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)

Single-ion nonlinear mechanical oscillator

International Nuclear Information System (INIS)

Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.

2010-01-01

We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

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)

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

Deterministic nonlinear phase gates induced by a single qubit

Science.gov (United States)

Park, Kimin; Marek, Petr; Filip, Radim

2018-05-01

We propose deterministic realizations of nonlinear phase gates by repeating a finite sequence of non-commuting Rabi interactions between a harmonic oscillator and only a single two-level ancillary qubit. We show explicitly that the key nonclassical features of the ideal cubic phase gate and the quartic phase gate are generated in the harmonic oscillator faithfully by our method. We numerically analyzed the performance of our scheme under realistic imperfections of the oscillator and the two-level system. The methodology is extended further to higher-order nonlinear phase gates. This theoretical proposal completes the set of operations required for continuous-variable quantum computation.

Progress Toward Single-Photon-Level Nonlinear Optics in Crystalline Microcavities

Science.gov (United States)

Kowligy, Abijith S.

Over the last two decades, the emergence of quantum information science has uncovered many practical applications in areas such as communications, imaging, and sensing where harnessing quantum features of Nature provides tremendous benefits over existing methods exploiting classical physical phenomena. In this effort, one of the frontiers of research has been to identify and utilize quantum phenomena that are not susceptible to environmental and parasitic noise processes. Quantum photonics has been at the forefront of these studies because it allows room-temperature access to its inherently quantum-mechanical features, and allows leveraging the mature telecommunication industry. Accompanying the weak environmental influence, however, are also weak optical nonlinearities. Efficient nonlinear optical interactions are indispensible for many of the existing protocols for quantum optical computation and communication, e.g. high-fidelity entangling quantum logic gates rely on large nonlinear responses at the one- or few-photon-level. While this has been addressed to a great extent by interfacing photons with single quantum emitters and cold atomic gases, scalability has remained elusive. In this work, we identify the macroscopic second-order nonlinear polarization as a robust platform to address this challenge, and utilize the recent advances in the burgeoning field of optical microcavities to enhance this nonlinear response. In particular, we show theoretically that by using the quantum Zeno effect, low-noise, single-photon-level optical nonlinearities can be realized in lithium niobate whispering-gallery-mode microcavities, and present experimental progress toward this goal. Using the measured strength of the second-order nonlinear response in lithium niobate, we modeled the nonlinear system in the strong coupling regime using the Schrodinger picture framework and theoretically demonstrated that the single-photon-level operation can be observed for cavity lifetimes in

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

Investigation on the growth, spectral, lifetime, mechanical analysis and third-order nonlinear optical studies of L-methionine admixtured D-mandelic acid single crystal: A promising material for nonlinear optical applications

Science.gov (United States)

Jayaprakash, P.; Sangeetha, P.; Kumari, C. Rathika Thaya; Caroline, M. Lydia

2017-08-01

A nonlinear optical bulk single crystal of L-methionine admixtured D-mandelic acid (LMDMA) has been grown by slow solvent evaporation technique using water as solvent at ambient temperature. The crystallized LMDMA single crystal subjected to single crystal X-ray diffraction study confirmed monoclinic system with the acentric space group P21. The FTIR analysis gives information about the modes of vibration in the various functional groups present in LMDMA. The UV-visible spectral analysis assessed the optical quality and linear optical properties such as extinction coefficient, reflectance, refractive index and from which optical conductivity and electric susceptibility were also evaluated. The frequency doubling efficiency was observed using Kurtz Perry powder technique. A multiple shot laser was utilized to evaluate the laser damage threshold energy of the crystal. Discrete thermodynamic properties were carried out by TG-DTA studies. The hardness, Meyer's index, yield strength, elastic stiffness constant, Knoop hardness, fracture toughness and brittleness index were analyzed using Vickers microhardness tester. Layer growth pattern and the surface defect were examined by chemical etching studies using optical microscope. Fluorescence emission spectrum was recorded and lifetime was also studied. The electric field response of crystal was investigated from the dielectric studies at various temperatures at different frequencies. The third-order nonlinear optical response in LMDMA has been investigated using Z-scan technique with He-Ne laser at 632.8 nm and nonlinear parameters such as refractive index (n2), absorption coefficient (β) and susceptibility (χ3) investigated extensively for they are in optical phase conjucation, high-speed optical switches and optical dielectric devices.

Nonlinear Phenomena in the Single-Mode Dynamics in an AFM Cantilever Beam

KAUST Repository

Ruzziconi, Laura; Lenci, Stefano; Younis, Mohammad I.

2016-01-01

This study deals with the nonlinear dynamics arising in an atomic force microscope cantilever beam. After analyzing the static behavior, a single degree of freedom Galerkin reduced order model is introduced, which describes the overall scenario

Nonlinear single-spin spectrum analyzer.

Science.gov (United States)

Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

2013-03-15

Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.

Single nano-hole as a new effective nonlinear element for third-harmonic generation

Science.gov (United States)

Melentiev, P. N.; Konstantinova, T. V.; Afanasiev, A. E.; Kuzin, A. A.; Baturin, A. S.; Tausenev, A. V.; Konyaschenko, A. V.; Balykin, V. I.

2013-07-01

In this letter, we report on a particularly strong optical nonlinearity at the nanometer scale in aluminum. A strong optical nonlinearity of the third order was demonstrated on a single nanoslit. Single nanoslits of different aspect ratio were excited by a laser pulse (120 fs) at the wavelength 1.5 μm, leading predominantly to third-harmonic generation (THG). It has been shown that strong surface plasmon resonance in a nanoslit allows the realization of an effective nanolocalized source of third-harmonic radiation. We show also that a nanoslit in a metal film has a significant advantage in nonlinear processes over its Babinet complementary nanostructure (nanorod): the effective abstraction of heat in a film with a slit makes it possible to use much higher laser radiation intensities.

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.

Higher-order techniques for some problems of nonlinear control

Directory of Open Access Journals (Sweden)

Sarychev Andrey V.

2002-01-01

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

Single nano-hole as a new effective nonlinear element for third-harmonic generation

International Nuclear Information System (INIS)

Melentiev, P N; Konstantinova, T V; Afanasiev, A E; Balykin, V I; Kuzin, A A; Baturin, A S; Tausenev, A V; Konyaschenko, A V

2013-01-01

In this letter, we report on a particularly strong optical nonlinearity at the nanometer scale in aluminum. A strong optical nonlinearity of the third order was demonstrated on a single nanoslit. Single nanoslits of different aspect ratio were excited by a laser pulse (120 fs) at the wavelength 1.5 μm, leading predominantly to third-harmonic generation (THG). It has been shown that strong surface plasmon resonance in a nanoslit allows the realization of an effective nanolocalized source of third-harmonic radiation. We show also that a nanoslit in a metal film has a significant advantage in nonlinear processes over its Babinet complementary nanostructure (nanorod): the effective abstraction of heat in a film with a slit makes it possible to use much higher laser radiation intensities. (letter)

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.

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

Synthesis, optical, experimental and theoretical investigation of third order nonlinear optical properties of 8-hydroxyquinolinium 2-carboxy-6-nitrophthalate monohydrate single crystal

Science.gov (United States)

Bharathi, M. Divya; Bhuvaneswari, R.; Srividya, J.; Vinitha, G.; Prithiviraajan, R. N.; Anbalagan, G.

2018-02-01

Single crystals of 8-hydroxyquinolinium 2-carboxy-6-nitrophthalate monohydrate (8HQNP) were obtained from slow evaporation solution growth method using methanol-water (1:1) as a solvent. Powder X-ray diffraction was utilized to compute the unit cell parameters and dislocation density of 8HQNP crystal. The crystalline perfection of the as-grown crystal was investigated by high-resolution X-ray diffraction at room temperature. The molecular structure was analyzed by identifying the functional groups from FT-IR and FT-Raman spectra. The cut-off wavelength and the corresponding optical band gap obtained from an optical spectrum were 376 nm and 3.29 eV respectively. The dispersion nature of refractive index was investigated by the single-oscillator Wemple and Di-Domenico model. Red emission was observed in the photoluminescence spectrum when excited with 376 nm. The low birefringence and high laser damage threshold (8.538 GW/cm2) values dictate the suitability of the crystal for optical devices. Z-scan studies revealed the third order nonlinear absorption coefficient (β) and refractive index (n2) of the 8HQNP crystal. The theoretical value of third order nonlinear susceptibility obtained from density function theory is good accordance with the experimental value. The frontier molecular orbital energy gap decreases with increasing external electric field in different directions which attributed to the enhancement of the second hyperpolarizability. The grown title crystal is thermally stable up to 102 °C which was identified using thermal analysis. Mechanical strength of 8HQNP was estimated by using Vicker's microhardness studies.

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)

Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR

Directory of Open Access Journals (Sweden)

Dong Zhang

2017-03-01

Full Text Available This article presents a new fractional-order sliding mode control (FOSMC strategy based on a linear-quadratic regulator (LQR for a class of uncertain nonlinear systems. First, input/output feedback linearization is used to linearize the nonlinear system and decouple tracking error dynamics. Second, LQR is designed to ensure that the tracking error dynamics converges to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding surface is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, the global stability of the closed-loop control system is analytically proved using Lyapunov stability theory. Finally, a typical single-input single-output system and a typical multi-input multi-output system are simulated to illustrate the effectiveness and advantages of the proposed control strategy. The results of the simulation indicate that the proposed control strategy exhibits excellent performance and robustness with system uncertainties. Compared to conventional integer-order sliding mode control, the high-frequency chattering of the control input is drastically depressed.

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

The Volterra's integral equation theory for accelerator single-freedom nonlinear components

International Nuclear Information System (INIS)

Wang Sheng; Xie Xi

1996-01-01

The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed

Report of the working group on single-particle nonlinear dynamics

International Nuclear Information System (INIS)

Bazzani, A.; Bongini, L.; Corbett, J.; Dome, G.; Fedorova, A.; Freguglia, P.; Ng, K.; Ohmi, K.; Owen, H.; Papaphilippou, Y.; Robin, D.; Safranek, J.; Scandale, W.; Terebilo, A.; Turchetti, G.; Todesco, E.; Warnock, R.; Zeitlin, M.

1999-01-01

The Working Group on single-particle nonlinear dynamics has developed a set of tools to study nonlinear dynamics in a particle accelerator. The design of rings with large dynamic apertures is still far from automatic. The Working Group has concluded that nonlinear single-particle dynamics limits the performance of accelerators. (AIP) copyright 1999 American Institute of Physics

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.

Dynamical Tangles in Third-Order Oscillator with Single Jump Function

Directory of Open Access Journals (Sweden)

Jiří Petržela

2014-01-01

Full Text Available This contribution brings a deep and detailed study of the dynamical behavior associated with nonlinear oscillator described by a single third-order differential equation with scalar jump nonlinearity. The relative primitive geometry of the vector field allows making an exhaustive numerical analysis of its possible solutions, visualizations of the invariant manifolds, and basins of attraction as well as proving the existence of chaotic motion by using the concept of both Shilnikov theorems. The aim of this paper is also to complete, carry out and link the previous works on simple Newtonian dynamics, and answer the question how individual types of the phenomenon evolve with time via understandable notes.

Multifunctional Bi2ZnOB2O6 single crystals for second and third order nonlinear optical applications

International Nuclear Information System (INIS)

Iliopoulos, K.; Kasprowicz, D.; Majchrowski, A.; Michalski, E.; Gindre, D.; Sahraoui, B.

2013-01-01

Bi 2 ZnOB 2 O 6 nonlinear optical single crystals were grown by means of the Kyropoulos method from stoichiometric melt. The second and third harmonic generation (SHG/THG) of Bi 2 ZnOB 2 O 6 crystals were investigated by the SHG/THG Maker fringes technique. Moreover, SHG microscopy studies were carried out providing two-dimensional SHG images as a function of the incident laser polarization. The high nonlinear optical efficiency combined with the possibility to grow high quality crystals make Bi 2 ZnOB 2 O 6 an excellent candidate for photonic applications

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) ≤

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

International Nuclear Information System (INIS)

Pelinovsky, Dmitry E.; Yang Jianke

2005-01-01

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

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

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.

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

International Nuclear Information System (INIS)

Xiao Yafeng; Xue Haili; Zhang Hongqing

2011-01-01

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

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.

On-demand single-photon state generation via nonlinear absorption

International Nuclear Information System (INIS)

Hong Tao; Jack, Michael W.; Yamashita, Makoto

2004-01-01

We propose a method for producing on-demand single-photon states based on collision-induced exchanges of photons and unbalanced linear absorption between two single-mode light fields. These two effects result in an effective nonlinear absorption of photons in one of the modes, which can lead to single-photon states. A quantum nonlinear attenuator based on such a mechanism can absorb photons in a normal input light pulse and terminate the absorption at a single-photon state. Because the output light pulses containing single photons preserve the properties of the input pulses, we expect this method to be a means for building a highly controllable single-photon source

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.

