fibich, G.; Ilan, B.; Tsynkov, S.

    2001-01-01

    The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

  1. Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

    International Nuclear Information System (INIS)

    Liu Chunliang; Xie Xi; Chen Yinbao

    1991-01-01

    The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

  2. CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

    International Nuclear Information System (INIS)

    Roldan, Omar

    2017-01-01

    We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instance, facilitate the search for primordial non-Gaussianity in future works. It also disentangles the non-linear ISW from other effects. Finally, we provide a method which can iteratively be used to obtain the lensing solution at the desired order.

  3. CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

    Energy Technology Data Exchange (ETDEWEB)

    Roldan, Omar, E-mail: oaroldan@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972, Rio de Janeiro, RJ (Brazil)

    2017-08-01

    We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instance, facilitate the search for primordial non-Gaussianity in future works. It also disentangles the non-linear ISW from other effects. Finally, we provide a method which can iteratively be used to obtain the lensing solution at the desired order.

  4. A novel nonlinear adaptive filter using a pipelined second-order Volterra recurrent neural network.

    Science.gov (United States)

    Zhao, Haiquan; Zhang, Jiashu

    2009-12-01

    To enhance the performance and overcome the heavy computational complexity of recurrent neural networks (RNN), a novel nonlinear adaptive filter based on a pipelined second-order Volterra recurrent neural network (PSOVRNN) is proposed in this paper. A modified real-time recurrent learning (RTRL) algorithm of the proposed filter is derived in much more detail. The PSOVRNN comprises of a number of simple small-scale second-order Volterra recurrent neural network (SOVRNN) modules. In contrast to the standard RNN, these modules of a PSOVRNN can be performed simultaneously in a pipelined parallelism fashion, which can lead to a significant improvement in its total computational efficiency. Moreover, since each module of the PSOVRNN is a SOVRNN in which nonlinearity is introduced by the recursive second-order Volterra (RSOV) expansion, its performance can be further improved. Computer simulations have demonstrated that the PSOVRNN performs better than the pipelined recurrent neural network (PRNN) and RNN for nonlinear colored signals prediction and nonlinear channel equalization. However, the superiority of the PSOVRNN over the PRNN is at the cost of increasing computational complexity due to the introduced nonlinear expansion of each module.

  5. Nonlinear massive spin-2 field generated by higher derivative gravity

    International Nuclear Information System (INIS)

    Magnano, Guido; Sokolowski, Leszek M.

    2003-01-01

    We present a systematic exposition of the Lagrangian field theory for the massive spin-2 field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well-known inconsistency of the theory for a linear massive spin-2 field interacting with Einstein's gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called '(Helmholtz-)Jordan frame' and 'Einstein frame'. In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-2 field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-2 field in Einstein frame are given, and a simple but non-trivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-2 field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-2 field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected

  6. Jacobian projection reduced-order models for dynamic systems with contact nonlinearities

    Science.gov (United States)

    Gastaldi, Chiara; Zucca, Stefano; Epureanu, Bogdan I.

    2018-02-01

    In structural dynamics, the prediction of the response of systems with localized nonlinearities, such as friction dampers, is of particular interest. This task becomes especially cumbersome when high-resolution finite element models are used. While state-of-the-art techniques such as Craig-Bampton component mode synthesis are employed to generate reduced order models, the interface (nonlinear) degrees of freedom must still be solved in-full. For this reason, a new generation of specialized techniques capable of reducing linear and nonlinear degrees of freedom alike is emerging. This paper proposes a new technique that exploits spatial correlations in the dynamics to compute a reduction basis. The basis is composed of a set of vectors obtained using the Jacobian of partial derivatives of the contact forces with respect to nodal displacements. These basis vectors correspond to specifically chosen boundary conditions at the contacts over one cycle of vibration. The technique is shown to be effective in the reduction of several models studied using multiple harmonics with a coupled static solution. In addition, this paper addresses another challenge common to all reduction techniques: it presents and validates a novel a posteriori error estimate capable of evaluating the quality of the reduced-order solution without involving a comparison with the full-order solution.

  7. Oscillation criteria for first-order forced nonlinear difference equations

    OpenAIRE

    Grace Said R; Agarwal Ravi P; Smith Tim

    2006-01-01

    Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form Δx(n)+q1(n)xμ(n+1) = q2(n)xλ(n+1)+e(n), where λ, μ are the ratios of positive odd integers 0 <μ < 1 and λ > 1, are established.

  8. Dynamic Flight Simulation Utilizing High Fidelity CFD-Based Nonlinear Reduced Order Model, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — The overall technical objective of the Phase I effort is to develop a nonlinear aeroelastic solver utilizing the FUN3D generated nonlinear aerodynamic Reduced Order...

  9. Investigation of the spatial distribution of second-order nonlinearity in thermally poled optical fibers.

    Science.gov (United States)

    An, Honglin; Fleming, Simon

    2005-05-02

    The spatial distribution of second-order nonlinearity in thermally poled optical fibers was characterized by second-harmonic microscopy. The second-order nonlinearity was found to be confined to a thin layer close to the anode surface and progressed further into the silica as the poling time increased. Position uncertainty of the anode metal wire was observed to have an effect, as the nonlinear layers were found not always symmetrically located around the nearest points between the anode and cathode. Optical microscopy results were obtained on etched poled fiber cross-sections and compared with those from second-harmonic microscopy.

  10. Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion

    International Nuclear Information System (INIS)

    Xian-Qiong, Zhong; An-Ping, Xiang

    2010-01-01

    Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the case of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity. (classical areas of phenomenology)

  11. Order and chaos in the nonlinear response of driven nuclear spin systems

    Energy Technology Data Exchange (ETDEWEB)

    Brun, E; Derighetti, B; Holzner, R; Ravani, M [Zurich Univ. (Switzerland). Inst. fuer Physik

    1984-01-01

    The authors report on observations of ordered and chaotic behavior of a nonlinear system of strongly polarized nuclear spins inside the tuning coil of an NMR detector. The combined system: spins plus LC-circuit, may act as a nonlinear bistable absorber or a spin-flip laser, depending on the sign of the nuclear spin polarization. For the NMR laser experimental evidence is presented for limit-cycle behavior, sequences of bifurcations which lead to chaos, intermittency, multistability, and pronounced hysteresis effects. The experimental facts are compared with computer solutions of appropriate Bloch equations for the macroscopic order parameters.

  12. Application of higher order spectral features and support vector machines for bearing faults classification.

    Science.gov (United States)

    Saidi, Lotfi; Ben Ali, Jaouher; Fnaiech, Farhat

    2015-01-01

    Condition monitoring and fault diagnosis of rolling element bearings timely and accurately are very important to ensure the reliability of rotating machinery. This paper presents a novel pattern classification approach for bearings diagnostics, which combines the higher order spectra analysis features and support vector machine classifier. The use of non-linear features motivated by the higher order spectra has been reported to be a promising approach to analyze the non-linear and non-Gaussian characteristics of the mechanical vibration signals. The vibration bi-spectrum (third order spectrum) patterns are extracted as the feature vectors presenting different bearing faults. The extracted bi-spectrum features are subjected to principal component analysis for dimensionality reduction. These principal components were fed to support vector machine to distinguish four kinds of bearing faults covering different levels of severity for each fault type, which were measured in the experimental test bench running under different working conditions. In order to find the optimal parameters for the multi-class support vector machine model, a grid-search method in combination with 10-fold cross-validation has been used. Based on the correct classification of bearing patterns in the test set, in each fold the performance measures are computed. The average of these performance measures is computed to report the overall performance of the support vector machine classifier. In addition, in fault detection problems, the performance of a detection algorithm usually depends on the trade-off between robustness and sensitivity. The sensitivity and robustness of the proposed method are explored by running a series of experiments. A receiver operating characteristic (ROC) curve made the results more convincing. The results indicated that the proposed method can reliably identify different fault patterns of rolling element bearings based on vibration signals. Copyright © 2014 ISA

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

    Science.gov (United States)

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

    2017-04-01

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

  14. Higher-Order Program Generation

    DEFF Research Database (Denmark)

    Rhiger, Morten

    for OCaml, a dialect of ML, that provides run-time code generation for OCaml programs. We apply these byte-code combinators in semantics-directed compilation for an imperative language and in run-time specialization using type-directed partial evaluation. Finally, we present an approach to compiling goal......This dissertation addresses the challenges of embedding programming languages, specializing generic programs to specific parameters, and generating specialized instances of programs directly as executable code. Our main tools are higher-order programming techniques and automatic program generation....... It is our thesis that they synergize well in the development of customizable software. Recent research on domain-specific languages propose to embed them into existing general-purpose languages. Typed higher-order languages have proven especially useful as meta languages because they provide a rich...

  15. On nonlinear control design for autonomous chaotic systems of integer and fractional orders

    International Nuclear Information System (INIS)

    Ahmad, Wajdi M.; Harb, Ahmad M.

    2003-01-01

    In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations

  16. Frontiers of higher order fuzzy sets

    CERN Document Server

    Tahayori, Hooman

    2015-01-01

    Frontiers of Higher Order Fuzzy Sets, strives to improve the theoretical aspects of general and Interval Type-2 fuzzy sets and provides a unified representation theorem for higher order fuzzy sets. Moreover, the book elaborates on the concept of gradual elements and their integration with the higher order fuzzy sets. This book also introduces new frameworks for information granulation based on general T2FSs, IT2FSs, Gradual elements, Shadowed sets and rough sets. In particular, the properties and characteristics of the new proposed frameworks are studied. Such new frameworks are shown to be more capable to be exploited in real applications. Higher order fuzzy sets that are the result of the integration of general T2FSs, IT2FSs, gradual elements, shadowed sets and rough sets will be shown to be suitable to be applied in the fields of bioinformatics, business, management, ambient intelligence, medicine, cloud computing and smart grids. Presents new variations of fuzzy set frameworks and new areas of applicabili...

  17. Higher-order quasi-phase matched second harmonic generation in periodically poled MgO-doped stoichiometric LiTaO3

    International Nuclear Information System (INIS)

    Yu, Nan Ei; Kurimura, Sunao; Kitamura, Kenji

    2005-01-01

    A periodically poled device was investigated by using fourth-order quasi-phase-matched (QPM) second harmonic generation (SHG) in MgO-doped stoichiometric lithium tantalate (LiTaO 3 ). The effective nonlinear coefficient was found be 2.4 pm/V by using fourth-order QPM SHG at the fundamental wavelength of 1064 nm. For first-order QPM SHG, the effective value of d 33 could be 9.2 pm/V. Using the sensitive higher-order QPM SHG method, we investigated the relationship between the domain duty ratio and the conversion efficiency.

  18. Higher order harmonics of reactor neutron equation

    International Nuclear Information System (INIS)

    Li Fu; Hu Yongming; Luo Zhengpei

    1996-01-01

    The flux mapping method using the higher order harmonics of the neutron equation is proposed. Based on the bi-orthogonality of the higher order harmonics, the process and formulas for higher order harmonics calculation are derived via the source iteration method with source correction. For the first time, not only any order harmonics for up-to-3-dimensional geometry are achieved, but also the preliminary verification to the capability for flux mapping have been carried out

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

    Science.gov (United States)

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

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

  20. Higher-Order Minimal Functional Graphs

    DEFF Research Database (Denmark)

    Jones, Neil D; Rosendahl, Mads

    1994-01-01

    We present a minimal function graph semantics for a higher-order functional language with applicative evaluation order. The semantics captures the intermediate calls performed during the evaluation of a program. This information may be used in abstract interpretation as a basis for proving...

  1. Periodic solutions of certain third order nonlinear differential systems with delay

    International Nuclear Information System (INIS)

    Tejumola, H.O.; Afuwape, A.U.

    1990-12-01

    This paper investigates the existence of 2π-periodic solutions of systems of third-order nonlinear differential equations, with delay, under varied assumptions. The results obtained extend earlier works of Tejumola and generalize to third order systems those of Conti, Iannacci and Nkashama as well as DePascale and Iannacci and Iannacci and Nkashama. 16 refs

  2. Higher-Order Generalized Invexity in Control Problems

    Directory of Open Access Journals (Sweden)

    S. K. Padhan

    2011-01-01

    Full Text Available We introduce a higher-order duality (Mangasarian type and Mond-Weir type for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal problems, higher-order duality results (weak duality, strong duality, and converse duality are derived for these pair of problems. Also, we establish few examples in support of our investigation.

  3. Higher-order rogue wave solutions of the three-wave resonant interaction equation via the generalized Darboux transformation

    International Nuclear Information System (INIS)

    Wang, Xin; Chen, Yong; Cao, Jianli

    2015-01-01

    In this paper, we utilize generalized Darboux transformation to study higher-order rogue wave solutions of the three-wave resonant interaction equation, which describes the propagation and mixing of waves with different frequencies in weakly nonlinear dispersive media. A general Nth-order rogue wave solution with two characteristic velocities structural parameters and 3N independent parameters under a determined plane-wave background and a specific parameter condition is derived. As an application, we show that four fundamental rogue waves with fundamental, two kinds of line and quadrilateral patterns, or six fundamental rogue waves with fundamental, triangular, two kinds of quadrilateral and circular patterns can emerge in the second-order rogue waves. Moreover, several important wave characteristics including the maximum values, the corresponding coordinate positions of the humps, and the stability problem for some special higher-order rogue wave solutions such as the fundamental and quadrilateral cases are discussed. (paper)

  4. Computation of nonlinear water waves with a high-order Boussinesq model

    DEFF Research Database (Denmark)

    Fuhrman, David R.; Madsen, Per A.; Bingham, Harry

    2005-01-01

    Computational highlights from a recently developed high-order Boussinesq model are shown. The model is capable of treating fully nonlinear waves (up to the breaking point) out to dimensionless depths of (wavenumber times depth) kh \\approx 25. Cases considered include the study of short......-crested waves in shallow/deep water, resulting in hexagonal/rectangular surface patterns; crescent waves, resulting from unstable perturbations of plane progressive waves; and highly-nonlinear wave-structure interactions. The emphasis is on physically demanding problems, and in eachcase qualitative and (when...

  5. Higher order antibunching in intermediate states

    International Nuclear Information System (INIS)

    Verma, Amit; Sharma, Navneet K.; Pathak, Anirban

    2008-01-01

    Since the introduction of binomial state as an intermediate state, different intermediate states have been proposed. Different nonclassical effects have also been reported in these intermediate states. But till now higher order antibunching is predicted in only one type of intermediate state, which is known as shadowed negative binomial state. Recently we have shown that the higher order antibunching is not a rare phenomenon [P. Gupta, P. Pandey, A. Pathak, J. Phys. B 39 (2006) 1137]. To establish our earlier claim further, here we have shown that the higher order antibunching can be seen in different intermediate states, such as binomial state, reciprocal binomial state, hypergeometric state, generalized binomial state, negative binomial state and photon added coherent state. We have studied the possibility of observing the higher order subpoissonian photon statistics in different limits of intermediate states. The effects of different control parameters on the depth of non classicality have also been studied in this connection and it has been shown that the depth of nonclassicality can be tuned by controlling various physical parameters

  6. Nonlinear spectroscopic studies of interfacial molecular ordering

    International Nuclear Information System (INIS)

    Superfine, R.

    1991-07-01

    The second order nonlinear optical processes of second harmonic generation and sum frequency generation are powerful new probes of surfaces. They possess unusual surface sensitivity due to the symmetry properties of the nonlinear susceptibility. In particular, infrared-visible sum frequency generation (SFG) can obtain the vibrational spectrum of sub-monolayer coverages of molecules. In this thesis, we explore the unique information that can be obtained from SFG. We take advantage of the sensitivity of SFG to the conformation of alkane chains to study the interaction between adsorbed liquid crystal molecules and surfactant treated surfaces. The sign of the SFG susceptibility depends on the sign of the molecular polarizability and the orientation, up or down, of the molecule. We experimentally determine the sign of the susceptibility and use it to determine the absolute orientation to obtain the sign of the molecular polarizability and show that this quantity contains important information about the dynamics of molecular charge distributions. Finally, we study the vibrational spectra and the molecular orientation at the pure liquid/vapor interface of methanol and water and present the most detailed evidence yet obtained for the structure of the pure water surface. 32 refs., 4 figs., 2 tabs

  7. A Higher-Order Colon Translation

    DEFF Research Database (Denmark)

    Danvy, Olivier; Nielsen, Lasse Reichstein

    2001-01-01

    A lambda-encoding such as the CPS transformation gives rise to administrative redexes. In his seminal article ``Call-by-name, call-by-value and the lambda-calculus'', 25 years ago, Plotkin tackled administrative reductions using a so-called ``colon translation.'' 10 years ago, Danvy and Filinski...... integrated administrative reductions in the CPS transformation, making it operate in one pass. The technique applies to other lambda-encodings (e.g., variants of CPS), but we do not see it used in practice--instead, Plotkin's colon translation appears to be favored. Therefore, in an attempt to link both...... techniques, we recast Plotkin's proof of Indifference and Simulation to the higher-order specification of the one-pass CPS transformation. To this end, we extend his colon translation from first order to higher order...

  8. A novel nature inspired firefly algorithm with higher order neural network: Performance analysis

    Directory of Open Access Journals (Sweden)

    Janmenjoy Nayak

    2016-03-01

    Full Text Available The applications of both Feed Forward Neural network and Multilayer perceptron are very diverse and saturated. But the linear threshold unit of feed forward networks causes fast learning with limited capabilities, while due to multilayering, the back propagation of errors exhibits slow training speed in MLP. So, a higher order network can be constructed by correlating between the input variables to perform nonlinear mapping using the single layer of input units for overcoming the above drawbacks. In this paper, a Firefly based higher order neural network has been proposed for data classification for maintaining fast learning and avoids the exponential increase of processing units. A vast literature survey has been conducted to review the state of the art of the previous developed models. The performance of the proposed method has been tested with various benchmark datasets from UCI machine learning repository and compared with the performance of other established models. Experimental results imply that the proposed method is fast, steady, reliable and provides better classification accuracy than others.

  9. Large third-order optical nonlinearity of silver colloids in silica glasses synthesized by ion implantation

    International Nuclear Information System (INIS)

    Ghosh, Binita; Chakraborty, Purushottam

    2011-01-01

    Silver ion implantations in fused silica glasses have been made to synthesize silver nanocluster-glass composites and a combination of 'Anti-Resonant Interferometric Nonlinear Spectroscopy (ARINS)' and 'Z-scan' techniques has been employed for the measurement of the third-order optical susceptibility of these nanocomposites. The ARINS technique utilizes the dressing of two unequal-intensity counter-propagating pulsed optical beams with differential nonlinear phases, which occurs upon traversing the sample. This difference in phase manifests itself in the intensity-dependent transmission, measurement of which enables us to extract the values of nonlinear refractive index (η 2 ) and nonlinear absorption coefficient (β), finally yielding the real and imaginary parts of the third-order dielectric susceptibility (χ (3) ). The real and imaginary parts of χ (3) are obtained in the orders of 10 -10 e.s.u for silver nanocluster-glass composites. The present value of χ (3) , to our knowledge, is extremely accurate and much more reliable compared to the values previously obtained by other workers for similar silver-glass nanocomposites using only Z-scan technique. Optical nonlinearity has been explained to be due to two-photon absorption in the present nanocomposite glasses and is essentially of electronic origin.

  10. A Paraconsistent Higher Order Logic

    DEFF Research Database (Denmark)

    Villadsen, Jørgen

    2004-01-01

    of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order...... of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens. Many non-classical logics are, at the propositional level, funny toys which work quite good, but when one wants...

  11. Third-order optical nonlinearity of N-doped graphene oxide nanocomposites at different GO ratios

    Science.gov (United States)

    Kimiagar, Salimeh; Abrinaei, Fahimeh

    2018-05-01

    In the present work, the influence of GO ratios on the structural, linear and nonlinear optical properties of nitrogen-doped graphene oxide nanocomposites (N-GO NCs) has been studied. N-GO NCs were synthesized by hydrothermal method. The XRD, FTIR, SEM, and TEM results confirmed the reduction of GO by nitrogen doping. The energy band gaps of N-GO NCs calculated from UV-Vis analyzed by using Tauc plot. To obtain further insight into potential optical changes in the N-GO NCs by increasing GO contents, Z-scan analysis was performed with nanosecond Nd-YAG laser at 532 nm. The nonlinear absorption coefficient, β, and nonlinear refractive index, n2, for N-GO NCs at the laser intensity of 113 MW/cm were measured and an increase was observed in both parameters after addition of nitrogen to GO. The third-order nonlinear optical susceptibilities of N-GO NCs were measured in the order of 10-9 esu. The results showed that N-GO NCs have negative nonlinearity which can be controlled by GO contents to obtain the highest values for nonlinear optical parameters. The nonlinear optical results not only imply that N-GO NCs can serve as an important material in the advancing of optoelectronics but also open new possibilities for the design of new graphene-based materials by variation of N and GO ratios as well as manufacturing conditions.

  12. Higher-order force gradient symplectic algorithms

    Science.gov (United States)

    Chin, Siu A.; Kidwell, Donald W.

    2000-12-01

    We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10, and 12, the new algorithms are approximately a factor of 103, 104, 104, and 105 better.

  13. Chaos control of third-order phase-locked loops using backstepping nonlinear controller

    International Nuclear Information System (INIS)

    Harb, Ahmad M.; Harb, Bassam A.

    2004-01-01

    Previous study showed that a third-order phase-locked loop (PLL) with sinusoidal phase detector characteristics experienced a Hopf bifurcation point as well as chaotic behavior. As a result, this behavior drives the PLL to the out-of-lock (unstable) state. The analysis was based on a modern nonlinear theory such as bifurcation and chaos. The main goal of this paper is to control this chaotic behavior. A nonlinear controller based on the theory of backstepping is designed. The study showed the effectiveness of the designed nonlinear controller in controlling the undesirable unstable behavior and pulling the PLL back to the in-lock state

  14. The non-linear ion trap. Part 5. Nature of non-linear resonances and resonant ion ejection

    Science.gov (United States)

    Franzen, J.

    1994-01-01

    The superposition of higher order multipole fields on the basic quadrupole field in ion traps generates a non-harmonic oscillator system for the ions. Fourier analyses of simulated secular oscillations in non-linear ion traps, therefore, not only reveal the sideband frequencies, well-known from the Mathieu theory, but additionally a commonwealth of multipole-specific overtones (or higher harmonics), and corresponding sidebands of overtones. Non-linear resonances occur when the overtone frequencies match sideband frequencies. It can be shown that in each of the resonance conditions, not just one overtone matches one sideband, instead, groups of overtones match groups of sidebands. The generation of overtones is studied by Fourier analysis of computed ion oscillations in the direction of thez axis. Even multipoles (octopole, dodecapole, etc.) generate only odd orders of higher harmonics (3, 5, etc.) of the secular frequency, explainable by the symmetry with regard to the planez = 0. In contrast, odd multipoles (hexapole, decapole, etc.) generate all orders of higher harmonics. For all multipoles, the lowest higher harmonics are found to be strongest. With multipoles of higher orders, the strength of the overtones decreases weaker with the order of the harmonics. Forz direction resonances in stationary trapping fields, the function governing the amplitude growth is investigated by computer simulations. The ejection in thez direction, as a function of timet, follows, at least in good approximation, the equation wheren is the order of multipole, andC is a constant. This equation is strictly valid for the electrically applied dipole field (n = 1), matching the secular frequency or one of its sidebands, resulting in a linear increase of the amplitude. It is valid also for the basic quadrupole field (n = 2) outside the stability area, giving an exponential increase. It is at least approximately valid for the non-linear resonances by weak superpositions of all higher odd

  15. Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models

    Science.gov (United States)

    Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.

    2011-01-01

    We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.

  16. Skinner-Rusk unified formalism for higher-order systems

    Science.gov (United States)

    Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

    2012-07-01

    The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, first-order and higher-order field theories, and higher-order autonomous systems. In this work we present a generalization of this formalism for higher-order non-autonomous mechanical systems.

  17. Nonlinear dynamics of an electrically actuated imperfect microbeam resonator: Experimental investigation and reduced-order modeling

    KAUST Repository

    Ruzziconi, Laura

    2013-06-10

    We present a study of the dynamic behavior of a microelectromechanical systems (MEMS) device consisting of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected, the first four experimental natural frequencies are identified and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. Several backward and forward frequency sweeps are acquired. The nonlinear behavior is highlighted, which includes ranges of multistability, where the nonresonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is also capable of capturing the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach. © 2013 IOP Publishing Ltd.

  18. Ablation and optical third-order nonlinearities in Ag nanoparticles

    Directory of Open Access Journals (Sweden)

    Carlos Torres-Torres

    2010-11-01

    Full Text Available Carlos Torres-Torres1, Néstor Peréa-López2, Jorge Alejandro Reyes-Esqueda3, Luis Rodríguez-Fernández3, Alejandro Crespo-Sosa3, Juan Carlos Cheang-Wong3, Alicia Oliver31Section of Graduate Studies and Research, School of Mechanical and Electrical Engineering, National Polytechnic Institute, Zacatenco, Distrito Federal, Mexico; 2Laboratory for Nanoscience and Nanotechnology Research and Advanced Materials Department, IPICYT, Camino a la Presa San Jose, San Luis Potosi, Mexico; 3Instituto de Física, Universidad Nacional Autónoma de México, A.P. 20-364, México, D.F. 01000, MéxicoAbstract: The optical damage associated with high intensity laser excitation of silver nanoparticles (NPs was studied. In order to investigate the mechanisms of optical nonlinearity of a nanocomposite and their relation with its ablation threshold, a high-purity silica sample implanted with Ag ions was exposed to different nanosecond and picosecond laser irradiations. The magnitude and sign of picosecond refractive and absorptive nonlinearities were measured near and far from the surface plasmon resonance (SPR of the Ag NPs with a self-diffraction technique. Saturable optical absorption and electronic polarization related to self-focusing were identified. Linear absorption is the main process involved in nanosecond laser ablation, but nonlinearities are important for ultrashort picosecond pulses when the absorptive process become significantly dependent on the irradiance. We estimated that near the resonance, picosecond intraband transitions allow an expanded distribution of energy among the NPs, in comparison to the energy distribution resulting in a case of far from resonance, when the most important absorption takes place in silica. We measured important differences in the ablation threshold and we estimated that the high selectiveness of the SPR of Ag NPs as well as their corresponding optical nonlinearities can be strongly significant for laser

  19. Explicit formulation of second and third order optical nonlinearity in the FDTD framework

    Science.gov (United States)

    Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

    2018-01-01

    The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

  20. Non-linear second-order periodic systems with non-smooth potential

    Indian Academy of Sciences (India)

    In this paper we study second order non-linear periodic systems driven by the ordinary vector -Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on ...

  1. Non-linear second-order periodic systems with non-smooth potential

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Abstract. In this paper we study second order non-linear periodic systems driven by the ordinary vector p-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth ...

