Dynamics of breathers in discrete nonlinear Schrodinger models

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge

1998-01-01

We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...

Stokes phenomena and monodromy deformation problem for nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Chowdury, A.R.; Naskar, M.

1986-01-01

Following Flaschka and Newell, the inverse problem for Painleve IV is formulated with the help of similarity variables. The Painleve IV arises as the eliminant of the two second-order ordinary differential equations originating from the nonlinear Schrodinger equation. Asymptotic expansions are obtained near the singularities at zero and infinity of the complex eigenvalue plane. The corresponding analysis then displays the Stokes phenomena. The monodromy matrices connecting the solution Y /sub j/ in the sector S /sub j/ to that in S /sub j+1/ are fixed in structure by the imposition of certain conditions. It is then shown that a deformation keeping the monodromy data fixed leads to the nonlinear Schrodinger equation. While Flaschka and Newell did not make any absolute determination of the Stokes parameters, the present approach yields the values of the Stokes parameters in an explicit way, which in turn can determine the matrix connecting the solutions near zero and infinity. Finally, it is shown that the integral equation originating from the analyticity and asymptotic nature of the problem leads to the similarity solution previously determined by Boiti and Pampinelli

Derivation and solution of a time-dependent, nonlinear, Schrodinger-like equation for the superconductivity order parameter

International Nuclear Information System (INIS)

Esrick, M.A.

1981-01-01

A time-dependent, nonlinear, Schrodinger-like equation for the superconductivity order parameter is derived from the Gor'kov equations. Three types of traveling wave solutions of the equation are discussed. The phases and amplitudes of these solutions propagate at different speeds. The first type of solution has an amplitude that propagates as a soliton and it is suggested that this solution might correspond to the recently observed propagating collective modes of the order parameter. The amplitude of the second type of solution propagates as a periodic disturbance in space and time. It is suggested that this type of solution might explain the recently observed multiple values of the superconductor energy gap as well as the spatially inhomogenous superconducting state. The third type of solution, which is of a more general character, might provide some insight into non-periodic, inhomogeneous states occuring in superconductors. It is also proposed that quasiparticle injection and microwave irradiation might generate soliton-like disturbances in superconductors

Asymptotic behavior for a quadratic nonlinear Schrodinger equation

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Pavel I. Naumkin

2008-02-01

Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.

Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems

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Hailiang Li

2003-09-01

Full Text Available This paper concerns the well-posedness and semiclassical limit of nonlinear Schrodinger-Poisson systems. We show the local well-posedness and the existence of semiclassical limit of the two models for initial data with Sobolev regularity, before shocks appear in the limit system. We establish the existence of a global solution and show the time-asymptotic behavior of a classical solutions of Schrodinger-Poisson system for a fixed re-scaled Planck constant.

Multiple solutions to some singular nonlinear Schrodinger equations

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Monica Lazzo

2001-01-01

Full Text Available We consider the equation $$ - h^2 Delta u + V_varepsilon(x u = |u|^{p-2} u $$ which arises in the study of standing waves of a nonlinear Schrodinger equation. We allow the potential $V_varepsilon$ to be unbounded below and prove existence and multiplicity results for positive solutions.

Semiclassical quantization of the nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Nohl, C.R.

1976-01-01

Using the functional integral technique of Dashen, Hasslacher, and Neveu, we perform a semiclassical quantization of the nonlinear Schrodinger equation (NLSE), which reproduces McGuire's exact result for the energy levels of the bound states of the theory. We show that the stability angle formalism leads to the one-loop normal ordering and self-energy renormalization expected from perturbation theory, and demonstrate that taking into account center-of-mass motion gives the correct nonrelativistic energy--momentum relation. We interpret the classical solution in the context of the quantum theory, relating it to the matrix element of the field operator between adjacent bound states in the limit of large quantum numbers. Finally, we quantize the NLSE as a theory of N component fermion fields and show that the semiclassical method yields the exact energy levels and correct degeneracies

Collapse arresting in an inhomogeneous quintic nonlinear Schrodinger model

DEFF Research Database (Denmark)

Gaididei, Yuri Borisovich; Schjødt-Eriksen, Jens; Christiansen, Peter Leth

1999-01-01

Collapse of (1 + 1)-dimensional beams in the inhomogeneous one-dimensional quintic nonlinear Schrodinger equation is analyzed both numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams in which the homogeneous medium would blow up...

Solutions to nonlinear Schrodinger equations for special initial data

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Takeshi Wada

2015-11-01

Full Text Available This article concerns the solvability of the nonlinear Schrodinger equation with gauge invariant power nonlinear term in one space dimension. The well-posedness of this equation is known only for $H^s$ with $s\\ge 0$. Under some assumptions on the nonlinearity, this paper shows that this equation is uniquely solvable for special but typical initial data, namely the linear combinations of $\\delta(x$ and p.v. (1/x, which belong to $H^{-1/2-0}$. The proof in this article allows $L^2$-perturbations on the initial data.

A discrete homotopy perturbation method for non-linear Schrodinger equation

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H. A. Wahab

2015-12-01

Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.

Gap solitons in periodic Schrodinger lattice system with nonlinear hopping

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Ming Cheng

2016-10-01

Full Text Available This article concerns the periodic discrete Schrodinger equation with nonlinear hopping on the infinite integer lattice. We obtain the existence of gap solitons by the linking theorem and concentration compactness method together with a periodic approximation technique. In addition, the behavior of such solutions is studied as $\\alpha\\to 0$. Notice that the nonlinear hopping can be sign changing.

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)

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

Staggered and short-period solutions of the saturable discrete nonlinear Schrodinger equation

DEFF Research Database (Denmark)

Khare, A.; Rasmussen, K.O.; Samuelsen, Mogens Rugholm

2009-01-01

We point out that the nonlinear Schrodinger lattice with a saturable nonlinearity also admits staggered periodic aswell as localized pulse-like solutions. Further, the same model also admits solutions with a short period. We examine the stability of these solutions and find that the staggered as ...

Collapse arresting in an inhomogeneous two-dimensional nonlinear Schrodinger model

DEFF Research Database (Denmark)

Schjødt-Eriksen, Jens; Gaididei, Yuri Borisovich; Christiansen, Peter Leth

2001-01-01

Collapse of (2 + 1)-dimensional beams in the inhomogeneous two-dimensional cubic nonlinear Schrodinger equation is analyzed numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams that in a homogeneous medium would collapse may...

Reduction of the state vector by a nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Pearle, P.

1976-01-01

It is hypothesized that the state vector describes the physical state of a single system in nature. Then it is necessary that the state vector of a macroscopic apparatus not assume the form of a superposition of macroscopically distinguishable state vectors. To prevent this, it is suggested that a nonlinear term be added to the Schrodinger equation, which rapidly drives the amplitude of one or another of the state vectors in such a superposition to one, and the rest to zero. It is proposed that it is the phase angles of the amplitudes immediately after a measurement which determine which amplitude is driven to one. A diffusion equation is arrived at to describe the reduction of an ensemble of state vectors corresponding to an ensemble of macroscopically identically prepared experiments. Then a nonlinear term to add to the Schrodinger equation is presented, and it is shown that this leads to the diffusion equation in a weak-coupling approximation

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

Exact solutions of nonlinear generalizations of the Klein Gordon and Schrodinger equations

International Nuclear Information System (INIS)

Burt, P.B.

1978-01-01

Exact solutions of sine Gordon and multiple sine Gordon equations are constructed in terms of solutions of a linear base equation, the Klein Gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. Further, exact solutions of nonlinear generalizations of the Schrodinger equation and of additional nonlinear generalizations of the Klein Gordon equation are constructed in terms of solutions of linear base equations. Finally, solutions with spherical symmetry, of nonlinear Klein Gordon equations are given. 14 references

Polynomially decaying transmission for the nonlinear schrodinger equation in a random medium

International Nuclear Information System (INIS)

Devillard, P.; Sovillard, B.

1986-01-01

This is the first study of one the transmission problems associate to the nonlinear Schrodinger equation with a random potential. We show that for almost every realization of the medium the rate of transmission vanishes when increasing the size of the medium; however, whereas it decays exponentially in the linear regime, it decays polynomially in the nonlinear one

Global well-posedness for nonlinear Schrodinger equations with energy-critical damping

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Binhua Feng

2015-01-01

Full Text Available We consider the Cauchy problem for the nonlinear Schrodinger equations with energy-critical damping. We prove the existence of global in-time solutions for general initial data in the energy space. Our results extend some results from [1,2].

Higher-order techniques for some problems of nonlinear control

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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.

Modified wave operators for nonlinear Schrodinger equations in one and two dimensions

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Nakao Hayashi

2004-04-01

Full Text Available We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13

Higher-Order Spectrum in Understanding Nonlinearity in EEG Rhythms

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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.

On a quantum version of conservation laws for derivative nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Sen, S.; Chowdhury, A.R.