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

International Nuclear Information System (INIS)

Frank, T D; Mongkolsakulvong, S

2015-01-01

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

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

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

Science.gov (United States)

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

2017-12-01

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

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.

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.

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...

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.

Single-order laser high harmonics in XUV for ultrafast photoelectron spectroscopy of molecular wavepacket dynamics

Directory of Open Access Journals (Sweden)

Mizuho Fushitani

2016-11-01

Full Text Available We present applications of extreme ultraviolet (XUV single-order laser harmonics to gas-phase ultrafast photoelectron spectroscopy. Ultrashort XUV pulses at 80 nm are obtained as the 5th order harmonics of the fundamental laser at 400 nm by using Xe or Kr as the nonlinear medium and separated from other harmonic orders by using an indium foil. The single-order laser harmonics is applied for real-time probing of vibrational wavepacket dynamics of I2 molecules in the bound and dissociating low-lying electronic states and electronic-vibrational wavepacket dynamics of highly excited Rydberg N2 molecules.

Single-order laser high harmonics in XUV for ultrafast photoelectron spectroscopy of molecular wavepacket dynamics.

Science.gov (United States)

Fushitani, Mizuho; Hishikawa, Akiyoshi

2016-11-01

We present applications of extreme ultraviolet (XUV) single-order laser harmonics to gas-phase ultrafast photoelectron spectroscopy. Ultrashort XUV pulses at 80 nm are obtained as the 5th order harmonics of the fundamental laser at 400 nm by using Xe or Kr as the nonlinear medium and separated from other harmonic orders by using an indium foil. The single-order laser harmonics is applied for real-time probing of vibrational wavepacket dynamics of I 2 molecules in the bound and dissociating low-lying electronic states and electronic-vibrational wavepacket dynamics of highly excited Rydberg N 2 molecules.

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.

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

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 Single Spin Spectrum Analayzer

Science.gov (United States)

Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

2014-05-01

Qubits are excellent probes of their environment. When operating in the linear regime, they can be used as linear spectrum analyzers of the noise processes surrounding them. These methods fail for strong non-Gaussian noise where the qubit response is no longer linear. Here we solve the problem of nonlinear spectral analysis, required for strongly coupled environments. Our non-perturbative analytic model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We developed a noise characterization scheme adapted to this non-linearity. We then applied it using a single trapped 88Sr+ ion as the a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. With this method, we attained a ten fold improvement over the standard Fourier limit. Finally, we experimentally compared the performance of equidistant vs. Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013), Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: National Institute of Standards and Tehcnology, Boulder, CO.

Studies on the growth aspects, structural, thermal, dielectric and third order nonlinear optical properties of solution grown 4-methylpyridinium p-nitrophenolate single crystal

Science.gov (United States)

Devi, S. Reena; Kalaiyarasi, S.; Zahid, I. MD.; Kumar, R. Mohan

2016-11-01

An ionic organic optical crystal of 4-methylpyridinium p-nitrophenolate was grown from methanol by slow evaporation method at ambient temperature. Powder and single crystal X-ray diffraction studies revealed the crystal system and its crystalline perfection. The rocking curve recorded from HRXRD study confirmed the crystal quality. FTIR spectral analysis confirmed the functional groups present in the title compound. UV-visible spectral study revealed the optical window and band gap of grown crystal. The thermal, electrical and surface laser damage threshold properties of harvested crystal were examined by using TGA/DTA, LCR/Impedance Analyzer and Nd:YAG laser system respectively. The third order nonlinear optical property of grown crystal was elucidated by Z-scan technique.

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.

Highly efficient single-pass sum frequency generation by cascaded nonlinear crystals

DEFF Research Database (Denmark)

Hansen, Anders Kragh; Andersen, Peter E.; Jensen, Ole Bjarlin

2015-01-01

, despite differences in the phase relations of the involved fields. An unprecedented 5.5 W of continuous-wave diffraction-limited green light is generated from the single-pass sum frequency mixing of two diode lasers in two periodically poled nonlinear crystals (conversion efficiency 50%). The technique......The cascading of nonlinear crystals has been established as a simple method to greatly increase the conversion efficiency of single-pass second-harmonic generation compared to a single-crystal scheme. Here, we show for the first time that the technique can be extended to sum frequency generation...... is generally applicable and can be applied to any combination of fundamental wavelengths and nonlinear crystals....

Higher-Order Spectrum in Understanding Nonlinearity in EEG Rhythms

Directory of Open Access Journals (Sweden)

Cauchy Pradhan

2012-01-01

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

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

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

Nonlinear dynamics of single-helicity neoclassical MHD tearing instabilities

International Nuclear Information System (INIS)

Spong, D.A.; Shaing, K.C.; Carreras, B.A.; Callen, J.D.; Garcia, L.

1988-10-01

Neoclassical magnetohydrodynamic (MHD) effects can significantly alter the nonlinear evolution of resistive tearing instabilities. This is studied numerically by using a flux-surface-averaged set of evolution equations that includes the lowest-order neoclassical MHD effects. The new terms in the equations are fluctuating bootstrap current, neoclassical modification of the resistivity, and neoclassical damping of the vorticity. Single-helicity tearing modes are studied in a cylindrical model over a range of neoclassical viscosities (μ/sub e//ν/sup e/) and values of the Δ' parameter of tearing mode theory. Increasing the neoclassical viscosity leads to increased growth rate and saturated island width as predicted analytically. The larger island width is caused by the fluctuating bootstrap current contribution in Ohm's law. The Δ' parameter no longer solely determines the island width, and finite-width saturated islands may be obtained even when Δ' is negative. The importance of the bootstrap current (/approximately/∂/rho///partial derivative/psi/) in the nonlinear dynamics leads us to examine the sensitivity of the results with respect to different models for the density evolution. 11 refs., 8 figs

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)

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.

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...

Nonlinear and Nonsymmetric Single-Molecule Electronic Properties Towards Molecular Information Processing.

Science.gov (United States)

Tamaki, Takashi; Ogawa, Takuji

2017-09-05

This review highlights molecular design for nonlinear and nonsymmetric single-molecule electronic properties such as rectification, negative differential resistance, and switching, which are important components of future single-molecule information processing devices. Perspectives on integrated "molecular circuits" are also provided. Nonlinear and nonsymmetric single-molecule electronics can be designed by utilizing (1) asymmetric molecular cores, (2) asymmetric anchoring groups, (3) an asymmetric junction environment, and (4) asymmetric electrode materials. This review mainly focuses on the design of molecular cores.

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.

Syntheses, structures and third-order non-linear optical properties of homometal clusters containing molybdenum

International Nuclear Information System (INIS)

Li Yong; Lu Jing; Cui Xiaobing; Xu Jiqing; Li Kechang; Sun Huaying; Li Guanghua; Pan Lingyun; Yang Qingxin

2005-01-01

Both the homometal cluster [P(ph 4 )] 2 [Mo 2 O 2 (μ-S) 2 (S 2 ) 2 ] (1) and [Mo 2 O 2 (μ-S) 2 (Et 2 dtc) 2 ] (2) (Et 2 dtc=diethyl-dithiocarbamate) were successfully synthesized by low-temperature solid-state reactions. X-ray single-crystal diffraction studies suggest that compound (1) is a dinuclear anion cluster, and compound (2) is a dinuclear neutral cluster. The two compounds were characterized by elemental analyses, IR spectra and UV-Vis spectra. The third-order non-linear optical (NLO) properties of the clusters were also investigated and all exhibited nice non-linear absorption and self-defocusing performance with moduli of the hyperpolarizabilities 5.145x10 -30 esu for (1) and 5.428x10 -30 esu for (2)

Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential

Science.gov (United States)

Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.

2018-03-01

We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p  >  0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.

Nonlinear ultrasonic fatigue crack detection using a single piezoelectric transducer

Science.gov (United States)

An, Yun-Kyu; Lee, Dong Jun

2016-04-01

This paper proposes a new nonlinear ultrasonic technique for fatigue crack detection using a single piezoelectric transducer (PZT). The proposed technique identifies a fatigue crack using linear (α) and nonlinear (β) parameters obtained from only a single PZT mounted on a target structure. Based on the different physical characteristics of α and β, a fatigue crack-induced feature is able to be effectively isolated from the inherent nonlinearity of a target structure and data acquisition system. The proposed technique requires much simpler test setup and less processing costs than the existing nonlinear ultrasonic techniques, but fast and powerful. To validate the proposed technique, a real fatigue crack is created in an aluminum plate, and then false positive and negative tests are carried out under varying temperature conditions. The experimental results reveal that the fatigue crack is successfully detected, and no positive false alarm is indicated.

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.

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

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.

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

Growth and characterization of benzaldehyde 4-nitro phenyl hydrazone (BPH) single crystal: A proficient second order nonlinear optical material

Science.gov (United States)

Saravanan, M.; Abraham Rajasekar, S.

2016-04-01

The crystals (benzaldehyde 4-nitro phenyl hydrazone (BPH)) appropriate for NLO appliance were grown by the slow cooling method. The solubility and metastable zone width measurement of BPH specimen was studied. The material crystallizes in the monoclinic crystal system with noncentrosymmetric space group of Cc. The optical precision in the whole visible region was found to be excellent for non-linear optical claim. Excellence of the grown crystal is ascertained by the HRXRD and etching studies. Laser Damage Threshold and Photoluminescence studies designate that the grown crystal contains less imperfection. The mechanical behaviour of BPH sample at different temperatures was investigated to determine the hardness stability of the grown specimen. The piezoelectric temperament and the relative Second Harmonic Generation (for diverse particle sizes) of the material were also studied. The dielectric studies were executed at varied temperatures and frequencies to investigate the electrical properties. Photoconductivity measurement enumerates consummate of inducing dipoles due to strong incident radiation and also divulge the nonlinear behaviour of the material. The third order nonlinear optical properties of BPH crystals were deliberate by Z-scan method.

Single-Wire Electric-Field Coupling Power Transmission Using Nonlinear Parity-Time-Symmetric Model with Coupled-Mode Theory

Directory of Open Access Journals (Sweden)

Xujian Shu

2018-03-01

Full Text Available The output power and transmission efficiency of the traditional single-wire electric-field coupling power transmission (ECPT system will drop sharply with the increase of the distance between transmitter and receiver, thus, in order to solve the above problem, in this paper, a new nonlinear parity-time (PT-symmetric model for single-wire ECPT system based on coupled-mode theory (CMT is proposed. The proposed model for single-wire ECPT system not only achieves constant output power but also obtains a high constant transmission efficiency against variable distance, and the steady-state characteristics of the single-wire ECPT system are analyzed. Based on the theoretical analysis and circuit simulation, it shows that the transmission efficiency with constant output power remains 60% over a transmission distance of approximately 34 m without the need for any tuning. Furthermore, the application of a nonlinear PT-symmetric circuit based on CMT enables robust electric power transfer to moving devices or vehicles.

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.

Nonlinear characterization of a single-axis acoustic levitator.

Science.gov (United States)

Andrade, Marco A B; Ramos, Tiago S; Okina, Fábio T A; Adamowski, Julio C

2014-04-01

The nonlinear behavior of a 20.3 kHz single-axis acoustic levitator formed by a Langevin transducer with a concave radiating surface and a concave reflector is experimentally investigated. In this study, a laser Doppler vibrometer is applied to measure the nonlinear sound field in the air gap between the transducer and the reflector. Additionally, an electronic balance is used in the measurement of the acoustic radiation force on the reflector as a function of the distance between the transducer and the reflector. The experimental results show some effects that cannot be described by the linear acoustic theory, such as the jump phenomenon, harmonic generation, and the hysteresis effect. The influence of these nonlinear effects on the acoustic levitation of small particles is discussed.

Nonlinear characterization of a single-axis acoustic levitator

International Nuclear Information System (INIS)

Andrade, Marco A. B.; Ramos, Tiago S.; Okina, Fábio T. A.; Adamowski, Julio C.