  2. Higher-order curvature terms and extended inflation

    International Nuclear Information System (INIS)

    Wang Yun

    1990-01-01

    We consider higher-order curvature terms in context of the Brans-Dicke theory of gravity, and investigate the effects of these terms on extended inflationary theories. We find that the higher-order curvature terms tend to speed up inflation, although the original extended-inflation solutions are stable when these terms are small. Analytical solutions are found for two extreme cases: when the higher-order curvature terms are small, and when they dominate. A conformal transformation is employed in solving the latter case, and some of the subtleties in this technique are discussed. We note that percolation is less likely to occur when the higher-order curvature terms are present. An upper bound on α is expected if we are to avoid excessive and inadequate percolation of true-vacuum bubbles

  3. Static aeroelastic analysis including geometric nonlinearities based on reduced order model

    Directory of Open Access Journals (Sweden)

    Changchuan Xie

    2017-04-01

    Full Text Available This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model (ROM. The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities; meanwhile, the non-planar effects of aerodynamics and follower force effect have been considered. ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method (FEM especially in aeroelastic solutions. The approach for structure modeling presented here is on the basis of combined modal/finite element (MFE method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis. Moreover, the non-planar aerodynamic force is computed by the non-planar vortex lattice method (VLM. Structure and aerodynamics can be coupled with the surface spline method. The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.

  4. Higher order mode optical fiber Raman amplifiers

    DEFF Research Database (Denmark)

    Rottwitt, Karsten; Friis, Søren Michael Mørk; Usuga Castaneda, Mario A.

    2016-01-01

    We review higher order mode Raman amplifiers and discuss recent theoretical as well as experimental results including system demonstrations.......We review higher order mode Raman amplifiers and discuss recent theoretical as well as experimental results including system demonstrations....

  5. Second order nonlinear optical properties of zinc oxide films deposited by low temperature dual ion beam sputtering

    International Nuclear Information System (INIS)

    Larciprete, M.C.; Passeri, D.; Michelotti, F.; Paoloni, S.; Sibilia, C.; Bertolotti, M.; Belardini, A.; Sarto, F.; Somma, F.; Lo Mastro, S.

    2005-01-01

    We investigated second order optical nonlinearity of zinc oxide thin films, grown on glass substrates by the dual ion beam sputtering technique under different deposition conditions. Linear optical characterization of the films was carried out by spectrophotometric optical transmittance and reflectance measurements, giving the complex refractive index dispersion. Resistivity of the films was determined using the four-point probe sheet resistance method. Second harmonic generation measurements were performed by means of the Maker fringes technique where the fundamental beam was originated by nanosecond laser at λ=1064 nm. We found a relatively high nonlinear optical response, and evidence of a dependence of the nonlinear coefficient on the deposition parameters for each sample. Moreover, the crystalline properties of the films were investigated by x-ray diffraction measurements and correlation with second order nonlinearity were analyzed. Finally, we investigated the influence of the oxygen flow rate during the deposition process on both the second order nonlinearity and the structural properties of the samples

  6. Nonlocal higher order evolution equations

    KAUST Repository

    Rossi, Julio D.

    2010-06-01

    In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.

  7. Third-order nonlinear optical properties of ADP crystal

    Science.gov (United States)

    Wang, Mengxia; Wang, Zhengping; Chai, Xiangxu; Sun, Yuxiang; Sui, Tingting; Sun, Xun; Xu, Xinguang

    2018-05-01

    By using the Z-scan method, we investigated the third-order nonlinear optical (NLO) properties of ADP crystal at different wavelengths (355, 532, and 1064 nm) and different orientations ([001], [100], [110], I and II). The experimental data were fitted by NLO theory, to give out the two photon absorption (TPA) coefficient β 2 and the nonlinear refractive index n 2. When the light source changed from a 40 ps, 1064 nm fundamental laser to a 30 ps, 355 nm third-harmonic-generation (THG) laser, the β 2 value increased about 5 times (0.2 × 10‑2 → 1 × 10‑2 cm GW‑1), and the n 2 value increased about 1.5 times (1.5 × 10‑16 → 2.2 × 10‑16 cm2 W‑1). Among all of the orientations, the [110] sample exhibits the smallest β 2, and the second smallest n 2. It indicates that this orientation and its surroundings will be the preferred directions for high-power laser applications of ADP crystal.

  8. Distributed ESO based cooperative tracking control for high-order nonlinear multiagent systems with lumped disturbance and application in multi flight simulators systems.

    Science.gov (United States)

    Cong, Zhang

    2018-03-01

    Based on extended state observer, a novel and practical design method is developed to solve the distributed cooperative tracking problem of higher-order nonlinear multiagent systems with lumped disturbance in a fixed communication topology directed graph. The proposed method is designed to guarantee all the follower nodes ultimately and uniformly converge to the leader node with bounded residual errors. The leader node, modeled as a higher-order non-autonomous nonlinear system, acts as a command generator giving commands only to a small portion of the networked follower nodes. Extended state observer is used to estimate the local states and lumped disturbance of each follower node. Moreover, each distributed controller can work independently only requiring the relative states and/or the estimated relative states information between itself and its neighbors. Finally an engineering application of multi flight simulators systems is demonstrated to test and verify the effectiveness of the proposed algorithm. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  9. Ultra-fast dynamics in the nonlinear optical response of silver nanoprism ordered arrays.

    Science.gov (United States)

    Sánchez-Esquivel, Héctor; Raygoza-Sanchez, Karen Y; Rangel-Rojo, Raúl; Kalinic, Boris; Michieli, Niccolò; Cesca, Tiziana; Mattei, Giovanni

    2018-03-15

    In this work we present the study of the ultra-fast dynamics of the nonlinear optical response of a honeycomb array of silver triangular nanoprisms, performed using a femtosecond pulsed laser tuned with the dipolar surface plasmon resonance of the nanoarray. Nonlinear absorption and refraction, and their time-dependence, were explored using the z-scan and time-resolved excite-probe techniques. Nonlinear absorption is shown to change sign with the input irradiance and the behavior was explained on the basis of a three-level model. The response time was determined to be in the picosecond regime. A technique based on a variable frequency chopper was also used in order to discriminate the thermal and electronic contributions to the nonlinearity, which were found to have opposite signs. All these findings propel the investigated nanoprism arrays as good candidates for applications in advanced ultra-fast nonlinear nanophotonic devices.

  10. Conceptualizing and Assessing Higher-Order Thinking in Reading

    Science.gov (United States)

    Afflerbach, Peter; Cho, Byeong-Young; Kim, Jong-Yun

    2015-01-01

    Students engage in higher-order thinking as they read complex texts and perform complex reading-related tasks. However, the most consequential assessments, high-stakes tests, are currently limited in providing information about students' higher-order thinking. In this article, we describe higher-order thinking in relation to reading. We provide a…

  11. Application of Mass Lumped Higher Order Finite Elements

    International Nuclear Information System (INIS)

    J. Chen, H.R. Strauss, S.C. Jardin, W. Park, L.E. Sugiyama, G. Fu, J. Breslau

    2005-01-01

    There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied

  12. Effect of higher order nonlinearity, directionality and finite water depth on wave statistics: Comparison of field data and numerical simulations

    Science.gov (United States)

    Fernández, Leandro; Monbaliu, Jaak; Onorato, Miguel; Toffoli, Alessandro

    2014-05-01

    This research is focused on the study of nonlinear evolution of irregular wave fields in water of arbitrary depth by comparing field measurements and numerical simulations.It is now well accepted that modulational instability, known as one of the main mechanisms for the formation of rogue waves, induces strong departures from Gaussian statistics. However, whereas non-Gaussian properties are remarkable when wave fields follow one direction of propagation over an infinite water depth, wave statistics only weakly deviate from Gaussianity when waves spread over a range of different directions. Over finite water depth, furthermore, wave instability attenuates overall and eventually vanishes for relative water depths as low as kh=1.36 (where k is the wavenumber of the dominant waves and h the water depth). Recent experimental results, nonetheless, seem to indicate that oblique perturbations are capable of triggering and sustaining modulational instability even if khthe aim of this research is to understand whether the combined effect of directionality and finite water depth has a significant effect on wave statistics and particularly on the occurrence of extremes. For this purpose, numerical experiments have been performed solving the Euler equation of motion with the Higher Order Spectral Method (HOSM) and compared with data of short crested wave fields for different sea states observed at the Lake George (Australia). A comparative analysis of the statistical properties (i.e. density function of the surface elevation and its statistical moments skewness and kurtosis) between simulations and in-situ data provides a confrontation between the numerical developments and real observations in field conditions.

  13. Third-order nonlinear optical properties of thin sputtered gold films

    Science.gov (United States)

    Xenogiannopoulou, E.; Aloukos, P.; Couris, S.; Kaminska, E.; Piotrowska, A.; Dynowska, E.

    2007-07-01

    Au films of thickness ranging between 5 and 52 nm were prepared by sputtering on quartz substrates and their third-order nonlinear optical response was investigated by Optical Kerr effect (OKE) and Z-scan techniques using 532 nm, 35 ps laser pulses. All prepared films were characterized by XRD, AFM and UV-VIS-NIR spectrophotometry while their third-order susceptibility χ(3) was measured and found to be of the order of 10 -9 esu. The real and imaginary parts of the third-order susceptibility were found in very good agreement with experimental results and theoretical predictions reported by Smith et al. [D.D. Smith, Y. Yoon, R.W. Boyd, Y.K. Cambell, L.A. Baker, R.M. Crooks, M. George, J. Appl. Phys. 86 (1999) 6200].

  14. Third-order nonlinear optical response of Ag-CdSe/PVA hybrid nanocomposite

    Energy Technology Data Exchange (ETDEWEB)

    Tripathi, S.K.; Kaur, Ramneek; Kaur, Jaspreet; Sharma, Mamta [Panjab University, Department of Physics, Center of Advanced Study in Physics, Chandigarh (India)

    2015-09-15

    Hybrid nanocomposites of II-VI semiconductor nanoparticles are gaining great interest in nonlinear optoelectronic devices. Present work includes the characterization of CdSe polymer nanocomposite prepared by chemical in situ technique. From X-ray diffraction, the hexagonal wurtzite structure of nanoparticles has been confirmed with spherical morphology from transmission electron microscopy. Ag-CdSe hybrid polymer nanocomposite has been prepared chemically at different Ag concentrations. The presence of Ag in hybrid nanocomposite has been confirmed with energy-dispersive X-ray spectroscopy. The effect of varying Ag concentration on the linear and nonlinear optical properties of the nanocomposites has been studied. In linear optical parameters, the linear absorption coefficient, refractive index, extinction coefficient and optical conductivity have been calculated. The third-order nonlinear optical properties have been observed with open- and closed-aperture Z-scan technique. The large nonlinear refractive index ∝10{sup -5} cm{sup 2}/W with self-focusing behaviour is due to the combined effect of quantum confinement and thermo-optical effects. The enhanced nonlinearity with increasing Ag content is due to the surface plasmon resonance, which enhances the local electric field near the nanoparticle surface. Thus, Ag-CdSe hybrid polymer nanocomposite has favourable nonlinear optical properties for various optoelectronic applications. (orig.)

  15. Third-order nonlinear optical response of Ag-CdSe/PVA hybrid nanocomposite

    International Nuclear Information System (INIS)

    Tripathi, S.K.; Kaur, Ramneek; Kaur, Jaspreet; Sharma, Mamta

    2015-01-01

    Hybrid nanocomposites of II-VI semiconductor nanoparticles are gaining great interest in nonlinear optoelectronic devices. Present work includes the characterization of CdSe polymer nanocomposite prepared by chemical in situ technique. From X-ray diffraction, the hexagonal wurtzite structure of nanoparticles has been confirmed with spherical morphology from transmission electron microscopy. Ag-CdSe hybrid polymer nanocomposite has been prepared chemically at different Ag concentrations. The presence of Ag in hybrid nanocomposite has been confirmed with energy-dispersive X-ray spectroscopy. The effect of varying Ag concentration on the linear and nonlinear optical properties of the nanocomposites has been studied. In linear optical parameters, the linear absorption coefficient, refractive index, extinction coefficient and optical conductivity have been calculated. The third-order nonlinear optical properties have been observed with open- and closed-aperture Z-scan technique. The large nonlinear refractive index ∝10 -5 cm 2 /W with self-focusing behaviour is due to the combined effect of quantum confinement and thermo-optical effects. The enhanced nonlinearity with increasing Ag content is due to the surface plasmon resonance, which enhances the local electric field near the nanoparticle surface. Thus, Ag-CdSe hybrid polymer nanocomposite has favourable nonlinear optical properties for various optoelectronic applications. (orig.)

  16. High-order optical nonlinearities in nanocomposite films dispersed with semiconductor quantum dots at high concentrations

    International Nuclear Information System (INIS)

    Tomita, Yasuo; Matsushima, Shun-suke; Yamagami, Ryu-ichi; Jinzenji, Taka-aki; Sakuma, Shohei; Liu, Xiangming; Izuishi, Takuya; Shen, Qing

    2017-01-01

    We describe the nonlinear optical properties of inorganic-organic nanocomposite films in which semiconductor CdSe quantum dots as high as 6.8 vol.% are dispersed. Open/closed Z-scan measurements, degenerate multi-wave mixing and femtosecond pump-probe/transient grating measurements are conducted. It is shown that the observed fifth-order optical nonlinearity has the cascaded third-order contribution that becomes prominent at high concentrations of CdSe QDs. It is also shown that there are picosecond-scale intensity-dependent and nanosecond-scale intensity-independent decay components in absorptive and refractive nonlinearities. The former is caused by the Auger process, while the latter comes from the electron-hole recombination process. (paper)

  17. Higher-order techniques in computational electromagnetics

    CERN Document Server

    Graglia, Roberto D

    2016-01-01

    Higher-Order Techniques in Computational Electromagnetics explains 'high-order' techniques that can significantly improve the accuracy, computational cost, and reliability of computational techniques for high-frequency electromagnetics, such as antennas, microwave devices and radar scattering applications.

  18. Nonclassical properties of a contradirectional nonlinear optical coupler

    Energy Technology Data Exchange (ETDEWEB)

    Thapliyal, Kishore [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); Pathak, Anirban, E-mail: anirban.pathak@gmail.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); RCPTM, Joint Laboratory of Optics of Palacky University and Institute of Physics of Academy of Science of the Czech Republic, Faculty of Science, Palacky University, 17. listopadu 12, 771 46 Olomouc (Czech Republic); Sen, Biswajit [Department of Physics, Vidyasagar Teachers' Training College, Midnapore 721101 (India); Perřina, Jan [RCPTM, Joint Laboratory of Optics of Palacky University and Institute of Physics of Academy of Science of the Czech Republic, Faculty of Science, Palacky University, 17. listopadu 12, 771 46 Olomouc (Czech Republic); Department of Optics, Palacky University, 17. listopadu 12, 771 46 Olomouc (Czech Republic)

    2014-10-24

    We investigate the nonclassical properties of output fields propagated through a contradirectional asymmetric nonlinear optical coupler consisting of a linear waveguide and a nonlinear (quadratic) waveguide operated by second harmonic generation. In contrast to the earlier results, all the initial fields are considered weak and a completely quantum-mechanical model is used here to describe the system. Perturbative solutions of Heisenberg's equations of motion for various field modes are obtained using Sen–Mandal technique. Obtained solutions are subsequently used to show the existence of single-mode and intermodal squeezing, single-mode and intermodal antibunching, two-mode and multi-mode entanglement in the output of contradirectional asymmetric nonlinear optical coupler. Further, existence of higher order nonclassicality is also established by showing the existence of higher order antibunching, higher order squeezing and higher order entanglement. Variation of observed nonclassical characters with different coupling constants and phase mismatch is discussed. - Highlights: • Nonclassicalities in fields propagating through a directional coupler is studied. • Completely quantum-mechanical description of the coupler is provided. • Analytic solutions of Heisenberg equations of motion for various modes are obtained. • Existence of lower order and higher order entanglement is shown. • Variation of nonclassicalities with phase-mismatch and coupling constants is studied.

  19. Studies on third-order optical nonlinearity and power limiting of conducting polymers using the z-scan technique for nonlinear optical applications

    International Nuclear Information System (INIS)

    Pramodini, S; Poornesh, P; Sudhakar, Y N; SelvaKumar, M

    2014-01-01

    We present the synthesis and characterization of third-order optical nonlinearity and optical limiting of the conducting polymers poly (aniline-co-o-anisidine) and poly (aniline-co-pyrrole). Nonlinear optical studies were carried out by employing the z-scan technique using a He–Ne laser operating in continuous wave mode at 633 nm. The copolymers exhibited a reverse saturable absorption process and self-defocusing properties under the experimental conditions. The estimated values of β eff , n 2 and χ (3) were found to be of the order of 10 −2  cm W −1 , 10 -5  esu and 10 −7  esu respectively. Self-diffraction rings were observed due to refractive index change when exposed to the laser beam. The copolymers possess a lower limiting threshold and clamping level, which is essential to a great extent for power limiting devices. Therefore, copolymers of aniline emerge as a potential candidate for nonlinear optical device applications. (paper)

  20. Studies on third-order optical nonlinearity and power limiting of conducting polymers using the z-scan technique for nonlinear optical applications

    Science.gov (United States)

    Pramodini, S.; Sudhakar, Y. N.; SelvaKumar, M.; Poornesh, P.

    2014-04-01

    We present the synthesis and characterization of third-order optical nonlinearity and optical limiting of the conducting polymers poly (aniline-co-o-anisidine) and poly (aniline-co-pyrrole). Nonlinear optical studies were carried out by employing the z-scan technique using a He-Ne laser operating in continuous wave mode at 633 nm. The copolymers exhibited a reverse saturable absorption process and self-defocusing properties under the experimental conditions. The estimated values of βeff, n2 and χ(3) were found to be of the order of 10-2 cm W-1, 10-5 esu and 10-7 esu respectively. Self-diffraction rings were observed due to refractive index change when exposed to the laser beam. The copolymers possess a lower limiting threshold and clamping level, which is essential to a great extent for power limiting devices. Therefore, copolymers of aniline emerge as a potential candidate for nonlinear optical device applications.

  1. Axion as a Cold Dark Matter Candidate: Proof to Fully Nonlinear Order

    Energy Technology Data Exchange (ETDEWEB)

    Noh, Hyerim [Center for Large Telescope, Korea Astronomy and Space Science Institute, Daejon (Korea, Republic of); Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu (Korea, Republic of); Park, Chan-Gyung [Division of Science Education and Institute of Fusion Science, Chonbuk National University, Jeonju (Korea, Republic of)

    2017-09-01

    We present proof of the axion as a cold dark matter (CDM) candidate to the fully nonlinear order perturbations based on Einstein’s gravity. We consider the axion as a coherently oscillating massive classical scalar field without interaction. We present the fully nonlinear and exact, except for ignoring the transverse-tracefree tensor-type perturbation, hydrodynamic equations for an axion fluid in Einstein’s gravity. We show that the axion has the characteristic pressure and anisotropic stress; the latter starts to appear from the second-order perturbation. But these terms do not directly affect the hydrodynamic equations in our axion treatment. Instead, what behaves as the effective pressure term in relativistic hydrodynamic equations is the perturbed lapse function and the relativistic result coincides exactly with the one known in the previous non-relativistic studies. The effective pressure term leads to a Jeans scale that is of the solar-system scale for conventional axion mass. As the fully nonlinear and relativistic hydrodynamic equations for an axion fluid coincide exactly with the ones of a zero-pressure fluid in the super-Jeans scale, we have proved the CDM nature of such an axion in that scale.

  2. Classification of stable solutions for non-homogeneous higher-order elliptic PDEs

    Directory of Open Access Journals (Sweden)

    Abdellaziz Harrabi

    2017-04-01

    Full Text Available Abstract Under some assumptions on the nonlinearity f, we will study the nonexistence of nontrivial stable solutions or solutions which are stable outside a compact set of R n $\\mathbb {R}^{n}$ for the following semilinear higher-order problem: ( − Δ k u = f ( u in  R n , $$\\begin{aligned} (-\\Delta^{k} u= f(u \\quad \\mbox{in }\\mathbb {R}^{n}, \\end{aligned}$$ with k = 1 , 2 , 3 , 4 $k=1,2,3,4$ . The main methods used are the integral estimates and the Pohozaev identity. Many classes of nonlinearity will be considered; even the sign-changing nonlinearity, which has an adequate subcritical growth at zero as for example f ( u = − m u + λ | u | θ − 1 u − μ | u | p − 1 u $f(u= -m u +\\lambda|u|^{\\theta-1}u-\\mu |u|^{p-1}u$ , where m ≥ 0 $m\\geq0$ , λ > 0 $\\lambda>0$ , μ > 0 $\\mu>0$ , p , θ > 1 $p, \\theta>1$ . More precisely, we shall revise the nonexistence theorem of Berestycki and Lions (Arch. Ration. Mech. Anal. 82:313-345, 1983 in the class of smooth finite Morse index solutions as the well known work of Bahri and Lions (Commun. Pure Appl. Math. 45:1205-1215, 1992. Also, the case when f ( u u $f(uu$ is a nonnegative function will be studied under a large subcritical growth assumption at zero, for example f ( u = | u | θ − 1 u ( 1 + | u | q $f(u=|u|^{\\theta-1}u(1 + |u|^{q}$ or f ( u = | u | θ − 1 u e | u | q $f(u= |u|^{\\theta-1}u e^{|u|^{q}}$ , θ > 1 $\\theta>1$ and q > 0 $q>0$ . Extensions to solutions which are merely stable are discussed in the case of supercritical growth with k = 1 $k=1$ .

  3. Analogy, higher order thinking, and education.

    Science.gov (United States)

    Richland, Lindsey Engle; Simms, Nina

    2015-01-01

    Analogical reasoning, the ability to understand phenomena as systems of structured relationships that can be aligned, compared, and mapped together, plays a fundamental role in the technology rich, increasingly globalized educational climate of the 21st century. Flexible, conceptual thinking is prioritized in this view of education, and schools are emphasizing 'higher order thinking', rather than memorization of a cannon of key topics. The lack of a cognitively grounded definition for higher order thinking, however, has led to a field of research and practice with little coherence across domains or connection to the large body of cognitive science research on thinking. We review literature on analogy and disciplinary higher order thinking to propose that relational reasoning can be productively considered the cognitive underpinning of higher order thinking. We highlight the utility of this framework for developing insights into practice through a review of mathematics, science, and history educational contexts. In these disciplines, analogy is essential to developing expert-like disciplinary knowledge in which concepts are understood to be systems of relationships that can be connected and flexibly manipulated. At the same time, analogies in education require explicit support to ensure that learners notice the relevance of relational thinking, have adequate processing resources available to mentally hold and manipulate relations, and are able to recognize both the similarities and differences when drawing analogies between systems of relationships. © 2015 John Wiley & Sons, Ltd.

  4. Clapeyron equation and phase equilibrium properties in higher dimensional charged topological dilaton AdS black holes with a nonlinear source

    Energy Technology Data Exchange (ETDEWEB)

    Li, Huai-Fan; Zhao, Hui-Hua; Zhang, Li-Chun; Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China)

    2017-05-15

    Using Maxwell's equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black hole with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in the P-v diagrams. The two-phase equilibrium curves in the P-T diagrams are plotted, and we take the first order approximation of volume v in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for a higher dimensional charged topological black hole with a nonlinear source. The latent heat of an isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems. (orig.)

  5. Photo-physics of third-order nonlinear optical processes in organic dyes

    International Nuclear Information System (INIS)

    Delysse, Stephane

    1997-01-01

    We study some aspects of the nonlinear picosecond photo-physics in organic dyes using Kerr ellipsometry. The aim is to establish link between the photo-physics and nonlinear optics in these compounds. First, we study coherent processes directly linked to the third-order susceptibility. Thus, we measure two-photon absorption spectra of large internal charge transfer dyes. We take into account all coupling between three electronic states which can interfere to explain the particular response of some stilbene dyes. On the second hand, we expose a more photophysical approach to determine the S 1 → S n transition energies and moments using the measurement of excited state absorption cross sections. These results allow the prediction of the susceptibilities relevant to alternative nonlinear optical methods. Nevertheless, the stationary approach hides the complex relaxation processes which can take place in organic dyes. As an illustration, we study the formation and disappearance of a TICT (Twisted intramolecular charge transfer) in a pyrylium salt in solvents of increasing viscosity. (author) [fr

  6. Conceptual Foundations of Transition to the Nonlinear Models of Higher Education in the Region

    Directory of Open Access Journals (Sweden)

    Garold Efimovich Zborovsky

    2016-12-01

    Full Text Available The subject matter of the analysis is the non-linear characteristics of the new model of higher education in relation to its resources and risk environment. The purpose of this article is to prove the need and the possibility of transition to the nonlinear model of higher education in the region on the basis of theoretical positions and the results of the study of non-linear socio-economic processes. In this connection, the socio-economic factors of such transition are characterized; the objective necessity of its implementation in the context of the economic and social uncertainty of a particular region, which is Ural Federal District, is shown. A new type of relationship between universities and their social partners is considered. The need for the change of interactions between educational communities; reliance on the use of a new wide range of economic, social and spiritual resources; the constant search for new mechanisms, educational programs, relations with the external environment, management decisions are argued. Ural Federal District is shown as one of the most advanced regions of the Russian Federation not only in the sphere of the economy, social and cultural life, but also in the sphere of higher education. This circumstance is related to the constant, intensive search for innovative approaches to the modernization of higher education in the region, including the formation of its non-linear model. The presented situation forms the basis of the hypothesis that the non-linear model of higher education can ensure its competitiveness in the global educational space, to enhance its role in the society and specific regions of the country and to turn it into a locomotive of the socio-economic and socio-cultural development. The study is based on an interdisciplinary methodology, including the potential of theoretical sociology, sociology of education, economic sociology, management theory, regional economy. The findings of the research

  7. On existence of soliton solutions of arbitrary-order system of nonlinear Schrodinger equations

    International Nuclear Information System (INIS)

    Zhestkov, S.V.

    2003-01-01

    The soliton solutions are constructed for the system of arbitrary-order coupled nonlinear Schrodinger equations . The necessary and sufficient conditions of existence of these solutions are obtained. It is shown that the maximum number of solitons in nondegenerate case is 4L, where L is order of the system. (author)

  8. Stability and square integrability of solutions of nonlinear fourth order differential equations

    Directory of Open Access Journals (Sweden)

    Moussadek Remili

    2016-05-01

    Full Text Available The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order.