1988-01-01

The authors derived the quantum mechanical versions of infinite number of conservation laws associated with Derivative Nonlinear Schrodinger equation with the help of a methodology used in string theory. The renormalised version of the conserved quantities are obtained with explicit forms of the counter terms

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

Cross-constrained problems for nonlinear Schrodinger equation with harmonic potential

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Runzhang Xu

2012-11-01

Full Text Available This article studies a nonlinear Schodinger equation with harmonic potential by constructing different cross-constrained problems. By comparing the different cross-constrained problems, we derive different sharp criterion and different invariant manifolds that separate the global solutions and blowup solutions. Moreover, we conclude that some manifolds are empty due to the essence of the cross-constrained problems. Besides, we compare the three cross-constrained problems and the three depths of the potential wells. In this way, we explain the gaps in [J. Shu and J. Zhang, Nonlinear Shrodinger equation with harmonic potential, Journal of Mathematical Physics, 47, 063503 (2006], which was pointed out in [R. Xu and Y. Liu, Remarks on nonlinear Schrodinger equation with harmonic potential, Journal of Mathematical Physics, 49, 043512 (2008].

A study on linear and nonlinear Schrodinger equations by the variational iteration method

International Nuclear Information System (INIS)

Wazwaz, Abdul-Majid

2008-01-01

In this work, we introduce a framework to obtain exact solutions to linear and nonlinear Schrodinger equations. The He's variational iteration method (VIM) is used for analytic treatment of these equations. Numerical examples are tested to show the pertinent features of this method

Solitary waves for a coupled nonlinear Schrodinger system with dispersion management

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Panayotis Panayotaros

2010-08-01

Full Text Available We consider a system of coupled nonlinear Schrodinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication. We use Lions's Concentration Compactness principle to show the existence of standing waves with prescribed L^2 norm in an averaged equation that approximates the coupled system. We also use the Mountain Pass Lemma to prove the existence of standing waves with prescribed frequencies.

Hs solutions for nonlinear Schrodinger equations with potentials superquadratic at infinity

International Nuclear Information System (INIS)

Zhang Guoping; Yajima, Kenji; Liu Fengshan

2006-01-01

In this Letter we study the initial value problem for the nonlinear Schrodinger equation with the potential V superquadratic at infinity. With the local smoothing property and Strichartz inequality obtained by the authors, we prove the existence and the uniqueness of the solution for H s -valued initial data and fractional s by combining the L 2 boundedness theory of pseudo differential operators and the fractional derivatives estimate

On Perturbative Cubic Nonlinear Schrodinger Equations under Complex Nonhomogeneities and Complex Initial Conditions

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Magdy A. El-Tawil

2009-01-01

Full Text Available A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.

Solitary excitations in discrete two-dimensional nonlinear Schrodinger models with dispersive dipole-dipole interactions

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.

1998-01-01

The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either...

Localized excitations in discrete nonlinear Schrodinger systems: Effects of nonlocal dispersive interactions and noise

DEFF Research Database (Denmark)

Rasmussen, Kim; Christiansen, Peter Leth; Johansson, Magnus

1998-01-01

A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exp...

Beam stabilization in the two-dimensional nonlinear Schrodinger equation with an attractive potential by beam splitting and radiation

DEFF Research Database (Denmark)

leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich

2004-01-01

The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...... losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials....

Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

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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.

Dynamical symmetries of semi-linear Schrodinger and diffusion equations

International Nuclear Information System (INIS)

Stoimenov, Stoimen; Henkel, Malte

2005-01-01

Conditional and Lie symmetries of semi-linear 1D Schrodinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrodinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf 3 ) C . We consider non-hermitian representations and also include a dimensionful coupling constant of the non-linearity. The corresponding representations of the parabolic and almost-parabolic subalgebras of (conf 3 ) C are classified and the complete list of conditionally invariant semi-linear Schrodinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed

Schrodinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav; Růžička, František; Zloshchastiev, K. G.

2017-01-01

Roč. 9, č. 8 (2017), č. článku 165. ISSN 2073-8994 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : PT symmetry * nonlinear Schrodinger equations * logarithmic nonlinearities Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.457, year: 2016

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

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.

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

Nonlinear Schrodinger equation: A testing ground for the quantization of nonlinear waves

International Nuclear Information System (INIS)

Klein, A.; Krejs, F.

1976-01-01

Quantization of the nonlinear Schrodinger equation is carried out by the method due to Kerman and Klein. A viable procedure is inferred from the quantum interpretation of the classical (soliton) solution. The ground-state energy for a system with n particles is calculated to an accuracy which includes the first quantum correction to the semiclassical result. It is demonstrated that the exact answer can be obtained systematically only at the next level of approximation. For the calculation of the first quantum correction, the quantum theory of the stability of periodic orbits in field theory is developed and discussed. Since one is dealing with a finite many-body problem, the field theory can be written so that no infinite terms are encountered, but the Hamiltonian can also be artificially rearranged so as to destory this feature. For learning purposes the calculations are carried out with the various alternatives, and our methods prove capable of providing a uniform final result

An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

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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.

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...

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...

The time dependent Schrodinger equation revisited I: quantum field and classical Hamilton-Jacobi routes to Schrodinger's wave equation

International Nuclear Information System (INIS)

Scully, M O

2008-01-01

The time dependent Schrodinger equation is frequently 'derived' by postulating the energy E → i h-bar (∂/∂t) and momentum p-vector → ( h-bar /i)∇ operator relations. In the present paper we review the quantum field theoretic route to the Schrodinger wave equation which treats time and space as parameters, not operators. Furthermore, we recall that a classical (nonlinear) wave equation can be derived from the classical action via Hamiltonian-Jacobi theory. By requiring the wave equation to be linear we again arrive at the Schrodinger equation, without postulating operator relations. The underlying philosophy is operational: namely 'a particle is what a particle detector detects.' This leads us to a useful physical picture combining the wave (field) and particle paradigms which points the way to the time-dependent Schrodinger equation

On the so called rogue waves in nonlinear Schrodinger equations

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Y. Charles Li

2016-04-01

Full Text Available The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial period limit to the homoclinic solutions. In this article, from the perspective of the phase space structure of these homoclinic orbits in the infinite dimensional phase space where the NLS defines a dynamical system, we examine the observability of these homoclinic orbits (and their approximations. Our conclusion is that these approximate homoclinic orbits are the most observable solutions, and they should correspond to the most common deep ocean waves rather than the rare rogue waves. We also discuss other possibilities for the mechanism of a rogue wave: rough dependence on initial data or finite time blow up.

Assessment of Schrodinger Eigenmaps for target detection

Science.gov (United States)

Dorado Munoz, Leidy P.; Messinger, David W.; Czaja, Wojtek

2014-06-01

Non-linear dimensionality reduction methods have been widely applied to hyperspectral imagery due to its structure as the information can be represented in a lower dimension without losing information, and because the non-linear methods preserve the local geometry of the data while the dimension is reduced. One of these methods is Laplacian Eigenmaps (LE), which assumes that the data lies on a low dimensional manifold embedded in a high dimensional space. LE builds a nearest neighbor graph, computes its Laplacian and performs the eigendecomposition of the Laplacian. These eigenfunctions constitute a basis for the lower dimensional space in which the geometry of the manifold is preserved. In addition to the reduction problem, LE has been widely used in tasks such as segmentation, clustering, and classification. In this regard, a new Schrodinger Eigenmaps (SE) method was developed and presented as a semi-supervised classification scheme in order to improve the classification performance and take advantage of the labeled data. SE is an algorithm built upon LE, where the former Laplacian operator is replaced by the Schrodinger operator. The Schrodinger operator includes a potential term V, that, taking advantage of the additional information such as labeled data, allows clustering of similar points. In this paper, we explore the idea of using SE in target detection. In this way, we present a framework where the potential term V is defined as a barrier potential: a diagonal matrix encoding the spatial position of the target, and the detection performance is evaluated by using different targets and different hyperspectral scenes.

The behavior of steady quasisolitons near the limit cases of third-order nonlinear Schrödinger equation

DEFF Research Database (Denmark)

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

2002-01-01

The behavior of steady quasisoliton solutions to the extended third-order nonlinear Schrodinger (NLS) equation is studied in two cases: (i) when the coefficients in the equation approach the Hirota conditions, and (ii) near the limit of the regular NLS equation. (C) 2002 Published by Elsevier...

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.

Fractional Schrodinger equations with new conditions

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Abderrazek Benhassine

2018-01-01

Full Text Available In this article, we study the nonlinear fractional Schrodinger equation $$\\displaylines{ (-\\Delta^{\\alpha}u+ V(xu= f(x,u\\cr u\\in H^{\\alpha}(\\mathbb{R}^{n},\\mathbb{R}, }$$ where $(-\\Delta^{\\alpha}(\\alpha \\in (0, 1$ stands for the fractional Laplacian of order $\\alpha$, $x\\in \\mathbb{R}^{n}$, $V\\in C(\\mathbb{R}^{n},\\mathbb{R}$ may change sign and f is only locally defined near the origin with respect to u. Under some new assumptions on V and f, we show that the above system has infinitely many solutions near the origin. Some examples are also given to illustrate our main theoretical result.

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.

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.

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.

Constructing and analysis of soliton-like solutions of (1 + 1), (2 + 1), (3 + 1)-dimensional Schrodinger equations with the third power nonlinearity law

International Nuclear Information System (INIS)

Zhestkov, S.V.; Romanenko, A.A.