2014-01-01

The nonlinear behavior of a 20.3 kHz single-axis acoustic levitator formed by a Langevin transducer with a concave radiating surface and a concave reflector is experimentally investigated. In this study, a laser Doppler vibrometer is applied to measure the nonlinear sound field in the air gap between the transducer and the reflector. Additionally, an electronic balance is used in the measurement of the acoustic radiation force on the reflector as a function of the distance between the transducer and the reflector. The experimental results show some effects that cannot be described by the linear acoustic theory, such as the jump phenomenon, harmonic generation, and the hysteresis effect. The influence of these nonlinear effects on the acoustic levitation of small particles is discussed

Nonlinear characterization of a single-axis acoustic levitator

Energy Technology Data Exchange (ETDEWEB)

Andrade, Marco A. B. [Institute of Physics, University of São Paulo, São Paulo (Brazil); Ramos, Tiago S.; Okina, Fábio T. A.; Adamowski, Julio C. [Department of Mechatronics and Mechanical Systems Engineering, Escola Politécnica, University of São Paulo, São Paulo (Brazil)

2014-04-15

The nonlinear behavior of a 20.3 kHz single-axis acoustic levitator formed by a Langevin transducer with a concave radiating surface and a concave reflector is experimentally investigated. In this study, a laser Doppler vibrometer is applied to measure the nonlinear sound field in the air gap between the transducer and the reflector. Additionally, an electronic balance is used in the measurement of the acoustic radiation force on the reflector as a function of the distance between the transducer and the reflector. The experimental results show some effects that cannot be described by the linear acoustic theory, such as the jump phenomenon, harmonic generation, and the hysteresis effect. The influence of these nonlinear effects on the acoustic levitation of small particles is discussed.

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.

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.

Graphical user interface for input output characterization of single variable and multivariable highly nonlinear systems

Directory of Open Access Journals (Sweden)

Shahrukh Adnan Khan M. D.

2017-01-01

Full Text Available This paper presents a Graphical User Interface (GUI software utility for the input/output characterization of single variable and multivariable nonlinear systems by obtaining the sinusoidal input describing function (SIDF of the plant. The software utility is developed on MATLAB R2011a environment. The developed GUI holds no restriction on the nonlinearity type, arrangement and system order; provided that output(s of the system is obtainable either though simulation or experiments. An insight to the GUI and its features are presented in this paper and example problems from both single variable and multivariable cases are demonstrated. The formulation of input/output behavior of the system is discussed and the nucleus of the MATLAB command underlying the user interface has been outlined. Some of the industries that would benefit from this software utility includes but not limited to aerospace, defense technology, robotics and automotive.

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

"E pluribus unum" or How to Derive Single-equation Descriptions for Output-quantities in Nonlinear Circuits using Differential Algebra

OpenAIRE

Gerbracht, Eberhard H. -A.

2008-01-01

In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear algebra to the system of differential equations which is used to model the analog circuit. For nonlinear circuits and their corresponding nonlinear differential equations, we show how to employ computer algebra tools implemented in Maple, which are based on diff...

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.

Nonlinear convergence active vibration absorber for single and multiple frequency vibration control

Science.gov (United States)

Wang, Xi; Yang, Bintang; Guo, Shufeng; Zhao, Wenqiang

2017-12-01

This paper presents a nonlinear convergence algorithm for active dynamic undamped vibration absorber (ADUVA). The damping of absorber is ignored in this algorithm to strengthen the vibration suppressing effect and simplify the algorithm at the same time. The simulation and experimental results indicate that this nonlinear convergence ADUVA can help significantly suppress vibration caused by excitation of both single and multiple frequency. The proposed nonlinear algorithm is composed of equivalent dynamic modeling equations and frequency estimator. Both the single and multiple frequency ADUVA are mathematically imitated by the same mechanical structure with a mass body and a voice coil motor (VCM). The nonlinear convergence estimator is applied to simultaneously satisfy the requirements of fast convergence rate and small steady state frequency error, which are incompatible for linear convergence estimator. The convergence of the nonlinear algorithm is mathematically proofed, and its non-divergent characteristic is theoretically guaranteed. The vibration suppressing experiments demonstrate that the nonlinear ADUVA can accelerate the convergence rate of vibration suppressing and achieve more decrement of oscillation attenuation than the linear ADUVA.

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.

Single shot trajectory design for region-specific imaging using linear and nonlinear magnetic encoding fields.

Science.gov (United States)

Layton, Kelvin J; Gallichan, Daniel; Testud, Frederik; Cocosco, Chris A; Welz, Anna M; Barmet, Christoph; Pruessmann, Klaas P; Hennig, Jürgen; Zaitsev, Maxim

2013-09-01

It has recently been demonstrated that nonlinear encoding fields result in a spatially varying resolution. This work develops an automated procedure to design single-shot trajectories that create a local resolution improvement in a region of interest. The technique is based on the design of optimized local k-space trajectories and can be applied to arbitrary hardware configurations that employ any number of linear and nonlinear encoding fields. The trajectories designed in this work are tested with the currently available hardware setup consisting of three standard linear gradients and two quadrupolar encoding fields generated from a custom-built gradient insert. A field camera is used to measure the actual encoding trajectories up to third-order terms, enabling accurate reconstructions of these demanding single-shot trajectories, although the eddy current and concomitant field terms of the gradient insert have not been completely characterized. The local resolution improvement is demonstrated in phantom and in vivo experiments. Copyright © 2012 Wiley Periodicals, Inc.

Photonic single nonlinear-delay dynamical node for information processing

Science.gov (United States)

Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel

2012-06-01

An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.

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.)

Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems

International Nuclear Information System (INIS)

Ge Zhengming; Chang Chingming; Chen Yensheng

2006-01-01

Anti-control of chaos of single time scale brushless dc motors (BLDCM) and chaos synchronization of different order systems are studied in this paper. By addition of an external nonlinear term, we can obtain anti-control of chaos. Then, by addition of the coupling terms, by the use of Lyapunov stability theorem and by the linearization of the error dynamics, chaos synchronization between a third-order BLDCM and a second-order Duffing system are presented

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

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.

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

Directory of Open Access Journals (Sweden)

Eleni Bisognin

2007-01-01

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

Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

Directory of Open Access Journals (Sweden)

Taher S. Hassan

2016-01-01

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

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%.

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

Nonlinear Growth Models as Measurement Models: A Second-Order Growth Curve Model for Measuring Potential.

Science.gov (United States)

McNeish, Daniel; Dumas, Denis

2017-01-01

Recent methodological work has highlighted the promise of nonlinear growth models for addressing substantive questions in the behavioral sciences. In this article, we outline a second-order nonlinear growth model in order to measure a critical notion in development and education: potential. Here, potential is conceptualized as having three components-ability, capacity, and availability-where ability is the amount of skill a student is estimated to have at a given timepoint, capacity is the maximum amount of ability a student is predicted to be able to develop asymptotically, and availability is the difference between capacity and ability at any particular timepoint. We argue that single timepoint measures are typically insufficient for discerning information about potential, and we therefore describe a general framework that incorporates a growth model into the measurement model to capture these three components. Then, we provide an illustrative example using the public-use Early Childhood Longitudinal Study-Kindergarten data set using a Michaelis-Menten growth function (reparameterized from its common application in biochemistry) to demonstrate our proposed model as applied to measuring potential within an educational context. The advantage of this approach compared to currently utilized methods is discussed as are future directions and limitations.

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.

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

International Nuclear Information System (INIS)

Bouard, Anne de; Debussche, Arnaud

2006-01-01

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

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))

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

Single-pulse CARS based multimodal nonlinear optical microscope for bioimaging.

Science.gov (United States)

Kumar, Sunil; Kamali, Tschackad; Levitte, Jonathan M; Katz, Ori; Hermann, Boris; Werkmeister, Rene; Považay, Boris; Drexler, Wolfgang; Unterhuber, Angelika; Silberberg, Yaron

2015-05-18

Noninvasive label-free imaging of biological systems raises demand not only for high-speed three-dimensional prescreening of morphology over a wide-field of view but also it seeks to extract the microscopic functional and molecular details within. Capitalizing on the unique advantages brought out by different nonlinear optical effects, a multimodal nonlinear optical microscope can be a powerful tool for bioimaging. Bringing together the intensity-dependent contrast mechanisms via second harmonic generation, third harmonic generation and four-wave mixing for structural-sensitive imaging, and single-beam/single-pulse coherent anti-Stokes Raman scattering technique for chemical sensitive imaging in the finger-print region, we have developed a simple and nearly alignment-free multimodal nonlinear optical microscope that is based on a single wide-band Ti:Sapphire femtosecond pulse laser source. Successful imaging tests have been realized on two exemplary biological samples, a canine femur bone and collagen fibrils harvested from a rat tail. Since the ultra-broad band-width femtosecond laser is a suitable source for performing high-resolution optical coherence tomography, a wide-field optical coherence tomography arm can be easily incorporated into the presented multimodal microscope making it a versatile optical imaging tool for noninvasive label-free bioimaging.

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

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)

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

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. ...

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)

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.

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

Nonlinear digital out-of-plane waveguide coupler based on nonlinear scattering of a single graphene layer

Science.gov (United States)

Asadi, Reza; Ouyang, Zhengbiao

2018-03-01

A new mechanism for out-of-plane coupling into a waveguide is presented and numerically studied based on nonlinear scattering of a single nano-scale Graphene layer inside the waveguide. In this mechanism, the refractive index nonlinearity of Graphene and nonhomogeneous light intensity distribution occurred due to the interference between the out-of-plane incident pump light and the waveguide mode provide a virtual grating inside the waveguide, coupling the out-of-plane pump light into the waveguide. It has been shown that the coupling efficiency has two distinct values with high contrast around a threshold pump intensity, providing suitable condition for digital optical applications. The structure operates at a resonance mode due to band edge effect, which enhances the nonlinearity and decreases the required threshold intensity.

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.

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.

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.

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...

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.

Mechano-optic logic gate controlled by third-order nonlinear optical properties in a rotating ZnO:Au thin film

International Nuclear Information System (INIS)

Carrillo-Delgado, C; Torres-Torres, C; García-Merino, J A; García-Gil, C I; Khomenko, A V; Trejo-Valdez, M; Martínez-Gutiérrez, H; Torres-Martínez, R

2016-01-01

Measurements of the third-order nonlinear optical properties exhibited by a ZnO thin solid film deposited on a SnO 2 substrate are presented. The samples were prepared by a spray pyrolysis processing route. Scanning electron microscopy analysis and UV–Vis spectroscopy studies were carried out. The picosecond response at 1064 nm was explored by the z-scan technique. A large optical Kerr effect with two-photon absorption was obtained. The inhibition of the nonlinear optical absorption together with a noticeable enhancement in the optical Kerr effect in the sample was achieved by the incorporation of Au nanoparticles into the ZnO film. Additionally, a two-wave mixing configuration at 532 nm was performed and an optical Kerr effect was identified as the main cause of the nanosecond third-order optical nonlinearity. The relaxation time of the photothermal response of the sample was estimated to be about 1 s when the sample was excited by nanosecond single-shots. The rotation of the sample during the nanosecond two-wave mixing experiments was analyzed. It was stated that a non-monotonic relation between rotating frequency and pulse repetition rate governs the thermal contribution to the nonlinear refractive index exhibited by a rotating film. Potential applications for switching photothermal interactions in rotating samples can be contemplated. A rotary logic system dependent on Kerr transmittance in a two-wave mixing experiment was proposed. (paper)

Growth and characterization of new nonlinear optical 1-phenyl-3-(4-dimethylamino phenyl) prop-2-en-1-one (PDAC) single crystals

Science.gov (United States)

Ravindraswami, K.; Janardhana, K.; Gowda, Jayaprakash; Moolya, B. Narayana

2018-04-01

Non linear optical 1-phenyl-3-(4-dimethylamino phenyl) prop-2-en-1-one (PDAC) was synthesized using Claisen - Schmidt condensation method and studied for optical nonlinearity with an emphasis on structure-property relationship. The structural confirmation studies were carried out using 1H-NMR, FT-IR and single crystal XRD techniques. The nonlinear absorption and nonlinear refraction parameters in z-scan with nano second laser pulses were obtained by measuring the profile of propagated beam through the samples. The real and imaginary parts of third-order bulk susceptibility χ(3) were evaluated. Thermo gravimetric analysis is carried out to investigate the thermal stability.

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.

Crucial role of molecular planarity on the second order nonlinear optical property of pyridine based chalcone single crystals

Science.gov (United States)

Menezes, Anthoni Praveen; Jayarama, A.; Ng, Seik Weng

2015-05-01

An efficient nonlinear optical material 2E-3-(4-bromophenyl)-1-(pyridin-3-yl) prop-2-en-1-one (BPP) was synthesized and single crystals were grown using slow evaporation solution growth technique at room temperature. Grown crystal had prismatic morphology and its structure was confirmed by various spectroscopic studies, elemental analysis, and single crystal X-ray diffraction (XRD) technique. The single crystal XRD of the crystal showed that BPP crystallizes in monoclinic system with noncentrosymmetric space group P21 and the cell parameters are a = 5.6428(7) Å, b = 3.8637(6) Å, c = 26.411(2) Å, β = 97.568(11) deg and v = 575.82(12) Å3. The UV-Visible spectrum reveals that the crystal is optically transparent and has high optical energy band gap of 3.1 eV. The powder second harmonic generation efficiency (SHG) of BPP is 6.8 times that of KDP. From thermal analysis it is found that the crystal melts at 139 °C and decomposes at 264 °C. High optical transparency down to blue region, higher powder SHG efficiency and better thermal stability than that of urea makes this chalcone derivative a promising candidate for SHG applications. Furthermore, effect of molecular planarity on SHG efficiency and role of pyridine ring adjacent to carbonyl group in forming noncentrosymmetric crystal systems of chalcone family is also discussed.