  9. Large third-order optical nonlinearity in vertically oriented mesoporous silica thin films embedded with Ag nanoparticles

    Energy Technology Data Exchange (ETDEWEB)

    Tan, Min; Liu, Qiming, E-mail: qmliu@whu.edu.cn [Wuhan University, Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology (China)

    2016-12-15

    Taking advantage of the channel confinement of mesoporous films to prevent the agglomeration of Ag nanoparticles to achieve large third-order optical nonlinearity in amorphous materials, Ag-loaded composite mesoporous silica film was prepared by the electrochemical deposition method on ITO substrate. Ag ions were firstly transported into the channels of mesoporous film by the diffusion and binding force of channels, which were reduced to nanoparticles by applying suitable voltage. The existence and uniform distribution of Ag nanoparticles ranging in 1–10 nm in the mesoporous silica thin films were exhibited by UV spectrophotometer, X-ray powder diffraction (XRD), transmission electron microscopy (TEM), and X-ray photoelectron spectroscopy (XPS) measurements. The third-order optical nonlinearity induced by Ag nanoparticles was studied by the Z-scan technique. Due to the local field surface plasmon resonance, the maximum third-order nonlinear optical susceptibility of Ag-loaded composite mesoporous silica film is 1.53×10{sup −10} esu, which is 1000 times larger than that of the Ag-contained chalcogenide glasses which showed large nonlinearity in amorphous materials.

  10. Higher order generalized perturbation theory for boiling water reactor in-core fuel management optimization

    International Nuclear Information System (INIS)

    Moore, B.R.; Turinsky, P.J.

    1998-01-01

    Boiling water reactor (BWR) loading pattern assessment requires solving the two-group, nodal form of the neutron diffusion equation and drift-flux form of the fluid equations simultaneously because these equation sets are strongly coupled via nonlinear feedback. To reduce the computational burden associated with the calculation of the core attributes (that is, core eigenvalue and thermal margins) of a perturbed BWR loading pattern, the analytical and numerical aspects of a higher order generalized perturbation theory (GPT) method, which correctly addresses the strong nonlinear feedbacks of two-phase flow, have been established. Inclusion of Jacobian information in the definition of the generalized flux adjoints provides for a rapidly convergent iterative method for solution of the power distribution and eigenvalue of a loading pattern perturbed from a reference state. Results show that the computational speedup of GPT compared with conventional forward solution methods demanding consistent accuracy is highly dependent on the number of spatial nodes utilized by the core simulator, varying from superior to inferior performance as the number of nodes increases

  11. Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II

    Directory of Open Access Journals (Sweden)

    Akira Shirai

    2015-01-01

    Full Text Available In this paper, we study the following nonlinear first order partial differential equation: \\[f(t,x,u,\\partial_t u,\\partial_x u=0\\quad\\text{with}\\quad u(0,x\\equiv 0.\\] The purpose of this paper is to determine the estimate of Gevrey order under the condition that the equation is singular of a totally characteristic type. The Gevrey order is indicated by the rate of divergence of a formal power series. This paper is a continuation of the previous papers [Convergence of formal solutions of singular first order nonlinear partial differential equations of totally characteristic type, Funkcial. Ekvac. 45 (2002, 187-208] and [Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type, Surikaiseki Kenkyujo Kokyuroku, Kyoto University 1431 (2005, 94-106]. Especially the last-mentioned paper is regarded as part I of this paper.

  12. Higher-order paraxial theory of the propagation of ring rippled laser beam in plasma: Relativistic ponderomotive regime

    International Nuclear Information System (INIS)

    Purohit, Gunjan; Rawat, Priyanka; Chauhan, Prashant; Mahmoud, Saleh T.

    2015-01-01

    This article presents higher-order paraxial theory (non-paraxial theory) for the ring ripple formation on an intense Gaussian laser beam and its propagation in plasma, taking into account the relativistic-ponderomotive nonlinearity. The intensity dependent dielectric constant of the plasma has been determined for the main laser beam and ring ripple superimposed on the main laser beam. The dielectric constant of the plasma is modified due to the contribution of the electric field vector of ring ripple. Nonlinear differential equations have been formulated to examine the growth of ring ripple in plasma, self focusing of main laser beam, and ring rippled laser beam in plasma using higher-order paraxial theory. These equations have been solved numerically for different laser intensities and plasma frequencies. The well established experimental laser and plasma parameters are used in numerical calculation. It is observed that the focusing of the laser beams (main and ring rippled) becomes fast in the nonparaxial region by expanding the eikonal and other relevant quantities up to the fourth power of r. The splitted profile of laser beam in the plasma is observed due to uneven focusing/defocusing of the axial and off-axial rays. The growths of ring ripple increase when the laser beam intensity increases. Furthermore, the intensity profile of ring rippled laser beam gets modified due to the contribution of growth rate

  13. Nonlinear coupling of flow harmonics: Hexagonal flow and beyond

    Science.gov (United States)

    Giacalone, Giuliano; Yan, Li; Ollitrault, Jean-Yves

    2018-05-01

    Higher Fourier harmonics of anisotropic flow (v4 and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one and allows us to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at s =2.76 TeV, we perform an application of our formalism to hexagonal flow, v6, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient χ624, which couples v6 to v2 and v4. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, and higher order moments recently analyzed by the ALICE Collaboration. The value of χ624 extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher order harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of v7 and v8.

  14. A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations

    KAUST Repository

    Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan; Yang, Yong

    2014-01-01

    © 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.

  15. Higher-order Jordan Osserman pseudo-Riemannian manifolds

    International Nuclear Information System (INIS)

    Gilkey, Peter B; Ivanova, Raina; Zhang Tan

    2002-01-01

    We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds

  16. Higher-order Jordan Osserman pseudo-Riemannian manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)

    2002-09-07

    We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.

  17. Third-order nonlinear optical response of colloidal gold nanoparticles prepared by sputtering deposition

    Energy Technology Data Exchange (ETDEWEB)

    Castro, Hemerson P. S.; Alencar, Márcio A. R. C.; Hickmann, Jandir M. [Optics and Materials Group–OPTMA, Universidade Federal de Alagoas, CAIXA POSTAL 2051, 57061-970 Maceió (Brazil); Wender, Heberton [Brazilian Synchrotron National Laboratory (LNLS), CNPEM, Rua Giuseppe Máximo Scolfaro 10.000, 13083-970 Campinas (Brazil); Department of Physics, Universidade Federal do Mato Grosso do Sul, 79070-900, Campo Grande (Brazil); Teixeira, Sergio R. [Institute of Physics, Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre (Brazil); Dupont, Jairton [Laboratory of Molecular Catalysis, Institute of Chemistry, Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre (Brazil)

    2013-11-14

    The nonlinear optical responses of gold nanoparticles dispersed in castor oil produced by sputtering deposition were investigated, using the thermally managed Z-scan technique. Particles with spherical shape and 2.6 nm of average diameter were obtained and characterized by transmission electron microscopy and small angle X-ray scattering. This colloid was highly stable, without the presence of chemical impurities, neither stabilizers. It was observed that this system presents a large refractive third-order nonlinear response and a negligible nonlinear absorption. Moreover, the evaluation of the all-optical switching figures of merit demonstrated that the colloidal nanoparticles prepared by sputtering deposition have a good potential for the development of ultrafast photonic devices.

  18. Neoclassical transport including collisional nonlinearity.

    Science.gov (United States)

    Candy, J; Belli, E A

    2011-06-10

    In the standard δf theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction δf is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlüter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.

  19. Support-Vector-Machine-Based Reduced-Order Model for Limit Cycle Oscillation Prediction of Nonlinear Aeroelastic System

    Directory of Open Access Journals (Sweden)

    Gang Chen

    2012-01-01

    Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.

  20. Transverse Field Dispersion in the Generalized Nonlinear Schrödinger Equation: Four Wave Mixing in a Higher Order Mode Fiber

    DEFF Research Database (Denmark)

    Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris

    2013-01-01

    An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...

  1. Dynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation

    DEFF Research Database (Denmark)

    Karpman, V.I.; Juul Rasmussen, J.; Shagalov, A.G.

    2001-01-01

    The dynamics of soliton and quasisoliton solutions of the cubic third-order nonlinear Schrodinger equation is studied. Regular solitons exist due to a balance between the nonlinear terms and (linear) third-order dispersion; they are not important at small alpha (3) (alpha (3) is the coefficient...... in the third derivative term) and vanish at alpha3 -->0. The most essential, at small alpha (3), is a quasisoliton emitting resonant radiation (resonantly radiating soliton). Its relationship with the other (steady) quasisoliton, called embedded soliton, is studied analytically and also in numerical...

  2. Participation of the Third Order Optical Nonlinearities in Nanostructured Silver Doped Zinc Oxide Thin Solid Films

    Directory of Open Access Journals (Sweden)

    C. Torres-Torres

    2012-01-01

    Full Text Available We report the transmittance modulation of optical signals in a nanocomposite integrated by two different silver doped zinc oxide thin solid films. An ultrasonic spray pyrolysis approach was employed for the preparation of the samples. Measurements of the third-order nonlinear optical response at a nonresonant 532 nm wavelength of excitation were performed using a vectorial two-wave mixing. It seems that the separated contribution of the optical nonlinearity associated with each film noticeable differs in the resulting nonlinear effects with respect to the additive response exhibited by the bilayer system. An enhancement of the optical Kerr nonlinearity is predicted for prime number arrays of the studied nanoclusters in a two-wave interaction. We consider that the nanostructured morphology of the thin solid films originates a strong modification of the third-order optical phenomena exhibited by multilayer films based on zinc oxide.

  3. Difference equations in massive higher order calculations

    International Nuclear Information System (INIS)

    Bierenbaum, I.; Bluemlein, J.; Klein, S.; Schneider, C.

    2007-07-01

    The calculation of massive 2-loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter N. We report on the solution of these sums through higher order difference equations using the summation package Sigma. (orig.)

  4. Higher accuracy analytical approximations to a nonlinear oscillator with discontinuity by He's homotopy perturbation method

    International Nuclear Information System (INIS)

    Belendez, A.; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A.

    2008-01-01

    He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient

  5. The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

    Directory of Open Access Journals (Sweden)

    Feng-Tao He

    2013-01-01

    Full Text Available We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton’s dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1 if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton’s width increases, while its amplitude and wave velocity reduce. (2 If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton’s width increases, while its amplitude and the wave velocity reduce.

  6. EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.

  7. Higher-order harmonics coupling in different free-electron laser codes

    Science.gov (United States)

    Giannessi, L.; Freund, H. P.; Musumeci, P.; Reiche, S.

    2008-08-01

    The capability for simulation of the dynamics of a free-electron laser including the higher-order harmonics in linear undulators exists in several existing codes as MEDUSA [H.P. Freund, S.G. Biedron, and S.V. Milton, IEEE J. Quantum Electron. 27 (2000) 243; H.P. Freund, Phys. Rev. ST-AB 8 (2005) 110701] and PERSEO [L. Giannessi, Overview of Perseo, a system for simulating FEL dynamics in Mathcad, , in: Proceedings of FEL 2006 Conference, BESSY, Berlin, Germany, 2006, p. 91], and has been recently implemented in GENESIS 1.3 [See ]. MEDUSA and GENESIS also include the dynamics of even harmonics induced by the coupling through the betatron motion. In addition MEDUSA, which is based on a non-wiggler averaged model, is capable of simulating the generation of even harmonics in the transversally cold beam regime, i.e. when the even harmonic coupling arises from non-linear effects associated with longitudinal particle dynamics and not to a finite beam emittance. In this paper a comparison between the predictions of the codes in different conditions is given.

  8. Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics

    NARCIS (Netherlands)

    Yu, Wenwu; Chen, Guanrong; Cao, Ming; Kurths, Juergen; Kurths, Jürgen

    This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a

  9. Higher-order harmonics of general limited diffraction Bessel beams

    International Nuclear Information System (INIS)

    Ding De-Sheng; Huang Jin-Huang

    2016-01-01

    In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m -th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. (special topic)

  10. An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

    KAUST Repository

    Xu, Tiantian

    2014-08-17

    Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

  11. Conservative fourth-order time integration of non-linear dynamic systems

    DEFF Research Database (Denmark)

    Krenk, Steen

    2015-01-01

    An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... the resulting time integrals of the inertia and stiffness terms via integration by parts. This process introduces the time derivatives of the state space variables, and these are then substituted from the original state-space differential equations. The resulting discrete form of the state-space equations...... is a direct fourth-order accurate representation of the original differential equations. This fourth-order form is energy conserving for systems with force potential in the form of a quartic polynomial in the displacement components. Energy conservation for a force potential of general form is obtained...

  12. Dynamical Properties in a Fourth-Order Nonlinear Difference Equation

    OpenAIRE

    Xianyi Li; Yunxin Chen

    2010-01-01

    The rule of trajectory structure for fourth-order nonlinear difference equation xn+1=(xan−2+xn−3)/(xan−2xn−3+1), n=0,1,2,…, where a∈[0,1) and the initial values x−3,x−2,x−1,x0∈[0,∞), is described clearly out in this paper. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is 4+,3−,1+,2−,2+,1−,1+, 1&#x...

  13. Multi-order nonlinear diffraction in second harmonic generation

    DEFF Research Database (Denmark)

    Saltiel, S. M.; Neshev, D.; Krolikowski, Wieslaw

    We analyze the emission patterns in the process of second harmonic (SH) generation in χ(2) nonlinear gratings and identify for the first time, to the best of our knowledge, the evidence of Raman-Nath type nonlinear diffraction in frequency doubling processes.......We analyze the emission patterns in the process of second harmonic (SH) generation in χ(2) nonlinear gratings and identify for the first time, to the best of our knowledge, the evidence of Raman-Nath type nonlinear diffraction in frequency doubling processes....

  14. Emergence of complex space-temporal order in nonlinear field theories

    International Nuclear Information System (INIS)

    Gleiser, Marcelo

    2006-01-01

    We investigate the emergence of time-dependent nonperturbative configurations during the evolution of nonlinear scalar field models with symmetric and asymmetric double-well potentials. Complex space-temporal behavior emerges as the system seeks to establish equipartition after a fast quench. We show that fast quenches may dramatically modify the decay rate of metastable states in first order phase transitions. We discuss possible applications in condensed matter systems and in inflationary cosmology. (author)

  15. High-order finite difference solution for 3D nonlinear wave-structure interaction

    DEFF Research Database (Denmark)

    Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter

    2010-01-01

    This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme O...

  16. Bilinear forms, N-soliton solutions and soliton interactions for a fourth-order dispersive nonlinear Schrödinger equation in condensed-matter physics and biophysics

    International Nuclear Information System (INIS)

    Liu, Rong-Xiang; Tian, Bo; Liu, Li-Cai; Qin, Bo; Lü, Xing

    2013-01-01

    In this paper we investigate a fourth-order dispersive nonlinear Schrödinger equation, which governs the dynamics of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain with the octuple–dipole interaction in condensed-matter physics as well as the alpha helical proteins with higher-order excitations and interactions in biophysics. Beyond the existing constraint, upon the introduction of an auxiliary function, bilinear forms and N-soliton solutions are constructed with the Hirota method. Asymptotic analysis on the two-soliton solutions indicates that the soliton interactions are elastic. Soliton velocity varies linearly with the coefficient of discreteness and higher-order magnetic interactions. Bound-state solitons can also exist under certain conditions. Period of a bound-state soliton is inversely correlated to the coefficient of discreteness and higher-order magnetic interactions. Interactions among the three solitons are all pairwise elastic

  17. Higher-order harmonics of general limited diffraction Bessel beams

    Science.gov (United States)

    Ding, De-Sheng; Huang, Jin-Huang

    2016-12-01

    In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).

  18. Reduced-order modeling of piezoelectric energy harvesters with nonlinear circuits under complex conditions

    Science.gov (United States)

    Xiang, Hong-Jun; Zhang, Zhi-Wei; Shi, Zhi-Fei; Li, Hong

    2018-04-01

    A fully coupled modeling approach is developed for piezoelectric energy harvesters in this work based on the use of available robust finite element packages and efficient reducing order modeling techniques. At first, the harvester is modeled using finite element packages. The dynamic equilibrium equations of harvesters are rebuilt by extracting system matrices from the finite element model using built-in commands without any additional tools. A Krylov subspace-based scheme is then applied to obtain a reduced-order model for improving simulation efficiency but preserving the key features of harvesters. Co-simulation of the reduced-order model with nonlinear energy harvesting circuits is achieved in a system level. Several examples in both cases of harmonic response and transient response analysis are conducted to validate the present approach. The proposed approach allows to improve the simulation efficiency by several orders of magnitude. Moreover, the parameters used in the equivalent circuit model can be conveniently obtained by the proposed eigenvector-based model order reduction technique. More importantly, this work establishes a methodology for modeling of piezoelectric energy harvesters with any complicated mechanical geometries and nonlinear circuits. The input load may be more complex also. The method can be employed by harvester designers to optimal mechanical structures or by circuit designers to develop novel energy harvesting circuits.

  19. Higher order QCD corrections in small x physics

    International Nuclear Information System (INIS)

    Chachamis, G.

    2006-11-01

    We study higher order QCD corrections in small x Physics. The numerical implementation of the full NLO photon impact factor is the remaining necessary piece for the testing of the NLO BFKL resummation against data from physical processes, such as γ * γ * collisions. We perform the numerical integration over phase space for the virtual corrections to the NLO photon impact factor. This, along with the previously calculated real corrections, makes feasible in the near future first estimates for the γ*γ* total cross section, since the convolution of the full impact factor with the NLO BFKL gluon Green's function is now straightforward. The NLO corrections for the photon impact factor are sizeable and negative. In the second part of this thesis, we estimate higher order correction to the BK equation. We are mainly interested in whether partonic saturation delays or not in rapidity when going beyond the leading order. In our investigation, we use the so called 'rapidity veto' which forbid two emissions to be very close in rapidity, to 'switch on' higher order corrections to the BK equation. From analytic and numerical analysis, we conclude that indeed saturation does delay in rapidity when higher order corrections are taken into account. In the last part, we investigate higher order QCD corrections as additional corrections to the Electroweak (EW) sector. The question of whether BFKL corrections are of any importance in the Regge limit for the EW sector seems natural; although they arise in higher loop level, the accumulation of logarithms in energy s at high energies, cannot be dismissed without an investigation. We focus on the process γγ→ZZ. We calculate the pQCD corrections in the forward region at leading logarithmic (LL) BFKL accuracy, which are of the order of few percent at the TeV energy scale. (orig.)

  20. Higher order QCD corrections in small x physics

    Energy Technology Data Exchange (ETDEWEB)

    Chachamis, G.

    2006-11-15

    We study higher order QCD corrections in small x Physics. The numerical implementation of the full NLO photon impact factor is the remaining necessary piece for the testing of the NLO BFKL resummation against data from physical processes, such as {gamma}{sup *}{gamma}{sup *} collisions. We perform the numerical integration over phase space for the virtual corrections to the NLO photon impact factor. This, along with the previously calculated real corrections, makes feasible in the near future first estimates for the {gamma}*{gamma}* total cross section, since the convolution of the full impact factor with the NLO BFKL gluon Green's function is now straightforward. The NLO corrections for the photon impact factor are sizeable and negative. In the second part of this thesis, we estimate higher order correction to the BK equation. We are mainly interested in whether partonic saturation delays or not in rapidity when going beyond the leading order. In our investigation, we use the so called 'rapidity veto' which forbid two emissions to be very close in rapidity, to 'switch on' higher order corrections to the BK equation. From analytic and numerical analysis, we conclude that indeed saturation does delay in rapidity when higher order corrections are taken into account. In the last part, we investigate higher order QCD corrections as additional corrections to the Electroweak (EW) sector. The question of whether BFKL corrections are of any importance in the Regge limit for the EW sector seems natural; although they arise in higher loop level, the accumulation of logarithms in energy s at high energies, cannot be dismissed without an investigation. We focus on the process {gamma}{gamma}{yields}ZZ. We calculate the pQCD corrections in the forward region at leading logarithmic (LL) BFKL accuracy, which are of the order of few percent at the TeV energy scale. (orig.)

  1. Nonlocal higher order evolution equations

    KAUST Repository

    Rossi, Julio D.; Schö nlieb, Carola-Bibiane

    2010-01-01

    In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove

  2. Run-up on a body in waves and current. Fully nonlinear and finite-order calculations

    DEFF Research Database (Denmark)

    Büchmann, Bjarne; Ferrant, P.; Skourup, J.

    2001-01-01

    Run-up on a large fixed body in waves and current have been calculated using both a fully nonlinear time-domain boundary element model and a finite-order time-domain boundary element model, the latter being correct to second order in the wave steepness and to first-order in the current strength...

  3. Unambiguous formalism for higher order Lagrangian field theories

    International Nuclear Information System (INIS)

    Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn; Vankerschaver, Joris

    2009-01-01

    The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.

  4. Improving Spiking Dynamical Networks: Accurate Delays, Higher-Order Synapses, and Time Cells.

    Science.gov (United States)

    Voelker, Aaron R; Eliasmith, Chris

    2018-03-01

    Researchers building spiking neural networks face the challenge of improving the biological plausibility of their model networks while maintaining the ability to quantitatively characterize network behavior. In this work, we extend the theory behind the neural engineering framework (NEF), a method of building spiking dynamical networks, to permit the use of a broad class of synapse models while maintaining prescribed dynamics up to a given order. This theory improves our understanding of how low-level synaptic properties alter the accuracy of high-level computations in spiking dynamical networks. For completeness, we provide characterizations for both continuous-time (i.e., analog) and discrete-time (i.e., digital) simulations. We demonstrate the utility of these extensions by mapping an optimal delay line onto various spiking dynamical networks using higher-order models of the synapse. We show that these networks nonlinearly encode rolling windows of input history, using a scale invariant representation, with accuracy depending on the frequency content of the input signal. Finally, we reveal that these methods provide a novel explanation of time cell responses during a delay task, which have been observed throughout hippocampus, striatum, and cortex.

  5. Transition of EMRIs through resonance: higher order corrections in resonant flux enhancement

    Science.gov (United States)

    Mihaylov, Deyan; Gair, Jonathan

    2017-01-01

    Extreme mass ratio inspirals (EMRIs) are candidate events for gravitational wave detection in the millihertz range (by detectors like LISA and eLISA). These events involve a stellar-mass black hole, or a similar compact object, descending into the gravitational field of a supermassive black hole, eventually merging with it. Properties of the inspiraling trajectory away from resonance are well known and have been studied extensively, however little is known about the behaviour of these binary systems at resonance, when the radial and lateral frequencies of the orbit become commensurate. There are two resonance models in the literature, the instantaneous frequency function by Gair, Bender, and Yunes, and the standard two timescales approach devised by Flanagan and Hinderer. We argue that the Gair, Bender and Yunes model provides a valid treatment of the resonance problem and extend this solution to higher order in the size of the on-resonance perturbation. The non-linear differential equations which arise in treating resonances are interesting from a mathematical view point. We present our algorithm for perturbative solutions and the results to third order in the infinitesimal parameter, and discuss the scope of this approach. Deyan Mihaylov is funded by the STFC.

  6. Study of third order nonlinearity of chalcogenide thin films using third harmonic generation measurements

    Science.gov (United States)

    Rani, Sunita; Mohan, Devendra; Kumar, Manish; Sanjay

    2018-05-01

    Third order nonlinear susceptibility of (GeSe3.5)100-xBix (x = 0, 10, 14) and ZnxSySe100-x-y (x = 2, y = 28; x = 4, y = 20; x = 6, y = 12; x = 8, y = 4) amorphous chalcogenide thin films prepared using thermal evaporation technique is estimated. The dielectric constant at incident and third harmonic wavelength is calculated using "PARAV" computer program. 1064 nm wavelength of Nd: YAG laser is incident on thin film and third harmonic signal at 355 nm wavelength alongwith fundamental light is obtained in reflection that is separated from 1064 nm using suitable optical filter. Reflected third harmonic signal is measured to trace the influence of Bi and Zn on third order nonlinear susceptibility and is found to increase with increase in Bi and Zn content in (GeSe3.5)100-xBix, and ZnxSySe100-x-y chalcogenide thin films respectively. The excellent optical nonlinear property shows the use of chalcogenide thin films in photonics for wavelength conversion and optical data processing.

  7. Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

    Energy Technology Data Exchange (ETDEWEB)

    Cobb, J.W.

    1995-02-01

    There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

  8. Optical rogue waves and soliton turbulence in nonlinear fibre optics

    DEFF Research Database (Denmark)

    Genty, G.; Dudley, J. M.; de Sterke, C. M.

    2009-01-01

    We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....

  9. Existence of solutions for nonlinear mixed type integrodifferential equation of second order

    Directory of Open Access Journals (Sweden)

    Haribhau Laxman Tidke

    2010-04-01

    Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.

  10. Higher-Order Fermi-Liquid Corrections for an Anderson Impurity Away from Half Filling

    Science.gov (United States)

    Oguri, Akira; Hewson, A. C.

    2018-03-01

    We study the higher-order Fermi-liquid relations of Kondo systems for arbitrary impurity-electron fillings, extending the many-body quantum theoretical approach of Yamada and Yosida. It includes, partly, a microscopic clarification of the related achievements based on Nozières' phenomenological description: Filippone, Moca, von Delft, and Mora [Phys. Rev. B 95, 165404 (2017), 10.1103/PhysRevB.95.165404]. In our formulation, the Fermi-liquid parameters such as the quasiparticle energy, damping, and transport coefficients are related to each other through the total vertex Γσ σ';σ'σ(ω ,ω';ω',ω ), which may be regarded as a generalized Landau quasiparticle interaction. We obtain exactly this function up to linear order with respect to the frequencies ω and ω' using the antisymmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half filling through the nonlinear susceptibilities. We also apply the formulation to nonequilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field.

  11. Higher-Order Fermi-Liquid Corrections for an Anderson Impurity Away from Half Filling.

    Science.gov (United States)

    Oguri, Akira; Hewson, A C

    2018-03-23

    We study the higher-order Fermi-liquid relations of Kondo systems for arbitrary impurity-electron fillings, extending the many-body quantum theoretical approach of Yamada and Yosida. It includes, partly, a microscopic clarification of the related achievements based on Nozières' phenomenological description: Filippone, Moca, von Delft, and Mora [Phys. Rev. B 95, 165404 (2017)PRBMDO2469-995010.1103/PhysRevB.95.165404]. In our formulation, the Fermi-liquid parameters such as the quasiparticle energy, damping, and transport coefficients are related to each other through the total vertex Γ_{σσ^{'};σ^{'}σ}(ω,ω^{'};ω^{'},ω), which may be regarded as a generalized Landau quasiparticle interaction. We obtain exactly this function up to linear order with respect to the frequencies ω and ω^{'} using the antisymmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half filling through the nonlinear susceptibilities. We also apply the formulation to nonequilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field.

  12. Higher-Order Approximation of Cubic-Quintic Duffing Model

    DEFF Research Database (Denmark)

    Ganji, S. S.; Barari, Amin; Babazadeh, H.

    2011-01-01

    We apply an Artificial Parameter Lindstedt-Poincaré Method (APL-PM) to find improved approximate solutions for strongly nonlinear Duffing oscillations with cubic-quintic nonlinear restoring force. This approach yields simple linear algebraic equations instead of nonlinear algebraic equations...