2009-01-01

The problem of existence of soliton-like solutions of (1+1), (2+1), (3+1)-dimensional Schrodinger equations with the third power nonlinearity law is investigated. The numerical-analytical method of constructing solitons is developed. (authors)

On the Schrodinger field

International Nuclear Information System (INIS)

Takahashi, Y.

1986-01-01

A brief but systematic discussion of the Schrodinger field is presented from the view point of quantized field theory. It is pointed out that the local momentum conservation equation is not of the usual continuity equation type when two-body potential interaction is presented and nevertheless the total momentum is globally conserved. The Schrodinger equation can be cast into a multicomponent equation containing only first order derivatives, depending on its spin contents. In case of spin 1/2, the g-factor is shown to be 2 even in purely non-relativistic Schrodinger field, in contrast with the general belief that g=2 is a relativistic effect

SOLUCIÓN DE LA ECUACIÓN NO LINEAL DE SCHRODINGER (1+1 EN UN MEDIO KERR

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Francis Armando Segovia

2015-12-01

Full Text Available Se presenta un marco teórico y se muestra una simulación numérica de la propagación de solitones. Con especial atención a los solitones ópticos espaciales, se calcula analíticamente el perfil de solitón correspondiente a la ecuación Schrodinger no-lineal para un medio Kerr. Los resultados muestran que los solitones ópticos son pulsos estables cuya forma y espectro son preservados en grandes distancias.Solution of the nonlinear Schrodinger equation (1+1 in a Kerr mediumABSTRACTThis document presents a theoretical framework and shows a numerical simulation for the propagation of solitons. With special attention to the spatial optical solitons, we calculates analytically the profile of solitón corresponding to the non-linear Schrodinger equation for a Kerr medium. The results show that the optical solitons are stable pulses whose shape and spectrum are preserved at great distances.Keywords: nonlinear optics, nonlinear Schrodinger equation, solitons.

Schrodinger cat state generation using a slow light

International Nuclear Information System (INIS)

Ham, B. S.; Kim, M. S.

2003-01-01

We show a practical application of giant Kerr nonlinearity to quantum information processing based on superposition of two distinct macroscopic states- Schrodinger cat state. The giant Kerr nonlinearity can be achieved by using electromagnetically induced transparency, in which light propagation should be slowed down so that a pi-phase shift can be easily obtained owing to increased interaction time.

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...

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.

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...

Scattering of quantized solitary waves in the cubic Schrodinger equation

International Nuclear Information System (INIS)

Dolan, L.

1976-01-01

The quantum mechanics for N particles interacting via a delta-function potential in one space dimension and one time dimension is known. The second-quantized description of this system has for its Euler-Lagrange equations of motion the cubic Schrodinger equation. This nonlinear differential equation supports solitary wave solutions. A quantization of these solitons reproduces the weak-coupling limit to the known quantum mechanics. The phase shift for two-body scattering and the energy of the N-body bound state is derived in this approximation. The nonlinear Schrodinger equation is contrasted with the sine-Gordon theory in respect to the ideas which the classical solutions play in the description of the quantum states

Self-similar solutions with compactly supported profile of some nonlinear Schrodinger equations

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Pascal Begout

2014-04-01

Full Text Available ``Sharp localized'' solutions (i.e. with compact support for each given time t of a singular nonlinear type Schr\\"odinger equation in the whole space $\\mathbb{R}^N$ are constructed here under the assumption that they have a self-similar structure. It requires the assumption that the external forcing term satisfies that $\\mathbf{f}(t,x=t^{-(\\mathbf{p}-2/2}\\mathbf{F}(t^{-1/2}x$ for some complex exponent $\\mathbf{p}$ and for some profile function $\\mathbf{F}$ which is assumed to be with compact support in $\\mathbb{R}^N$. We show the existence of solutions of the form $\\mathbf{u}(t,x=t^{\\mathbf{p}/2}\\mathbf{U}(t^{-1/2}x$, with a profile $\\mathbf{U}$, which also has compact support in $\\mathbb{R}^N$. The proof of the localization of the support of the profile $\\mathbf{U}$ uses some suitable energy method applied to the stationary problem satisfied by $\\mathbf{U}$ after some unknown transformation.

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

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

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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.

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

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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.

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.

On the representation of contextual probabilistic dynamics in the complex Hilbert space: Linear and nonlinear evolutions, Schrodinger dynamics

International Nuclear Information System (INIS)

Khrennikov, A.

2005-01-01

We constructed the representation of contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function can be considered as Hilbert space projection of realistic dynamics in a pre space. The basic condition for representing the pre space-dynamics is the law of statistical conservation of energy-conservation of probabilities. The construction of the dynamical representation is an important step in the development of contextual statistical viewpoint of quantum processes. But the contextual statistical model is essentially more general than the quantum one. Therefore in general the Hilbert space projection of the pre space dynamics can be nonlinear and even irreversible (but it is always unitary). There were found conditions of linearity and reversibility of the Hilbert space dynamical projection. We also found conditions for the conventional Schrodinger dynamics (including time-dependent Hamiltonians). We remark that in general even the Schrodinger dynamics is based just on the statistical conservation of energy; for individual systems the law of conservation of energy can be violated (at least in our theoretical model)

Uniform decay for a local dissipative Klein-Gordon-Schrodinger type system

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Marilena N. Poulou

2012-10-01

Full Text Available In this article, we consider a nonlinear Klein-Gordon-Schrodinger type system in $mathbb{R}^n$, where the nonlinear term exists and the damping term is effective. We prove the existence and uniqueness of a global solution and its exponential decay. The result is achieved by using the multiplier technique.

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Rasmussen, Kim; Henning, D.; Gabriel, H.

1996-01-01

We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...

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)

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.

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.

Schr\\"odinger group and quantum finance

OpenAIRE

Romero, Juan M.; Lavana, Ulises; Martínez, Elio

2013-01-01

Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black-Scholes equation is invariant under Schr\\"odinger group. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited. To get the Black-Scholes equation symmetries, the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schr\\"odinger algebra representation is co...

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.

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

Erwin Schrodinger

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education. Erwin Schrodinger. Articles written in Resonance – Journal of Science Education. Volume 4 Issue 2 February 1999 pp 92-103 Classics. The Fundamental Idea of Wave Mechanics · Erwin Schrodinger · More Details Fulltext PDF ...

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

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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.

Asymptotic Expansions for Higher-Order Scalar Difference Equations

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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.

Asymptotic Expansions for Higher-Order Scalar Difference Equations

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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.

Construction of wave operator for two-dimensional Klein-Gordon-Schrodinger systems with Yukawa coupling

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Kai Tsuruta

2013-05-01

Full Text Available We prove the existence of the wave operator for the Klein-Gordon-Schrodinger system with Yukawa coupling. This non-linearity type is below Strichartz scaling, and therefore classic perturbation methods will fail in any Strichartz space. Instead, we follow the "first iteration method" to handle these critical non-linearities.

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.

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.

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) )

An Algorithm for Higher Order Hopf Normal Forms

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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.

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)

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.

Existence and concentration of semiclassical states for nonlinear Schrodinger equations

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Shaowei Chen

2012-05-01

Full Text Available In this article, we study the semilinear Schrodinger equation $$ -epsilon^2Delta u+ u+ V(xu=f(u,quad uin H^1(mathbb{R}^N, $$ where $Ngeq 2$ and $epsilon>0$ is a small parameter. The function $V$ is bounded in $mathbb{R}^N$, $inf_{mathbb{R}^N}(1+V(x>0$ and it has a possibly degenerate isolated critical point. Under some conditions on f, we prove that as $epsilono 0$, this equation has a solution which concentrates at the critical point of V.

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.

Existence of solutions to quasilinear Schrodinger equations with indefinite potential

Directory of Open Access Journals (Sweden)

Zupei Shen

2015-04-01

Full Text Available In this article, we study the existence and multiplicity of solutions of the quasilinear Schrodinger equation $$ -u''+V(xu-(|u| ^2''u=f(u $$ on $\\mathbb{R}$, where the potential $V$ allows sign changing and the nonlinearity satisfies conditions weaker than the classical Ambrosetti-Rabinowitz condition. By a local linking theorem and the fountain theorem, we obtain the existence and multiplicity of solutions for the equation.

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.

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.

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.

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.

New travelling wave solutions of the (1 + 1-dimensional cubic nonlinear Schrodinger equation using novel (G′/G-expansion method

Directory of Open Access Journals (Sweden)

M.G. Hafez

2016-06-01

Full Text Available In this paper, the novel (G′/G-expansion method is applied to construct exact travelling wave solutions of the cubic nonlinear Schrodinger equation. This technique is straightforward and simple to use, and gives more new general solutions than the other existing methods. Various types of solitary and periodic wave solutions of this equation are derived. The obtained results may be helpful to describe the wave propagation in soliton physics, such as soliton propagation in optical fibers, modulus instability in plasma physics, etc. and provided us the firm mathematical foundation in soliton physics or any varied instances. Furthermore, three-dimensional modules plot of the solutions are also given to visualize the dynamics of the equation.

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)

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

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.