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

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.

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

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...

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

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.

MD1831: Single Bunch Instabilities with Q" and Non-Linear Corrections

CERN Document Server

Carver, Lee Robert; De Maria, Riccardo; Li, Kevin Shing Bruce; Amorim, David; Biancacci, Nicolo; Buffat, Xavier; Maclean, Ewen Hamish; Metral, Elias; Lasocha, Kacper; Lefevre, Thibaut; Levens, Tom; Salvant, Benoit; CERN. Geneva. ATS Department

2017-01-01

During MD1751, it was observed that both a full single beam and 964 non-colliding bunches in Beam 1 (B1) and Beam 2 (B2) were both stable at the End of Squeeze (EOS) for 0A in the Landau Octupoles. At ß* = 40cm there is also a significant Q" arising from the lattice, as well as uncorrected non-linearities in the Insertion Regions (IRs). Each of these effects could be capable of fully stabilising the beam. This MD made first use of a Q" knob through variation of the Main Sextupoles (MS) by stabilising a single bunch at Flat Top, before showing at EOS that the non-linearities were the main contributors to the beam stability.

The role of dendritic non-linearities in single neuron computation

Directory of Open Access Journals (Sweden)

Boris Gutkin

2014-05-01

Full Text Available Experiment has demonstrated that summation of excitatory post-synaptic protientials (EPSPs in dendrites is non-linear. The sum of multiple EPSPs can be larger than their arithmetic sum, a superlinear summation due to the opening of voltage-gated channels and similar to somatic spiking. The so-called dendritic spike. The sum of multiple of EPSPs can also be smaller than their arithmetic sum, because the synaptic current necessarily saturates at some point. While these observations are well-explained by biophysical models the impact of dendritic spikes on computation remains a matter of debate. One reason is that dendritic spikes may fail to make the neuron spike; similarly, dendritic saturations are sometime presented as a glitch which should be corrected by dendritic spikes. We will provide solid arguments against this claim and show that dendritic saturations as well as dendritic spikes enhance single neuron computation, even when they cannot directly make the neuron fire. To explore the computational impact of dendritic spikes and saturations, we are using a binary neuron model in conjunction with Boolean algebra. We demonstrate using these tools that a single dendritic non-linearity, either spiking or saturating, combined with somatic non-linearity, enables a neuron to compute linearly non-separable Boolean functions (lnBfs. These functions are impossible to compute when summation is linear and the exclusive OR is a famous example of lnBfs. Importantly, the implementation of these functions does not require the dendritic non-linearity to make the neuron spike. Next, We show that reduced and realistic biophysical models of the neuron are capable of computing lnBfs. Within these models and contrary to the binary model, the dendritic and somatic non-linearity are tightly coupled. Yet we show that these neuron models are capable of linearly non-separable computations.

Analytical results for a conditional phase shift between single-photon pulses in a nonlocal nonlinear medium

Science.gov (United States)

Viswanathan, Balakrishnan; Gea-Banacloche, Julio

2018-03-01

It has been suggested that second-order nonlinearities could be used for quantum logic at the single-photon level. Specifically, successive two-photon processes in principle could accomplish the phase shift (conditioned on the presence of two photons in the low-frequency modes) |011 〉→i |100 〉→-|011 〉 . We have analyzed a recent scheme proposed by Xia et al. [Phys. Rev. Lett. 116, 023601 (2016)], 10.1103/PhysRevLett.116.023601 to induce such a conditional phase shift between two single-photon pulses propagating at different speeds through a nonlinear medium with a nonlocal response. We present here an analytical solution for the most general case, i.e., for an arbitrary response function, initial state, and pulse velocity, which supports their numerical observation that a π phase shift with unit fidelity is possible, in principle, in an appropriate limit. We also discuss why this is possible in this system, despite the theoretical objections to the possibility of conditional phase shifts on single photons that were raised some time ago by Shapiro [Phys. Rev. A 73, 062305 (2006)], 10.1103/PhysRevA.73.062305 and by Gea-Banacloche [Phys. Rev. A 81, 043823 (2010)], 10.1103/PhysRevA.81.043823 one of us.

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.

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

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.

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 ...

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.

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.

Summary report of the group on single-particle nonlinear dynamics

International Nuclear Information System (INIS)

Axinescu, S.; Bartolini, R.; Bazzani, A.

1996-10-01

This report summarizes the research on single-particle nonlinear beam dynamics. It discusses the following topics: analytical and semi-analytical tools; early prediction of the dynamic aperture; how the results are commonly presented; Is the mechanism of the dynamic aperture understand; ripple effects; and beam-beam effects

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

Nonlinear evolution of single spike in Richtmyer-Meshkov instability

International Nuclear Information System (INIS)

Fukuda, Y.; Nishihara, K.; Wouchuk, J.G.

2000-01-01

Nonlinear evolution of single spike structure and vortex in the Richtmyer-Meshkov instability is investigated with the use of a two-dimensional hydrodynamic code. It is shown that singularity appears in the vorticity left by transmitted and reflected shocks at a corrugated interface. This singularity results in opposite sign of vorticity along the interface that causes double spiral structure of the spike. (authors)

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.

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.

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)

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...

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.

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.

Polarized dependence of nonlinear susceptibility in a single layer graphene system in infrared region

Energy Technology Data Exchange (ETDEWEB)

Solookinejad, G., E-mail: ghsolooki@gmail.com

2016-09-15

In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.

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.

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

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

International Nuclear Information System (INIS)

Zhestkov, S.V.

2003-01-01

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

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.

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...

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.

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.

An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

Directory of Open Access Journals (Sweden)

Eman S. Alaidarous

2013-01-01

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

Importance of the alignment of polar π conjugated molecules inside carbon nanotubes in determining second-order non-linear optical properties.

Science.gov (United States)

Yumura, Takashi; Yamamoto, Wataru

2017-09-20

We employed density functional theory (DFT) calculations with dispersion corrections to investigate energetically preferred alignments of certain p,p'-dimethylaminonitrostilbene (DANS) molecules inside an armchair (m,m) carbon nanotube (n × DANS@(m,m)), where the number of inner molecules (n) is no greater than 3. Here, three types of alignments of DANS are considered: a linear alignment in a parallel fashion and stacking alignments in parallel and antiparallel fashions. According to DFT calculations, a threshold tube diameter for containing DANS molecules in linear or stacking alignments was found to be approximately 1.0 nm. Nanotubes with diameters smaller than 1.0 nm result in the selective formation of linearly aligned DANS molecules due to strong confinement effects within the nanotubes. By contrast, larger diameter nanotubes allow DANS molecules to align in a stacking and linear fashion. The type of alignment adopted by the DANS molecules inside a nanotube is responsible for their second-order non-linear optical properties represented by their static hyperpolarizability (β 0 values). In fact, we computed β 0 values of DANS assemblies taken from optimized n × DANS@(m,m) structures, and their values were compared with those of a single DANS molecule. DFT calculations showed that β 0 values of DANS molecules depend on their alignment, which decrease in the following order: linear alignment > parallel stacking alignment > antiparallel stacking alignment. In particular, a linear alignment has a β 0 value more significant than that of the same number of isolated molecules. Therefore, the linear alignment of DANS molecules, which is only allowed inside smaller diameter nanotubes, can strongly enhance their second-order non-linear optical properties. Since the nanotube confinement determines the alignment of DANS molecules, a restricted nanospace can be utilized to control their second-order non-linear optical properties. These DFT findings can assist in the

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.

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.

Ordered macro-microporous metal-organic framework single crystals

KAUST Repository

Shen, Kui

2018-01-16

We constructed highly oriented and ordered macropores within metal-organic framework (MOF) single crystals, opening up the area of three-dimensional-ordered macro-microporous materials (that is, materials containing both macro- and micropores) in single-crystalline form. Our methodology relies on the strong shaping effects of a polystyrene nanosphere monolith template and a double-solvent-induced heterogeneous nucleation approach. This process synergistically enabled the in situ growth of MOFs within ordered voids, rendering a single crystal with oriented and ordered macro-microporous structure. The improved mass diffusion properties of such hierarchical frameworks, together with their robust single-crystalline nature, endow them with superior catalytic activity and recyclability for bulky-molecule reactions, as compared with conventional, polycrystalline hollow, and disordered macroporous ZIF-8.

Ordered macro-microporous metal-organic framework single crystals

Science.gov (United States)

Shen, Kui; Zhang, Lei; Chen, Xiaodong; Liu, Lingmei; Zhang, Daliang; Han, Yu; Chen, Junying; Long, Jilan; Luque, Rafael; Li, Yingwei; Chen, Banglin

2018-01-01

We constructed highly oriented and ordered macropores within metal-organic framework (MOF) single crystals, opening up the area of three-dimensional–ordered macro-microporous materials (that is, materials containing both macro- and micropores) in single-crystalline form. Our methodology relies on the strong shaping effects of a polystyrene nanosphere monolith template and a double-solvent–induced heterogeneous nucleation approach. This process synergistically enabled the in situ growth of MOFs within ordered voids, rendering a single crystal with oriented and ordered macro-microporous structure. The improved mass diffusion properties of such hierarchical frameworks, together with their robust single-crystalline nature, endow them with superior catalytic activity and recyclability for bulky-molecule reactions, as compared with conventional, polycrystalline hollow, and disordered macroporous ZIF-8.

Ordered macro-microporous metal-organic framework single crystals

KAUST Repository

Shen, Kui; Zhang, Lei; Chen, Xiaodong; Liu, Lingmei; Zhang, Daliang; Han, Yu; Chen, Junying; Long, Jilan; Luque, Rafael; Li, Yingwei; Chen, Banglin

2018-01-01

We constructed highly oriented and ordered macropores within metal-organic framework (MOF) single crystals, opening up the area of three-dimensional-ordered macro-microporous materials (that is, materials containing both macro- and micropores) in single-crystalline form. Our methodology relies on the strong shaping effects of a polystyrene nanosphere monolith template and a double-solvent-induced heterogeneous nucleation approach. This process synergistically enabled the in situ growth of MOFs within ordered voids, rendering a single crystal with oriented and ordered macro-microporous structure. The improved mass diffusion properties of such hierarchical frameworks, together with their robust single-crystalline nature, endow them with superior catalytic activity and recyclability for bulky-molecule reactions, as compared with conventional, polycrystalline hollow, and disordered macroporous ZIF-8.

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...

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.

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.

A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids

International Nuclear Information System (INIS)

Li-Feng, Wang; Wen-Hua, Ye; Zheng-Feng, Fan; Chuang, Xue; Ying-Jun, Li

2009-01-01

A weakly nonlinear model is proposed for the Kelvin–Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling. (fundamental areas of phenomenology (including applications))

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

Directory of Open Access Journals (Sweden)

Feng-Tao He

2013-01-01

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

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.

Nonlinear free vibration of single walled Carbone NanoTubes conveying fluid

Directory of Open Access Journals (Sweden)

Azrar A.

2014-04-01

Full Text Available Nonlinear free vibration of single-walled carbon nanotubes (CNTs conveying fluid are modeled and numerically simulated based on von Kármán geometric nonlinearity and Eringen’s nonlocal elasticity theory. The CNTs are modelled as nanobeams where the effects of transverse shear deformation and rotary inertia are considered within the framework of Timoshenko beam theory. The governing equations and boundary conditions are derived using the Hamilton’s principle and the nonlinear equation of motion is solved by the Galerkin’s method. The small scale parameter and the fluid-tube interaction effects on the dynamic behaviours of the CNT-fluid system as well as the instabilities induced by the fluid-velocity can be investigated. The critical fluid-velocity and frequency-amplitude relationships as well as the flutter and divergence instability types and the associated time responses are obtained based on the presented methodological approach.