  13. Distributed robust adaptive control of high order nonlinear multi agent systems.

    Science.gov (United States)

    Hashemi, Mahnaz; Shahgholian, Ghazanfar

    2018-03-01

    In this paper, a robust adaptive neural network based controller is presented for multi agent high order nonlinear systems with unknown nonlinear functions, unknown control gains and unknown actuator failures. At first, Neural Network (NN) is used to approximate the nonlinear uncertainty terms derived from the controller design procedure for the followers. Then, a novel distributed robust adaptive controller is developed by combining the backstepping method and the Dynamic Surface Control (DSC) approach. The proposed controllers are distributed in the sense that the designed controller for each follower agent only requires relative state information between itself and its neighbors. By using the Young's inequality, only few parameters need to be tuned regardless of NN nodes number. Accordingly, the problems of dimensionality curse and explosion of complexity are counteracted, simultaneously. New adaptive laws are designed by choosing the appropriate Lyapunov-Krasovskii functionals. The proposed approach proves the boundedness of all the closed-loop signals in addition to the convergence of the distributed tracking errors to a small neighborhood of the origin. Simulation results indicate that the proposed controller is effective and robust. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  14. Third-order nonlinear optical studies of anthraquinone dyes using a CW He–Ne laser

    International Nuclear Information System (INIS)

    Pramodini, S; Poornesh, P

    2014-01-01

    We present investigations on the third-order optical nonlinearity and optical power limiting of anthraquinone dyes. Z-scan measurements were performed using a continuous wave He–Ne laser at 633 nm wavelength as an excitation source. The nonlinear refraction studies exhibited self-defocusing behavior of the dyes. The nonlinear absorption in the dyes was dominated by a reverse saturable absorption process. Self-diffraction ring patterns were observed due to the change in refractive index and thermal lensing. Increase of the electron donating ability of the substituents resulted in enhanced values of the nonlinear optical parameters, establishing the structure–property relationship. The optical limiting study revealed that the dyes possess a lower limiting threshold and clamping level which is very important for eye and sensor protection. Hence, the dyes investigated here emerge as promising candidates for future opto-electronic and photonic device applications such as optical power limiters. (paper)

  15. Third-order nonlinear optical studies of anthraquinone dyes using a CW He-Ne laser

    Science.gov (United States)

    Pramodini, S.; Poornesh, P.

    2014-05-01

    We present investigations on the third-order optical nonlinearity and optical power limiting of anthraquinone dyes. Z-scan measurements were performed using a continuous wave He-Ne laser at 633 nm wavelength as an excitation source. The nonlinear refraction studies exhibited self-defocusing behavior of the dyes. The nonlinear absorption in the dyes was dominated by a reverse saturable absorption process. Self-diffraction ring patterns were observed due to the change in refractive index and thermal lensing. Increase of the electron donating ability of the substituents resulted in enhanced values of the nonlinear optical parameters, establishing the structure-property relationship. The optical limiting study revealed that the dyes possess a lower limiting threshold and clamping level which is very important for eye and sensor protection. Hence, the dyes investigated here emerge as promising candidates for future opto-electronic and photonic device applications such as optical power limiters.

  16. Third-order nonlinear optical properties of GeSe2-Ga2Se3-PbI2 glasses

    International Nuclear Information System (INIS)

    Tang Gao; Liu Cunming; Luo Lan; Chen Wei

    2010-01-01

    The third-order nonlinear optical (NLO) properties of new selenium-based GeSe 2 -Ga 2 Se 3 -PbI 2 glasses have been measured using the optical Kerr effect (OKE) technique, with picosecond and femtosecond laser pulses. The 0.70GeSe 2 -0.15Ga 2 Se 3 -0.15PbI 2 glass has the largest third-order optical nonlinear susceptibility in GeSe 2 -Ga 2 Se 3 -PbI 2 glass system with χ (3) of 5.28x10 12 esu. In addition, the response time of glasses is sub-picosecond, which is predominantly associated with electron cloud. Local structure of the glasses has been identified by using Raman studies, while the origins of the observed nonlinear optical response are discussed. The [Ge(Ga)Se 4 ] tetrahedral and lone-pair electrons from highly polarizable Pb atom in glasses play an important role in enhanced NLO response. These results as well as their good chemical stability indicate that GeSe 2 -Ga 2 Se 3 -PbI 2 glasses are promising materials for photonic applications of third-order nonlinear optical signal processing.

  17. Traveling solitary wave solutions to evolution equations with nonlinear terms of any order

    International Nuclear Information System (INIS)

    Feng Zhaosheng

    2003-01-01

    Many physical phenomena in one- or higher-dimensional space can be described by nonlinear evolution equations, which can be reduced to ordinary differential equations such as the Lienard equation. Thus, to study those ordinary differential equations is of significance not only in mathematics itself, but also in physics. In this paper, a kind of explicit exact solutions to the Lienard equation is obtained. The applications of the solutions to the nonlinear RR-equation and the compound KdV-type equation are presented, which extend the results obtained in the previous literature

  18. Time-Discrete Higher-Order ALE Formulations: Stability

    KAUST Repository

    Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.

    2013-01-01

    on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time

  19. The Meaning of Higher-Order Factors in Reflective-Measurement Models

    Science.gov (United States)

    Eid, Michael; Koch, Tobias

    2014-01-01

    Higher-order factor analysis is a widely used approach for analyzing the structure of a multidimensional test. Whenever first-order factors are correlated researchers are tempted to apply a higher-order factor model. But is this reasonable? What do the higher-order factors measure? What is their meaning? Willoughby, Holochwost, Blanton, and Blair…

  20. Nil Bohr-sets and almost automorphy of higher order

    CERN Document Server

    Huang, Wen; Ye, Xiangdong

    2016-01-01

    Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d\\in \\mathbb{N} does the collection of \\{n\\in \\mathbb{Z}: S\\cap (S-n)\\cap\\ldots\\cap (S-dn)\

  1. Application of power spectrum, cepstrum, higher order spectrum and neural network analyses for induction motor fault diagnosis

    Science.gov (United States)

    Liang, B.; Iwnicki, S. D.; Zhao, Y.

    2013-08-01

    The power spectrum is defined as the square of the magnitude of the Fourier transform (FT) of a signal. The advantage of FT analysis is that it allows the decomposition of a signal into individual periodic frequency components and establishes the relative intensity of each component. It is the most commonly used signal processing technique today. If the same principle is applied for the detection of periodicity components in a Fourier spectrum, the process is called the cepstrum analysis. Cepstrum analysis is a very useful tool for detection families of harmonics with uniform spacing or the families of sidebands commonly found in gearbox, bearing and engine vibration fault spectra. Higher order spectra (HOS) (also known as polyspectra) consist of higher order moment of spectra which are able to detect non-linear interactions between frequency components. For HOS, the most commonly used is the bispectrum. The bispectrum is the third-order frequency domain measure, which contains information that standard power spectral analysis techniques cannot provide. It is well known that neural networks can represent complex non-linear relationships, and therefore they are extremely useful for fault identification and classification. This paper presents an application of power spectrum, cepstrum, bispectrum and neural network for fault pattern extraction of induction motors. The potential for using the power spectrum, cepstrum, bispectrum and neural network as a means for differentiating between healthy and faulty induction motor operation is examined. A series of experiments is done and the advantages and disadvantages between them are discussed. It has been found that a combination of power spectrum, cepstrum and bispectrum plus neural network analyses could be a very useful tool for condition monitoring and fault diagnosis of induction motors.

  2. Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

    Science.gov (United States)

    Ho, Yuh-Shan

    2006-01-01

    A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

  3. Efficient Estimation of Extreme Non-linear Roll Motions using the First-order Reliability Method (FORM)

    DEFF Research Database (Denmark)

    Jensen, Jørgen Juncher

    2007-01-01

    In on-board decision support systems efficient procedures are needed for real-time estimation of the maximum ship responses to be expected within the next few hours, given on-line information on the sea state and user defined ranges of possible headings and speeds. For linear responses standard...... frequency domain methods can be applied. To non-linear responses like the roll motion, standard methods like direct time domain simulations are not feasible due to the required computational time. However, the statistical distribution of non-linear ship responses can be estimated very accurately using...... the first-order reliability method (FORM), well-known from structural reliability problems. To illustrate the proposed procedure, the roll motion is modelled by a simplified non-linear procedure taking into account non-linear hydrodynamic damping, time-varying restoring and wave excitation moments...

  4. Gradient-based optimization in nonlinear structural dynamics

    DEFF Research Database (Denmark)

    Dou, Suguang

    The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider......, frequency stabilization, and disk resonator gyroscope. For advanced design of these structures, it is of considerable value to extend current optimization in linear structural dynamics into nonlinear structural dynamics. In this thesis, we present a framework for modelling, analysis, characterization......, and optimization of nonlinear structural dynamics. In the modelling, nonlinear finite elements are used. In the analysis, nonlinear frequency response and nonlinear normal modes are calculated based on a harmonic balance method with higher-order harmonics. In the characterization, nonlinear modal coupling...

  5. Higher order cumulants in colorless partonic plasma

    Energy Technology Data Exchange (ETDEWEB)

    Cherif, S. [Sciences and Technologies Department, University of Ghardaia, Ghardaia, Algiers (Algeria); Laboratoire de Physique et de Mathématiques Appliquées (LPMA), ENS-Kouba (Bachir El-Ibrahimi), Algiers (Algeria); Ahmed, M. A. A. [Department of Physics, College of Science, Taibah University Al-Madinah Al-Mounawwarah KSA (Saudi Arabia); Department of Physics, Taiz University in Turba, Taiz (Yemen); Laboratoire de Physique et de Mathématiques Appliquées (LPMA), ENS-Kouba (Bachir El-Ibrahimi), Algiers (Algeria); Ladrem, M., E-mail: mladrem@yahoo.fr [Department of Physics, College of Science, Taibah University Al-Madinah Al-Mounawwarah KSA (Saudi Arabia); Laboratoire de Physique et de Mathématiques Appliquées (LPMA), ENS-Kouba (Bachir El-Ibrahimi), Algiers (Algeria)

    2016-06-10

    Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to the thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.

  6. Long wavelength limit of evolution of nonlinear cosmological perturbations

    International Nuclear Information System (INIS)

    Hamazaki, Takashi

    2008-01-01

    In the general matter composition where the multiple scalar fields and the multiple perfect fluids coexist, in the leading order of the gradient expansion, we construct all of the solutions of the nonlinear evolutions of the locally homogeneous universe. From the momentum constraint, we derive the constraints which the solution constants of the locally homogeneous universe must satisfy. We construct the gauge invariant perturbation variables in the arbitrarily higher order nonlinear cosmological perturbation theory around the spatially flat Friedmann-Robertson-Walker universe. We construct the nonlinear long wavelength limit formula representing the long wavelength limit of the evolution of the nonlinear gauge invariant perturbation variables in terms of perturbations of the evolutions of the locally homogeneous universe. By using the long wavelength limit formula, we investigate the evolution of nonlinear cosmological perturbations in the universe dominated by the multiple slow rolling scalar fields with an arbitrary potential. The τ function and the N potential introduced in this paper make it possible to write the evolution of the multiple slow rolling scalar fields with an arbitrary interaction potential and the arbitrarily higher order nonlinear Bardeen parameter at the end of the slow rolling phase analytically. It is shown that the nonlinear parameters such as f NL and g NL are suppressed by the slow rolling expansion parameters.

  7. Oscillating nonlinear acoustic shock waves

    DEFF Research Database (Denmark)

    Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth

    2016-01-01

    We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show that at resona......We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....

  8. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Science.gov (United States)

    Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

    2017-07-01

    This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  9. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Directory of Open Access Journals (Sweden)

    Shahid Hasnain

    2017-07-01

    Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  10. On the expressiveness and decidability of higher-order process calculi

    NARCIS (Netherlands)

    Lanese, Ivan; Perez, Jorge A.; Sangiorgi, Davide; Schmitt, Alan

    In higher-order process calculi, the values exchanged in communications may contain processes. A core calculus of higher-order concurrency is studied; it has only the operators necessary to express higher-order communications: input prefix, process output, and parallel composition. By exhibiting a

  11. Multilevel Fast Multipole Method for Higher Order Discretizations

    DEFF Research Database (Denmark)

    Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik

    2014-01-01

    The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower...... order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined....

  12. New Chiral Bis-Dipolar 6,6'-Disubstituted-Binaphthol Derivatives for Second-Order Nonlinear Optics

    DEFF Research Database (Denmark)

    Deussen, Heinz-Josef; Boutton, Carlo; Thorup, Niels

    1998-01-01

    (S)everal chiral molecules with C-2 symmetry derived from two geometries of the binaphthol (BN) system substituted with different accepters have been synthesized in order to study the possibility of producing noncentrosymmetric crystals formed from these chiral structures. All the molecules possess...... cancel out exactly despite the noncentrosymmetry. The crystal structure of racemic 9,14-dicyanodinaphtho[2,1-d:1',2'-f][1,3]-dioxepin (2b) was found to be centrosymmetric. The new compounds were investigated for second-harmonic generation (including BN derivatives reported earlier) by the Kurtz......-Perry powder test to evaluate the second-order nonlinear optical (NLO) properties of polycrystalline samples. Although chirality ensures noncentrosymmetric crystals, only modest (approximate to 2-methyl-4-nitroaniline) or no nonlinearities were observed in the powder test, For a representative selection...

  13. Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

    Science.gov (United States)

    Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

    2017-12-01

    An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

  14. Generating higher-order quantum dissipation from lower-order parametric processes

    Science.gov (United States)

    Mundhada, S. O.; Grimm, A.; Touzard, S.; Vool, U.; Shankar, S.; Devoret, M. H.; Mirrahimi, M.

    2017-06-01

    The stabilisation of quantum manifolds is at the heart of error-protected quantum information storage and manipulation. Nonlinear driven-dissipative processes achieve such stabilisation in a hardware efficient manner. Josephson circuits with parametric pump drives implement these nonlinear interactions. In this article, we propose a scheme to engineer a four-photon drive and dissipation on a harmonic oscillator by cascading experimentally demonstrated two-photon processes. This would stabilise a four-dimensional degenerate manifold in a superconducting resonator. We analyse the performance of the scheme using numerical simulations of a realisable system with experimentally achievable parameters.

  15. The second order extended Kalman filter and Markov nonlinear filter for data processing in interferometric systems

    International Nuclear Information System (INIS)

    Ermolaev, P; Volynsky, M

    2014-01-01

    Recurrent stochastic data processing algorithms using representation of interferometric signal as output of a dynamic system, which state is described by vector of parameters, in some cases are more effective, compared with conventional algorithms. Interferometric signals depend on phase nonlinearly. Consequently it is expedient to apply algorithms of nonlinear stochastic filtering, such as Kalman type filters. An application of the second order extended Kalman filter and Markov nonlinear filter that allows to minimize estimation error is described. Experimental results of signals processing are illustrated. Comparison of the algorithms is presented and discussed.

  16. Engineering high-order nonlinear dissipation for quantum superconducting circuits

    Science.gov (United States)

    Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.

    Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.

  17. Order-disorder transitions in time-discrete mean field systems with memory: a novel approach via nonlinear autoregressive models

    International Nuclear Information System (INIS)

    Frank, T D; Mongkolsakulvong, S

    2015-01-01

    In a previous study strongly nonlinear autoregressive (SNAR) models have been introduced as a generalization of the widely-used time-discrete autoregressive models that are known to apply both to Markov and non-Markovian systems. In contrast to conventional autoregressive models, SNAR models depend on process mean values. So far, only linear dependences have been studied. We consider the case in which process mean values can have a nonlinear impact on the processes under consideration. It is shown that such models describe Markov and non-Markovian many-body systems with mean field forces that exhibit a nonlinear impact on single subsystems. We exemplify that such nonlinear dependences can describe order-disorder phase transitions of time-discrete Markovian and non-Markovian many-body systems. The relevant order parameter equations are derived and issues of stability and stationarity are studied. (paper)

  18. Higher-order rewriting and partial evaluation

    DEFF Research Database (Denmark)

    Danvy, Olivier; Rose, Kristoffer H.

    1998-01-01

    We demonstrate the usefulness of higher-order rewriting techniques for specializing programs, i.e., for partial evaluation. More precisely, we demonstrate how casting program specializers as combinatory reduction systems (CRSs) makes it possible to formalize the corresponding program...

  19. Higher-Order Separation Logic in Isabelle/HOLCF

    DEFF Research Database (Denmark)

    Varming, Carsten; Birkedal, Lars

    2008-01-01

    We formalize higher-order separation logic for a first-order imperative language with procedures and local variables in Isabelle/HOLCF. The assertion language is modeled in such a way that one may use any theory defined in Isabelle/HOLCF to construct assertions, e.g., primitive recursion, least o...

  20. Meta-Logical Reasoning in Higher-Order Logic

    DEFF Research Database (Denmark)

    Villadsen, Jørgen; Schlichtkrull, Anders; Hess, Andreas Viktor

    The semantics of first-order logic (FOL) can be described in the meta-language of higher-order logic (HOL). Using HOL one can prove key properties of FOL such as soundness and completeness. Furthermore, one can prove sentences in FOL valid using the formalized FOL semantics. To aid...

  1. Two (multi point nonlinear Lyapunov systems associated with an n th order nonlinear system of differential equations – existence and uniqueness

    Directory of Open Access Journals (Sweden)

    Murty K. N.

    2000-01-01

    Full Text Available This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with an n th order nonlinear Lyapunov system. A variation of parameters formula is developed and used as a tool to obtain existence and uniqueness. We discuss solution of the second order problem by the ADI method and develop a fixed point method to find the general solution of the n th order Lyapunov system. The results of Barnett (SIAM J. Appl. Anal. 24(1, 1973 are a particular case.

  2. Stability analysis of embedded solitons in the generalized third-order nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Pelinovsky, Dmitry E.; Yang Jianke

    2005-01-01

    We study the generalized third-order nonlinear Schroedinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons

  3. Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell–Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model

    International Nuclear Information System (INIS)

    Lorin, E; Bandrauk, A D; Lytova, M; Memarian, A

    2015-01-01

    This paper is dedicated to the exploration of non-conventional nonlinear optics models for intense and short electromagnetic fields propagating in a gas. When an intense field interacts with a gas, usual nonlinear optics models, such as cubic nonlinear Maxwell, wave and Schrödinger equations, derived by perturbation theory may become inaccurate or even irrelevant. As a consequence, and to include in particular the effect of free electrons generated by laser–molecule interaction, several heuristic models, such as UPPE, HOKE models, etc, coupled with Drude-like models [1, 2], were derived. The goal of this paper is to present alternative approaches based on non-heuristic principles. This work is in particular motivated by the on-going debate in the filamentation community, about the effect of high order nonlinearities versus plasma effects due to free electrons, in pulse defocusing occurring in laser filaments [3–9]. The motivation of our work goes beyond filamentation modeling, and is more generally related to the interaction of any external intense and (short) pulse with a gas. In this paper, two different strategies are developed. The first one is based on the derivation of an evolution equation on the polarization, in order to determine the response of the medium (polarization) subject to a short and intense electromagnetic field. Then, we derive a combined semi-heuristic model, based on Lewenstein’s strong field approximation model and the usual perturbative modeling in nonlinear optics. The proposed model allows for inclusion of high order nonlinearities as well as free electron plasma effects. (paper)

  4. Higher-Order and Symbolic Computation

    DEFF Research Database (Denmark)

    Danvy, Olivier; Mason, Ian

    2008-01-01

    a series of implementaions that properly account for multiple invocations of the derivative-taking opeatro. In "Adapting Functional Programs to Higher-Order Logic," Scott Owens and Konrad Slind present a variety of examples of terminiation proofs of functional programs written in HOL proof systems. Since......-calculus programs, historically. The anaylsis determines the possible locations of ambients and mirrors the temporla sequencing of actions in the structure of types....

  5. Fermat collocation method for the solutions of nonlinear system of second order boundary value problems

    Directory of Open Access Journals (Sweden)

    Salih Yalcinbas

    2016-01-01

    Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.

  6. Creating large second-order optical nonlinearity in optical waveguides written by femtosecond laser pulses in boro-aluminosilicate glass

    Science.gov (United States)

    An, Hong-Lin; Arriola, Alexander; Gross, Simon; Fuerbach, Alexander; Withford, Michael J.; Fleming, Simon

    2014-01-01

    The thermal poling technique was applied to optical waveguides embedded in a commercial boro-aluminosilicate glass, resulting in high levels of induced second-order optical nonlinearity. The waveguides were fabricated using the femtosecond laser direct-write technique, and thermally poled samples were characterized with second harmonic optical microscopy to reveal the distribution profile of the induced nonlinearity. It was found that, in contrast to fused silica, the presence of waveguides in boro-aluminosilicate glass led to an enhancement of the creation of the second-order nonlinearity, which is larger in the laser written waveguiding regions when compared to the un-modified substrate. The magnitude of the nonlinear coefficient d33 achieved in the core of the laser-written waveguides, up to 0.2 pm/V, was comparable to that in thermally poled fused silica, enabling the realization of compact integrated electro-optic devices in boro-aluminosilicate glasses.

  7. All-fiber Raman Probe using Higher Order Modes

    DEFF Research Database (Denmark)

    Larsen, Stine Højer Møller; Rishøj, Lars Søgaard; Rottwitt, Karsten

    2013-01-01

    We demonstrate the first all-fiber Raman probe utilizing higher order modes for the excitation. The spectrum of cyclohexane is measured using both the fundamental mode as well as in-fiber-generated Bessel-like modes.......We demonstrate the first all-fiber Raman probe utilizing higher order modes for the excitation. The spectrum of cyclohexane is measured using both the fundamental mode as well as in-fiber-generated Bessel-like modes....

  8. On the origin of higher braces and higher-order derivations

    Czech Academy of Sciences Publication Activity Database

    Markl, Martin

    2015-01-01

    Roč. 10, č. 3 (2015), s. 637-667 ISSN 2193-8407 Institutional support: RVO:67985840 Keywords : Koszul braces * Börjeseon braces * higher-order derivation Subject RIV: BA - General Mathematics Impact factor: 0.600, year: 2015 http://link.springer.com/article/10.1007/s40062-014-0079-2

  9. ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.

  10. Classical higher-order processes

    DEFF Research Database (Denmark)

    Montesi, Fabrizio

    2017-01-01

    Classical Processes (CP) is a calculus where the proof theory of classical linear logic types processes à la Π-calculus, building on a Curry-Howard correspondence between session types and linear propositions. We contribute to this research line by extending CP with process mobility, inspired...... by the Higher-Order Π-calculus. The key to our calculus is that sequents are asymmetric: one side types sessions as in CP and the other types process variables, which can be instantiated with process values. The controlled interaction between the two sides ensures that process variables can be used at will......, but always respecting the linear usage of sessions expected by the environment....

  11. Higher order nonlinear equations for the dust-acoustic waves in a dusty plasma with two temperature-ions and nonextensive electrons

    International Nuclear Information System (INIS)

    Emamuddin, M.; Yasmin, S.; Mamun, A. A.

    2013-01-01

    The nonlinear propagation of dust-acoustic waves in a dusty plasma whose constituents are negatively charged dust, Maxwellian ions with two distinct temperatures, and electrons following q-nonextensive distribution, is investigated by deriving a number of nonlinear equations, namely, the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV), and the Gardner equations. The basic characteristics of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two temperature ions and electron nonextensivity on the basic features of DA K-dV, mK-dV, and Gardner solitons are also examined. It has been observed that the DA Gardner solitons exhibit negative (positive) solitons for q c (q>q c ) (where q c is the critical value of the nonextensive parameter q). The implications of our results in understanding the localized nonlinear electrostatic perturbations existing in stellar polytropes, quark-gluon plasma, protoneutron stars, etc. (where ions with different temperatures and nonextensive electrons exist) are also briefly addressed.

  12. Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators

    KAUST Repository

    Talukdar, Abdul Hafiz

    2011-05-01

    Exceptional behaviours of Memristor are illustrated in Memristor based second order (Wien oscillator) and third order (phase shift oscillator) oscillator systems in this Thesis. Conventional concepts about sustained oscillation have been argued by demonstrating the possibility of sustained oscillation with oscillating resistance and dynamic poles. Mathematical models are also proposed for analysis and simulations have been presented to support the surprising characteristics of the Memristor based oscillator systems. This thesis also describes a comparative study among the Wien family oscillators with one Memristor. In case of phase shift oscillator, one Memristor and three Memristors systems are illustrated and compared to generalize the nonlinear dynamics observed for both 2nd order and 3rd order system. Detail explanations are provided with analytical models to simplify the unconventional properties of Memristor based oscillatory systems.

  13. CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

    OpenAIRE

    Roldan, Omar

    2017-01-01

    We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instan...

  14. Higher-Order Cyclostationarity Detection for Spectrum Sensing

    Directory of Open Access Journals (Sweden)

    Julien Renard

    2010-01-01

    Full Text Available Recent years have shown a growing interest in the concept of Cognitive Radios (CRs, able to access portions of the electromagnetic spectrum in an opportunistic operating way. Such systems require efficient detectors able to work in low Signal-to-Noise Ratio (SNR environments, with little or no information about the signals they are trying to detect. Energy detectors are widely used to perform such blind detection tasks, but quickly reach the so-called SNR wall below which detection becomes impossible Tandra (2005. Cyclostationarity detectors are an interesting alternative to energy detectors, as they exploit hidden periodicities present in man-made signals, but absent in noise. Such detectors use quadratic transformations of the signals to extract the hidden sine-waves. While most of the literature focuses on the second-order transformations of the signals, we investigate the potential of higher-order transformations of the signals. Using the theory of Higher-Order Cyclostationarity (HOCS, we derive a fourth-order detector that performs similarly to the second-order ones to detect linearly modulated signals, at SNR around 0 dB, which may be used if the signals of interest do not exhibit second-order cyclostationarity. More generally this paper reviews the relevant aspects of the cyclostationary and HOCS theory, and shows their potential for spectrum sensing.