A conservative local discontinuous Galerkin method for the solution of nonlinear Schr(o)dinger equation in two dimensions

Institute of Scientific and Technical Information of China (English)

ZHANG RongPei; YU XiJun; LI MingJun; LI XiangGui

2017-01-01

In this study,we present a conservative local discontinuous Galerkin (LDG) method for numerically solving the two-dimensional nonlinear Schr(o)dinger (NLS) equation.The NLS equation is rewritten as a firstorder system and then we construct the LDG formulation with appropriate numerical flux.The mass and energy conserving laws for the semi-discrete formulation can be proved based on different choices of numerical fluxes such as the central,alternative and upwind-based flux.We will propose two kinds of time discretization methods for the semi-discrete formulation.One is based on Crank-Nicolson method and can be proved to preserve the discrete mass and energy conservation.The other one is Krylov implicit integration factor (ⅡF) method which demands much less computational effort.Various numerical experiments are presented to demonstrate the conservation law of mass and energy,the optimal rates of convergence,and the blow-up phenomenon.

Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Directory of Open Access Journals (Sweden)

Khaled A. Gepreel

2013-01-01

Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

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

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

Critical behavior from Schrodinger representation

International Nuclear Information System (INIS)

Suranyi, P.

1992-01-01

In this paper, the Schrodinger equation for φ 4 field theory is reduced to an infinite set of integral equations. A systematic truncation scheme is proposed and it is solved in second order to obtain the approximate critical behavior of the renormalized mass. The correlation exponent is given as a solution of a transcendental equation. It is in good agreement with the Ising model in all physical dimensions

Analytic smoothing effect for the cubic hyperbolic Schrodinger equation in two space dimensions

Directory of Open Access Journals (Sweden)

Gaku Hoshino

2016-01-01

Full Text Available We study the Cauchy problem for the cubic hyperbolic Schrodinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.

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...

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.

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)

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.

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.

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

Supersymmetric extensions of Schrodinger-invariance

International Nuclear Information System (INIS)

Henkel, Malte; Unterberger, Jeremie

2006-01-01

The set of dynamic symmetries of the scalar free Schrodinger equation in d space dimensions gives a realization of the Schrodinger algebra that may be extended into a representation of the conformal algebra in d+2 dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin-12 Levy-Leblond equation. An N=2 supersymmetric extension of these equations leads, respectively, to a 'super-Schrodinger' model and to the (3 vertical bar 2)-supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras osp(2 vertical bar 2)-bar sh(2 vertical bar 2) and osp(2 vertical bar 4), respectively. The Schrodinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schrodinger-Neveu-Schwarz algebra sns (N) with N supercharges. Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of osp(2 vertical bar 4). If one includes both N=2 supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values

Curvature-induced symmetry breaking in nonlinear Schrodinger models

DEFF Research Database (Denmark)

Gaididei, Yuri Borisovich; Mingaleev, S. F.; Christiansen, Peter Leth

2000-01-01

We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states...

Numerical study of fractional nonlinear Schrodinger equations

KAUST Repository

Klein, Christian

2014-10-08

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

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.

Infinitely many solutions for fractional Schr\\"odinger equations in R^N

Directory of Open Access Journals (Sweden)

Caisheng Chen

2016-03-01

Full Text Available Using variational methods we prove the existence of infinitely many solutions to the fractional Schrodinger equation $$ (-\\Delta^su+V(xu=f(x,u, \\quad x\\in\\mathbb{R}^N, $$ where $N\\ge 2, s\\in (0,1$. $(-\\Delta^s$ stands for the fractional Laplacian. The potential function satisfies $V(x\\geq V_0>0$. The nonlinearity f(x,u is superlinear, has subcritical growth in u, and may or may not satisfy the (AR condition.

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.)

Breatherlike impurity modes in discrete nonlinear lattices

DEFF Research Database (Denmark)

Hennig, D.; Rasmussen, Kim; Tsironis, G. P.

1995-01-01

We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...

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.

Schrodinger representation in renormalizable quantum field theory

International Nuclear Information System (INIS)

Symanzik, K.

1983-01-01

The problem of the Schrodinger representation arose from work on the Nambu-Goto Ansatz for integration over surfaces. Going beyond semiclassical approximation leads to two problems of nonrenormalizibility and of whether Dirichlet boundary conditions can be imposed on a ''Euclidean'' quantum field theory. The Schrodinger representation is constructed in a way where the principles of general renormalization theory can be refered to. The Schrodinger function of surface terms is studied, as well as behaviour at the boundary. The Schrodinger equation is derived. Completeness, unitarity, and computation of expectation values are considered. Extensions of these methods into other Bose field theories such as Fermi fields and Marjorana fields is straightforward

Spike-layer solutions to nonlinear fractional Schrodinger equations with almost optimal nonlinearities

Directory of Open Access Journals (Sweden)

Jinmyoung Seok

2015-07-01

Full Text Available In this article, we are interested in singularly perturbed nonlinear elliptic problems involving a fractional Laplacian. Under a class of nonlinearity which is believed to be almost optimal, we construct a positive solution which exhibits multiple spikes near any given local minimum components of an exterior potential of the problem.

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.

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.

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.

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

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.

Finite element method for time-space-fractional Schrodinger equation

Directory of Open Access Journals (Sweden)

Xiaogang Zhu

2017-07-01

Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.

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.

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.

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.

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.

Nonlinear Optics and Applications

Science.gov (United States)

Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)

2007-01-01

Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.

Nonlinear excitations in two-dimensional molecular structures with impurities

DEFF Research Database (Denmark)

Gaididei, Yuri Borisovich; Rasmussen, Kim; Christiansen, Peter Leth

1995-01-01

We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence...... of the impurity. Transforming the equation to the noninertial frame of reference coupled with the center of mass we investigate the soliton behavior in the close vicinity of the impurity. With the help of the lens transformation we show that the soliton width is governed by an Ermakov-Pinney equation. We also...... excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation....

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)

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.

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.)

Breatherlike excitations in discrete lattices with noise and nonlinear damping

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yuri B.; Johansson, Magnus

1997-01-01

We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects...

Reflectionless discrete Schr\\"odinger operators are spectrally atypical

OpenAIRE

VandenBoom, Tom

2017-01-01

We prove that, if an isospectral torus contains a discrete Schr\\"odinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense in which finite unions of nondegenerate closed intervals having capacity one are not the spectrum of any reflectionless discrete Schr\\"odinger operator. We also show that the only reflectionless discrete Schr\\"odinger operators having zero, one, or two spectral gaps are periodic.

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)

Comparison of the Schrodinger and Salpeter equations

International Nuclear Information System (INIS)

Jacobs, S.; Olsson, M.G.

1985-01-01

A unified approach to the solution of the Schrodinger and spinless Salpeter equations is presented. Fits to heavy quark bound state energies using various potential models are employed to determine whether the Salpeter equation provides a better description of heavy quark systems than the Schrodinger equation

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

On localization in the discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Bang, O.; Juul Rasmussen, J.; Christiansen, P.L.

1993-01-01

For some values of the grid resolution, depending on the nonlinearity, the discrete nonlinear Schrodinger equation with arbitrary power nonlinearity can be approximated by the corresponding continuum version of the equation. When the discretization becomes too coarse, the discrete equation exhibits...

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.

Quantum Computer Games: Schrodinger Cat and Hounds

Science.gov (United States)

Gordon, Michal; Gordon, Goren

2012-01-01

The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements and…

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

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%.

The construction of partner potential from the general potential anharmonic in D-dimensional Schrodinger system

Science.gov (United States)

Suparmi; Cari, C.; Wea, K. N.; Wahyulianti

2018-03-01

The Schrodinger equation is the fundamental equation in quantum physics. The characteristic of the particle in physics potential field can be explained by using the Schrodinger equation. In this study, the solution of 4 dimensional Schrodinger equation for the anharmonic potential and the anharmonic partner potential have done. The method that used to solve the Schrodinger equation was the ansatz wave method, while to construction the partner potential was the supersymmetric method. The construction of partner potential used to explain the experiment result that cannot be explained by the original potential. The eigenvalue for anharmonic potential and the anharmonic partner potential have the same characteristic. Every increase of quantum orbital number the eigenvalue getting smaller. This result corresponds to Bohrn’s atomic theory that the eigenvalue is inversely proportional to the atomic shell. But the eigenvalue for the anharmonic partner potential higher than the eigenvalue for the anharmonic original potential.

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)

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.

Newton-Cartan supergravity with torsion and Schrodinger supergravity

NARCIS (Netherlands)

Bergshoeff, Eric; Rosseel, Jan; Zojer, Thomas

2015-01-01

We derive a torsionfull version of three-dimensional N - 2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The "superconformal" theory that we start with is Schrodinger supergravity which we obtain by gauging the Schrodinger superalgebra. We present

Local well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices

Directory of Open Access Journals (Sweden)

Xavier Carvajal

2004-01-01

Full Text Available We prove that the initial value problem associated with $$ partial_tu+ialpha partial^2_x u+Beta partial^3_x u +igamma|u|^2u = 0, quad x,t in mathbb{R}, $$ is locally well-posed in $H^s$ for $s>-1/4$.

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...