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

Fractional-Order Control of a Nonlinear Time-Delay System: Case Study in Oxygen Regulation in the Heart-Lung Machine

Directory of Open Access Journals (Sweden)

S. J. Sadati

2012-01-01

Full Text Available A fractional-order controller will be proposed to regulate the inlet oxygen into the heart-lung machine. An analytical approach will be explained to satisfy some requirements together with practical implementation of some restrictions for the first time. Primarily a nonlinear single-input single-output (SISO time-delay model which was obtained previously in the literature is introduced for the oxygen generation process in the heart-lung machine system and we will complete it by adding some new states to control it. Thereafter, the system is linearized using the state feedback linearization approach to find a third-order time-delay dynamics. Consequently classical PID and fractional order controllers are gained to assess the quality of the proposed technique. A set of optimal parameters of those controllers are achieved through the genetic algorithm optimization procedure through minimizing a cost function. Our design method focuses on minimizing some famous performance criterions such as IAE, ISE, and ITSE. In the genetic algorithm, the controller parameters are chosen as a random population. The best relevant values are achieved by reducing the cost function. A time-domain simulation signifies the performance of controller with respect to a traditional optimized PID controller.

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...

SPP propagation in nonlinear glass-metal interface

KAUST Repository

Sagor, Rakibul Hasan

2011-12-01

The non-linear propagation of Surface-Plasmon-Polaritons (SPP) in single interface of metal and chalcogenide glass (ChG) is considered. A time domain simulation algorithm is developed using the Finite Difference Time Domain (FDTD) method. The general polarization algorithm incorporated in the auxiliary differential equation (ADE) is used to model frequency-dependent dispersion relation and third-order nonlinearity of ChG. The main objective is to observe the nonlinear behavior of SPP propagation and study the dynamics of the whole structure. © 2011 IEEE.

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.

Simulation of nonlinear wave run-up with a high-order Boussinesq model

DEFF Research Database (Denmark)

Fuhrman, David R.; Madsen, Per A.

2008-01-01

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions....... As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions...... cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability...

Non-linear phenomena in electronic systems consisting of coupled single-electron oscillators

International Nuclear Information System (INIS)

Kikombo, Andrew Kilinga; Hirose, Tetsuya; Asai, Tetsuya; Amemiya, Yoshihito

2008-01-01

This paper describes non-linear dynamics of electronic systems consisting of single-electron oscillators. A single-electron oscillator is a circuit made up of a tunneling junction and a resistor, and produces simple relaxation oscillation. Coupled with another, single electron oscillators exhibit complex behavior described by a combination of continuous differential equations and discrete difference equations. Computer simulation shows that a double-oscillator system consisting of two coupled oscillators produces multi-periodic oscillation with a single attractor, and that a quadruple-oscillator system consisting of four oscillators also produces multi-periodic oscillation but has a number of possible attractors and takes one of them determined by initial conditions

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...

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.

Growth and characterization of nonlinear optical single crystal: Nicotinic L-tartaric

Energy Technology Data Exchange (ETDEWEB)

Sheelarani, V.; Shanthi, J., E-mail: shanthinelson@gmail.com [Department of Physics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore-641043 (India)

2015-06-24

Nonlinear optical single crystals were grown from Nicotinic and L-Tartaric acid by slow evaporation technique at room temperature. Structure of the grown crystal was confirmed by single crystal X-ray diffraction studies, The crystallinity of the Nicotinic L-Tartaric (NLT) crystals was confirmed from the powder XRD pattern. The transparent range and cut off wavelength of the grown crystal was studied by the UV–Vis spectroscopic analysis.The thermal stability of the crystal was studied by TG-DTA. The second harmonic generation (SHG) efficiency of NLT was confirmed by Kurtz Perry technique.

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.

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

Directory of Open Access Journals (Sweden)

Ahmad Bashir

2010-01-01

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

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)

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

Science.gov (United States)

Pramodini, S.; Poornesh, P.

2014-05-01

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

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

International Nuclear Information System (INIS)

Tang Gao; Liu Cunming; Luo Lan; Chen Wei

2010-01-01

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

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

Science.gov (United States)

Ho, Yuh-Shan

2006-01-01

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

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

DEFF Research Database (Denmark)

Jensen, Jørgen Juncher

2007-01-01

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

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

Science.gov (United States)

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

2017-07-01

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

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

Directory of Open Access Journals (Sweden)

Shahid Hasnain

2017-07-01

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

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

DEFF Research Database (Denmark)

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

1998-01-01

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

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

Science.gov (United States)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

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

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

International Nuclear Information System (INIS)

Ermolaev, P; Volynsky, M

2014-01-01

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

Engineering high-order nonlinear dissipation for quantum superconducting circuits

Science.gov (United States)

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

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

Qualitative aspects of nonlinear wave motion: Complexity and simplicity

International Nuclear Information System (INIS)

Engelbrecht, J.

1993-01-01

The nonlinear wave processes possess many qualitative properties which cannot be described by linear theories. In this presentation, an attempt is made to systematize the main aspects of this fascinating area. The sources of nonlinearities are analyzed in order to understand why and how the nonlinear mathematical models are formulated. The technique of evolution equations is discussed then as a main mathematical tool to separate multiwave processes into single waves. The evolution equations give concise but in many cases sufficient description of wave processes in solids permitting to analyze spectral changes, phase changes and velocities, coupling of waves, and interaction of nonlinearities with other physical effects of the same order. Several new problems are listed. Knowing the reasons, the seemingly complex problems can be effectively analyzed. 61 refs

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

Directory of Open Access Journals (Sweden)

Murty K. N.

2000-01-01

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

NLSEmagic: Nonlinear Schrödinger equation multi-dimensional Matlab-based GPU-accelerated integrators using compact high-order schemes

Science.gov (United States)

Caplan, R. M.

2013-04-01

We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schrödinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes graphic processing unit (GPU) parallel architectures. The codes running on the GPU are many times faster than their serial counterparts, and are much cheaper to run than on standard parallel clusters. The codes are developed with usability and portability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files. Catalogue identifier: AEOJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOJ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 124453 No. of bytes in distributed program, including test data, etc.: 4728604 Distribution format: tar.gz Programming language: C, CUDA, MATLAB. Computer: PC, MAC. Operating system: Windows, MacOS, Linux. Has the code been vectorized or parallelized?: Yes. Number of processors used: Single CPU, number of GPU processors dependent on chosen GPU card (max is currently 3072 cores on GeForce GTX 690). Supplementary material: Setup guide, Installation guide. RAM: Highly dependent on dimensionality and grid size. For typical medium-large problem size in three dimensions, 4GB is sufficient. Keywords: Nonlinear Schröodinger Equation, GPU, high-order finite difference, Bose-Einstien condensates. Classification: 4.3, 7.7. Nature of problem: Integrate solutions of the time-dependent one-, two-, and three-dimensional cubic nonlinear Schrödinger equation. Solution method: The integrators utilize a fully-explicit fourth-order Runge-Kutta scheme in time

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

International Nuclear Information System (INIS)

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

2015-01-01

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

Investigation of inorganic nonlinear optical potassium penta borate tetra hydrate (PPBTH) single crystals grown by slow evaporation method

Science.gov (United States)

Arivuselvi, R.; Babu, P. Ramesh

2018-03-01

Borates family crystals were plays vital role in the field of non linear optics (NLO) due to needs of wide range of applications. In this report, NLO crystals (potassium penta borate tetra hydrate (KB5H8O12) are grown by slow evaporation method at room temperature (28° C) and studied their physical properties. The harvested single crystals are transparent with the dimension of 12 × 10 × 6 mm3 and colourless. X-ray diffraction of single crystals reveals that the grown crystal belongs to orthorhombic system with non-centrosymmetric space group Pba2. All the absorbed functional groups are present in the order of inorganic compounds expect 1688 cm-1 because of water (Osbnd H sbnd O blending) molecule present in the pristine. Crystals show transparent in the entire visible region with 5.9 eV optical band gap and also it shows excellence in both second and third order nonlinear optical properties. Crystals can withstand upto 154 °C without any phase changes which is observed using thermal (TGA/DTA) analysis.

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

Directory of Open Access Journals (Sweden)

Salih Yalcinbas

2016-01-01

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

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

Science.gov (United States)

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

2014-01-01

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

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

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

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

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.

Nonlinear evolution of single spike structure and vortex in Richtmeyer-Meshkov instability

International Nuclear Information System (INIS)

Fukuda, Yuko O.; Nishihara, Katsunobu; Okamoto, Masayo; Nagatomo, Hideo; Matsuoka, Chihiro; Ishizaki, Ryuichi; Sakagami, Hitoshi

1999-01-01

Nonlinear evolution of single spike structure and vortex in the Richtmyer-Meshkov instability is investigated for two dimensional case, and axial symmetric and non axial symmetric cases with the use of a three-dimensional hydrodynamic code. It is shown that singularity appears in the vorticity left by transmitted and reflected shocks at a corrugated interface. This singularity results in opposite sign of vorticity along the interface that causes double spiral structure of the spike. Difference of nonlinear growth rate and double spiral structure among three cases is also discussed by visualization of simulation data. In a case that there is no slip-off of initial spike axis, vorticity ring is relatively stable, but phase rotation occurs. (author)

FRF decoupling of nonlinear systems

Science.gov (United States)

Kalaycıoğlu, Taner; Özgüven, H. Nevzat

2018-03-01

Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.

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

KAUST Repository

Talukdar, Abdul Hafiz

2011-05-01

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

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

OpenAIRE

Roldan, Omar

2017-01-01

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

Construction of a single/multiple wavelength RZ optical pulse source at 40 GHz by use of wavelength conversion in a high-nonlinearity DSF-NOLM

DEFF Research Database (Denmark)

Yu, Jianjun; Yujun, Qian; Jeppesen, Palle

2001-01-01

A single or multiple wavelength RZ optical pulse source at 40 GHz is successfully obtained by using wavelength conversion in a nonlinear optical loop mirror consisting of high nonlinearity-dispersion shifted fiber.......A single or multiple wavelength RZ optical pulse source at 40 GHz is successfully obtained by using wavelength conversion in a nonlinear optical loop mirror consisting of high nonlinearity-dispersion shifted fiber....

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

International Nuclear Information System (INIS)

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

2008-01-01

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

Growth, structural, thermal, dielectric and nonlinear optical properties of potassium hexachloro cadmate (IV) a novel single crystal

Science.gov (United States)

Umarani, P.; Jagannathan, K.

2018-02-01

The Potassium hexachloro cadmate (IV) (PHC) single crystal was grown from the aqueous of the solution by a controlled evaporation method. Single crystal XRD solved the structure. FTIR is used to identify the functional groups of grown crystal. The UV-Vis-NIR spectrometer was used to find out the UV cut off region and to calculate the optical band gap of the Potassium hexachloro cadmate (IV) single crystal. The EDAX spectrum has been used to identify the compounds present in title compound. The TG-DTA profile shows the thermal stability of the grown crystal of Potassium hexachloro cadmate (IV). The Vicker's hardness measurement was used to calculate the material hardness of the title compound. The dielectric loss and constant varied with frequencies and activation energy is also calculated. The solid state parameters like plasma energy, Penn gap, Fermi energy, electronic polarizability using Penn analysis and Clausius-Mossotti equation were also calculated for the title compound. The Z-scan technique is used to calculate the third order nonlinear susceptibility of a real and imaginary part.

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

International Nuclear Information System (INIS)

Choi, Chan Kyu; Yoo, Hong Hee

2012-01-01

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

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

Science.gov (United States)

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

2018-04-01

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

Oscillating nonlinear acoustic shock waves

DEFF Research Database (Denmark)

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

2016-01-01

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

Validity testing of third-order nonlinear models for synchronous generators

Energy Technology Data Exchange (ETDEWEB)

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

2009-06-15

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

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

Science.gov (United States)

Chen, Yong; Yan, Zhenya

2016-03-22

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

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

Directory of Open Access Journals (Sweden)

Aydin Tiryaki

2014-06-01

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

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)

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...

Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity

DEFF Research Database (Denmark)

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

2010-01-01

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

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

International Nuclear Information System (INIS)

Brandt, H.E.

1983-01-01

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

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.

Cumulants of heat transfer across nonlinear quantum systems

Science.gov (United States)

Li, Huanan; Agarwalla, Bijay Kumar; Li, Baowen; Wang, Jian-Sheng

2013-12-01

We consider thermal conduction across a general nonlinear phononic junction. Based on two-time observation protocol and the nonequilibrium Green's function method, heat transfer in steady-state regimes is studied, and practical formulas for the calculation of the cumulant generating function are obtained. As an application, the general formalism is used to study anharmonic effects on fluctuation of steady-state heat transfer across a single-site junction with a quartic nonlinear on-site pinning potential. An explicit nonlinear modification to the cumulant generating function exact up to the first order is given, in which the Gallavotti-Cohen fluctuation symmetry is found still valid. Numerically a self-consistent procedure is introduced, which works well for strong nonlinearity.

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.

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

Data.gov (United States)

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

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.

Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Yan, R.; Aluie, H.; Betti, R.; Sanz, J.; Liu, B.; Frank, A.