  15. Synthesis, crystal structure, growth, optical and third order nonlinear optical studies of 8HQ2C5N single crystal - An efficient third-order nonlinear optical material

    Energy Technology Data Exchange (ETDEWEB)

    Divya Bharathi, M.; Ahila, G.; Mohana, J. [Department of Physics, Presidency College, Chennai 600005 (India); Chakkaravarthi, G. [Department of Physics, CPCL Polytechnic College, Chennai 600068 (India); Anbalagan, G., E-mail: anbu24663@yahoo.co.in [Department of Nuclear Physics, University of Madras, Chennai 600025 (India)

    2017-05-01

    A neoteric organic third order nonlinear optical material 8-hydroxyquinolinium 2-chloro-5-nitrobenzoate dihydrate (8HQ2C5N) was grown by slow cooling technique using ethanol: water (1:1) mixed solvent. The calculated low value of average etch pit solidity (4.12 × 10{sup 3} cm{sup −2}) indicated that the title crystal contain less defects. From the single crystal X-ray diffraction data, it was endowed that 8HQ2C5N crystal belongs to the monoclinic system with centrosymmetric space group P2{sub 1}/c and the cell parameters values, a = 9.6546 (4) Ǻ, b = 7.1637(3) Ǻ, c = 24.3606 (12) Ǻ, α = γ = 90°, β = 92.458(2)° and volume = 1683.29(13) Ǻ{sup 3}. The FT-IR and FT-Raman spectrum were used to affirm the functional group of the title compound. The chemical structure of 8HQ2C5N was scrutinized by {sup 13}C and {sup 1}H NMR spectral analysis and thermal stability through the differential scanning calorimetry study. Using optical studies the lower cut-off wavelength and optical band gap of 8HQ2C5N were found to be 364 nm and 3.17 eV respectively. Using the single oscillator model suggested by Wemple – Didomenico, the oscillator energy (E{sub o}), the dispersion energy (E{sub d}) and static dielectric constant (ε{sub o}) were estimated. The third-order susceptibility were determined as Im χ{sup (3)} = 2.51 × 10{sup −5} esu and Re χ{sup (3)} = 4.46 × 10{sup −7} esu. The theoretical third-order nonlinear optical susceptibility χ{sup (3)} was calculated and the results were compared with experimental value. Photoluminescence spectrum of 8HQ2C5N crystal showed the yellow emission. The crystal had the single shot laser damage threshold of 5.562 GW/cm{sup 2}. Microhardness measurement showed that 8HQ2C5N belongs to a soft material category. - Highlights: • A new organic single crystals were grown and the crystal structure was reported. • Crystal possess, good transmittance, thermal and mechanical stability. • Single shot LDT value is found to be

  16. Internal crisis in a second-order non-linear non-autonomous electronic oscillator

    International Nuclear Information System (INIS)

    Stavrinides, S.G.; Deliolanis, N.C.; Miliou, A.N.; Laopoulos, Th.; Anagnostopoulos, A.N.

    2008-01-01

    The internal crisis of a second-order non-linear non-autonomous chaotic electronic circuit is studied. The phase portraits consist of two interacting sub-attractors, a chaotic and a periodic one. Maximal Lyapunov exponents were calculated, for both the periodic and the chaotic waveforms, in order to confirm their nature. Transitions between the chaotic and the periodic sub-attractors become more frequent by increasing the circuit driving frequency. The frequency distribution of the corresponding laminar lengths and their average values indicate that an internal crisis takes place in this circuit, manifested in the intermittent behaviour of the corresponding orbits

  17. Higher-order tensors in diffusion imaging

    NARCIS (Netherlands)

    Schultz, T.; Fuster, A.; Ghosh, A.; Deriche, R.; Florack, L.M.J.; Lim, L.H.; Westin, C.-F.; Vilanova, A.; Burgeth, B.

    2014-01-01

    Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion

  18. Propagation of sech2-type solitary waves in higher-order KdV-type systems

    International Nuclear Information System (INIS)

    Ilison, O.; Salupere, A.

    2005-01-01

    Wave propagation in microstructured media is essentially influenced by nonlinear and dispersive effects. The simplest model governing these effects results in the Korteweg-de Vries (KdV) equation. In the present paper a KdV-type evolution equation, including the third- and fifth-order dispersive and the fourth-order nonlinear terms, is used for modelling the wave propagation in microstructured solids like martensitic-austenitic alloys. The model equation is solved numerically under localised initial conditions. Possible solution types are defined and discussed. The existence of a threshold is established. Below the threshold, the relatively small solitary waves decay in time. However, if the amplitude exceeds a certain threshold, i.e., the critical value, then such a solitary wave can propagate with nearly a constant speed and amplitude and consequently conserve the energy

  19. Uncertainty analysis of nonlinear systems employing the first-order reliability method

    International Nuclear Information System (INIS)

    Choi, Chan Kyu; Yoo, Hong Hee

    2012-01-01

    In most mechanical systems, properties of the system elements have uncertainties due to several reasons. For example, mass, stiffness coefficient of a spring, damping coefficient of a damper or friction coefficients have uncertain characteristics. The uncertain characteristics of the elements have a direct effect on the system performance uncertainty. It is very important to estimate the performance uncertainty since the performance uncertainty is directly related to manufacturing yield and consumer satisfaction. Due to this reason, the performance uncertainty should be estimated accurately and considered in the system design. In this paper, performance measures are defined for nonlinear vibration systems and the performance measure uncertainties are estimated employing the first order reliability method (FORM). It was found that the FORM could provide good results in spite of the system nonlinear characteristics. Comparing to the results obtained by Monte Carlo Simulation (MCS), the accuracy of the uncertainty analysis results obtained by the FORM is validated

  20. Third-order nonlinear optical properties of 1,3-bis(3,4-dimethoxyphenyl) prop-2-en-1-one under femtosecond laser pulses

    Science.gov (United States)

    Maidur, Shivaraj R.; Patil, Parutagouda Shankaragouda; Rao, S. Venugopal

    2018-04-01

    In this paper, we present the third-order nonlinear optical (NLO) studies of 1,3-bis(3,4-dimethoxyphenyl)prop-2-en-1-one (abbreviated as VDMC). The chalcone was synthesized by Claisen-Schmidt condensation method. The third-order nonlinear optical properties were evaluated using standard, well-known Z-scan technique under femtosecond laser regime (150 fs, 900 nm) with two different laser repetition rates 500 Hz and 80 MHz. Open aperture studies showed that the molecule possess two photon absorption with the coefficients in the order 10-9 cmW-1. The closed aperture studies have resulted the negative nonlinear refraction with the coefficients in the order 10-14 cm2W-1. The two-photon absorption cross sections were estimated. Optical limiting properties have been studied and the limiting threshold values were found to be in the range 0.86-2.3 mJ/cm2, which suggests that VDMC has better applications in the field of nonlinear optics.

  1. Theorem Proving In Higher Order Logics

    Science.gov (United States)

    Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene

    2002-01-01

    The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.

  2. Third order nonlinear optical properties of a paratellurite single crystal

    Science.gov (United States)

    Duclère, J.-R.; Hayakawa, T.; Roginskii, E. M.; Smirnov, M. B.; Mirgorodsky, A.; Couderc, V.; Masson, O.; Colas, M.; Noguera, O.; Rodriguez, V.; Thomas, P.

    2018-05-01

    The (a,b) plane angular dependence of the third-order nonlinear optical susceptibility, χ(3) , of a c-cut paratellurite (α-TeO2) single crystal was quantitatively evaluated here by the Z-scan technique, using a Ti:sapphire femtosecond laser operated at 800 nm. In particular, the mean value Re( ⟨χ(3)⟩a,b )(α-TeO2) of the optical tensor has been extracted from such experiments via a direct comparison with the data collected for a fused silica reference glass plate. A R e (⟨χ(3)⟩(a,b )(α-TeO2)):R e (χ(3))(SiO2 glass) ratio roughly equal to 49.1 is found, and our result compares thus very favourably with the unique experimental value (a ratio of ˜50) reported by Kim et al. [J. Am. Ceram. Soc. 76, 2486 (1993)] for a pure TeO2 glass. In addition, it is shown that the angular dependence of the phase modulation within the (a,b) plane can be fully understood in the light of the strong dextro-rotatory power known for TeO2 materials. Taking into account the optical activity, some analytical model serving to estimate the diagonal and non-diagonal components of the third order nonlinear susceptibility tensor has been thus developed. Finally, Re( χxxxx(3) ) and Re( χxxyy(3) ) values of 95.1 ×10-22 m 2/V2 and 42.0 ×10-22 m2/V2 , respectively, are then deduced for a paratellurite single crystal, considering fused silica as a reference.

  3. Multi-bi- and tri-stability using nonlinear plasmonic Fano resonators

    KAUST Repository

    Amin, Muhammad

    2013-09-01

    A plasmonic Fano resonator embedding Kerr nonlinearity is used to achieve multi-bi- and tri-stability. Fano resonance is obtained by inducing higher-order plasmon modes on metallic surfaces via geometrical symmetry breaking. The presence of the multiple higher order plasmon modes provides the means for producing multi-bi- or tri-stability in the response of the resonator when it is loaded with a material with Kerr nonlinearity. The multi-stability in the response of the proposed resonator enables its use in three-state all optical memory and switching applications. © 2013 IEEE.

  4. Validity testing of third-order nonlinear models for synchronous generators

    Energy Technology Data Exchange (ETDEWEB)

    Arjona, M.A. [Division de Estudios de Posgrado e Investigacion, Instituto Tecnologico de La Laguna Torreon, Coah. (Mexico); Escarela-Perez, R. [Universidad Autonoma Metropolitana - Azcapotzalco, Departamento de Energia, Av. San Pablo 180, Col. Reynosa, C.P. 02200 (Mexico); Espinosa-Perez, G. [Division de Estudios Posgrado de la Facultad de Ingenieria Universidad Nacional Autonoma de Mexico (Mexico); Alvarez-Ramirez, J. [Universidad Autonoma Metropolitana -Iztapalapa, Division de Ciencias Basicas e Ingenieria (Mexico)

    2009-06-15

    Third-order nonlinear models are commonly used in control theory for the analysis of the stability of both open-loop and closed-loop synchronous machines. However, the ability of these models to describe the electrical machine dynamics has not been tested experimentally. This work focuses on this issue by addressing the parameters identification problem for third-order models for synchronous generators. For a third-order model describing the dynamics of power angle {delta}, rotor speed {omega} and quadrature axis transient EMF E{sub q}{sup '}, it is shown that the parameters cannot be identified because of the effects of the unknown initial condition of E{sub q}{sup '}. To avoid this situation, a model that incorporates the measured electrical power dynamics is considered, showing that state measurements guarantee the identification of the model parameters. Data obtained from a 7 kVA lab-scale synchronous generator and from a 150 MVA finite-element simulation were used to show that, at least for the worked examples, the estimated parameters display only moderate variations over the operating region. This suggests that third-order models can suffice to describe the main dynamical features of synchronous generators, and that third-order models can be used to design and tune power system stabilizers and voltage regulators. (author)

  5. Ring vortex solitons in nonlocal nonlinear media

    DEFF Research Database (Denmark)

    Briedis, D.; Petersen, D.E.; Edmundson, D.

    2005-01-01

    We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single...... or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction....

  6. Spectral methods for a nonlinear initial value problem involving pseudo differential operators

    International Nuclear Information System (INIS)

    Pasciak, J.E.

    1982-01-01

    Spectral methods (Fourier methods) for approximating the solution of a nonlinear initial value problem involving pseudo differential operators are defined and analyzed. A semidiscrete approximation to the nonlinear equation based on an L 2 projection is described. The semidiscrete L 2 approximation is shown to be a priori stable and convergent under sufficient decay and smoothness assumptions on the initial data. It is shown that the semidiscrete method converges with infinite order, that is, higher order decay and smoothness assumptions imply higher order error bounds. Spectral schemes based on spacial collocation are also discussed

  7. Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials.

    Science.gov (United States)

    Chen, Yong; Yan, Zhenya

    2016-03-22

    Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.

  8. Complete modulational-instability gain spectrum of nonlinear quasi-phase-matching gratings

    DEFF Research Database (Denmark)

    Corney, Joel F.; Bang, Ole

    2004-01-01

    We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phasematching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher-order gain bands....

  9. Sturm-Picone type theorems for second-order nonlinear differential equations

    Directory of Open Access Journals (Sweden)

    Aydin Tiryaki

    2014-06-01

    Full Text Available The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations $$\\displaylines{ (p_1(t|x'|^{\\alpha-1}x''+q_1(tf_1(x=0 \\cr (p_2(t|y'|^{\\alpha-1}y''+q_2(tf_2(y=0,\\quad t_1

  10. Self-similarity of higher-order moving averages

    Science.gov (United States)

    Arianos, Sergio; Carbone, Anna; Türk, Christian

    2011-10-01

    In this work, higher-order moving average polynomials are defined by straightforward generalization of the standard moving average. The self-similarity of the polynomials is analyzed for fractional Brownian series and quantified in terms of the Hurst exponent H by using the detrending moving average method. We prove that the exponent H of the fractional Brownian series and of the detrending moving average variance asymptotically agree for the first-order polynomial. Such asymptotic values are compared with the results obtained by the simulations. The higher-order polynomials correspond to trend estimates at shorter time scales as the degree of the polynomial increases. Importantly, the increase of polynomial degree does not require to change the moving average window. Thus trends at different time scales can be obtained on data sets with the same size. These polynomials could be interesting for those applications relying on trend estimates over different time horizons (financial markets) or on filtering at different frequencies (image analysis).

  11. Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity

    DEFF Research Database (Denmark)

    Sfahania, M. G.; Ganji, S. S.; Barari, Amin

    2010-01-01

    This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presen...

  12. Formulation of nonlinear chromaticity in circular accelerators by canonical perturbation method

    International Nuclear Information System (INIS)

    Takao, Masaru

    2005-01-01

    The formulation of nonlinear chromaticity in circular accelerators based on the canonical perturbation method is presented. Since the canonical perturbation method directly relates the tune shift to the perturbation Hamiltonian, it greatly simplifies the calculation of the nonlinear chromaticity. The obtained integral representation for nonlinear chromaticity can be systematically extended to higher orders

  13. Symmetry of the complete second-order nonlinear conductivity tensor for an unmagnetized relativistic turbulent plasma

    International Nuclear Information System (INIS)

    Brandt, H.E.

    1983-01-01

    A new exact symmetry is proved for the complete second-order nonlinear conductivity tensor of an unmagnetized relativistic turbulent plasma. The symmetry is not limited to principal parts. If Cerenkov resonance is ignored, the new symmetry reduces to the well-known symmetry related to the Manley--Rowe relations, crossing symmetry, and nondissipation of the principal part of the nonlinear current. Also, a new utilitarian representation for the complete tensor is obtained in which all derivatives are removed and the pole structure is clearly exhibited

  14. Compiler-Directed Transformation for Higher-Order Stencils

    Energy Technology Data Exchange (ETDEWEB)

    Basu, Protonu [Univ. of Utah, Salt Lake City, UT (United States); Hall, Mary [Univ. of Utah, Salt Lake City, UT (United States); Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Straalen, Brian Van [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oliker, Leonid [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Colella, Phillip [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

    2015-07-20

    As the cost of data movement increasingly dominates performance, developers of finite-volume and finite-difference solutions for partial differential equations (PDEs) are exploring novel higher-order stencils that increase numerical accuracy and computational intensity. This paper describes a new compiler reordering transformation applied to stencil operators that performs partial sums in buffers, and reuses the partial sums in computing multiple results. This optimization has multiple effect son improving stencil performance that are particularly important to higher-order stencils: exploits data reuse, reduces floating-point operations, and exposes efficient SIMD parallelism to backend compilers. We study the benefit of this optimization in the context of Geometric Multigrid (GMG), a widely used method to solvePDEs, using four different Jacobi smoothers built from 7-, 13-, 27-and 125-point stencils. We quantify performance, speedup, andnumerical accuracy, and use the Roofline model to qualify our results. Ultimately, we obtain over 4× speedup on the smoothers themselves and up to a 3× speedup on the multigrid solver. Finally, we demonstrate that high-order multigrid solvers have the potential of reducing total data movement and energy by several orders of magnitude.

  15. Non-critically phase-matched second harmonic generation and third order nonlinearity in organic crystal glucuronic acid γ-lactone

    Science.gov (United States)

    Saripalli, Ravi Kiran; Katturi, Naga Krishnakanth; Soma, Venugopal Rao; Bhat, H. L.; Elizabeth, Suja

    2017-12-01

    The linear, second order, and third order nonlinear optical properties of glucuronic acid γ-lactone single crystals were investigated. The optic axes and principal dielectric axes were identified through optical conoscopy and the principal refractive indices were obtained using the Brewster's angle method. Conic sections were observed which is perceived to be due to spontaneous non-collinear phase matching. The direction of collinear phase matching was determined and the deff evaluated in this direction was 0.71 pm/V. Open and closed aperture Z-scan measurements with femtosecond pulses revealed high third order nonlinearity in the form of self-defocusing, two-photon absorption, as well as saturable absorption.

  16. Higher-Order Components for Grid Programming

    CERN Document Server

    Dünnweber, Jan

    2009-01-01

    Higher-Order Components were developed within the CoreGRID European Network of Excellence and have become an optional extension of the popular Globus middleware. This book provides the reader with hands-on experience, describing a collection of example applications from various fields of science and engineering, including biology and physics.

  17. Higher order aberrations of the eye: Part one

    Directory of Open Access Journals (Sweden)

    Marsha Oberholzer

    2016-06-01

    Full Text Available This article is the first in a series of two articles that provide a comprehensive literature review of higher order aberrations (HOAs of the eye. The present article mainly explains the general principles of such HOAs as well as HOAs of importance, and the measuring apparatus used to measure HOAs of the eye. The second article in the series discusses factors contributing to variable results in measurements of HOAs of the eye. Keywords: Higher order aberrations; wavefront aberrations; aberrometer

  18. Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems

    International Nuclear Information System (INIS)

    Prieto-Martinez, Pedro Daniel; Roman-Roy, Narciso

    2011-01-01

    The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view. (paper)

  19. Higher Order Lagrange Finite Elements In M3D

    International Nuclear Information System (INIS)

    Chen, J.; Strauss, H.R.; Jardin, S.C.; Park, W.; Sugiyama, L.E.; Fu, G.; Breslau, J.

    2004-01-01

    The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles

  20. Femtosecond single-beam direct laser poling of stable and efficient second-order nonlinear optical properties in glass

    International Nuclear Information System (INIS)

    Papon, G.; Marquestaut, N.; Royon, A.; Canioni, L.; Petit, Y.; Dussauze, M.; Rodriguez, V.; Cardinal, T.

    2014-01-01

    We depict a new approach for the localized creation in three dimensions (3D) of a highly demanded nonlinear optical function for integrated optics, namely second harmonic generation. We report on the nonlinear optical characteristics induced by single-beam femtosecond direct laser writing in a tailored silver-containing phosphate glass. The original spatial distribution of the nonlinear pattern, composed of four lines after one single laser writing translation, is observed and modeled with success, demonstrating the electric field induced origin of the second harmonic generation. These efficient second-order nonlinear structures (with χ eff (2)  ∼ 0.6 pm V −1 ) with sub-micron scale are impressively stable under thermal constraint up to glass transition temperature, which makes them very promising for new photonic applications, especially when 3D nonlinear architectures are desired

  1. Higher-Order Hybrid Gaussian Kernel in Meshsize Boosting Algorithm

    African Journals Online (AJOL)

    In this paper, we shall use higher-order hybrid Gaussian kernel in a meshsize boosting algorithm in kernel density estimation. Bias reduction is guaranteed in this scheme like other existing schemes but uses the higher-order hybrid Gaussian kernel instead of the regular fixed kernels. A numerical verification of this scheme ...

  2. Nonlinear Parameter-Varying AeroServoElastic Reduced Order Model for Aerostructural Sensing and Control, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — The overall goal of the project is to develop reliable reduced order modeling technologies to automatically generate nonlinear, parameter-varying (PV),...

  3. Sinusoidal oscillators with lower gain requirements at higher frequencies based on an explicit tanh(x) nonlinearity

    KAUST Repository

    Elwakil, Ahmed S.

    2009-04-28

    Two novel sinusoidal oscillator structures with an explicit tanh(x) nonlinearity are proposed. The oscillators have the attractive feature: the higher the operating frequency, the lower the necessary gain required to start oscillations. A nonlinear model for the two oscillators is derived and verified numerically. Spice simulations using AMS BiCMOS 0.35 μ model parameters and experimental results are shown. Copyright © 2009 John Wiley & Sons, Ltd.

  4. On some nonlinear effects in ultrasonic fields

    Science.gov (United States)

    Tjotta

    2000-03-01

    Nonlinear effects associated with intense sound fields in fluids are considered theoretically. Special attention is directed to the study of higher effects that cannot be described within the standard propagation models of nonlinear acoustics (the KZK and Burgers equations). The analysis is based on the fundamental equations of motion for a thermoviscous fluid, for which thermal equations of state exist. Model equations are derived and used to analyze nonlinear sources for generation of flow and heat, and other changes in the ambient state of the fluid. Fluctuations in the coefficients of viscosity and thermal conductivity caused by the sound field, are accounted for. Also considered are nonlinear effects induced in the fluid by flexural vibrations. The intensity and absorption of finite amplitude sound waves are calculated, and related to the sources for generation of higher order effects.

  5. High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

    Science.gov (United States)

    Fisher, Travis C.; Carpenter, Mark H.

    2013-01-01

    Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

  6. Higher Order and Fractional Diffusive Equations

    Directory of Open Access Journals (Sweden)

    D. Assante

    2015-07-01

    Full Text Available We discuss the solution of various generalized forms of the Heat Equation, by means of different tools ranging from the use of Hermite-Kampé de Fériet polynomials of higher and fractional order to operational techniques. We show that these methods are useful to obtain either numerical or analytical solutions.

  7. On the physical contributions to the third-order nonlinear optical response in plasmonic nanocomposites

    International Nuclear Information System (INIS)

    Fernández-Hernández, Roberto Carlos; Gleason-Villagran, Roberto; Rodríguez-Fernández, Luis; Crespo-Sosa, Alejandro; Cheang-Wong, Juan Carlos; López-Suárez, Alejandra; Oliver, Alicia; Reyes-Esqueda, Jorge Alejandro; Torres-Torres, Carlos; Rangel-Rojo, Raúl

    2012-01-01

    Au and Ag isotropic and anisotropic nanocomposites were prepared using the ion implantation technique. Their optical properties were studied at several wavelengths in the optical range 300–800 nm, across their plasmon resonances. The linear regime was characterized by measuring the absorption spectrum and the third-order nonlinear regime by means of the Z-scan technique using a tunable picosecond pulsed laser system (26 ps). Open-aperture Z-scan traces show a superposition of different optical nonlinear absorption (NLA) processes in the whole range studied. We associate these phenomena with the excitation of inter- and intra-band electronic transitions, which contribute with a positive sign to NLA, and to the formation of hot-electrons, which contribute with opposite sign to NLA. Closed-aperture traces for measuring nonlinear refraction (NLR) show different signs for Au and Ag samples, and a change of sign in Au is found when purely inter-band transitions are excited. In this work, for the appropriate wavelength, it is worth remarking on the free-electron response to the exciting light and its strong contribution to the nonlinear optical properties for low (intra-band) and high (hot-electrons) irradiances. (paper)

  8. Generating higher-order Lie algebras by expanding Maurer-Cartan forms

    International Nuclear Information System (INIS)

    Caroca, R.; Merino, N.; Salgado, P.; Perez, A.

    2009-01-01

    By means of a generalization of the Maurer-Cartan expansion method, we construct a procedure to obtain expanded higher-order Lie algebras. The expanded higher-order Maurer-Cartan equations for the case G=V 0 +V 1 are found. A dual formulation for the S-expansion multialgebra procedure is also considered. The expanded higher-order Maurer-Cartan equations are recovered from S-expansion formalism by choosing a special semigroup. This dual method could be useful in finding a generalization to the case of a generalized free differential algebra, which may be relevant for physical applications in, e.g., higher-spin gauge theories.

  9. Modular specification and verification for higher-order languages with state

    DEFF Research Database (Denmark)

    Svendsen, Kasper

    The overall topic of this thesis is modular reasoning for higher-order languages with state. The thesis consists of four mostly independent chapters that each deal with a different aspect of reasoning about higher-order languages with state. The unifying theme throughout all four chapters is higher....... The third chapter of the thesis is a case study of the C# joins library. What makes this library interesting as a case study is that it combines a lot of advanced features (higher-order code with effects, concurrency, recursion through the store, shared mutable state, and fine-grained synchronization...

  10. Experimental study of the third-order nonlinearity of atomic and molecular gases using 10-μm laser pulses

    Science.gov (United States)

    Pigeon, J. J.; Tochitsky, S. Ya.; Welch, E. C.; Joshi, C.

    2018-04-01

    We present measurements of the third-order optical nonlinearity of Kr, Xe, N2, O2, and air at a wavelength near 10 µm by using four-wave mixing of ˜15 -GW /c m2 , 200-ps (full width at half maximum) C O2 laser pulses. Measurements in molecular gases resulted in an asymmetric four-wave mixing spectrum indicating that the nonlinear response is strongly affected by the delayed, rotational contribution to the effective nonlinear refractive index. Within the uncertainty of our measurements, we have found that the long-wavelength nonlinear refractive indices of these gases are consistent with measurements performed in the near IR.

  11. Numerical simulation of the nonlinear dynamics of packets of spiral density waves

    International Nuclear Information System (INIS)

    Korchagin, V.I.

    1987-01-01

    In a numerical experiment, the behavior of nonlinear packets of spiral density waves in a gas disk has been investigated for different initial wave amplitudes. If the amplitude of the density perturbations is small (<5%), the wave packet is drawn toward the center or toward the periphery of the disk in accordance with the linear theory. The behavior of linear packets of waves with wavelength comparable to the disk radius (R/sub d//lambda = 4) exhibits good agreement with the conclusions of the linear theory of tightly wound spiral waves. The dynamics of wave packets with initial density amplitudes 16, 30, 50% demonstrates the nonlinear nature of the behavior. THe behavior is governed by whether or not the nonlinear effects of higher than third order in the wave amplitude play a part. If the wave packet dynamics is determined by the cubic nonlinearity, the results of the numerical experiment are in qualitative and quantitative agreement with the nonlinear theory of short waves, although the characteristic scale of the packet and the wavelength are of the order of the disk radius. In the cases when the nonlinear effects of higher orders in the amplitude play an important part, the behavior of a packet does not differ qualitatively from the behavior predicted by the theory of cubic nonlinearity, but the nonlinear spreading of the packet takes place more rapidly

  12. Finding Higher Order Differentials of MISTY1

    Science.gov (United States)

    Tsunoo, Yukiyasu; Saito, Teruo; Kawabata, Takeshi; Nakagawa, Hirokatsu

    MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it is recommended for Japanese e-Government ciphers by the CRYPTREC project. In this paper, we report on 12th order differentials in 3-round MISTY1 with FL functions and 44th order differentials in 4-round MISTY1 with FL functions both previously unknown. We also report that both data complexity and computational complexity of higher order differential attacks on 6-round MISTY1 with FL functions and 7-round MISTY1 with FL functions using the 46th order differential can be reduced to as much as 1/22 of the previous values by using multiple 44th order differentials simultaneously.