Well-posedness and exact controllability of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation

Directory of Open Access Journals (Sweden)

Ruili Wen

2016-08-01

Full Text Available We consider an open-loop system of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation. Using the multiplier method on Riemannian manifold we show that that the system is well-posed in the sense of Salamon. This implies that the exponential stability of the closed-loop system under the direct proportional output feedback control and the exact controllability of open-loop system are equivalent. So in order to conclude feedback stabilization from well-posedness, we study the exact controllability under a uniqueness assumption by presenting the observability inequality for the dual system. In addition, we show that the system is regular in the sense of Weiss, and that the feedthrough operator is zero.

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.

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.

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.)

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.

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

Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.

1996-01-01

Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...

Defocusing regimes of nonlinear waves in media with negative dispersion

DEFF Research Database (Denmark)

Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.

1996-01-01

Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...

PERSAMAAN SCHRODINGER D-DIMENSI BAGIAN SUDUT POTENSIAL POSCHL-TELLER HIPERBOLIK TERDEFORMASI Q PLUS ROSEN-MORSE TRIGONOMETRI MENGGUNAKAN METODE NIKIFOROV-UVAROV

Directory of Open Access Journals (Sweden)

S. Suparmi

2016-11-01

Full Text Available Metode Nikivarof Uvarov merupakan metode penyelesaian persamaan diferensial orde dua dengan mengubah persamaan diferensial orde dua yang umum (persamaan Schrodinger menjadi persamaan diferensial tipe hipergeometrik melalui substitusi variabel yang sesuai untuk memperoleh eigen value dan fungsi gelombang bagian sudut. Penelitian ini merupakan studi literatur untuk menyelesaikan persamaan Schrodinger D-dimensi bagian sudut dengan potensial Poschl-Teller Hiperbolik Terdeformasi q plus Rosen Morse Trigonometri Terdeformasi q menggunakan metode Nikiforov-Uvarov (NU. Pada penelitian ini bertujuan untuk mengetahui bagaimana fungsi gelombang bagian sudut persamaan schrodinger D-dimensi  untuk potensial Poschl-Teller Hiperbolik Terdeformasi q plus Rosen Morse Trigonometri Terdeformasi q menggunakan metode Nikiforov-Uvarov (NU.Nikivarof Uvarov is a method to solve second order differential equations by changing general second order differential equation to hyper-geometric differential equation type through substituting relevant variable to obtain eigenvalues and the angle of wave function. This is a literature study to solve the D-dimensional Schrodinger equation with a corner section q Deformed Hyperbolic Poschl Teller plus q Deformed Trigonometric Rosen-Morse Potential using Nikiforov-Uvarov (NU. This study aims to determine the way the angle of wave function of D-dimensional Schrodinger equation for q-Deformed Hyperbolic Poschl Teller plus q Deformed  Trigonometric Rosen-Morse Potential using Nikiforov-Uvarov (NU. 

Nonlinear Electron Waves in Strongly Magnetized Plasmas

DEFF Research Database (Denmark)

Pécseli, Hans; Juul Rasmussen, Jens

1980-01-01

Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...... dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed....

Nonlocal description of X waves in quadratic nonlinear materials

DEFF Research Database (Denmark)

Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole

2006-01-01

We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...

The Schrodinger Eigenvalue March

Science.gov (United States)

Tannous, C.; Langlois, J.

2011-01-01

A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…

Three-dimensional solutions in media with spatial dependence of nonlinear refractive index

International Nuclear Information System (INIS)

Kovachev, L.M.; Kaymakanova, N.I.; Dakova, D.Y.; Pavlov, L.I.; Donev, S.G.; Pavlov, R.L.

2004-01-01

We investigate a nonparaxial vector generalization of the scalar 3D+1 Nonlinear Schrodinger Equation (NSE). Exact analytical 3D+1 soliton solutions are obtained for the first time in media of spatial dependence of the nonlinear refractive index

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.

Existence of standing waves for Schrodinger equations involving the fractional Laplacian

Directory of Open Access Journals (Sweden)

Everaldo S. de Medeiros

2017-03-01

Full Text Available We study a class of fractional Schrodinger equations of the form $$ \\varepsilon^{2\\alpha}(-\\Delta^\\alpha u+ V(xu = f(x,u \\quad\\text{in } \\mathbb{R}^N, $$ where $\\varepsilon$ is a positive parameter, $0 < \\alpha < 1$, $2\\alpha < N$, $(-\\Delta^\\alpha$ is the fractional Laplacian, $V:\\mathbb{R}^{N}\\to \\mathbb{R}$ is a potential which may be bounded or unbounded and the nonlinearity $f:\\mathbb{R}^{N}\\times \\mathbb{R}\\to \\mathbb{R}$ is superlinear and behaves like $|u|^{p-2}u$ at infinity for some $2

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.

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.

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

Null controllability of a cascade system of Schrodinger equations

Directory of Open Access Journals (Sweden)

Marcos Lopez-Garcia

2016-03-01

Full Text Available This article presents a control problem for a cascade system of two linear N-dimensional Schrodinger equations. We address the problem of null controllability by means of a control supported in a region not satisfying the classical geometrical control condition. The proof is based on the application of a Carleman estimate with degenerate weights to each one of the equations and a careful analysis of the system in order to prove null controllability with only one control force.

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)

Schr"odinger's Unified Field Theory: Physics by Public Relations

Science.gov (United States)

Halpern, Paul

2009-05-01

We will explore the circumstances surrounding Erwin Schr"odinger's announcement in January 1947 that he had developed a comprehensive unified field theory of gravitation and electromagnetism. We will speculate on Schr"odinger's motivations for the mode and tone of his statements, consider the reaction of the international press within the context of the postwar era, and examine Einstein's response.

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.

Canonical action-angle formalism for quantized nonlinear fields

International Nuclear Information System (INIS)

Garbaczewki, P.

1987-01-01

The canonical quantizations of field and action-angle coordinates which (locally) parameterize the phase manifold for the same nonlinear field theory model (e.g. sine-Gordon and nonlinear Schrodinger with the attractive coupling) are reconciled on the common for both cases state space. The classical-quantum relationship is maintained in the mean: coherent state expectation values of operators give rise to classical objects

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.

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) ≤

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

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

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.

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 ...

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.

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.

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.

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.

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.

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.

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.

Nonlinear Evolution of Alfvenic Wave Packets

Science.gov (United States)

Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.

1998-01-01

Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.

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.

Collective spin by linearization of the Schrodinger equation for nuclear collective motion

International Nuclear Information System (INIS)

Greiner, M.; Scheid, W.; Herrmann, R.

1988-01-01

The free Schrodinger equation for multipole degrees of freedom is linearized so that energy and momentum operators appear only in first order. As an example, the authors demonstrate the linearization procedure for quadrupole degrees of freedom. The wave function solving this equation carries a spin. The authors derive the operator of the collective spin and its eigen values depending on multipolarity

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

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.

Quantum field theory in flat Robertson-Walker space-time functional Schrodinger picture

International Nuclear Information System (INIS)

Pi, S.Y.

1990-01-01

Quantum field theory in Robertson-Walker space-time is intrinsically time-dependent and the functional Schrodinger picture provides a useful description. This paper discusses free and self-interacting bosonic quantum field theories: Schrodinger picture quantization, time-dependent Gaussian approximations based on variational principles describing time evolution of pure and mixed states, and renormalizability of the Schrodinger picture. The technique introduced can be used to study various dynamical questions in early universe processes

Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Directory of Open Access Journals (Sweden)

Khaled A. Gepreel

2012-01-01

Full Text Available We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

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.

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...

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.

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

Image denoising using the squared eigenfunctions of the Schrodinger operator

KAUST Repository

Kaisserli, Zineb; Laleg-Kirati, Taous-Meriem

2015-01-01

This study introduces a new image denoising method based on the spectral analysis of the semi-classical Schrodinger operator. The noisy image is considered as a potential of the Schrodinger operator, and the denoised image is reconstructed using the discrete spectrum of this operator. First results illustrating the performance of the proposed approach are presented and compared to the singular value decomposition method.

Image denoising using the squared eigenfunctions of the Schrodinger operator

KAUST Repository

Kaisserli, Zineb

2015-02-02

This study introduces a new image denoising method based on the spectral analysis of the semi-classical Schrodinger operator. The noisy image is considered as a potential of the Schrodinger operator, and the denoised image is reconstructed using the discrete spectrum of this operator. First results illustrating the performance of the proposed approach are presented and compared to the singular value decomposition method.

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.

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.

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....

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

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.

Variational Principles, Lie Point Symmetries, and Similarity Solutions of the Vector Maxwell Equations in Non-linear Optics

DEFF Research Database (Denmark)

Webb, Garry; Sørensen, Mads Peter; Brio, Moysey

2004-01-01

the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr nonlinearity, are shown to reduce...... the properties of Maxwell's equations in nonlinear optics, without resorting to the commonly used nonlinear Schr\\"odinger (NLS) equation approximation in which a high frequency carrier wave is modulated on long length and time scales due to nonlinear sideband wave interactions. This is important in femto......-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field $E$, in terms of the the canonical variables, with possible multiple real roots for $E$. In order...

Nonlinear evolution of astrophysical Alfven waves

Science.gov (United States)

Spangler, S. R.

1984-01-01

Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth.

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.

Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

Science.gov (United States)

Costiner, Sorin; Taasan, Shlomo

1994-01-01

This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

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.