2016-01-01

The nonlinear evolution of the single-mode ablative Rayleigh-Taylor instability is studied in three dimensions. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the three-dimensional (3D) terminal bubble velocity greatly exceeds both the two-dimensional (2D) value and the classical 3D bubble velocity. Unlike in 2D, the 3D short-wavelength bubble velocity does not saturate. The growing 3D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. The vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes to the ablated plasma filling the bubble volume

Analysis of second order harmonic distortion due to transmitter non-linearity and chromatic and modal dispersion of optical OFDM SSB modulated signals in SMF-MMF fiber links

Science.gov (United States)

Patel, Dhananjay; Singh, Vinay Kumar; Dalal, U. D.

2017-01-01

Single mode fibers (SMF) are typically used in Wide Area Networks (WAN), Metropolitan Area Networks (MAN) and also find applications in Radio over Fiber (RoF) architectures supporting data transmission in Fiber to the Home (FTTH), Remote Antenna Units (RAUs), in-building networks etc. Multi-mode fibers (MMFs) with low cost, ease of installation and low maintenance are predominantly (85-90%) deployed in-building networks providing data access in local area networks (LANs). The transmission of millimeter wave signals through the SMF in WAN and MAN, along with the reuse of MMF in-building networks will not levy fiber reinstallation cost. The transmission of the millimeter waves experiences signal impairments due to the transmitter non-linearity and modal dispersion of the MMF. The MMF exhibiting large modal dispersion limits the bandwidth-length product of the fiber. The second and higher-order harmonics present in the optical signal fall within the system bandwidth. This causes degradation in the received signal and an unwanted radiation of power at the RAU. The power of these harmonics is proportional to the non-linearity of the transmitter and the modal dispersion of the MMF and should be maintained below the standard values as per the international norms. In this paper, a mathematical model is developed for Second-order Harmonic Distortion (HD2) generated due to non-linearity of the transmitter and chromatic-modal dispersion of the SMF-MMF optic link. This is also verified using a software simulation. The model consists of a Mach Zehnder Modulator (MZM) that generates two m-QAM OFDM Single Sideband (SSB) signals based on phase shift of the hybrid coupler (90° and 120°). Our results show that the SSB signal with 120° hybrid coupler has suppresses the higher-order harmonics and makes the system more robust against the HD2 in the SMF-MMF optic link.

Nonlinear polarization effects in a birefringent single mode optical fiber

International Nuclear Information System (INIS)

Ishiekwene, G.C.; Mensah, S.Y.; Brown, C.S.

2001-04-01

The nonlinear polarization effects in a birefringent single mode optical fiber is studied using Jacobi elliptic functions. We find that the polarization state of the propagating beam depends on the initial polarization as well as the intensity of the input light in a complicated way. The Stokes polarization parameters are either periodic or aperiodic depending on the value of the Jacobian modulus. Our calculations suggest that the effective beat length of the fiber can become infinite at a higher critical value of the input power when polarization dependent losses are considered. (author)

Nonlinear beam mechanics

NARCIS (Netherlands)

Westra, H.J.R.

2012-01-01

In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

Science.gov (United States)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

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.

Dye molecules as single-photon sources and large optical nonlinearities on a chip

International Nuclear Information System (INIS)

Hwang, J; Hinds, E A

2011-01-01

We point out that individual organic dye molecules, deposited close to optical waveguides on a photonic chip, can act as single-photon sources. A thin silicon nitride strip waveguide is expected to collect 28% of the photons from a single dibenzoterrylene molecule. These molecules can also provide large, localized optical nonlinearities, which are enough to discriminate between one photon or two through a differential phase shift of 2 0 per photon. This new atom-photon interface may be used as a resource for processing quantum information.

On the physical contributions to the third-order nonlinear optical response in plasmonic nanocomposites

International Nuclear Information System (INIS)

Fernández-Hernández, Roberto Carlos; Gleason-Villagran, Roberto; Rodríguez-Fernández, Luis; Crespo-Sosa, Alejandro; Cheang-Wong, Juan Carlos; López-Suárez, Alejandra; Oliver, Alicia; Reyes-Esqueda, Jorge Alejandro; Torres-Torres, Carlos; Rangel-Rojo, Raúl

2012-01-01

Au and Ag isotropic and anisotropic nanocomposites were prepared using the ion implantation technique. Their optical properties were studied at several wavelengths in the optical range 300–800 nm, across their plasmon resonances. The linear regime was characterized by measuring the absorption spectrum and the third-order nonlinear regime by means of the Z-scan technique using a tunable picosecond pulsed laser system (26 ps). Open-aperture Z-scan traces show a superposition of different optical nonlinear absorption (NLA) processes in the whole range studied. We associate these phenomena with the excitation of inter- and intra-band electronic transitions, which contribute with a positive sign to NLA, and to the formation of hot-electrons, which contribute with opposite sign to NLA. Closed-aperture traces for measuring nonlinear refraction (NLR) show different signs for Au and Ag samples, and a change of sign in Au is found when purely inter-band transitions are excited. In this work, for the appropriate wavelength, it is worth remarking on the free-electron response to the exciting light and its strong contribution to the nonlinear optical properties for low (intra-band) and high (hot-electrons) irradiances. (paper)

Ring vortex solitons in nonlocal nonlinear media

DEFF Research Database (Denmark)

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

2005-01-01

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

Experimental study of the third-order nonlinearity of atomic and molecular gases using 10-μm laser pulses

Science.gov (United States)

Pigeon, J. J.; Tochitsky, S. Ya.; Welch, E. C.; Joshi, C.

2018-04-01

We present measurements of the third-order optical nonlinearity of Kr, Xe, N2, O2, and air at a wavelength near 10 µm by using four-wave mixing of ˜15 -GW /c m2 , 200-ps (full width at half maximum) C O2 laser pulses. Measurements in molecular gases resulted in an asymmetric four-wave mixing spectrum indicating that the nonlinear response is strongly affected by the delayed, rotational contribution to the effective nonlinear refractive index. Within the uncertainty of our measurements, we have found that the long-wavelength nonlinear refractive indices of these gases are consistent with measurements performed in the near IR.

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.

Zeolite Y Films as Ideal Platform for Evaluation of Third-Order Nonlinear Optical Quantum Dots

Directory of Open Access Journals (Sweden)

Hyun Sung Kim

2016-01-01

Full Text Available Zeolites are ideal host material for generation and stabilization of regular ultrasmall quantum dots (QDs array with the size below 1.5 nm. Quantum dots (QDs with high density and extinction absorption coefficient have been expected to give high level of third-order nonlinear optical (3rd-NLO and to have great potential applications in optoelectronics. In this paper, we carried out a systematic elucidation of the third-order nonlinear optical response of various types of QDs including PbSe, PbS, CdSe, CdS, ZnSe, ZnS, Ag2Se, and Ag2S by manipulation of QDs into zeolites Y pores. In this respect, we could demonstrate that the zeolite offers an ideal platform for capability comparison 3rd-NLO response of various types of QDs with high sensitivities.

Self-Similar Nanocavity Design with Ultrasmall Mode Volume for Single-Photon Nonlinearities

DEFF Research Database (Denmark)

Choi, Hyeongrak; Heuck, Mikkel; Englund, Dirk R.

2017-01-01

We propose a photonic crystal nanocavity design with self-similar electromagnetic boundary conditions, achieving ultrasmall mode volume (V-eff). The electric energy density of a cavity mode can be maximized in the air or dielectric region, depending on the choice of boundary conditions. We illust...... at the single-photon level. These features open new directions in cavity quantum electrodynamics, spectroscopy, and quantum nonlinear optics....

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.

Multiple periodic solutions for a class of second-order nonlinear neutral delay equations

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available By means of a variational structure and Z 2 -group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the form0, au>0$"> x ″ ( t − τ + λ ( t f ( t , x ( t , x ( t − τ , x ( t − 2 τ = x ( t , λ ( t > 0 , τ > 0 .

Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems.

Science.gov (United States)

Mei, Jie; Ren, Wei; Li, Bing; Ma, Guangfu

2015-09-01

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

Interacting wave fronts and rarefaction waves in a second order model of nonlinear thermoviscous fluids : Interacting fronts and rarefaction waves

DEFF Research Database (Denmark)

Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich

2011-01-01

A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hami...... is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.......A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...... the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions...

Testing for one Generalized Linear Single Order Parameter

DEFF Research Database (Denmark)

Ellegaard, Niels Langager; Christensen, Tage Emil; Dyre, Jeppe

We examine a linear single order parameter model for thermoviscoelastic relaxation in viscous liquids, allowing for a distribution of relaxation times. In this model the relaxation of volume and entalpy is completely described by the relaxation of one internal order parameter. In contrast to prior...... work the order parameter may be chosen to have a non-exponential relaxation. The model predictions contradict the general consensus of the properties of viscous liquids in two ways: (i) The model predicts that following a linear isobaric temperature step, the normalized volume and entalpy relaxation...... responses or extrapolate from measurements of a glassy state away from equilibrium. Starting from a master equation description of inherent dynamics, we calculate the complex thermodynamic response functions. We device a way of testing for the generalized single order parameter model by measuring 3 complex...

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

Science.gov (United States)

Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

2018-06-01

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

Generalized effective potential in nonlinear theories of the 4-th order

International Nuclear Information System (INIS)

Ananikyan, N.S.; Savvidy, G.K.

1980-01-01

By means of the Legendre transformations in the framework of nonlinear theories of the 4-th order a generalized effective potential GITA(phi, G, H, S) is constructed. It depends on PHI, a possible expectation value of the quantum field; on G, H, possible expectation values of the 2- a.nd 3-point connected Green functions and on S= a possible expectation value of the classical action. The expansion for the functional GITA(phi, G, H, S) is obtained, which is similar to the loop expansion for the effective action GITA(phi)

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

Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

Science.gov (United States)

Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

2015-12-01

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

Full 3D modelling of pulse propagation enables efficient nonlinear frequency conversion with low energy laser pulses in a single-element tripler

Science.gov (United States)

Kardaś, Tomasz M.; Nejbauer, Michał; Wnuk, Paweł; Resan, Bojan; Radzewicz, Czesław; Wasylczyk, Piotr

2017-02-01

Although new optical materials continue to open up access to more and more wavelength bands where femtosecond laser pulses can be generated, light frequency conversion techniques are still indispensable in filling the gaps on the ultrafast spectral scale. With high repetition rate, low pulse energy laser sources (oscillators) tight focusing is necessary for a robust wave mixing and the efficiency of broadband nonlinear conversion is limited by diffraction as well as spatial and temporal walk-off. Here we demonstrate a miniature third harmonic generator (tripler) with conversion efficiency exceeding 30%, producing 246 fs UV pulses via cascaded second order processes within a single laser beam focus. Designing this highly efficient and ultra compact frequency converter was made possible by full 3-dimentional modelling of propagation of tightly focused, broadband light fields in nonlinear and birefringent media.

A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives

Directory of Open Access Journals (Sweden)

Duan Jun-Sheng

2017-12-01

Full Text Available We conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative. For each of the two vibration systems, we consider the stiffness contribution factor and damping contribution factor of the term of fractional derivatives, the amplitude and the phase difference for the response. The effects of driving frequency on these response quantities are discussed. Also the influences of the order α of the fractional derivative and the parameter γ parameterizing the weight function in the distributed-order derivative are analyzed. Two cases display similar response behaviors, but the stiffness contribution factor and damping contribution factor of the distributed-order derivative are almost monotonic change with the parameter γ, not exactly like the case of single fractional-order derivative for the order α. The case of the distributed-order derivative provides us more options for the weight function and parameters.

Third-order optical nonlinearities in bulk and fs-laser inscribed waveguides in strengthened alkali aluminosilcate glass

Science.gov (United States)

Almeida, Gustavo F. B.; Almeida, Juliana M. P.; Martins, Renato J.; De Boni, Leonardo; Arnold, Craig B.; Mendonca, Cleber R.

2018-01-01

The development of advanced photonics devices requires materials with large optical nonlinearities, fast response times and high optical transparency, while at the same time allowing for the micro/nano-processing needed for integrated photonics. In this context, glasses have been receiving considerable attention given their relevant optical properties which can be specifically tailored by compositional control. Corning Gorilla® Glass (strengthened alkali aluminosilicate glass) is well-known for its use as a protective screen in mobile devices, and has attracted interest as a potential candidate for optical devices. Therefore, it is crucial not only to expand the knowledge on the fabrication of waveguides in Gorilla Glass under different regimes, but also to determine its nonlinear optical response, both using fs-laser pulses. Thus, this paper reports, for the first time, characterization of the third-order optical nonlinearities of Gorilla Glass, as well as linear and nonlinear characterization of waveguide written with femtosecond pulses under the low repetition rate regime (1 kHz).