  13. Practical implementation of a higher order transverse leakage approximation

    International Nuclear Information System (INIS)

    Prinsloo, Rian H.; Tomašević

    2011-01-01

    Transverse integrated nodal diffusion methods currently represent the standard in full core neutronic simulation. The primary shortcoming in this approach, be it via the Analytic Nodal Method or Nodal Expansion Method, is the utilization of the quadratic transverse leakage approximation. This approach, although proven to work well for typical LWR problems, is not consistent with the formulation of nodal methods and can cause accuracy and convergence problems. In this work an improved, consistent quadratic leakage approximation is formulated, which derives from the class of higher order nodal methods developed some years ago. In this new approach, only information relevant to describing the transverse leak- age terms in the zero-order nodal equations are obtained from the higher order formalism. The method yields accuracy comparable to full higher order methods, but does not suffer from the same computational burden which these methods typically incur. (author)

  14. Higher class groups of Eichler orders

    International Nuclear Information System (INIS)

    Guo Xuejun; Kuku, Aderemi

    2003-11-01

    In this paper, we prove that if A is a quaternion algebra and Λ an Eichler order in A, then the only p-torsion possible in even dimensional higher class groups Cl 2n (Λ) (n ≥ 1) are for those rational primes p which lie under prime ideals of O F at which Λ are not maximal. (author)

  15. Zeolite Y Films as Ideal Platform for Evaluation of Third-Order Nonlinear Optical Quantum Dots

    Directory of Open Access Journals (Sweden)

    Hyun Sung Kim

    2016-01-01

    Full Text Available Zeolites are ideal host material for generation and stabilization of regular ultrasmall quantum dots (QDs array with the size below 1.5 nm. Quantum dots (QDs with high density and extinction absorption coefficient have been expected to give high level of third-order nonlinear optical (3rd-NLO and to have great potential applications in optoelectronics. In this paper, we carried out a systematic elucidation of the third-order nonlinear optical response of various types of QDs including PbSe, PbS, CdSe, CdS, ZnSe, ZnS, Ag2Se, and Ag2S by manipulation of QDs into zeolites Y pores. In this respect, we could demonstrate that the zeolite offers an ideal platform for capability comparison 3rd-NLO response of various types of QDs with high sensitivities.

  16. Higher-Order Integral Equation Methods in Computational Electromagnetics

    DEFF Research Database (Denmark)

    Jørgensen, Erik; Meincke, Peter

    Higher-order integral equation methods have been investigated. The study has focused on improving the accuracy and efficiency of the Method of Moments (MoM) applied to electromagnetic problems. A new set of hierarchical Legendre basis functions of arbitrary order is developed. The new basis...

  17. Time-Discrete Higher-Order ALE Formulations: Stability

    KAUST Repository

    Bonito, Andrea

    2013-01-01

    Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.

  18. The Higher Order Structure of Environmental Attitudes: A Cross-Cultural Examination

    Directory of Open Access Journals (Sweden)

    Taciano L. Milfont

    2010-01-01

    Full Text Available Past research has suggested that Preservation and Utilization are the two higher order dimensions forming the hierarchical structure of environmental attitudes. This means that these two higher order dimensions could group all kinds of perceptions or beliefs regarding the natural environment people have. A crosscultural study was conducted in Brazil, New Zealand, and South Africa to test this hierarchical structure of environmental attitudes. Results from single- and multi-group confirmatory factor analyses demonstrated that environmental attitudes are a multidimensional construct, and that their first-order factors associate to each other to form a vertical structure. However, the question whether the vertical structure comprise a single higher order factor or two higher order factors still remains unanswered. These results are discussed and directions for future research trying to demonstrate that Preservation and Utilization, taken as distinct second-order environmental attitudes factors, are more empirically meaningful than a single and generalised environmental attitudes higher order factor are presented.

  19. Piezoelectric Field Enhanced Second-Order Nonlinear Optical Susceptibilities in Wurtzite GaN/AlGaN Quantum Wells

    Science.gov (United States)

    Liu, Ansheng; Chuang, S.-L.; Ning, C. Z.; Woo, Alex (Technical Monitor)

    1999-01-01

    Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.

  20. Micro-/nanoscale multi-field coupling in nonlinear photonic devices

    Science.gov (United States)

    Yang, Qing; Wang, Yubo; Tang, Mingwei; Xu, Pengfei; Xu, Yingke; Liu, Xu

    2017-08-01

    The coupling of mechanics/electronics/photonics may improve the performance of nanophotonic devices not only in the linear region but also in the nonlinear region. This review letter mainly presents the recent advances on multi-field coupling in nonlinear photonic devices. The nonlinear piezoelectric effect and piezo-phototronic effects in quantum wells and fibers show that large second-order nonlinear susceptibilities can be achieved, and second harmonic generation and electro-optic modulation can be enhanced and modulated. Strain engineering can tune the lattice structures and induce second order susceptibilities in central symmetry semiconductors. By combining the absorption-based photoacoustic effect and intensity-dependent photobleaching effect, subdiffraction imaging can be achieved. This review will also discuss possible future applications of these novel effects and the perspective of their research. The review can help us develop a deeper knowledge of the substance of photon-electron-phonon interaction in a micro-/nano- system. Moreover, it can benefit the design of nonlinear optical sensors and imaging devices with a faster response rate, higher efficiency, more sensitivity and higher spatial resolution which could be applied in environmental detection, bio-sensors, medical imaging and so on.

  1. Multiple periodic solutions for a class of second-order nonlinear neutral delay equations

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available By means of a variational structure and Z 2 -group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the form0, au>0$"> x ″ ( t − τ + λ ( t f ( t , x ( t , x ( t − τ , x ( t − 2 τ = x ( t , λ ( t > 0 , τ > 0 .

  2. Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems.

    Science.gov (United States)

    Mei, Jie; Ren, Wei; Li, Bing; Ma, Guangfu

    2015-09-01

    In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

  3. Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR

    Directory of Open Access Journals (Sweden)

    Dong Zhang

    2017-03-01

    Full Text Available This article presents a new fractional-order sliding mode control (FOSMC strategy based on a linear-quadratic regulator (LQR for a class of uncertain nonlinear systems. First, input/output feedback linearization is used to linearize the nonlinear system and decouple tracking error dynamics. Second, LQR is designed to ensure that the tracking error dynamics converges to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding surface is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, the global stability of the closed-loop control system is analytically proved using Lyapunov stability theory. Finally, a typical single-input single-output system and a typical multi-input multi-output system are simulated to illustrate the effectiveness and advantages of the proposed control strategy. The results of the simulation indicate that the proposed control strategy exhibits excellent performance and robustness with system uncertainties. Compared to conventional integer-order sliding mode control, the high-frequency chattering of the control input is drastically depressed.

  4. Higher-order stochastic differential equations and the positive Wigner function

    Science.gov (United States)

    Drummond, P. D.

    2017-12-01

    General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

  5. Interacting wave fronts and rarefaction waves in a second order model of nonlinear thermoviscous fluids : Interacting fronts and rarefaction waves

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich

    2011-01-01

    A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hami...... is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.......A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...... the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions...

  6. Finite-time output feedback stabilization of high-order uncertain nonlinear systems

    Science.gov (United States)

    Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

    2018-06-01

    This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

  7. Generalized effective potential in nonlinear theories of the 4-th order

    International Nuclear Information System (INIS)

    Ananikyan, N.S.; Savvidy, G.K.

    1980-01-01

    By means of the Legendre transformations in the framework of nonlinear theories of the 4-th order a generalized effective potential GITA(phi, G, H, S) is constructed. It depends on PHI, a possible expectation value of the quantum field; on G, H, possible expectation values of the 2- a.nd 3-point connected Green functions and on S= a possible expectation value of the classical action. The expansion for the functional GITA(phi, G, H, S) is obtained, which is similar to the loop expansion for the effective action GITA(phi)

  8. Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

    Energy Technology Data Exchange (ETDEWEB)

    Troisi, Antonio [Universita degli Studi di Salerno, Dipartimento di Fisica ' ' E.R. Caianiello' ' , Salerno (Italy)

    2017-03-15

    Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f(R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R) = f{sub 0}R{sup n} the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions. (orig.)

  9. New developments in state estimation for Nonlinear Systems

    DEFF Research Database (Denmark)

    Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole

    2000-01-01

    Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a mult......-known estimators, such as the extended Kalman filter (EKF) and its higher-order relatives, in most practical applications....

  10. Nonlinear ultrasonic imaging with X wave

    Science.gov (United States)

    Du, Hongwei; Lu, Wei; Feng, Huanqing

    2009-10-01

    X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.

  11. Higher order multipoles and splines in plasma simulations

    International Nuclear Information System (INIS)

    Okuda, H.; Cheng, C.Z.

    1978-01-01

    The reduction of spatial grid effects in plasma simulations has been studied numerically using higher order multipole expansions and the spline method in one dimension. It is found that, while keeping the higher order moments such as quadrupole and octopole moments substantially reduces the grid effects, quadratic and cubic splines in general have better stability properties for numerical plasma simulations when the Debye length is much smaller than the grid size. In particular the spline method may be useful in three-dimensional simulations for plasma confinement where the grid size in the axial direction is much greater than the Debye length. (Auth.)

  12. Higher-order multipoles and splines in plasma simulations

    International Nuclear Information System (INIS)

    Okuda, H.; Cheng, C.Z.

    1977-12-01

    Reduction of spatial grid effects in plasma simulations has been studied numerically using higher order multipole expansions and spline method in one dimension. It is found that, while keeping the higher order moments such as quadrupole and octopole moments substantially reduces the grid effects, quadratic and cubic splines in general have better stability properties for numerical plasma simulations when the Debye length is much smaller than the grid size. In particular, spline method may be useful in three dimensional simulations for plasma confinement where the grid size in the axial direction is much greater than the Debye length

  13. Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

    Science.gov (United States)

    Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

    2015-12-01

    This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

  14. Third-order optical nonlinearities in bulk and fs-laser inscribed waveguides in strengthened alkali aluminosilcate glass

    Science.gov (United States)

    Almeida, Gustavo F. B.; Almeida, Juliana M. P.; Martins, Renato J.; De Boni, Leonardo; Arnold, Craig B.; Mendonca, Cleber R.

    2018-01-01

    The development of advanced photonics devices requires materials with large optical nonlinearities, fast response times and high optical transparency, while at the same time allowing for the micro/nano-processing needed for integrated photonics. In this context, glasses have been receiving considerable attention given their relevant optical properties which can be specifically tailored by compositional control. Corning Gorilla® Glass (strengthened alkali aluminosilicate glass) is well-known for its use as a protective screen in mobile devices, and has attracted interest as a potential candidate for optical devices. Therefore, it is crucial not only to expand the knowledge on the fabrication of waveguides in Gorilla Glass under different regimes, but also to determine its nonlinear optical response, both using fs-laser pulses. Thus, this paper reports, for the first time, characterization of the third-order optical nonlinearities of Gorilla Glass, as well as linear and nonlinear characterization of waveguide written with femtosecond pulses under the low repetition rate regime (1 kHz).

  15. Physical origin of third order non-linear optical response of porphyrin nanorods

    International Nuclear Information System (INIS)

    Mongwaketsi, N.; Khamlich, S.; Pranaitis, M.; Sahraoui, B.; Khammar, F.; Garab, G.; Sparrow, R.; Maaza, M.

    2012-01-01

    The non-linear optical properties of porphyrin nanorods were studied using Z-scan, Second and Third harmonic generation techniques. We investigated in details the heteroaggregate behaviour formation of [H 4 TPPS 4 ] 2- and [SnTPyP] 2+ mixture by means of the UV-VIS spectroscopy and aggregates structure and morphology by transmission electron microscopy. The porphyrin nanorods under investigation were synthesized by self assembly and molecular recognition method. They have been optimized in view of future application in the construction of the light harvesting system. The focus of this study was geared towards understanding the influence of the type of solvent used on these porphyrins nanorods using spectroscopic and microscopic techniques. Highlights: ► We synthesized porphyrin nanorods by self assembly and molecular recognition method. ► TEM images confirmed solid cylindrical shapes. ► UV-VIS spectroscopy showed the decrease in the absorbance peaks of the precursors. ► The enhanced third-order nonlinearities were observed.

  16. Passive impedance-based second-order sliding mode control for non-linear teleoperators

    Directory of Open Access Journals (Sweden)

    Luis G García-Valdovinos

    2017-02-01

    Full Text Available Bilateral teleoperation systems have attracted significant attention in the last decade mainly because of technological advancements in both the communication channel and computers performance. In addition, non-linear multi-degree-of-freedom bilateral teleoperators along with state observers have become an open research area. In this article, a model-free exact differentiator is used to estimate the full state along with a chattering-free second-order sliding mode controller to guarantee a robust impedance tracking under both constant and an unknown time delay of non-linear multi-degree-of-freedom robots. The robustness of the proposed controller is improved by introducing a change of coordinates in terms of a new nominal reference similar to that used in adaptive control theory. Experimental results that validate the predicted behaviour are presented and discussed using a Phantom Premium 1.0 as the master robot and a Catalyst-5 virtual model as the slave robot. The dynamics of the Catalyst-5 system is solved online.

  17. Global Well-Posedness for Cubic NLS with Nonlinear Damping

    KAUST Repository

    Antonelli, Paolo

    2010-11-04

    We study the Cauchy problem for the cubic nonlinear Schrödinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions. © Taylor & Francis Group, LLC.

  18. The cubic-quintic-septic complex Ginzburg-Landau equation formulation of optical pulse propagation in 3D doped Kerr media with higher-order dispersions

    Science.gov (United States)

    Djoko, Martin; Kofane, T. C.

    2018-06-01

    We investigate the propagation characteristics and stabilization of generalized-Gaussian pulse in highly nonlinear homogeneous media with higher-order dispersion terms. The optical pulse propagation has been modeled by the higher-order (3+1)-dimensional cubic-quintic-septic complex Ginzburg-Landau [(3+1)D CQS-CGL] equation. We have used the variational method to find a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links. The variational equations we obtained have been integrated numerically by the means of the fourth-order Runge-Kutta (RK4) method, which also allows us to investigate the evolution of the generalized-Gaussian beam and the pulse evolution along an optical doped fiber. Then, we have solved the original nonlinear (3+1)D CQS-CGL equation with the split-step Fourier method (SSFM), and compare the results with those obtained, using the variational approach. A good agreement between analytical and numerical methods is observed. The evolution of the generalized-Gaussian beam has shown oscillatory propagation, and bell-shaped dissipative optical bullets have been obtained under certain parameter values in both anomalous and normal chromatic dispersion regimes. Using the natural control parameter of the solution as it evolves, named the total energy Q, our numerical simulations reveal the existence of 3D stable vortex dissipative light bullets, 3D stable spatiotemporal optical soliton, stationary and pulsating optical bullets, depending on the used initial input condition (symmetric or elliptic).

  19. Higher-order dynamical effects in Coulomb dissociation

    International Nuclear Information System (INIS)

    Esbensen, H.

    1994-06-01

    We study the effect of higher-order processes in Coulomb dissociation of 11 Li by numerically solving the three-dimensional time-dependent Schroedinger equation for the relative motion of a di-neutron and the 9 Li core. Comparisons are made to first-order perturbation theory and to measurements. The calculated Coulomb reacceleration effects improve the agreement with experiment, but some discrepancy remains. The effects are much smaller in the dissociation of 11 Be, and they decrease with increasing beam energy. (orig.)

  20. Higher Order Mode Fibers

    DEFF Research Database (Denmark)

    Israelsen, Stine Møller

    This PhD thesis considers higher order modes (HOMs) in optical fibers. That includes their excitation and characteristics. Within the last decades, HOMs have been applied both for space multiplexing in optical communications, group velocity dispersion management and sensing among others......-radial polarization as opposed to the linear polarization of the LP0X modes. The effect is investigated numerically in a double cladding fiber with an outer aircladding using a full vectorial modesolver. Experimentally, the bowtie modes are excited using a long period grating and their free space characteristics...... and polarization state are investigated. For this fiber, the onset of the bowtie effect is shown numerically to be LP011. The characteristics usually associated with Bessel-likes modes such as long diffraction free length and selfhealing are shown to be conserved despite the lack of azimuthal symmetry...

  1. Nonlinear surface elastic modes in crystals

    Science.gov (United States)

    Gorentsveig, V. I.; Kivshar, Yu. S.; Kosevich, A. M.; Syrkin, E. S.

    1990-03-01

    The influence of nonlinearity on shear horizontal surface elastic waves in crystals is described on the basis of the effective nonlinear Schrödinger equation. It is shown that the corresponding solutions form a set of surface modes and the simplest mode coincides with the solution proposed by Mozhaev. The higher order modes have internal frequencies caused by the nonlinearity. All these modes decay in the crystal as uoexp(- z/ zo) atz≫ zo- u o-1 ( z is the distance from the crystal surface, uo the wave amplitude at the surface). The creation of the modes from a localized surface excitation has a threshold. The stability of the modes is discussed.

  2. The differential geometry of higher order jets and tangent bundles

    International Nuclear Information System (INIS)

    De Leon, M.; Rodrigues, P.R.

    1985-01-01

    This chapter is devoted to the study of basic geometrical notions required for the development of the main object of the text. Some facts about Jet theory are reviewed. A particular case of Jet manifolds is considered: the tangent bundle of higher order. It is shown that this jet bundle possesses in a canonical way a certain kind of geometric structure, the so called almost tangent structure of higher order, and which is a generalization of the almost tangent geometry of the tangent bundle. Another important fact examined is the extension of the notion of 'spray' to higher order tangent bundles. (Auth.)

  3. Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion

    Science.gov (United States)

    Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin

    2014-09-01

    We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

  4. Linear matrix differential equations of higher-order and applications

    Directory of Open Access Journals (Sweden)

    Mustapha Rachidi

    2008-07-01

    Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.

  5. Conductivity of higher dimensional holographic superconductors with nonlinear electrodynamics

    Science.gov (United States)

    Sheykhi, Ahmad; Hashemi Asl, Doa; Dehyadegari, Amin

    2018-06-01

    We investigate analytically as well as numerically the properties of s-wave holographic superconductors in d-dimensional spacetime and in the presence of Logarithmic nonlinear electrodynamics. We study three aspects of this kind of superconductors. First, we obtain, by employing analytical Sturm-Liouville method as well as numerical shooting method, the relation between critical temperature and charge density, ρ, and disclose the effects of both nonlinear parameter b and the dimensions of spacetime, d, on the critical temperature Tc. We find that in each dimension, Tc /ρ 1 / (d - 2) decreases with increasing the nonlinear parameter b while it increases with increasing the dimension of spacetime for a fixed value of b. Then, we calculate the condensation value and critical exponent of the system analytically and numerically and observe that in each dimension, the dimensionless condensation get larger with increasing the nonlinear parameter b. Besides, for a fixed value of b, it increases with increasing the spacetime dimension. We confirm that the results obtained from our analytical method are in agreement with the results obtained from numerical shooting method. This fact further supports the correctness of our analytical method. Finally, we explore the holographic conductivity of this system and find out that the superconducting gap increases with increasing either the nonlinear parameter or the spacetime dimension.

  6. Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

    Science.gov (United States)

    Liu, Changying; Iserles, Arieh; Wu, Xinyuan

    2018-03-01

    The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

  7. Higher order corrections in quantum electrodynamics

    International Nuclear Information System (INIS)

    Rafael, E.

    1977-01-01

    Theoretical contributions to high-order corrections in purely leptonic systems, such as electrons and muons, muonium (μ + e - ) and positronium (e + e - ), are reviewed to establish the validity of quantum electrodynamics (QED). Two types of QED contributions to the anomalous magnetic moments are considered, from diagrams with one fermion type lines and those witn two fermion type lines. The contributions up to eighth order are compared to the data available with a different accuracy. Good agreement is stated within the experimental errors. The experimental accuracy of the muonium hyperfine structure and of the radiative corrections to the decay of positronium are compared to the one attainable in theoretical calculations. The need for a higher precision in both experimental data and theoretical calculations is stated

  8. Errors of first-order probe correction for higher-order probes in spherical near-field antenna measurements

    DEFF Research Database (Denmark)

    Laitinen, Tommi; Nielsen, Jeppe Majlund; Pivnenko, Sergiy

    2004-01-01

    An investigation is performed to study the error of the far-field pattern determined from a spherical near-field antenna measurement in the case where a first-order (mu=+-1) probe correction scheme is applied to the near-field signal measured by a higher-order probe.......An investigation is performed to study the error of the far-field pattern determined from a spherical near-field antenna measurement in the case where a first-order (mu=+-1) probe correction scheme is applied to the near-field signal measured by a higher-order probe....

  9. Multi-frequency Defect Selective Imaging via Nonlinear Ultrasound

    Science.gov (United States)

    Solodov, Igor; Busse, Gerd

    The concept of defect-selective ultrasonic nonlinear imaging is based on visualization of strongly nonlinear inclusions in the form of localized cracked defects. For intense excitation, the ultrasonic response of defects is affected by mechanical constraint between their fragments that makes their vibrations extremely nonlinear. The cracked flaws, therefore, efficiently generate multiple new frequencies, which can be used as a nonlinear "tag" to detect and image them. In this paper, the methodologies of nonlinear scanning laser vibrometry (NSLV) and nonlinear air-coupled emission (NACE) are applied for nonlinear imaging of various defects in hi-tech and constructional materials. A broad database obtained demonstrates evident advantages of the nonlinear approach over its linear counterpart. The higher-order nonlinear frequencies provide increase in signal-to-noise ratio and enhance the contrast of imaging. Unlike conventional ultrasonic instruments, the nonlinear approach yields abundant multi-frequency information on defect location. The application of image recognition and processing algorithms is described and shown to improve reliability and quality of ultrasonic imaging.

  10. Four Wave Mixing using Intermodal Nonlinearities

    DEFF Research Database (Denmark)

    Rishøj, Lars Søgaard

    The nonlinear process of four-wave mixing (FWM) enables coupling of energy between wavelengths. This is useful for both optical amplification and wavelength conversion. A crucial prerequisite for the process is phase matching. This PhD project investigates how higher order modes (HOMs) in fibers...

  11. MIMO processing based on higher-order Poincaré spheres

    Science.gov (United States)

    Fernandes, Gil M.; Muga, Nelson J.; Pinto, Armando N.

    2017-08-01

    A multi-input multi-output (MIMO) algorithm based on higher-order Poincaré spheres is demonstrated for space-division multiplexing (SDM) systems. The MIMO algorithm is modulation format agnostic, robust to frequency offset and does not require training sequences. In this approach, the space-multiplexed signal is decomposed in sets of two tributary signals, with each set represented in a higher-order Poincaré sphere. For any arbitrary complex modulation format, the samples of two tributaries can be represented in a given higher-order Poincaré sphere with a symmetry plane. The crosstalk along propagation changes the spatial orientation of this plane and, therefore, it can be compensated by computing and realigning the best fit plane. We show how the transmitted signal can be successfully recovered using this procedure for all possible combinations of tributaries. Moreover, we analyze the convergence speed for the MIMO technique considering several optical-to-noise ratios.

  12. Response to Comment on 'On Higher-Order Corrections to Gyrokinetic Vlasov-Poisson Equations in the Long Wavelength Limit [Phys. Plasmas 16,044506 (2009)]'

    International Nuclear Information System (INIS)

    Lee, W.W.; Kolesnikov, R.A.

    2009-01-01

    We show in this Response that the nonlinear Poisson's equation in our original paper derived from the drift kinetic approach can be verified by using the nonlinear gyrokinetic Poisson's equation of Dubin et al. (Phys. Fluids 26, 3524 (1983)). This nonlinear contribution in φ 2 is indeed of the order of k # perpendicular# 4 in the long wavelength limit and remains finite for zero ion temperature, in contrast to the nonlinear term by Parra and Catto (Plasma Phys. Control. Fusion 50, 065014 (2008)), which is of the order of k # perpendicular# 2 and diverges for T i → 0. For comparison, the leading term for the gyrokinetic Poisson's equation in this limit is of the order of k # perpendicular# 2 φ.

  13. Probing the interatomic potential of solids with strong-field nonlinear phononics

    Science.gov (United States)

    von Hoegen, A.; Mankowsky, R.; Fechner, M.; Först, M.; Cavalleri, A.

    2018-03-01

    Nonlinear optical techniques at visible frequencies have long been applied to condensed matter spectroscopy. However, because many important excitations of solids are found at low energies, much can be gained from the extension of nonlinear optics to mid-infrared and terahertz frequencies. For example, the nonlinear excitation of lattice vibrations has enabled the dynamic control of material functions. So far it has only been possible to exploit second-order phonon nonlinearities at terahertz field strengths near one million volts per centimetre. Here we achieve an order-of-magnitude increase in field strength and explore higher-order phonon nonlinearities. We excite up to five harmonics of the A1 (transverse optical) phonon mode in the ferroelectric material lithium niobate. By using ultrashort mid-infrared laser pulses to drive the atoms far from their equilibrium positions, and measuring the large-amplitude atomic trajectories, we can sample the interatomic potential of lithium niobate, providing a benchmark for ab initio calculations for the material. Tomography of the energy surface by high-order nonlinear phononics could benefit many aspects of materials research, including the study of classical and quantum phase transitions.

  14. Comment on 'On higher order corrections to gyrokinetic Vlasov-Poisson equations in the long wavelength limit' [Phys. Plasmas 16, 044506 (2009)

    International Nuclear Information System (INIS)

    Parra, Felix I.; Catto, Peter J.

    2009-01-01

    A recent publication [F. I. Parra and P. J. Catto, Plasma Phys. Controlled Fusion 50, 065014 (2008)] warned against the use of the lower order gyrokinetic Poisson equation at long wavelengths because the long wavelength, radial electric field must remain undetermined to the order the equation is obtained. Another reference [W. W. Lee and R. A. Kolesnikov, Phys. Plasmas 16, 044506 (2009)] criticizes these results by arguing that the higher order terms neglected in the most common gyrokinetic Poisson equation are formally smaller than the terms that are retained. This argument is flawed and ignores that the lower order terms, although formally larger, must cancel without determining the long wavelength, radial electric field. The reason for this cancellation is discussed. In addition, the origin of a nonlinear term present in the gyrokinetic Poisson equation [F. I. Parra and P. J. Catto, Plasma Phys. Controlled Fusion 50, 065014 (2008)] is explained.

  15. Ward identities of higher order Virasoro algebra

    International Nuclear Information System (INIS)

    Zha Chaozeng; Dolate, S.

    1994-11-01

    The general formulations of primary fields versus quasi-primary ones in the context of high order Virasoro algebra (HOVA) and the corresponding Ward identity are explored. The primary fields of conformal spins up to 8 are given in terms of quasi-primary fields, and the general features of the higher order expressions are also discussed. It is observed that the local fields, either primary of quasi-primary, carry the same numbers of central charges, and not all the primary fields contribute to the anomalies in the Ward identities. (author). 6 refs

  16. Multi-bunch energy distribution due to higher order modes in a travelling-wave constant gradient structure

    International Nuclear Information System (INIS)

    Yamamoto, M.; Higo, T.; Matsumoto, H.; Takeda, S.; Oide, K.; Takata, K.

    1993-01-01

    In order to accept the beam from an injector linac to a damping ring of Accelerator Test Facility (ATF), a multi-bunch energy distribution must be within ±0.3% of the beam energy. Most of the multi-bunch energy distribution linear by depends on a bunch number and this linear term can be corrected by the energy conpesention cavities. So non-linear term was calculated. It was found that the non-linear term is within ±0.3%. (author)

  17. Higher order perturbation theory - An example for discussion

    International Nuclear Information System (INIS)

    Lewins, J.D.; Parks, G.; Babb, A.L.