Collapse of solitary excitations in the nonlinear Schrödinger equation with nonlinear damping and white noise

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim

1996-01-01

in an exponentially decreasing width of the solution in the long-time limit. We also find that a sufficiently large noise variance may cause an initially localized distribution to spread instead of contracting, and that the critical variance necessary to cause dispersion will for small damping be the same......We study the effect of adding noise and nonlinear damping in the two-dimensional nonlinear Schrodinger equation (NLS). Using a collective approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead...

Functionals Hartree-Fock equations in the Schrodinger representation of quantum field theory

International Nuclear Information System (INIS)

Gamboa, J.

1989-08-01

Hartree-Fock equations for a scalar field theory in the Schrodinger representation are derived. It is shown that renormalization of the total energy in the functional Schrodinger equation is enterely contained in the eigenvalues of the Hartree-Fock hamiltonian. (A.C.A.S.) [pt

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

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

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....

Nonlinear Schrodinger elliptic systems involving exponential critical growth in R^2

Directory of Open Access Journals (Sweden)

Francisco S. B. Albuquerque Albuquerque

2014-02-01

Full Text Available This article concerns the existence and multiplicity of solutions for elliptic systems with weights, and nonlinearities having exponential critical growth. Our approach is based on the Trudinger-Moser inequality and on a minimax theorem.

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

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.

Properties of Energy Spectra of Molecular Crystals Investigated by Nonlinear Theory

Science.gov (United States)

Pang, Xiao-Feng; Zhang, Huai-Wu

We calculate the quantum energy spectra of molecular crystals, such as acetanilide, by using discrete nonlinear Schrodinger equation, containing various interactions, appropriate to the systems. The energy spectra consist of many energy bands, in each energy band there are a lot of energy levels including some higher excited states. The result of energy spectrum is basically consistent with experimental values obtained by infrared absorption and Raman scattering in acetanilide and can also explain some experimental results obtained by Careri et al. Finally, we further discuss the influences of variously characteristic parameters on the energy spectra of the systems.

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.

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.

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.

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.

On Schr\\"odinger's cat

OpenAIRE

de Silva, Nalin

2010-01-01

Schr\\"odinger's cat appears to have been harassed in a chamber during the past eighty years or so by interpreting the role of the observer as a person, who sets an experiment and then observes results, may be after some time. The realist position tells us that the physical processes would take place independent of the observer with well defined properties, whereas the positivist position wants us to believe that nothing can be said of a system when it is not being observed. In this paper we q...

Adiabatic invariants and asymptotic behavior of Lyapunov exponents of the Schrodinger equation

International Nuclear Information System (INIS)

Delyon, F.; Foulon, P.

1986-01-01

We give an upper bound for the high-energy behavior of the Lyapunov exponent of the one-dimensional Schrodinger equation. We relate this behavior to the diffrentiability properties of the potential. As an application, this result provides an upper bound for the asymptotic length of the gaps of the Schrodinger equation

A solution of the Schrodinger equation with two-body correlations included

International Nuclear Information System (INIS)

Fabre de la Ripelle, M.

1984-01-01

A procedure for introducing the two-body correlations in the solution of the Schrodinger equation is described. The N-body Schrodinger equation for nucleons subject to two-(or many)-body N-N interaction has never been solved with accuracy except for few-body systems. Indeed it is difficult to take the two-body correlations generated by the interaction into account in the wave function

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

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...

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.

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

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.

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.

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.

Nonlinear dynamics of a parametrically driven sine-Gordon system

DEFF Research Database (Denmark)

Grønbech-Jensen, Niels; Kivshar, Yuri S.; Samuelsen, Mogens Rugholm

1993-01-01

We consider a sine-Gordon system, driven by an ac parametric force in the presence of loss. It is demonstrated that a breather can be maintained in a steady state at half of the external frequency. In the small-amplitude limit the effect is described by an effective nonlinear Schrodinger equation...

Random-walk simulation of the Schrodinger equation: H+3

International Nuclear Information System (INIS)

Anderson, J.B.

1975-01-01

A simple random-walk method for obtaining ab initio solutions of the Schrodinger equation is examined in its application to the case of the molecular ion H + 3 in the equilateral triangle configuration with side length R=1.66 bohr. The method, which is based on the similarity of the Schrodinger equation and the diffusion equation, involves the random movement of imaginary particles (psips) in electron configuration space subject to a variable chance of multiplication or disappearance. The computation requirements for high accuracy in determining energies of H + 3 are greater than those of existing LCAO--MO--SCF--CI methods. For more complex molecular systems the method may be competitive. (auth)

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

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.

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.

Remarks on the spectral theory for the multiparticle-type Schrodinger operator

International Nuclear Information System (INIS)

Yafaev, D.R.

1985-01-01

Mourre's method is used to prove the limiting absorption principle for the multiparticle Schrodinger operator under the same assumptions on the pair potentials as in the two-particle problem. It is shown that at high energies this principle is valid under wider conditions than on the whole spectral axis. The scattering theory for a Schrodinger operator whose potential decays at infinity in an essentially anisotropic manner is constructed in analogy with the three-particle problem

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

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.

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

Massively Parallel Algorithms for Solution of Schrodinger Equation

Science.gov (United States)

Fijany, Amir; Barhen, Jacob; Toomerian, Nikzad

1994-01-01

In this paper massively parallel algorithms for solution of Schrodinger equation are developed. Our results clearly indicate that the Crank-Nicolson method, in addition to its excellent numerical properties, is also highly suitable for massively parallel computation.

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.

Stabilization of nonlinear excitations by disorder

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.

1998-01-01

Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem...... are investigated. We find that otherwise unstable excitations can be stabilized by the presence of disorder in the continuum problem. For the very narrow excitations of the discrete problem we find that the disorder has no effect on the averaged behavior. Finally, we show that the disorder can be applied to induce...... a high degree of controllability of the spatial extent of the stable excitations in the continuum system....

Stationary states of the two-dimensional nonlinear Schrödinger model with disorder

DEFF Research Database (Denmark)

Gaididei, Yuri Borisovich; Hendriksen, D.; Christiansen, Peter Leth

1998-01-01

Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder...

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.

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.

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.

The effects of relativistic and non-local non-linearities on modulational instabilities in non-uniform plasma

International Nuclear Information System (INIS)

Mohamed, B.F.; El-Shorbagy, Kh.H.

2000-01-01

A general detailed analysis for the nonlinear generation of localized fields due to the existence of a strong pump field inside the non-uniform plasma has been considered. We have taken into account the effects of relativistic and non-local nonlinearities on the structure of plasma resonance region. The nonlinear Schrodinger equation described the localized fields are investigated. Besides, the generalized dispersion relation is obtained to study the modulational instabilities in different cases. Keywords: Wave-plasma interaction, Nonlinear effects, Modulation instabilities

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...

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.

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.

Parametric autoresonant excitation of the nonlinear Schrödinger equation.

Science.gov (United States)

Friedland, L; Shagalov, A G

2016-10-01

Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the driving wave for entering the autoresonant regime. It is shown that above the threshold, a flat (spatially independent) NLS solution can be fully converted into a traveling wave. A simplified, few spatial harmonics expansion approach is also developed for studying this nonlinear mode conversion process, allowing interpretation as autoresonant interaction within triads of spatial harmonics.

Soliton solutions for a quasilinear Schrodinger equation

Directory of Open Access Journals (Sweden)

Duchao Liu

2013-12-01

Full Text Available In this article, critical point theory is used to show the existence of nontrivial weak solutions to the quasilinear Schrodinger equation $$ -\\Delta_p u-\\frac{p}{2^{p-1}}u\\Delta_p(u^2=f(x,u $$ in a bounded smooth domain $\\Omega\\subset\\mathbb{R}^{N}$ with Dirichlet boundary conditions.

Torsional Newton-Cartan geometry and the Schrodinger algebra

NARCIS (Netherlands)

Bergshoeff, Eric A.; Hartong, Jelle; Rosseel, Jan

2015-01-01

We show that by gauging the Schrodinger algebra with critical exponent z and imposing suitable curvature constraints, that make diffeomorphisms equivalent to time and space translations, one obtains a geometric structure known as (twistless) torsional Newton-Cartan geometry (TTNC). This is a version

Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method

Directory of Open Access Journals (Sweden)

Hassan A. Zedan

2012-01-01

Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.

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.

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

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

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...

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.

Light-Front Holography and the Light-Front Schrodinger Equation

Energy Technology Data Exchange (ETDEWEB)

Brodsky, Stanley J.; de Teramond, Guy

2012-08-15

One of the most important nonperturbative methods for solving QCD is quantization at fixed light-front time {tau} = t+z=c - Dirac's 'Front Form'. The eigenvalues of the light-front QCD Hamiltonian predict the hadron spectrum and the eigensolutions provide the light-front wavefunctions which describe hadron structure. More generally, we show that the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrodinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. We outline a method for computing the required potential from first principles in QCD. The holographic mapping of gravity in AdS space to QCD, quantized at fixed light-front time, yields the same light front Schrodinger equation; in fact, the soft-wall AdS/QCD approach provides a model for the light-front potential which is color-confining and reproduces well the light-hadron spectrum. One also derives via light-front holography a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent first approximation of the color-confining dynamics, spectroscopy, and excitation spectra of relativistic light-quark bound states in QCD.