Nonlinear Optical Properties of XPh4 (X = B-, C, N+, P+): A New Class of Molecules with a Negative Third-Order Polarizability

KAUST Repository

Gieseking, Rebecca L.; Ensley, Trenton R.; Hu, Honghua; Hagan, David J.; Risko, Chad; Van Stryland, Eric W.; Bredas, Jean-Luc

2015-01-01

Organic π-conjugated materials have been widely used for a variety of nonlinear optical (NLO) applications. Molecules with negative real components Re(γ) of the third-order polarizability, which leads to nonlinear refraction in macroscopic systems, have important benefits for several NLO applications. However, few organic systems studied to date have negative Re(γ) in the long wavelength limit, and all inorganic materials show positive nonlinear refraction in this limit. Here, we introduce a new class of molecules of the form X(C6H5)4, where X = B-, C, N+, and P+, that have negative Re(γ). The molecular mechanism for the NLO properties in these systems is very different from those in typical linear conjugated systems: these systems have a band of excited states involving single-electron excitations within the π-system, several of which have significant coupling to the ground state. Thus, Re(γ) cannot be understood in terms of a simplified essential-state model and must be analyzed in the context of the full sum-over-states expression. Although Re(γ) is significantly smaller than that of other commonly-studied NLO chromophores, the introduction of a new molecular architecture offering the potential for a negative Re(γ) introduces new avenues of molecular design for NLO applications.

Nonlinear Optical Properties of XPh4 (X = B-, C, N+, P+): A New Class of Molecules with a Negative Third-Order Polarizability

KAUST Repository

Gieseking, Rebecca L.

2015-06-22

Organic π-conjugated materials have been widely used for a variety of nonlinear optical (NLO) applications. Molecules with negative real components Re(γ) of the third-order polarizability, which leads to nonlinear refraction in macroscopic systems, have important benefits for several NLO applications. However, few organic systems studied to date have negative Re(γ) in the long wavelength limit, and all inorganic materials show positive nonlinear refraction in this limit. Here, we introduce a new class of molecules of the form X(C6H5)4, where X = B-, C, N+, and P+, that have negative Re(γ). The molecular mechanism for the NLO properties in these systems is very different from those in typical linear conjugated systems: these systems have a band of excited states involving single-electron excitations within the π-system, several of which have significant coupling to the ground state. Thus, Re(γ) cannot be understood in terms of a simplified essential-state model and must be analyzed in the context of the full sum-over-states expression. Although Re(γ) is significantly smaller than that of other commonly-studied NLO chromophores, the introduction of a new molecular architecture offering the potential for a negative Re(γ) introduces new avenues of molecular design for NLO applications.

Temperature-dependent of Nonlinear Optical Conductance of Graphene-based Systems in High-intensity Terahertz Field

Institute of Scientific and Technical Information of China (English)

Jing Lv; Rui-yang Yuan; Hui Yan

2014-01-01

For multi-photon processed with the linear dispersion in the high-intensity terahertz(THz) field,we have systematically investigated the temperature-dependent nonlinear optical response of graphene-based systems, including single layer graphene, graphene superlattice and gapped graphene. In the intrinsic single layer graphene system, it demonstrates that, at low temperature, nonlinear optical conductivities of the thirdand fifth-order are respectively five and ten orders of magnitude larger than the universal conductivity with high-intensity and low frequency THz wave.In the graphene superlattice and gapped graphene systems, the optical responses enhanced because of the anisotropic massless and massive Dirac fermions.

Physical origin of third order non-linear optical response of porphyrin nanorods

International Nuclear Information System (INIS)

Mongwaketsi, N.; Khamlich, S.; Pranaitis, M.; Sahraoui, B.; Khammar, F.; Garab, G.; Sparrow, R.; Maaza, M.

2012-01-01

The non-linear optical properties of porphyrin nanorods were studied using Z-scan, Second and Third harmonic generation techniques. We investigated in details the heteroaggregate behaviour formation of [H 4 TPPS 4 ] 2- and [SnTPyP] 2+ mixture by means of the UV-VIS spectroscopy and aggregates structure and morphology by transmission electron microscopy. The porphyrin nanorods under investigation were synthesized by self assembly and molecular recognition method. They have been optimized in view of future application in the construction of the light harvesting system. The focus of this study was geared towards understanding the influence of the type of solvent used on these porphyrins nanorods using spectroscopic and microscopic techniques. Highlights: ► We synthesized porphyrin nanorods by self assembly and molecular recognition method. ► TEM images confirmed solid cylindrical shapes. ► UV-VIS spectroscopy showed the decrease in the absorbance peaks of the precursors. ► The enhanced third-order nonlinearities were observed.

Passive impedance-based second-order sliding mode control for non-linear teleoperators

Directory of Open Access Journals (Sweden)

Luis G García-Valdovinos

2017-02-01

Full Text Available Bilateral teleoperation systems have attracted significant attention in the last decade mainly because of technological advancements in both the communication channel and computers performance. In addition, non-linear multi-degree-of-freedom bilateral teleoperators along with state observers have become an open research area. In this article, a model-free exact differentiator is used to estimate the full state along with a chattering-free second-order sliding mode controller to guarantee a robust impedance tracking under both constant and an unknown time delay of non-linear multi-degree-of-freedom robots. The robustness of the proposed controller is improved by introducing a change of coordinates in terms of a new nominal reference similar to that used in adaptive control theory. Experimental results that validate the predicted behaviour are presented and discussed using a Phantom Premium 1.0 as the master robot and a Catalyst-5 virtual model as the slave robot. The dynamics of the Catalyst-5 system is solved online.

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

Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion

Science.gov (United States)

Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin

2014-09-01

We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

Science.gov (United States)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

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.

Terahertz Nonlinear Optics in Semiconductors

DEFF Research Database (Denmark)

Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.

2013-01-01

We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...... breathing of a single-cycle THz pulse in a semiconductor....

Laterally Loaded Single Pile Response Considering the Influence of Suction and Non-Linear Behaviour of Reinforced Concrete Sections

Directory of Open Access Journals (Sweden)

Stefano Stacul

2017-12-01

Full Text Available A hybrid BEM-p-y curves approach was developed for the single pile analysis with free/fixed head restraint conditions. The method considers the soil non-linear behaviour by means of p-y curves in series to a multi-layered elastic half-space. The non-linearity of reinforced concrete pile sections, also considering the influence of tension-stiffening, has been considered. The model reproduces the influence of suction by increasing the stress state and hence the stiffness of shallow soil-layers. Suction is modeled using the Modified-Kovacs model. The hybrid BEM-py curves method was validated by comparing results from data of 22 load tests on single piles. In addition, a detailed comparison is presented between measured and computed data on a large-diameter reinforced concrete bored single pile.

Attitude Control of a Single Tilt Tri-Rotor UAV System: Dynamic Modeling and Each Channel's Nonlinear Controllers Design

Directory of Open Access Journals (Sweden)

Juing-Shian Chiou

2013-01-01

Full Text Available This paper has implemented nonlinear control strategy for the single tilt tri-rotor aerial robot. Based on Newton-Euler’s laws, the linear and nonlinear mathematical models of tri-rotor UAVs are obtained. A numerical analysis using Newton-Raphson method is chosen for finding hovering equilibrium point. Back-stepping nonlinear controller design is based on constructing Lyapunov candidate function for closed-loop system. By imitating the linguistic logic of human thought, fuzzy logic controllers (FLCs are designed based on control rules and membership functions, which are much less rigid than the calculations computers generally perform. Effectiveness of the controllers design scheme is shown through nonlinear simulation model on each channel.

A study of single multiplicative neuron model with nonlinear filters for hourly wind speed prediction

International Nuclear Information System (INIS)

Wu, Xuedong; Zhu, Zhiyu; Su, Xunliang; Fan, Shaosheng; Du, Zhaoping; Chang, Yanchao; Zeng, Qingjun

2015-01-01

Wind speed prediction is one important methods to guarantee the wind energy integrated into the whole power system smoothly. However, wind power has a non–schedulable nature due to the strong stochastic nature and dynamic uncertainty nature of wind speed. Therefore, wind speed prediction is an indispensable requirement for power system operators. Two new approaches for hourly wind speed prediction are developed in this study by integrating the single multiplicative neuron model and the iterated nonlinear filters for updating the wind speed sequence accurately. In the presented methods, a nonlinear state–space model is first formed based on the single multiplicative neuron model and then the iterated nonlinear filters are employed to perform dynamic state estimation on wind speed sequence with stochastic uncertainty. The suggested approaches are demonstrated using three cases wind speed data and are compared with autoregressive moving average, artificial neural network, kernel ridge regression based residual active learning and single multiplicative neuron model methods. Three types of prediction errors, mean absolute error improvement ratio and running time are employed for different models’ performance comparison. Comparison results from Tables 1–3 indicate that the presented strategies have much better performance for hourly wind speed prediction than other technologies. - Highlights: • Developed two novel hybrid modeling methods for hourly wind speed prediction. • Uncertainty and fluctuations of wind speed can be better explained by novel methods. • Proposed strategies have online adaptive learning ability. • Proposed approaches have shown better performance compared with existed approaches. • Comparison and analysis of two proposed novel models for three cases are provided

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

Science.gov (United States)

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

2017-11-01

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

Visual aftereffects and sensory nonlinearities from a single statistical framework

Science.gov (United States)

Laparra, Valero; Malo, Jesús

2015-01-01

When adapted to a particular scenery our senses may fool us: colors are misinterpreted, certain spatial patterns seem to fade out, and static objects appear to move in reverse. A mere empirical description of the mechanisms tuned to color, texture, and motion may tell us where these visual illusions come from. However, such empirical models of gain control do not explain why these mechanisms work in this apparently dysfunctional manner. Current normative explanations of aftereffects based on scene statistics derive gain changes by (1) invoking decorrelation and linear manifold matching/equalization, or (2) using nonlinear divisive normalization obtained from parametric scene models. These principled approaches have different drawbacks: the first is not compatible with the known saturation nonlinearities in the sensors and it cannot fully accomplish information maximization due to its linear nature. In the second, gain change is almost determined a priori by the assumed parametric image model linked to divisive normalization. In this study we show that both the response changes that lead to aftereffects and the nonlinear behavior can be simultaneously derived from a single statistical framework: the Sequential Principal Curves Analysis (SPCA). As opposed to mechanistic models, SPCA is not intended to describe how physiological sensors work, but it is focused on explaining why they behave as they do. Nonparametric SPCA has two key advantages as a normative model of adaptation: (i) it is better than linear techniques as it is a flexible equalization that can be tuned for more sensible criteria other than plain decorrelation (either full information maximization or error minimization); and (ii) it makes no a priori functional assumption regarding the nonlinearity, so the saturations emerge directly from the scene data and the goal (and not from the assumed function). It turns out that the optimal responses derived from these more sensible criteria and SPCA are

Nonlinear optical susceptibilities in the diffusion modified AlxGa1-xN/GaN single quantum well

Science.gov (United States)

Das, T.; Panda, S.; Panda, B. K.

2018-05-01

Under thermal treatment of the post growth AlGaN/GaN single quantum well, the diffusion of Al and Ga atoms across the interface is expected to form the diffusion modified quantum well with diffusion length as a quantitative parameter for diffusion. The modification of confining potential and position-dependent effective mass in the quantum well due to diffusion is calculated taking the Fick's law. The built-in electric field which arises from spontaneous and piezoelectric polarizations in the wurtzite structure is included in the effective mass equation. The electronic states are calculated from the effective mass equation using the finite difference method for several diffusion lengths. Since the effective well width decreases with increasing diffusion length, the energy levels increase with it. The intersubband energy spacing in the conduction band decreases with diffusion length due to built-in electric field and reduction of effective well width. The linear susceptibility for first-order and the nonlinear second-order and third-order susceptibilities are calculated using the compact density matrix approach taking only two levels. The calculated susceptibilities are red shifted with increase in diffusion lengths due to decrease in intersubband energy spacing.

Communication: atomic force detection of single-molecule nonlinear optical vibrational spectroscopy.

Science.gov (United States)

Saurabh, Prasoon; Mukamel, Shaul

2014-04-28

Atomic Force Microscopy (AFM) allows for a highly sensitive detection of spectroscopic signals. This has been first demonstrated for NMR of a single molecule and recently extended to stimulated Raman in the optical regime. We theoretically investigate the use of optical forces to detect time and frequency domain nonlinear optical signals. We show that, with proper phase matching, the AFM-detected signals closely resemble coherent heterodyne-detected signals. Applications are made to AFM-detected and heterodyne-detected vibrational resonances in Coherent Anti-Stokes Raman Spectroscopy (χ((3))) and sum or difference frequency generation (χ((2))).