    1986-01-01

    Higher order perturbation theory is developed in the form of a Taylor series expansion to third order to calculate the thermal utilization of a nonuniform cell. The development takes advantage of the self-adjoint property of the diffusion operator to provide a simple development of this illustration of generalized perturbation theory employing scalar perturbation parameters. The results show how a designer might employ a second-order theory to quantify proposed design improvements, together with the limitations of second- and third-order theory. The chosen example has an exact optimization solution and thus provides a clear understanding of the role of perturbation theory at its various orders. Convergence and the computational advantages and disadvantages of the method are discussed

  18. Application of Higher-Order Cumulant in Fault Diagnosis of Rolling Bearing

    International Nuclear Information System (INIS)

    Shen, Yongjun; Yang, Shaopu; Wang, Junfeng

    2013-01-01

    In this paper a new method of pattern recognition based on higher-order cumulant and envelope analysis is presented. The core of this new method is to construct analytical signals from the given signals and obtain the envelope signals firstly, then compute and compare the higher-order cumulants of the envelope signals. The higher-order cumulants could be used as a characteristic quantity to distinguish these given signals. As an example, this method is applied in fault diagnosis for 197726 rolling bearing of freight locomotive. The comparisons of the second-order, third-order and fourth-order cumulants of the envelope signals from different vibration signals of rolling bearing show this new method could discriminate the normal and two fault signals distinctly

  19. Three-dimensional freak waves and higher-order wave-wave resonances

    Science.gov (United States)

    Badulin, S. I.; Ivonin, D. V.; Dulov, V. A.

    2012-04-01

    Quite often the freak wave phenomenon is associated with the mechanism of modulational (Benjamin-Feir) instability resulted from resonances of four waves with close directions and scales. This weakly nonlinear model reflects some important features of the phenomenon and is discussing in a great number of studies as initial stage of evolution of essentially nonlinear water waves. Higher-order wave-wave resonances attract incomparably less attention. More complicated mathematics and physics explain this disregard partially only. The true reason is a lack of adequate experimental background for the study of essentially three-dimensional water wave dynamics. We start our study with the classic example of New Year Wave. Two extreme events: the famous wave 26.5 meters and one of smaller 18.5 meters height (formally, not freak) of the same record, are shown to have pronounced features of essentially three-dimensional five-wave resonant interactions. The quasi-spectra approach is used for the data analysis in order to resolve adequately frequencies near the spectral peak fp ≈ 0.057Hz and, thus, to analyze possible modulations of the dominant wave component. In terms of the quasi-spectra the above two anomalous waves show co-existence of the peak harmonic and one at frequency f5w = 3/2fp that corresponds to maximum of five-wave instability of weakly nonlinear waves. No pronounced marks of usually discussed Benjamin-Feir instability are found in the record that is easy to explain: the spectral peak frequency fp corresponds to the non-dimensional depth parameter kD ≈ 0.92 (k - wavenumber, D ≈ 70 meters - depth at the Statoil platform Draupner site) that is well below the shallow water limit of the instability kD = 1.36. A unique data collection of wave records of the Marine Hydrophysical Institute in the Katsiveli platform (Black Sea) has been analyzed in view of the above findings of possible impact of the five-wave instability on freak wave occurrence. The data cover

  20. Higher-order risk preferences in social settings.

    Science.gov (United States)

    Heinrich, Timo; Mayrhofer, Thomas

    2018-01-01

    We study prudence and temperance (next to risk aversion) in social settings. Previous experimental studies have shown that these higher-order risk preferences affect the choices of individuals deciding privately on lotteries that only affect their own payoff. Yet, many risky and financially relevant decisions are made in the social settings of households or organizations. We elicit higher-order risk preferences of individuals and systematically vary how an individual's decision is made (alone or while communicating with a partner) and who is affected by the decision (only the individual or the partner as well). In doing so, we can isolate the effects of other-regarding concerns and communication on choices. Our results reveal that the majority of choices are risk averse, prudent, and temperate across social settings. We also observe that individuals are influenced significantly by the preferences of a partner when they are able to communicate and choices are payoff-relevant for both of them.

  1. Mathematics Teachers’ Interpretation of Higher-Order Thinking in Bloom’s Taxonomy

    OpenAIRE

    Tony Thompson

    2008-01-01

    This study investigated mathematics teachers’ interpretation of higher-order thinking in Bloom’s Taxonomy. Thirty-two high school mathematics teachers from the southeast U.S. were asked to (a) define lower- and higher-order thinking, (b) identify which thinking skills in Bloom’s Taxonomy represented lower- and higher-order thinking, and (c) create an Algebra I final exam item representative of each thinking skill. Results indicate that mathematics teachers have difficulty interpreting the thi...

  2. Higher-Order Finite Element Solutions of Option Prices

    DEFF Research Database (Denmark)

    Raahauge, Peter

    2004-01-01

    Kinks and jumps in the payoff function of option contracts prevent an effectiveimplementation of higher-order numerical approximation methods. Moreover, thederivatives (the greeks) are not easily determined around such singularities, even withstandard lower-order methods. This paper suggests...... for prices as well as for first and second order derivatives(delta and gamma). Unlike similar studies, numerical approximation errors aremeasured both as weighted averages and in the supnorm over a state space includingtime-to-maturities down to a split second.KEYWORDS: Numerical option pricing, Transformed...

  3. Nonlinear optics principles and applications

    CERN Document Server

    Rottwitt, Karsten

    2014-01-01

    IntroductionReview of linear opticsInduced polarizationHarmonic oscillator modelLocal field correctionsEstimated nonlinear responseSummaryTime-domain material responseThe polarization time-response functionThe Born-Oppenheimer approximationRaman scattering response function of silicaSummaryMaterial response in the frequency domain, susceptibility tensorsThe susceptibility tensorThe induced polarization in the frequency domainSum of monochromatic fieldsThe prefactor to the induced polarizationThird-order polarization in the Born-Oppenheimer approximation in the frequency domainKramers-Kronig relationsSummarySymmetries in nonlinear opticsSpatial symmetriesSecond-order materialsThird-order nonlinear materialsCyclic coordinate-systemContracted notation for second-order susceptibility tensorsSummaryThe nonlinear wave equationMono and quasi-monochromatic beamsPlane waves - the transverse problemWaveguidesVectorial approachNonlinear birefringenceSummarySecond-order nonlinear effectsGeneral theoryCoupled wave theoryP...

  4. The Cauchy problem for higher order abstract differential equations

    CERN Document Server

    Xiao, Ti-Jun

    1998-01-01

    This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.

  5. Long-Term Aging Diagnosis of Rotor Steel Using Acoustic Nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Chung Seok; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of); Park, Ik Keun; Hyun, Chang Yong [Seoul National University of Science and Tecnology, Seoul (Korea, Republic of)

    2011-12-15

    The long-term aging of ferritic 2.25CrMo steel was characterized using the acoustic nonlinear effect in order to apply to diagnose the degradation behavior of structural materials. We measured the acoustic nonlinearity parameter for each thermally aged specimen by the higher harmonic-generation technique. The acoustic nonlinearity parameter increased with aging time due to equilibrium M6C carbide precipitation, and has a favorable linear relation with Rockwell hardness. This study suggests that acoustic nonlinearity testing may be applicable to diagnostics on strength degradation in rotor steels.

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

    Science.gov (United States)

    Benhammouda, Brahim

    2016-01-01

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

  7. Comparing higher order models for the EORTC QLQ-C30

    DEFF Research Database (Denmark)

    Gundy, Chad M; Fayers, Peter M; Grønvold, Mogens

    2012-01-01

    To investigate the statistical fit of alternative higher order models for summarizing the health-related quality of life profile generated by the EORTC QLQ-C30 questionnaire.......To investigate the statistical fit of alternative higher order models for summarizing the health-related quality of life profile generated by the EORTC QLQ-C30 questionnaire....

  8. Scalar brane backgrounds in higher order curvature gravity

    International Nuclear Information System (INIS)

    Charmousis, Christos; Davis, Stephen C.; Dufaux, Jean-Francois

    2003-01-01

    We investigate maximally symmetric brane world solutions with a scalar field. Five-dimensional bulk gravity is described by a general lagrangian which yields field equations containing no higher than second order derivatives. This includes the Gauss-Bonnet combination for the graviton. Stability and gravitational properties of such solutions are considered, and we particularly emphasise the modifications induced by the higher order terms. In particular it is shown that higher curvature corrections to Einstein theory can give rise to instabilities in brane world solutions. A method for analytically obtaining the general solution for such actions is outlined. Generically, the requirement of a finite volume element together with the absence of a naked singularity in the bulk imposes fine-tuning of the brane tension. A model with a moduli scalar field is analysed in detail and we address questions of instability and non-singular self-tuning solutions. In particular, we discuss a case with a normalisable zero mode but infinite volume element. (author)

  9. Higher-order RANS turbulence models for separated flows

    Data.gov (United States)

    National Aeronautics and Space Administration — Higher-order Reynolds-averaged Navier-Stokes (RANS) models are developed to overcome the shortcomings of second-moment RANS models in predicting separated flows....

  10. Higher order mode damping of a higher harmonic superconducting cavity for SSRF

    International Nuclear Information System (INIS)

    Yu Haibo; Liu Jianfei; Hou Hongtao; Ma Zhenyu; Feng Xiqiang; Mao Dongqing

    2012-01-01

    Adopting a higher harmonic cavity on a synchrotron radiation facility can increase the beam lifetime and suppress the beam instability. In this paper, we report the simulation and preliminary design on higher order modes (HOMs) damping of the designed and fabricated higher harmonic superconducting cavity for Shanghai Synchrotron Radiation Facility (SSRF). The requirements for the HOM damping are analyzed, and the length and location of the HOM damper are optimized by using the SEAFISH code. The results show that the design can provide heavy damping for harmful HOMs with decreased impedance, and the beam instability requirement of SSRF can be satisfied. By using the ABCI code, the loss factor is obtained and the HOM power is estimated. (authors)

  11. The power of non-determinism in higher-order implicit complexity

    DEFF Research Database (Denmark)

    Kop, Cynthia Louisa Martina; Simonsen, Jakob Grue

    2017-01-01

    We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice. Cons-freeness roughly means that data constructors cannot occur...... in function bodies and all manipulation of storage space thus has to happen indirectly using the call stack. While cons-free programs have previously been used by several authors to characterise complexity classes, the work on non-deterministic programs has almost exclusively considered programs of data order...... 0. Previous work has shown that adding explicit non-determinism to consfree programs taking data of order 0 does not increase expressivity; we prove that this—dramatically—is not the case for higher data orders: adding non-determinism to programs with data order at least 1 allows...

  12. PRE-SERVICE MATHEMATICS TEACHERS’ CONCEPTION OF HIGHER-ORDER THINKING LEVEL IN BLOOM'S TAXONOMY

    OpenAIRE

    Damianus D Samo

    2017-01-01

    The purpose of this study is to explore pre-service mathematics teachers' conception of higher-order thinking in Bloom's Taxonomy, to explore pre-service mathematics teachers' ability in categorizing six cognitive levels of Bloom's Taxonomy as lower-order thinking and higher-order thinking, and pre-service mathematics teachers' ability in identifying some questionable items as lower-order and higher-order thinking. The higher-order thinking is the type of non-algorithm thinking which include ...

  13. Wigner higher-order spectra: definition, properties, computation and application to transient signal analysis

    OpenAIRE

    Rodríguez Fonollosa, Javier; Nikias, Chrysostomos L.

    1993-01-01

    The Wigner higher order moment spectra (WHOS) are defined as extensions of the Wigner-Ville distribution (WD) to higher order moment spectra domains. A general class of time-frequency higher order moment spectra is also defined in terms of arbitrary higher order moments of the signal as generalizations of the Cohen’s general class of time-frequency representations. The properties of the general class of time-frequency higher order moment spectra can be related to the properties...

  14. Statistical Signal Processing by Using the Higher-Order Correlation between Sound and Vibration and Its Application to Fault Detection of Rotational Machine

    Directory of Open Access Journals (Sweden)

    Hisako Masuike

    2008-01-01

    Full Text Available In this study, a stochastic diagnosis method based on the changing information of not only a linear correlation but also a higher-order nonlinear correlation is proposed in a form suitable for online signal processing in time domain by using a personal computer, especially in order to find minutely the mutual relationship between sound and vibration emitted from rotational machines. More specifically, a conditional probability hierarchically reflecting various types of correlation information is theoretically derived by introducing an expression on the multidimensional probability distribution in orthogonal expansion series form. The effectiveness of the proposed theory is experimentally confirmed by applying it to the observed data emitted from a rotational machine driven by an electric motor.

  15. Application of He’s Variational Iteration Method to Nonlinear Helmholtz Equation and Fifth-Order KDV Equation

    DEFF Research Database (Denmark)

    Miansari, Mo; Miansari, Me; Barari, Amin

    2009-01-01

    In this article, He’s variational iteration method (VIM), is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely c...

  16. Higher-order Skyrme hair of black holes

    Science.gov (United States)

    Gudnason, Sven Bjarke; Nitta, Muneto

    2018-05-01

    Higher-order derivative terms are considered as replacement for the Skyrme term in an Einstein-Skyrme-like model in order to pinpoint which properties are necessary for a black hole to possess stable static scalar hair. We find two new models able to support stable black hole hair in the limit of the Skyrme term being turned off. They contain 8 and 12 derivatives, respectively, and are roughly the Skyrme-term squared and the so-called BPS-Skyrme-term squared. In the twelfth-order model we find that the lower branches, which are normally unstable, become stable in the limit where the Skyrme term is turned off. We check this claim with a linear stability analysis. Finally, we find for a certain range of the gravitational coupling and horizon radius, that the twelfth-order model contains 4 solutions as opposed to 2. More surprisingly, the lowest part of the would-be unstable branch turns out to be the stable one of the 4 solutions.

  17. Dispersion of the resonant second order nonlinearity in 2D semiconductors probed by femtosecond continuum pulses

    Directory of Open Access Journals (Sweden)

    Mohammad Mokim

    2017-10-01

    Full Text Available We demonstrate an effective microspectroscopy technique by tracing the dispersion of second order nonlinear susceptibility (χ(2 in a monolayer tungsten diselenide (WSe2. The χ(2 dispersion obtained with better than 3 meV photon energy resolution showed peak value being within 6.3-8.4×10-19 m2/V range. We estimate the fundamental bandgap to be at 2.2 eV. Sub-structure in the χ(2 dispersion reveals a contribution to the nonlinearity due to exciton transitions with exciton binding energy estimated to be at 0.7 eV.

  18. Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides

    DEFF Research Database (Denmark)

    Reddy, D. V.; Raymer, M. G.; McKinstrie, C. J.

    2013-01-01

    in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process...... in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion....

  19. Higher order mode damping in Kaon factory RF cavities

    International Nuclear Information System (INIS)

    Enegren, T.; Poirier, R.; Griffin, J.; Walling, L.; Thiessen, H.A.; Smythe, W.R.

    1989-05-01

    Proposed designs for Kaon factory accelerators require that the rf cavities support beam currents on the order of several amperes. The beam current has Fourier components at all multiples of the rf frequency. Empty rf buckets produce additional components at all multiples of the revolution frequency. If a Fourier component of the beam coincides with the resonant frequency of a higher order mode of the cavity, which is inevitable if the cavity has a large frequency swing, significant excitation of this mode can occur. The induced voltage may then excite coupled bunch mode instabilities. Effective means are required to damp higher order modes without significantly affecting the fundamental mode. A mode damping scheme based on coupled transmission lines has been investigated and is report

  20. Syntheses, structures and third-order non-linear optical properties of homometal clusters containing molybdenum

    International Nuclear Information System (INIS)

    Li Yong; Lu Jing; Cui Xiaobing; Xu Jiqing; Li Kechang; Sun Huaying; Li Guanghua; Pan Lingyun; Yang Qingxin

    2005-01-01

    Both the homometal cluster [P(ph 4 )] 2 [Mo 2 O 2 (μ-S) 2 (S 2 ) 2 ] (1) and [Mo 2 O 2 (μ-S) 2 (Et 2 dtc) 2 ] (2) (Et 2 dtc=diethyl-dithiocarbamate) were successfully synthesized by low-temperature solid-state reactions. X-ray single-crystal diffraction studies suggest that compound (1) is a dinuclear anion cluster, and compound (2) is a dinuclear neutral cluster. The two compounds were characterized by elemental analyses, IR spectra and UV-Vis spectra. The third-order non-linear optical (NLO) properties of the clusters were also investigated and all exhibited nice non-linear absorption and self-defocusing performance with moduli of the hyperpolarizabilities 5.145x10 -30 esu for (1) and 5.428x10 -30 esu for (2)

  1. A framework for simulating ultrasound imaging based on first order nonlinear pressure–velocity relations

    DEFF Research Database (Denmark)

    Du, Yigang; Fan, Rui; Li, Yong

    2016-01-01

    An ultrasound imaging framework modeled with the first order nonlinear pressure–velocity relations (NPVR) based simulation and implemented by a half-time staggered solution and pseudospectral method is presented in this paper. The framework is capable of simulating linear and nonlinear ultrasound...... propagation and reflections in a heterogeneous medium with different sound speeds and densities. It can be initialized with arbitrary focus, excitation and apodization for multiple individual channels in both 2D and 3D spatial fields. The simulated channel data can be generated using this framework......, and ultrasound image can be obtained by beamforming the simulated channel data. Various results simulated by different algorithms are illustrated for comparisons. The root mean square (RMS) errors for each compared pulses are calculated. The linear propagation is validated by an angular spectrum approach (ASA...

  2. Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics.

    Science.gov (United States)

    Taheri, Mehdi; Sheikholeslam, Farid; Najafi, Majddedin; Zekri, Maryam

    2017-07-01

    In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  3. Handbook of Nonlinear Partial Differential Equations

    CERN Document Server

    Polyanin, Andrei D

    2011-01-01

    New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with Maple(t), Mathematica(R), and MATLAB(R) Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They

  4. Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

    Science.gov (United States)

    Fink, P. W.; Wilton, D. R.; Dobbins, J. A.

    2002-01-01

    In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required

  5. Higher Order Thinking Skills among Secondary School Students in Science Learning

    Science.gov (United States)

    Saido, Gulistan Mohammed; Siraj, Saedah; Bin Nordin, Abu Bakar; Al Amedy, Omed Saadallah

    2015-01-01

    A central goal of science education is to help students to develop their higher order thinking skills to enable them to face the challenges of daily life. Enhancing students' higher order thinking skills is the main goal of the Kurdish Science Curriculum in the Iraqi-Kurdistan region. This study aimed at assessing 7th grade students' higher order…

  6. Second-order nonlinear optical microscopy of spider silk

    Science.gov (United States)

    Zhao, Yue; Hien, Khuat Thi Thu; Mizutani, Goro; Rutt, Harvey N.

    2017-06-01

    Asymmetric β-sheet protein structures in spider silk should induce nonlinear optical interaction such as second harmonic generation (SHG) which is experimentally observed for a radial line and dragline spider silk using an imaging femtosecond laser SHG microscope. By comparing different spider silks, we found that the SHG signal correlates with the existence of the protein β-sheets. Measurements of the polarization dependence of SHG from the dragline indicated that the β-sheet has a nonlinear response depending on the direction of the incident electric field. We propose a model of what orientation the β-sheet takes in spider silk.

  7. Student's Perceived Level and Teachers' Teaching Strategies of Higher Order Thinking Skills: A Study on Higher Educational Institutions in Thailand

    Science.gov (United States)

    Shukla, Divya; Dungsungnoen, Aj Pattaradanai

    2016-01-01

    Higher order thinking skills (HOTS) has portrayed immense industry demand and the major goal of educational institution in imparting education is to inculcate higher order thinking skills. This compiles and mandate the institutions and instructor to develop the higher order thinking skills among students in order to prepare them for effective…

  8. Large third-order nonlinearity of nonpolar A-plane GaN film at 800 nm determined by Z-scan technology

    Science.gov (United States)

    Zhang, Feng; Han, Xiangyun

    2014-09-01

    We report an investigation on the optical third-order nonlinear property of the nonpolar A-plane GaN film. The film sample with a thickness of ~2 μm was grown on an r-plane sapphire substrate by metal-organic chemical vapor deposition system. By performing the Z-scan method combined with a mode-locked femtosecond Ti:sapphire laser (800 nm, 50 fs), the optical nonlinearity of the nonpolar A-plane GaN film was measured with the electric vector E of the laser beam being polarized parallel (//) and perpendicular (⊥) to the c axis of the film. The results show that both the third-order nonlinear absorption coefficient β and the nonlinear refractive index n2 of the sample film possess negative and large values, i.e. β// = -135 ± 29 cm/GW, n2// = -(4.0 ± 0.3) × 10-3 cm2/GW and β⊥ = -234 ± 29 cm/GW, n2⊥ = -(4.9 ± 0.4) × 10-3 cm2/GW, which are much larger than those of conventional C-plane GaN film, GaN bulk, and even the other oxide semiconductors.

  9. Thermoviscous Model Equations in Nonlinear Acoustics

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne

    Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

  10. Growth and Characterization of Lithium Potassium Phthalate (LiKP) Single Crystals for Third Order Nonlinear Optical Applications

    Energy Technology Data Exchange (ETDEWEB)

    Sivakumar, B.; Mohan, R. [Preidency College, Bangalore (India); Raj, S. Gokul [RR and Dr. SR Technical Univ., Avadi (India); Kumar, G. Ramesh [Anna Univ., Arni (India)

    2012-11-15

    Single crystals of lithium potassium phthalate (LiKP) were successfully grown from aqueous solution by solvent evaporation technique. The grown crystals were characterized by single crystal X-ray diffraction. The lithium potassium phthalate C{sub 16} H{sub 12} K Li{sub 3} O{sub 11} belongs to triclinic system with the following unit-cell dimensions at 298(2) K; a = 7.405(5) A; b = 9.878(5) A; c = 13.396(5) A; α = 71.778(5) .deg.; β = 87.300(5) .deg.; γ = 85.405(5) .deg.; having a space group P1. Mass spectrometric analysis provides the molecular weight of the compound and possible ways of fragmentations occurs in the compound. Thermal stability of the crystal was also studied by both simultaneous TGA/DTA analyses. The UV-Vis-NIR spectrum shows a good transparency in the whole of Visible and as well as in the near IR range. Third order nonlinear optical studies have also been studied by Z-scan technique. Nonlinear absorption and nonlinear refractive index were found out and the third order bulk susceptibility of compound was also estimated.

  11. The fourth-order non-linear sigma models and asymptotic freedom in four dimensions

    International Nuclear Information System (INIS)

    Buchbinder, I.L.; Ketov, S.V.

    1991-01-01

    Starting with the most general Lagrangian of the fourth-order non-linear sigma model in four space-time dimensions, we calculate the one-loop, on-shell ultra-violet-divergent part of the effective action. The formalism is based on the background field method and the generalised Schwinger-De Witt technique. The multiplicatively renormalisable case is investigated in some detail. The renormalisation group equations are obtained, and the conditions for a realisation of asymptotic freedom are considered. (orig.)

  12. Effective potentials in nonlinear polycrystals and quadrature formulae

    Science.gov (United States)

    Michel, Jean-Claude; Suquet, Pierre

    2017-08-01

    This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471, 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

  13. LOO: a low-order nonlinear transport scheme for acceleration of method of characteristics

    International Nuclear Information System (INIS)

    Li, Lulu; Smith, Kord; Forget, Benoit; Ferrer, Rodolfo

    2015-01-01

    This paper presents a new physics-based multi-grid nonlinear acceleration method: the low-order operator method, or LOO. LOO uses a coarse space-angle multi-group method of characteristics (MOC) neutron transport calculation to accelerate the fine space-angle MOC calculation. LOO is designed to capture more angular effects than diffusion-based acceleration methods through a transport-based low-order solver. LOO differs from existing transport-based acceleration schemes in that it emphasizes simplified coarse space-angle characteristics and preserves physics in quadrant phase-space. The details of the method, including the restriction step, the low-order iterative solver and the prolongation step are discussed in this work. LOO shows comparable convergence behavior to coarse mesh finite difference on several two-dimensional benchmark problems while not requiring any under-relaxation, making it a robust acceleration scheme. (author)

  14. Validation of a RANS transition model using a high-order weighted compact nonlinear scheme

    Science.gov (United States)

    Tu, GuoHua; Deng, XiaoGang; Mao, MeiLiang

    2013-04-01

    A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.

  15. Verifying object-oriented programs with higher-order separation logic in Coq

    DEFF Research Database (Denmark)

    Bengtson, Jesper; Jensen, Jonas Braband; Sieczkowski, Filip

    2011-01-01

    We present a shallow Coq embedding of a higher-order separation logic with nested triples for an object-oriented programming language. Moreover, we develop novel specification and proof patterns for reasoning in higher-order separation logic with nested triples about programs that use interfaces...... and interface inheritance. In particular, we show how to use the higher-order features of the Coq formalisation to specify and reason modularly about programs that (1) depend on some unknown code satisfying a specification or that (2) return objects conforming to a certain specification. All of our results have...

  16. Higher-order structure of Saccharomyces cerevisiae chromatin

    International Nuclear Information System (INIS)

    Lowary, P.T.; Widom, J.

    1989-01-01

    We have developed a method for partially purifying chromatin from Saccharomyces cerevisiae (baker's yeast) to a level suitable for studies of its higher-order folding. This has required the use of yeast strains that are free of the ubiquitous yeast killer virus. Results from dynamic light scattering, electron microscopy, and x-ray diffraction show that the yeast chromatin undergoes a cation-dependent folding into 30-nm filaments that resemble those characteristic of higher-cell chromatin; moreover, the packing of nucleosomes within the yeast 30-nm filaments is similar to that of higher cells. These results imply that yeast has a protein or protein domain that serves the role of the histone H 1 found in higher cells; physical and genetic studies of the yeast activity could help elucidate the structure and function of H 1. Images of the yeast 30-nm filaments can be used to test crossed-linker models for 30-nm filament structure

  17. Single-photon blockade in a hybrid cavity-optomechanical system via third-order nonlinearity

    Science.gov (United States)

    Sarma, Bijita; Sarma, Amarendra K.

    2018-04-01

    Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2)(0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.

  18. Higher-order force moments of active particles

    Science.gov (United States)

    Nasouri, Babak; Elfring, Gwynn J.

    2018-04-01

    Active particles moving through fluids generate disturbance flows due to their activity. For simplicity, the induced flow field is often modeled by the leading terms in a far-field approximation of the Stokes equations, whose coefficients are the force, torque, and stresslet (zeroth- and first-order force moments) of the active particle. This level of approximation is quite useful, but may also fail to predict more complex behaviors that are observed experimentally. In this study, to provide a better approximation, we evaluate the contribution of the second-order force moments to the flow field and, by reciprocal theorem, present explicit formulas for the stresslet dipole, rotlet dipole, and potential dipole for an arbitrarily shaped active particle. As examples of this method, we derive modified Faxén laws for active spherical particles and resolve higher-order moments for active rod-like particles.