Numerical solution of the Schrodinger equation for stationary bound states using nodel theorem

International Nuclear Information System (INIS)

Chen Zhijiang; Kong Fanmei; Din Yibin

1987-01-01

An iterative procedure for getting the numerical solution of Schrodinger equation on stationary bound states is introduced. The theoretical foundtion, the practical steps and the method are presented. An example is added at the end. Comparing with other methods, the present one requires less storage, less running time but posesses higher accuracy. It can be run on the personal computer or microcomputer with 256 K memory and 16 bit word length such as IBM/PC, MC68000/83/20, PDP11/23 etc

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.

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.

Switching between bistable states in a discrete nonlinear model with long-range dispersion

DEFF Research Database (Denmark)

Johansson, Magnus; Gaididei, Yuri B.; Christiansen, Peter Leth

1998-01-01

In the framework of a discrete nonlinear Schrodinger equation with long-range dispersion, we propose a general mechanism for obtaining a controlled switching between bistable localized excitations. We show that the application of a spatially symmetric kick leads to the excitation of an internal...

New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source

International Nuclear Information System (INIS)

Abdou, M.A.

2008-01-01

The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics

Chaotic synchronization of symbolic information in the discrete nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Pando L, C.L.

2003-08-01

We have studied the discrete nonlinear Schrodinger equation (DNLSE) with on-site defects and periodic boundary conditions. When the array dynamics becomes chaotic, the otherwise quasiperiodic amplitude correlations between the oscillators are destroyed. However, we show that synchronization of symbolic information of suitable amplitude signals is possible in this hamiltonian system. (author)

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.)

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

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...

Stationary solutions and self-trapping in discrete quadratic nonlinear systems

DEFF Research Database (Denmark)

Bang, Ole; Christiansen, Peter Leth; Clausen, Carl A. Balslev

1998-01-01

We consider the simplest equations describing coupled quadratic nonlinear (chi((2))) systems, which each consists of a fundamental mode resonantly interacting with its second harmonic. Such discrete equations apply, e.g., to optics, where they can describe arrays of chi((2)) waveguides...... the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, which is integrable. We show how the stationary solutions to the two systems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system...

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.

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)

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)

Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma

Science.gov (United States)

Vasquez, Bernard J.

1993-01-01

The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p Schrodinger (DNLS) equation.

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...

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.

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.

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

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

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.

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.

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))

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

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.

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.

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

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)

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

Institute of Scientific and Technical Information of China (English)

无

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.

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)

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...

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.

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)

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.

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.

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. ...

Spectral bisection algorithm for solving Schrodinger equation using upper and lower solutions

Directory of Open Access Journals (Sweden)

Qutaibeh Deeb Katatbeh

2007-10-01

Full Text Available This paper establishes a new criteria for obtaining a sequence of upper and lower bounds for the ground state eigenvalue of Schr"odinger equation $ -Deltapsi(r+V(rpsi(r=Epsi(r$ in $N$ spatial dimensions. Based on this proposed criteria, we prove a new comparison theorem in quantum mechanics for the ground state eigenfunctions of Schrodinger equation. We determine also lower and upper solutions for the exact wave function of the ground state eigenfunctions using the computed upper and lower bounds for the eigenvalues obtained by variational methods. In other words, by using this criteria, we prove that the substitution of the lower(upper bound of the eigenvalue in Schrodinger equation leads to an upper(lower solution. Finally, two proposed iteration approaches lead to an exact convergent sequence of solutions. The first one uses Raielgh-Ritz theorem. Meanwhile, the second approach uses a new numerical spectral bisection technique. We apply our results for a wide class of potentials in quantum mechanics such as sum of power-law potentials in quantum mechanics.

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

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.

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.

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.

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

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.

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.

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...

Orbital stability of Gausson solutions to logarithmic Schrodinger equations

Directory of Open Access Journals (Sweden)

Alex H. Ardila

2016-12-01

Full Text Available In this article we prove of the orbital stability of the ground state for logarithmic Schrodinger equation in any dimension and under nonradial perturbations. This general stability result was announced by Cazenave and Lions [9, Remark II.3], but no details were given there.

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.

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)

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.

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

Ground state solutions for asymptotically periodic Schrodinger equations with critical growth

Directory of Open Access Journals (Sweden)

Hui Zhang

2013-10-01

Full Text Available Using the Nehari manifold and the concentration compactness principle, we study the existence of ground state solutions for asymptotically periodic Schrodinger equations with critical growth.

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.

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...

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

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...

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.

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

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.

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...

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

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.

A model for the stochastic origins of Schrodinger's equation

OpenAIRE

Davidson, Mark P.

2001-01-01

A model for the motion of a charged particle in the vacuum is presented which, although purely classical in concept, yields Schrodinger's equation as a solution. It suggests that the origins of the peculiar and nonclassical features of quantum mechanics are actually inherent in a statistical description of the radiative reactive force.

Self-induced dipole force and filamentation instability of a matter wave

DEFF Research Database (Denmark)

Saffman, M.

1998-01-01

The interaction of copropagating electromagnetic and matter waves is described with a set of coupled higher-order nonlinear Schrodinger equations. Optical self-focusing modulates an initially planar wave leading to the generation of dipole forces on the atoms. Atomic channeling due to the dipole...... forces leads, in the nonlinear regime, to filamentation of the atomic beam. Instability growth rates are calculated for atomic beams with both low and high phase space densities. In one transverse dimension an exact solution is found that describes a coupled optical and atomic soliton....

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)

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...

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

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

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...

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.

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.

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

Science.gov (United States)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

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...

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.

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.

Boundary triples for Schrodinger operators with singular interactions on hypersurfaces

Czech Academy of Sciences Publication Activity Database

Behrndt, J.; Langer, M.; Lotoreichik, Vladimir

2016-01-01

Roč. 7, č. 2 (2016), s. 290-302 ISSN 2220-8054 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : boundary triple * Weyl function * Schrodinger operator * singular potential * delta-interaction * hypersurface Subject RIV: BE - Theoretical Physics

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

Inverse scattering solution of non-linear evolution equations in one space dimension: an introduction

International Nuclear Information System (INIS)

Alvarez-Estrada, R.F.

1979-01-01

A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly

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

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.

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.

Ground state solutions for non-local fractional Schrodinger equations

Directory of Open Access Journals (Sweden)

Yang Pu

2015-08-01

Full Text Available In this article, we study a time-independent fractional Schrodinger equation with non-local (regional diffusion $$ (-\\Delta^{\\alpha}_{\\rho}u + V(xu = f(x,u \\quad \\text{in }\\mathbb{R}^{N}, $$ where $\\alpha \\in (0,1$, $N > 2\\alpha$. We establish the existence of a non-negative ground state solution by variational methods.

Dynamics in discrete two-dimensional nonlinear Schrödinger equations in the presence of point defects

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim

1996-01-01

The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties...... of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-dimensional dynamics of the traveling pulses is demonstrated. The typical scenario of the two-dimensional quasicollapse of a moving intense pulse represents the formation of standing trapped...... narrow spikes. The influence of the point impurities on this dynamics is also investigated....

Numerical reconstruction of wave field spatial distributions at the output and input planes of nonlinear medium with use of digital holography

International Nuclear Information System (INIS)

Nalegaev, S S; Petrov, N V; Bespalov, V G

2014-01-01

A numerical reconstruction of spatial distributions of optical radiation propagating through a volume of nonlinear medium at input and output planes of the medium was demonstrated using a scheme of digital holography. A nonlinear Schrodinger equation with Fourier Split-Step method was used as a tool to propagate wavefront in the volume of the medium. Time dependence of the refractive index change was not taken into account.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

Science.gov (United States)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Stochastic solutions to the Schrodinger equation for fermions

International Nuclear Information System (INIS)

Arnow, D.M.

1981-01-01

An exact stochastic method has been developed for generating the antisymmetric eigensolution of lowest index and its associated eigenvalue for the Schrodinger wave equation in 3N dimensions. The method is called the Green's function Monte Carlo method for fermions (FGFMC) because it is based on a Monte Carlo solution to the integral form of the Schrodinger equation (using Green's function) and because it is the fermion class of particles in physics which require antisymmetric solutions. The solution consists of two sets of 3N-dimensional points, [R/sub j/ + ] and [R/sub j/ - ], distributed by density functions psi + and psi - , whose difference, psi + -psi - , is proportional to the eigensolution, psi/sub F/. The FGFMC method is successfully applied to a one dimensional problem and a nine dimensional problem, the results of which are presented here. These results demonstrate that this method can be successfully applied to small physical problems on medium-scale computing machines. The key to this success was the transformation of the problem from exponential to linear cost as a function of accuracy. The strong dependence on dimensionality, however, currently results in an exponential cost as a function of problem size, and this, until overcome, imposes a severe barrier to calculations on large systems

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.

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

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.

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 ...

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 ...

Nonlinear electron-acoustic rogue waves in electron-beam plasma system with non-thermal hot electrons

Science.gov (United States)

Elwakil, S. A.; El-hanbaly, A. M.; Elgarayh, A.; El-Shewy, E. K.; Kassem, A. I.