  19. Analysis and Improvement of the Generic Higher-Order Masking Scheme of FSE 2012

    OpenAIRE

    Roy, Arnab; Venkatesh, Srinivas Vivek

    2013-01-01

    Masking is a well-known technique used to prevent block cipher implementations from side-channel attacks. Higher-order side channel attacks (e.g. higher-order DPA attack) on widely used block cipher like AES have motivated the design of efficient higher-order masking schemes. Indeed, it is known that as the masking order increases, the difficulty of side-channel attack increases exponentially. However, the main problem in higher-order masking is to design an efficient and secure technique for...

  20. Analysis of second order harmonic distortion due to transmitter non-linearity and chromatic and modal dispersion of optical OFDM SSB modulated signals in SMF-MMF fiber links

    Science.gov (United States)

    Patel, Dhananjay; Singh, Vinay Kumar; Dalal, U. D.

    2017-01-01

    Single mode fibers (SMF) are typically used in Wide Area Networks (WAN), Metropolitan Area Networks (MAN) and also find applications in Radio over Fiber (RoF) architectures supporting data transmission in Fiber to the Home (FTTH), Remote Antenna Units (RAUs), in-building networks etc. Multi-mode fibers (MMFs) with low cost, ease of installation and low maintenance are predominantly (85-90%) deployed in-building networks providing data access in local area networks (LANs). The transmission of millimeter wave signals through the SMF in WAN and MAN, along with the reuse of MMF in-building networks will not levy fiber reinstallation cost. The transmission of the millimeter waves experiences signal impairments due to the transmitter non-linearity and modal dispersion of the MMF. The MMF exhibiting large modal dispersion limits the bandwidth-length product of the fiber. The second and higher-order harmonics present in the optical signal fall within the system bandwidth. This causes degradation in the received signal and an unwanted radiation of power at the RAU. The power of these harmonics is proportional to the non-linearity of the transmitter and the modal dispersion of the MMF and should be maintained below the standard values as per the international norms. In this paper, a mathematical model is developed for Second-order Harmonic Distortion (HD2) generated due to non-linearity of the transmitter and chromatic-modal dispersion of the SMF-MMF optic link. This is also verified using a software simulation. The model consists of a Mach Zehnder Modulator (MZM) that generates two m-QAM OFDM Single Sideband (SSB) signals based on phase shift of the hybrid coupler (90° and 120°). Our results show that the SSB signal with 120° hybrid coupler has suppresses the higher-order harmonics and makes the system more robust against the HD2 in the SMF-MMF optic link.

  1. Quantum corrections to nonlinear ion acoustic wave with Landau damping

    Energy Technology Data Exchange (ETDEWEB)

    Mukherjee, Abhik; Janaki, M. S. [Saha Institute of Nuclear Physics, Calcutta (India); Bose, Anirban [Serampore College, West Bengal (India)

    2014-07-15

    Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.

  2. Recurrent activity in higher order, modality non-specific brain regions

    DEFF Research Database (Denmark)

    Lou, Hans Olav Christensen; Joensson, Morten; Biermann-Ruben, Katja

    2011-01-01

    It has been proposed that the workings of the brain are mainly intrinsically generated recurrent neuronal activity, with sensory inputs as modifiers of such activity in both sensory and higher order modality non-specific regions. This is supported by the demonstration of recurrent neuronal activity...... in the visual system as a response to visual stimulation. In contrast recurrent activity has never been demonstrated before in higher order modality non-specific regions. Using magneto-encephalography and Granger causality analysis, we tested in a paralimbic network the hypothesis that stimulation may enhance...... causal recurrent interaction between higher-order, modality non-specific regions. The network includes anterior cingulate/medial prefrontal and posterior cingulate/medial parietal cortices together with pulvinar thalami, a network known to be effective in autobiographic memory retrieval and self...

  3. Visualization and processing of higher order descriptors for multi-valued data

    CERN Document Server

    Schultz, Thomas

    2015-01-01

    Modern imaging techniques and computational simulations yield complex multi-valued data that require higher-order mathematical descriptors. This book addresses topics of importance when dealing with such data, including frameworks for image processing, visualization, and statistical analysis of higher-order descriptors. It also provides examples of the successful use of higher-order descriptors in specific applications and a glimpse of the next generation of diffusion MRI. To do so, it combines contributions on new developments, current challenges in this area, and state-of-the-art surveys.   Compared to the increasing importance of higher-order descriptors in a range of applications, tools for analysis and processing are still relatively hard to come by. Even though application areas such as medical imaging, fluid dynamics, and structural mechanics are very different in nature they face many shared challenges. This book provides an interdisciplinary perspective on this topic with contributions from key rese...

  4. Efficient Model Order Reduction for the Dynamics of Nonlinear Multilayer Sheet Structures with Trial Vector Derivatives

    Directory of Open Access Journals (Sweden)

    Wolfgang Witteveen

    2014-01-01

    Full Text Available The mechanical response of multilayer sheet structures, such as leaf springs or car bodies, is largely determined by the nonlinear contact and friction forces between the sheets involved. Conventional computational approaches based on classical reduction techniques or the direct finite element approach have an inefficient balance between computational time and accuracy. In the present contribution, the method of trial vector derivatives is applied and extended in order to obtain a-priori trial vectors for the model reduction which are suitable for determining the nonlinearities in the joints of the reduced system. Findings show that the result quality in terms of displacements and contact forces is comparable to the direct finite element method but the computational effort is extremely low due to the model order reduction. Two numerical studies are presented to underline the method’s accuracy and efficiency. In conclusion, this approach is discussed with respect to the existing body of literature.

  5. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

    Directory of Open Access Journals (Sweden)

    Veyis Turut

    2013-01-01

    Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

  6. Method for conducting nonlinear electrochemical impedance spectroscopy

    Science.gov (United States)

    Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.

    2015-06-02

    A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.

  7. Pressure tunable cascaded third order nonlinearity and temporal pulse switching

    DEFF Research Database (Denmark)

    Eilenberger, Falk; Bache, Morten; Minardi, Stefano

    2013-01-01

    Effects based on the χ(3)-nonlinearity are arguably the most commonly discussed nonlinear interactions in photonics. In the description of pulse propagation, however, the generation of the third harmonic (TH) is commonly neglected, because it is strongly phase mismatched in most materials...

  8. Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

    Directory of Open Access Journals (Sweden)

    Omar Abu Arqub

    2014-01-01

    Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.

  9. Describing pediatric dysphonia with nonlinear dynamic parameters

    Science.gov (United States)

    Meredith, Morgan L.; Theis, Shannon M.; McMurray, J. Scott; Zhang, Yu; Jiang, Jack J.

    2008-01-01

    Objective Nonlinear dynamic analysis has emerged as a reliable and objective tool for assessing voice disorders. However, it has only been tested on adult populations. In the present study, nonlinear dynamic analysis was applied to normal and dysphonic pediatric populations with the goal of collecting normative data. Jitter analysis was also applied in order to compare nonlinear dynamic and perturbation measures. This study’s findings will be useful in creating standards for the use of nonlinear dynamic analysis as a tool to describe dysphonia in the pediatric population. Methods The study included 38 pediatric subjects (23 children with dysphonia and 15 without). Recordings of sustained vowels were obtained from each subject and underwent nonlinear dynamic analysis and percent jitter analysis. The resulting correlation dimension (D2) and percent jitter values were compared across the two groups using t-tests set at a significance level of p = 0.05. Results It was shown that D2 values covary with the presence of pathology in children. D2 values were significantly higher in dysphonic children than in normal children (p = 0.002). Standard deviations indicated a higher level of variation in normal children’s D2 values than in dysphonic children’s D2 values. Jitter analysis showed markedly higher percent jitter in dysphonic children than in normal children (p = 0.025) and large standard deviations for both groups. Conclusion This study indicates that nonlinear dynamic analysis could be a viable tool for the detection and assessment of dysphonia in children. Further investigations and more normative data are needed to create standards for using nonlinear dynamic parameters for the clinical evaluation of pediatric dysphonia. PMID:18947887

  10. The geometry of higher-order Lagrange spaces applications to mechanics and physics

    CERN Document Server

    Miron, Radu

    1997-01-01

    This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1 A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with Applications to higher-order analytical mechanics and theoretical physics are included as well Audience This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology

  11. A non-linear reduced order methodology applicable to boiling water reactor stability analysis

    International Nuclear Information System (INIS)

    Prill, Dennis Paul

    2013-01-01

    Thermal-hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers of boiling water reactor (BWR) stability behavior. High-power low-flow conditions in connection with unfavorable power distributions can lead the BWR system into unstable regions where power oscillations can be triggered. This important threat to operational safety requires careful analysis for proper understanding. Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs), saving computational cost and improving the physical understanding. Presently within reactor dynamics, no general and automatic prediction of high-dimensional ROMs based on detailed BWR models are available. In this thesis a systematic self-contained model order reduction (MOR) technique is derived which is applicable for several classes of dynamical problems, and in particular to BWRs of any degree of details. Expert knowledge can be given by operational, experimental or numerical transient data and is transfered into an optimal basis function representation. The methodology is mostly automated and provides the framework for the reduction of various different systems of any level of complexity. Only little effort is necessary to attain a reduced version within this self-written code which is based on coupling of sophisticated commercial software. The methodology reduces a complex system in a grid-free manner to a small system able to capture even non-linear dynamics. It is based on an optimal choice of basis functions given by the so-called proper orthogonal decomposition (POD). Required steps to achieve reliable and numerical stable ROM are given by a distinct calibration road-map. In validation and verification steps, a wide spectrum of representative test examples is systematically studied regarding a later BWR application. The first example is non-linear and has a dispersive character

  12. Higher-order neural network software for distortion invariant object recognition

    Science.gov (United States)

    Reid, Max B.; Spirkovska, Lilly

    1991-01-01

    The state-of-the-art in pattern recognition for such applications as automatic target recognition and industrial robotic vision relies on digital image processing. We present a higher-order neural network model and software which performs the complete feature extraction-pattern classification paradigm required for automatic pattern recognition. Using a third-order neural network, we demonstrate complete, 100 percent accurate invariance to distortions of scale, position, and in-plate rotation. In a higher-order neural network, feature extraction is built into the network, and does not have to be learned. Only the relatively simple classification step must be learned. This is key to achieving very rapid training. The training set is much smaller than with standard neural network software because the higher-order network only has to be shown one view of each object to be learned, not every possible view. The software and graphical user interface run on any Sun workstation. Results of the use of the neural software in autonomous robotic vision systems are presented. Such a system could have extensive application in robotic manufacturing.

  13. Evaluation of polymer based third order nonlinear integrated optics devices

    NARCIS (Netherlands)

    Driessen, A.; Hoekstra, Hugo; Blom, F.C.; Horst, F.; Horst, F.; Krijnen, Gijsbertus J.M.; van Schoot, J.B.P.; van Schoot, J.B.P.; Lambeck, Paul; Popma, T.J.A.; Diemeer, Mart

    Nonlinear polymers are promising materials for high speed active integrated optics devices. In this paper we evaluate the perspectives polymer based nonlinear optical devices can offer. Special attention is directed to the materials aspects. In our experimental work we applied mainly Akzo Nobel DANS

  14. Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

    Directory of Open Access Journals (Sweden)

    Bin Wang

    2016-01-01

    Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.

  15. Nonlinear electromagnetic susceptibilities of unmagnetized plasmas

    International Nuclear Information System (INIS)

    Yoon, Peter H.

    2005-01-01

    Fully electromagnetic nonlinear susceptibilities of unmagnetized plasmas are analyzed in detail. Concrete expressions of the second-order nonlinear susceptibility are found in various forms in the literature, usually in connection with the discussions of various three-wave decay processes, but the third-order susceptibilities are rarely discussed. The second-order susceptibility is pertinent to nonlinear wave-wave interactions (i.e., the decay/coalescence), whereas the third-order susceptibilities affect nonlinear wave-particle interactions (i.e., the induced scattering). In the present article useful approximate analytical expressions of these nonlinear susceptibilities that can be readily utilized in various situations are derived

  16. Covariant quantization of infinite spin particle models, and higher order gauge theories

    International Nuclear Information System (INIS)

    Edgren, Ludde; Marnelius, Robert

    2006-01-01

    Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in the quantization process. A consistent covariant quantization is shown to exist. Also a recently proposed supersymmetric version for half-odd integer spins is quantized. A general algorithm to derive gauge invariances of higher order Lagrangians is given and applied to the infinite spin particle model, and to a new higher order model for a spinning particle which is proposed here, as well as to a previously given higher order rigid particle model. The latter two models are also covariantly quantized

  17. 4-N, N-bis(4-methoxylphenyl) aniline substituted anthraquinone: X-ray crystal structures, theoretical calculations and third-order nonlinear optical properties

    Science.gov (United States)

    Xu, Liang; Zhang, Dingfeng; Zhou, Yecheng; Zheng, Yusen; Cao, Liu; Jiang, Xiao-Fang; Lu, Fushen

    2017-08-01

    In this paper, mono- and di-4-N,N-bis(4-methoxylphenyl)aniline-substituted anthraquinone have been designed and synthesized through Suzuki reaction. For mono-4-N,N-bis(4-methoxylphenyl)aniline-substituted anthraquinone, polymorphous crystal structures have been obtained in different crystallization conditions. Electrochemical characterization combined with theoretical calculation suggests that the addition of a second triphenylamine unit causes a larger band gap with higher lying LUMO (Lowest Unoccupied Molecular Orbital) and HOMO (Highest Occupied Molecular Orbital). The linear optical property shows that the introduction of a second triphenylamine unit bring about a significant hyperchromic effect with the extinction coefficients increasing from 11199 M-1 cm-1 to 22136 M-1 cm-1. The third-order nonlinear optical properties indicate that the introduction of a second triphenylamine unit lead to a much larger nonlinear absorption coefficient and two-photon absorption cross section, with the relevant value increasing from 2.04 × 10-12 cm W-1 to 3.91 × 10-12 cm W-1, and from 148 GM to 286 GM, respectively.

  18. High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform.

    Science.gov (United States)

    Gui, Tao; Lu, Chao; Lau, Alan Pak Tao; Wai, P K A

    2017-08-21

    In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.

  19. Synthesis, growth, crystal structure, optical and third order nonlinear optical properties of quinolinium derivative single crystal: PNQI

    Science.gov (United States)

    Karthigha, S.; Krishnamoorthi, C.

    2018-03-01

    An organic quinolinium derivative nonlinear optical (NLO) crystal, 1-ethyl-2-[2-(4-nitro-phenyl)-vinyl]-quinolinium iodide (PNQI) was synthesized and successfully grown by slow evaporation solution growth technique. Formation of a crystalline compound was confirmed by single crystal X-ray diffraction. The quinolinium compound PNQI crystallizes in the triclinic crystal system with a centrosymmetric space group of P-1 symmetry. The molecular structure of PNQI was confirmed by 1H NMR and 13C NMR spectral studies. The thermal properties of the crystal have been investigated by thermogravimetric (TG) and differential scanning calorimetry (DSC) studies. The optical characteristics obtained from UV-Vis-NIR spectral data were described and the cut-off wavelength observed at 506 nm. The etching study was performed to analyse the growth features of PNQI single crystal. The third order NLO properties such as nonlinear refractive index (n2), nonlinear absorption coefficient (β) and nonlinear susceptibility (χ (3)) of the crystal were investigated using Z-scan technique at 632.8 nm of Hesbnd Ne laser.

  20. An efficient higher order family of root finders

    Science.gov (United States)

    Petkovic, Ljiljana D.; Rancic, Lidija; Petkovic, Miodrag S.

    2008-06-01

    A one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial, based on a cubically convergent Hansen-Patrick's family, is studied. We show that the convergence of the basic family of the fourth order can be increased to five and six using Newton's and Halley's corrections, respectively. Since these corrections use the already calculated values, the computational efficiency of the accelerated methods is significantly increased. Further acceleration is achieved by applying the Gauss-Seidel approach (single-step mode). One of the most important problems in solving nonlinear equations, the construction of initial conditions which provide both the guaranteed and fast convergence, is considered for the proposed accelerated family. These conditions are computationally verifiable; they depend only on the polynomial coefficients, its degree and initial approximations, which is of practical importance. Some modifications of the considered family, providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions, are also studied. Numerical examples demonstrate the convergence properties of the presented family of root-finding methods.

  1. A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

    Science.gov (United States)

    Diosady, Laslo T.; Murman, Scott M.

    2018-01-01

    A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

  2. Higher-order-mode damper as beam-position monitors; Higher-Order-Mode Daempfer als Stahllagemonitore

    Energy Technology Data Exchange (ETDEWEB)

    Peschke, C.

    2006-03-15

    In the framework of this thesis a beam-position monitor was developed, which can only because of the signals from the HOM dampers of a linear-accelerator structure determine the beam position with high accuracy. For the unique determination of the beam position in the plane a procedure was developed, which uses the amplitudes and the start-phase difference between a dipole mode and a higher monopole mode. In order tocheck the suitability of the present SBLC-HOM damper as beam position monitor three-dimensional numerical field calculations in the frequency and time range and measurements on the damper cell were performed. For the measurements without beam a beam simulator was constructed, which allows computer-driven measurements with variable depositions of the simulated beam with a resolution of 1.23 {mu}m. Because the complete 6 m long, 180-cell accelerator structure was not available for measurements and could also with the available computers not be three-dimensionally simulated simulated, a one-dimensional equivalent-circuit based model of the multi-cell was studied. The equivalent circuits with 879 concentrated components regards the detuning from cell to cell, the cell losses, the damper losses, and the beam excitation in dependence on the deposition. the measurements and simulations let a resolution of the ready beam-position monitor on the 180-cell in the order of magnitude of 1-10 {mu}m and a relative accuracy smaller 6.2% be expected.

  3. On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

    Directory of Open Access Journals (Sweden)

    Youliang Fu

    2016-01-01

    Full Text Available This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.

  4. Higher-Order Hierarchical Legendre Basis Functions in Applications

    DEFF Research Database (Denmark)

    Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter

    2007-01-01

    The higher-order hierarchical Legendre basis functions have been developed for effective solution of integral equations with the method of moments. They are derived from orthogonal Legendre polynomials modified to enforce normal continuity between neighboring mesh elements, while preserving a high...

  5. Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

    International Nuclear Information System (INIS)

    Adcock, T. A. A.; Taylor, P. H.

    2016-01-01

    The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum

  6. ℋ∞ Adaptive observer for nonlinear fractional-order systems

    KAUST Repository

    Ndoye, Ibrahima

    2016-06-23

    In this paper, an adaptive observer is proposed for the joint estimation of states and parameters of a fractional nonlinear system with external perturbations. The convergence of the proposed observer is derived in terms of linear matrix inequalities (LMIs) by using an indirect Lyapunov method.The proposed ℋ∞ adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü\\'s systems. © 2016 John Wiley & Sons, Ltd.

  7. Higher order BLG supersymmetry transformations from 10-dimensional super Yang Mills

    Energy Technology Data Exchange (ETDEWEB)

    Hall, John [Alumnus of Physics Department, Imperial College,South Kensington, London, SW7 2AZ (United Kingdom); Low, Andrew [Physics Department, Wimbledon High School,Mansel Road, London, SW19 4AB (United Kingdom)

    2014-06-26

    We study a Simple Route for constructing the higher order Bagger-Lambert-Gustavsson theory - both supersymmetry transformations and Lagrangian - starting from knowledge of only the 10-dimensional Super Yang Mills Fermion Supersymmetry transformation. We are able to uniquely determine the four-derivative order corrected supersymmetry transformations, to lowest non-trivial order in Fermions, for the most general three-algebra theory. For the special case of Euclidean three-algbera, we reproduce the result presented in arXiv:1207.1208, with significantly less labour. In addition, we apply our method to calculate the quadratic fermion terms in the higher order BLG fermion supersymmetry transformation.

  8. Hamiltonian formulation of theory with higher order derivatives

    International Nuclear Information System (INIS)

    Gitman, D.M.; Lyakhovich, S.L.; Tyutin, I.V.

    1983-01-01

    A method of ''hamiltonization'' of a special theory with higher order derivatives is described. In a nonspecial case the result coincides with the known Ostrogradsky formulation. It is shown that in the nonspecial theory the lagrange equations of motion are reduced to the normal form

  9. Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model

    Energy Technology Data Exchange (ETDEWEB)

    Ghorbanpour Arani, A., E-mail: aghorban@kashanu.ac.ir [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of); Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan (Iran, Islamic Republic of); Zarei, M.Sh.; Amir, S.; Khoddami Maraghi, Z. [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of)

    2013-02-01

    In this work nonlinear vibration of double-walled carbon nanotube (DWCNT) embedded in an elastic medium and subjected to an axial fluid flow (incompressible and non-viscose) is investigated. The elastic medium is simulated using Pasternak foundation in which adjacent layer interactions are assumed to have been coupled by van der Waals (VdW) force. The higher-order equation of motion is derived using Hamilton's principle and nonlocal-nonlinear shell theory. Galerkin and averaging methods are adopted to solve the higher-order governing equations. Elastic medium, small scale parameter, velocity and fluid density are taken into account to calculate the effects of axial and circumferential wave numbers in this study. Results reveal that increasing circumferential wave number, leads to enhanced nonlinearity. Critical flow velocities of DWCNT are inversely related to the non-local parameter (e{sub 0}a), so that increase in the later lead to reduced critical flow velocities.

  10. Nonlinear generalization of the Kallen-Welton formula

    International Nuclear Information System (INIS)

    Kargin, A.Yu.

    1982-01-01

    Nonlinear dissipative-fluctuation relations permitting to find spectral correlation functions of (n+1) order for fluctuations of different electrodynamic values in plasma using the given value of tensor of nonlinear response of n order have been obtained for equilibrium plasma. At n=1 the relations obtained transform to the Kallen-Welton dissipative-fluctuation relation. Transformation of the nonlinear dissipative-fluctuation relation for cubical nonlinearity permitting to find nonlinear electric plasma susceptibility from the Known spectral correlation function of fourth order for charge density fluctUations in the absence of particle interaction is considered as an example. A compact expression for tensor of nonlinear plasma response has been obtained for an arbitrary order of nonlinearity

  11. Nonlinear Growth Models as Measurement Models: A Second-Order Growth Curve Model for Measuring Potential.

    Science.gov (United States)

    McNeish, Daniel; Dumas, Denis

    2017-01-01

    Recent methodological work has highlighted the promise of nonlinear growth models for addressing substantive questions in the behavioral sciences. In this article, we outline a second-order nonlinear growth model in order to measure a critical notion in development and education: potential. Here, potential is conceptualized as having three components-ability, capacity, and availability-where ability is the amount of skill a student is estimated to have at a given timepoint, capacity is the maximum amount of ability a student is predicted to be able to develop asymptotically, and availability is the difference between capacity and ability at any particular timepoint. We argue that single timepoint measures are typically insufficient for discerning information about potential, and we therefore describe a general framework that incorporates a growth model into the measurement model to capture these three components. Then, we provide an illustrative example using the public-use Early Childhood Longitudinal Study-Kindergarten data set using a Michaelis-Menten growth function (reparameterized from its common application in biochemistry) to demonstrate our proposed model as applied to measuring potential within an educational context. The advantage of this approach compared to currently utilized methods is discussed as are future directions and limitations.

  12. Higher order polynomial expansion nodal method for hexagonal core neutronics analysis

    International Nuclear Information System (INIS)

    Jin, Young Cho; Chang, Hyo Kim

    1998-01-01

    A higher-order polynomial expansion nodal(PEN) method is newly formulated as a means to improve the accuracy of the conventional PEN method solutions to multi-group diffusion equations in hexagonal core geometry. The new method is applied to solving various hexagonal core neutronics benchmark problems. The computational accuracy of the higher order PEN method is then compared with that of the conventional PEN method, the analytic function expansion nodal (AFEN) method, and the ANC-H method. It is demonstrated that the higher order PEN method improves the accuracy of the conventional PEN method and that it compares very well with the other nodal methods like the AFEN and ANC-H methods in accuracy

  13. Perturbation method for periodic solutions of nonlinear jerk equations

    International Nuclear Information System (INIS)

    Hu, H.

    2008-01-01

    A Lindstedt-Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton's method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method

  14. Coaxial higher-order mode damper employing a high-pass filter

    International Nuclear Information System (INIS)

    Kang, Y.W.; Jiang, X.

    1997-01-01

    Two different types of coaxial higher-order mode (HOM) dampers have been investigated for the Advanced Photon Source (APS) storage ring cavities: e-probe dampers and h-loop dampers. Realization of the h-loop dampers has been difficult because the loop antenna couples not only to the HOMs but also to the accelerating mode and results in loss of Q at the fundamental frequency. Previously, a first-order fundamental rejection filter was tested with unsatisfactory rejection characteristics. This problem can be overcome by using a higher-order high-pass filter between the loop and the matched load. Prototype dampers have been fabricated and tested in a storage ring single-cell cavity and the damping characteristic was analyzed

  15. A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

    Science.gov (United States)

    Bilyeu, David

    This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For

  16. Nonlinear waves in waveguides with stratification

    CERN Document Server

    Leble, Sergei B

    1991-01-01

    S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.

  17. Unidirectional reflection and invisibility in nonlinear media with an incoherent nonlinearity

    Science.gov (United States)

    Mostafazadeh, Ali; Oflaz, Neslihan

    2017-11-01

    We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.

  18. Nonlinear optics

    CERN Document Server

    Bloembergen, Nicolaas

    1996-01-01

    Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe

  19. A finite deformation theory of higher-order gradient crystal plasticity

    DEFF Research Database (Denmark)

    Kuroda, Mitsutoshi; Tvergaard, Viggo

    2008-01-01

    crystal plasticity that is based on an assumption of the existence of higher-order stresses. Furthermore, a boundary-value problem for simple shear of a constrained thin strip is studied numerically, and some characteristic features of finite deformation are demonstrated through a comparison to a solution......For higher-order gradient crystal plasticity, a finite deformation formulation is presented. The theory does not deviate much from the conventional crystal plasticity theory. Only a back stress effect and additional differential equations for evolution of the geometrically necessary dislocation...

  20. Heterotic non-linear sigma models with anti-de Sitter target spaces

    International Nuclear Information System (INIS)

    Michalogiorgakis, Georgios; Gubser, Steven S.

    2006-01-01

    We calculate the beta function of non-linear sigma models with S D+1 and AdS D+1 target spaces in a 1/D expansion up to order 1/D 2 and to all orders in α ' . This beta function encodes partial information about the spacetime effective action for the heterotic string to all orders in α ' . We argue that a zero of the beta function, corresponding to a worldsheet CFT with AdS D+1 target space, arises from competition between the one-loop and higher-loop terms, similarly to the bosonic and supersymmetric cases studied previously in [J.J. Friess, S.S. Gubser, Non-linear sigma models with anti-de Sitter target spaces, Nucl. Phys. B 750 (2006) 111-141]. Various critical exponents of the non-linear sigma model are calculated, and checks of the calculation are presented