2014-11-01

The properties of nonlinear electron-acoustic rogue waves have been investigated in an unmagnetized collisionless four-component plasma system consisting of a cold electron fluid, non-thermal hot electrons obeying a non-thermal distribution, an electron beam and stationary ions. It is found that the basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of rogue wave profiles on the electron beam and energetic population parameter are discussed. The results of the present investigation may be applicable in auroral zone plasma.

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

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.

Generic singular continuous spectrum for ergodic Schr\\"odinger operators

OpenAIRE

Avila, Artur; Damanik, David

2004-01-01

We consider Schr\\"odinger operators with ergodic potential $V_\\omega(n)=f(T^n(\\omega))$, $n \\in \\Z$, $\\omega \\in \\Omega$, where $T:\\Omega \\to \\Omega$ is a non-periodic homeomorphism. We show that for generic $f \\in C(\\Omega)$, the spectrum has no absolutely continuous component. The proof is based on approximation by discontinuous potentials which can be treated via Kotani Theory.

The Neutrosophic Logic View to Schrodinger's Cat Paradox, Revisited

Directory of Open Access Journals (Sweden)

Florentin Smarandache

2008-07-01

Full Text Available The present article discusses Neutrosophic logic view to Schrodinger's cat paradox. We argue that this paradox involves some degree of indeterminacy (unknown which Neutrosophic logic can take into consideration, whereas other methods including Fuzzy logic cannot. To make this proposition clear, we revisit our previous paper by offering an illustration using modified coin tossing problem, known as Parrondo's game.

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....

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

Science.gov (United States)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

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

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.

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.

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.

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.

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…

A direct algebraic method applied to obtain complex solutions of some nonlinear partial differential equations

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.

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

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.

On the Schrodinger equation in fluid-dynamical form

International Nuclear Information System (INIS)

Wong, C.Y.

1976-01-01

The fluid-dynamical form of the Schrodinger equations is studied to examine the nature of the quantum forces arising from the quantum potential of Madelung and Bohm. It is found that they are in the form of a stress tensor having diagonal and nondiagonal components. Future studies of these quantum stress tensors in a many-body system may shed some light on the mechanism of spontaneous symmetry breaking and the generation of vorticity in many nuclear systems

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].

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.)

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.)

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)

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.

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.

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)

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.

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

Science.gov (United States)

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

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.

Non-accretive Schrodinger operators and exponential decay of their eigenfunctions

Czech Academy of Sciences Publication Activity Database

Krejčiřík, David; Raymond, N.; Royer, J.; Siegl, Petr

2017-01-01

Roč. 221, č. 2 (2017), s. 779-802 ISSN 0021-2172 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : non-self-adjoint electromagnetic Schrodinger operators * Dirichlet realisation * Agmon-type exponential decay Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.796, year: 2016

Preparing Schrodinger cat states by parametric pumping

Science.gov (United States)

Leghtas, Zaki; Touzard, Steven; Pop, Ioan; Vlastakis, Brian; Zalys-Geller, Evan; Albert, Victor V.; Jiang, Liang; Frunzio, Luigi; Schoelkopf, Robert J.; Mirrahimi, Mazyar; Devoret, Michel H.

2014-03-01

Maintaining a quantum superposition state of light in a cavity has important applications for quantum error correction. We present an experimental protocol based on parametric pumping and Josephson circuits, which could prepare a Schrodinger cat state in a cavity. This is achieved by engineering a dissipative environment, which exchanges only pairs or quadruples of photons with our cavity mode. The dissipative nature of this preparation would lead to the observation of a dynamical Zeno effect, where the competition between a coherent drive and the dissipation reveals non trivial dynamics. Work supported by: IARPA, ARO, and NSF.

A Large Class of Exact Solutions to the One-Dimensional Schrodinger Equation

Science.gov (United States)

Karaoglu, Bekir

2007-01-01

A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement. (Contains 1 table and 1 figure.)

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 $k=1$ .

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.

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.)

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

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

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.

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.

Exact solutions of a Schrodinger equation based on the Lambert function

International Nuclear Information System (INIS)

Williams, Brian Wesley

2005-01-01

An exactly solvable Schrodinger equation of the confluent Natanzon class is derived using the differential properties of the Lambert W function. This potential involves two constant parameters and is defined along the entire real line. Specific spatial forms demonstrating wells and deformed positive barriers are presented

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

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.

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

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.

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.

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

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.

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.

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.

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.

The propagation of nonlinear rayleigh waves in layered elastic half-space

International Nuclear Information System (INIS)

Ahmetolan, S.

2004-01-01

In this work, the propagation of small but finite amplitude generalized Rayleigh waves in an elastic half-space covered by a different elastic layer of uniform and finite thickness is considered. The constituent materials are assumed to be homogeneous, isotropic, compressible hyperelastic. Excluding the harmonic resonance phenomena, it is shown that the nonlinear self modulation of generalized Rayleigh waves is governed asymptotically by a nonlinear Schrodinger (NLS) equation. The stability of the solutions and the existence of solitary wave-type solutions a NLS are strongly depend on the sign of the product of the coefficients of the nonlinear and dipersion terms of the equation.Therefore the analysis continues with the examination of dependence of these coefficients on the nonlinear material parameters. Three different models have been considered which are nonlinear layer-nonlinear half space, linear layer-nonlinear half space and nonlinear layer-linear half space. The behavior of the coefficients of the NLS equation was also analyzed the limit as h(thickness of the layer) goes to zero and k(the wave number) is constant. Then conclusions are drawn about the effect of nonlinear material parameters on the wave modulation. In the numerical investigations both hypothetical and real material models are used

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...

Approximation of Schrodinger operators with delta-interactions supported on hypersurfaces

Czech Academy of Sciences Publication Activity Database

Behrndt, J.; Exner, Pavel; Holzmann, M.; Lotoreichik, Vladimir

2017-01-01

Roč. 290, 8-9 (2017), s. 1215-1248 ISSN 0025-584X R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Schrodinger operators * delta-interactions supported on hypersurfaces * approximation by scaled regular potentials * norm resolvent convergence * spectral convergence Subject RIV: BE - Theoretical Physics OBOR OECD: Pure mathematics Impact factor: 0.742, year: 2016

Existence of high-energy solutions for supercritical fractional Schrodinger equations in R^N

Directory of Open Access Journals (Sweden)

Lu Gan

2016-12-01

Full Text Available In this article, we study supercritical fractional Schr\\"odinger equations. Applying the finite-dimensional reduction method and the penalization method, we obtain the high-energy solutions for this equation.

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.

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.)

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

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

Institute of Scientific and Technical Information of China (English)

无

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.

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.

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

On the bound states of Schrodinger operators with -interactions on conical surfaces

Czech Academy of Sciences Publication Activity Database

Lotoreichik, Vladimir; Ourmieres-Bonafos, T.

2016-01-01

Roč. 41, č. 6 (2016), s. 999-1028 ISSN 0360-5302 Institutional support: RVO:61389005 Keywords : conical and hyperconical surfaces * delta-interaction * existence of bound states * Schrodinger operator * spectral asymptotics Subject RIV: BE - Theoretical Physics Impact factor: 1.608, year: 2016

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)

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.

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...

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...

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....

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)

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...

Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces

Directory of Open Access Journals (Sweden)

Xavier Carvajal Paredes

2010-11-01

Full Text Available In this article, we prove that the initial value problem associated with the Korteweg-de Vries equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq 2heta ge 2$ and the initial value problem associated with the nonlinear Schrodinger equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq heta geq 1$. Persistence property has been proved by approximation of the solutions and using a priori estimates.

Huygens' principle, the free Schrodinger particle and the quantum anti-centrifugal force

DEFF Research Database (Denmark)

Cirone, M.A.; Dahl, Jens Peder; Fedorov, M.

2002-01-01

Huygens' principle following from the d'Alembert wave equation is not valid in two-dimensional space. A Schrodinger particle of vanishing angular momentum moving freely in two dimensions experiences an attractive force-the quantum anti-centrifugal force-towards its centre. We connect these two...

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

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

Science.gov (United States)

Karney, C. F. F.

1977-01-01

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

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).

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.

Construction of two-dimensional Schrodinger operator with given scattering amplitude at fixed energy

International Nuclear Information System (INIS)

Novikov, R.G.

1986-01-01

The classical necessary properties of the scattering amplitude (reciprocity and unitarity) are, provided its L 2 norm is small, sufficient for the existence of a two-dimensional Schrodinger operator with the given scattering amplitude at fixed energy

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.)

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.)

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

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...

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.

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.

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.

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.

Infinitely many large energy solutions of superlinear Schrodinger-Maxwell equations

Directory of Open Access Journals (Sweden)

Lin Li

2012-12-01

Full Text Available In this article we study the existence of infinitely many large energy solutions for the superlinear Schrodinger-Maxwell equations $$displaylines{ -Delta u+V(xu+ phi u=f(x,u quad hbox{in }mathbb{R}^3,cr -Delta phi=u^2, quad hbox{in }mathbb{R}^3, }$$ via the Fountain Theorem in critical point theory. In particular, we do not use the classical Ambrosetti-Rabinowitz condition.

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.

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....

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.

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.

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.

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...

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.

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)