Nonlinear optics principles and applications

CERN Document Server

Rottwitt, Karsten

2014-01-01

IntroductionReview of linear opticsInduced polarizationHarmonic oscillator modelLocal field correctionsEstimated nonlinear responseSummaryTime-domain material responseThe polarization time-response functionThe Born-Oppenheimer approximationRaman scattering response function of silicaSummaryMaterial response in the frequency domain, susceptibility tensorsThe susceptibility tensorThe induced polarization in the frequency domainSum of monochromatic fieldsThe prefactor to the induced polarizationThird-order polarization in the Born-Oppenheimer approximation in the frequency domainKramers-Kronig relationsSummarySymmetries in nonlinear opticsSpatial symmetriesSecond-order materialsThird-order nonlinear materialsCyclic coordinate-systemContracted notation for second-order susceptibility tensorsSummaryThe nonlinear wave equationMono and quasi-monochromatic beamsPlane waves - the transverse problemWaveguidesVectorial approachNonlinear birefringenceSummarySecond-order nonlinear effectsGeneral theoryCoupled wave theoryP...

Theory of plasmonic effects in nonlinear optics: the case of graphene

Science.gov (United States)

Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration

The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).

Nonlinear piezoelectricity in PZT ceramics for generating ultrasonic phase conjugate waves

Science.gov (United States)

Yamamoto; Kokubo; Sakai; Takagi

2000-03-01

We have succeeded in the generation of acoustic phase conjugate waves with nonlinear PZT piezoelectric ceramics and applied them to ultrasonic imaging systems. Our aim is to make a phase conjugator with 100% efficiency. For this purpose, it is important to clarify the mechanism of acoustic phase conjugation through nonlinear piezoelectricity. The process is explained by the parametric interaction via the third-order nonlinear piezoelectricity between the incident acoustic wave at angular frequency omega and the pump electric field at 2 omega. We solved the coupling equations including the third-ordered nonlinear piezoelectricity and theoretically derived the amplitude efficiency of the acoustic phase conjugation. We compared the efficiencies between the theoretical and experimental values for PZT ceramics with eight different compositions. Pb[(Zn1/3Nb2/3)(1 - x)Tix]O3 (X = 0.09, PZNT91/9) piezoelectric single crystals have been investigated for high-performance ultrasonic transducer application, because these have large piezoelectric constants, high electrical-mechanical coupling factors and high dielectric constants. We found that they have third-order nonlinear piezoelectric constants much larger than PZT and are hopeful that the material as a phase conjugator has over 100% efficiency.

Application of He’s Variational Iteration Method to Nonlinear Helmholtz Equation and Fifth-Order KDV Equation

DEFF Research Database (Denmark)

Miansari, Mo; Miansari, Me; Barari, Amin

2009-01-01

In this article, He’s variational iteration method (VIM), is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely c...

Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

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Iman Eshraghi

2016-09-01

Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.

Dispersion of the resonant second order nonlinearity in 2D semiconductors probed by femtosecond continuum pulses

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Mohammad Mokim

2017-10-01

Full Text Available We demonstrate an effective microspectroscopy technique by tracing the dispersion of second order nonlinear susceptibility (χ(2 in a monolayer tungsten diselenide (WSe2. The χ(2 dispersion obtained with better than 3 meV photon energy resolution showed peak value being within 6.3-8.4×10-19 m2/V range. We estimate the fundamental bandgap to be at 2.2 eV. Sub-structure in the χ(2 dispersion reveals a contribution to the nonlinearity due to exciton transitions with exciton binding energy estimated to be at 0.7 eV.

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides

DEFF Research Database (Denmark)

Reddy, D. V.; Raymer, M. G.; McKinstrie, C. J.

2013-01-01

in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process...... in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion....

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.

Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models

Science.gov (United States)

Low, Ian; Yin, Zhewei

2018-02-01

We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the Adler's zero is guaranteed for S -matrix elements, and gives rise to a subleading single soft theorem that is valid at the quantum level and to all orders in the Goldstone decay constant. For tree amplitudes, the Ward identity leads to a novel Berends-Giele recursion relation as well as an explicit form of the subleading single soft factor. Furthermore, interactions of the cubic biadjoint scalar theory associated with the single soft limit, which was previously discovered using the Cachazo-He-Yuan representation of tree amplitudes, can be seen to emerge from matrix elements of conserved currents corresponding to the generalized shift symmetry.

Probabilistically cloning two single-photon states using weak cross-Kerr nonlinearities

International Nuclear Information System (INIS)

Zhang, Wen; Rui, Pinshu; Zhang, Ziyun; Yang, Qun

2014-01-01

By using quantum nondemolition detectors (QNDs) based on weak cross-Kerr nonlinearities, we propose an experimental scheme for achieving 1→2 probabilistic quantum cloning (PQC) of a single-photon state, secretly choosing from a two-state set. In our scheme, after a QND is performed on the to-be-cloned photon and the assistant photon, a single-photon projection measurement is performed by a polarization beam splitter (PBS) and two single-photon trigger detectors (SPTDs). The measurement is to judge whether the PQC should be continued. If the cloning fails, a cutoff is carried out and some operations are omitted. This makes our scheme economical. If the PQC is continued according to the measurement result, two more QNDs and some unitary operations are performed on the to-be-cloned photon and the cloning photon to achieve the PQC in a nearly deterministic way. Our experimental scheme for PQC is feasible for future technology. Furthermore, the quantum logic network of our PQC scheme is presented. In comparison with similar networks, our PQC network is simpler and more economical. (paper)

A framework for simulating ultrasound imaging based on first order nonlinear pressure–velocity relations

DEFF Research Database (Denmark)

Du, Yigang; Fan, Rui; Li, Yong

2016-01-01

An ultrasound imaging framework modeled with the first order nonlinear pressure–velocity relations (NPVR) based simulation and implemented by a half-time staggered solution and pseudospectral method is presented in this paper. The framework is capable of simulating linear and nonlinear ultrasound...... propagation and reflections in a heterogeneous medium with different sound speeds and densities. It can be initialized with arbitrary focus, excitation and apodization for multiple individual channels in both 2D and 3D spatial fields. The simulated channel data can be generated using this framework......, and ultrasound image can be obtained by beamforming the simulated channel data. Various results simulated by different algorithms are illustrated for comparisons. The root mean square (RMS) errors for each compared pulses are calculated. The linear propagation is validated by an angular spectrum approach (ASA...

Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics.

Science.gov (United States)

Taheri, Mehdi; Sheikholeslam, Farid; Najafi, Majddedin; Zekri, Maryam

2017-07-01

In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Second-order nonlinear optical microscopy of spider silk

Science.gov (United States)

Zhao, Yue; Hien, Khuat Thi Thu; Mizutani, Goro; Rutt, Harvey N.

2017-06-01

Asymmetric β-sheet protein structures in spider silk should induce nonlinear optical interaction such as second harmonic generation (SHG) which is experimentally observed for a radial line and dragline spider silk using an imaging femtosecond laser SHG microscope. By comparing different spider silks, we found that the SHG signal correlates with the existence of the protein β-sheets. Measurements of the polarization dependence of SHG from the dragline indicated that the β-sheet has a nonlinear response depending on the direction of the incident electric field. We propose a model of what orientation the β-sheet takes in spider silk.

Temp erature-dep endent of Nonlinear Optical Conductance of Graphene-based Systems in High-intensity Terahertz Field

Institute of Scientific and Technical Information of China (English)

Jing Lv; Rui-yang Yuan; Hui Yan

2014-01-01

For multi-photon processed with the linear dispersion in the high-intensity terahertz (THz) field, we have systematically investigated the temperature-dependent nonlinear optical response of graphene-based systems, including single layer graphene, graphene superlattice and gapped graphene. In the intrinsic single layer graphene system, it demonstrates that, at low temperature, nonlinear optical conductivities of the third-and fifth-order are respectively five and ten orders of magnitude larger than the universal conductivity with high-intensity and low frequency THz wave.In the graphene superlattice and gapped graphene systems, the optical responses enhanced because of the anisotropic massless and massive Dirac fermions.

Large third-order nonlinearity of nonpolar A-plane GaN film at 800 nm determined by Z-scan technology

Science.gov (United States)

Zhang, Feng; Han, Xiangyun

2014-09-01

We report an investigation on the optical third-order nonlinear property of the nonpolar A-plane GaN film. The film sample with a thickness of ~2 μm was grown on an r-plane sapphire substrate by metal-organic chemical vapor deposition system. By performing the Z-scan method combined with a mode-locked femtosecond Ti:sapphire laser (800 nm, 50 fs), the optical nonlinearity of the nonpolar A-plane GaN film was measured with the electric vector E of the laser beam being polarized parallel (//) and perpendicular (⊥) to the c axis of the film. The results show that both the third-order nonlinear absorption coefficient β and the nonlinear refractive index n2 of the sample film possess negative and large values, i.e. β// = -135 ± 29 cm/GW, n2// = -(4.0 ± 0.3) × 10-3 cm2/GW and β⊥ = -234 ± 29 cm/GW, n2⊥ = -(4.9 ± 0.4) × 10-3 cm2/GW, which are much larger than those of conventional C-plane GaN film, GaN bulk, and even the other oxide semiconductors.

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.

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)

Nonlinear behavior of multiple-helicity resistive interchange modes near marginally stable states

International Nuclear Information System (INIS)

Sugama, Hideo; Nakajima, Noriyoshi; Wakatani, Masahiro.

1991-05-01

Nonlinear behavior of resistive interchange modes near marginally stable states is theoretically studied under the multiple-helicity condition. Reduced fluid equations in the sheared slab configuration are used in order to treat a local transport problem. With the use of the invariance property of local reduced fluid model equations under a transformation between the modes with different rational surfaces, weakly nonlinear theories for single-helicity modes by Hamaguchi and Nakajima are extended to the multiple-helicity case and applied to the resistive interchange modes. We derive the nonlinear amplitude equations of the multiple-helicity modes, from which the convective transport in the saturated state is obtained. It is shown how the convective transport is enhanced by nonlinear interaction between modes with different rational surfaces compared with the single-helicity case. We confirm that theoretical results are in good agreement with direct numerical simulations. (author)

The fourth-order non-linear sigma models and asymptotic freedom in four dimensions

International Nuclear Information System (INIS)

Buchbinder, I.L.; Ketov, S.V.

1991-01-01

Starting with the most general Lagrangian of the fourth-order non-linear sigma model in four space-time dimensions, we calculate the one-loop, on-shell ultra-violet-divergent part of the effective action. The formalism is based on the background field method and the generalised Schwinger-De Witt technique. The multiplicatively renormalisable case is investigated in some detail. The renormalisation group equations are obtained, and the conditions for a realisation of asymptotic freedom are considered. (orig.)

Nonlinear oscillations

CERN Document Server

Nayfeh, Ali Hasan

1995-01-01

Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim

LOO: a low-order nonlinear transport scheme for acceleration of method of characteristics

International Nuclear Information System (INIS)

Li, Lulu; Smith, Kord; Forget, Benoit; Ferrer, Rodolfo

2015-01-01

This paper presents a new physics-based multi-grid nonlinear acceleration method: the low-order operator method, or LOO. LOO uses a coarse space-angle multi-group method of characteristics (MOC) neutron transport calculation to accelerate the fine space-angle MOC calculation. LOO is designed to capture more angular effects than diffusion-based acceleration methods through a transport-based low-order solver. LOO differs from existing transport-based acceleration schemes in that it emphasizes simplified coarse space-angle characteristics and preserves physics in quadrant phase-space. The details of the method, including the restriction step, the low-order iterative solver and the prolongation step are discussed in this work. LOO shows comparable convergence behavior to coarse mesh finite difference on several two-dimensional benchmark problems while not requiring any under-relaxation, making it a robust acceleration scheme. (author)

Validation of a RANS transition model using a high-order weighted compact nonlinear scheme

Science.gov (United States)

Tu, GuoHua; Deng, XiaoGang; Mao, MeiLiang

2013-04-01

A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.

Output-Feedback Nonlinear Adaptive Control Strategy of the Single-Phase Grid-Connected Photovoltaic System

Directory of Open Access Journals (Sweden)

Abdelmajid Abouloifa

2018-01-01

Full Text Available This paper addresses the problem of controlling the single-phase grid connected to the photovoltaic system through a full bridge inverter with LCL-filter. The control aims are threefold: (i imposing the voltage in the output of PV panel to track a reference provided by the MPPT block; (ii regulating the DC-link voltage to guarantee the power exchange between the source and AC grid; (iii ensuring a satisfactory power factor correction (PFC. The problem is dealt with using a cascade nonlinear adaptive controller that is developed making use of sliding-mode technique and observers in order to estimate the state variables and grid parameters, by measuring only the grid current, PV voltage, and the DC bus voltage. The control problem addressed by this work involves several difficulties, including the uncertainty of some parameters of the system and the numerous state variables are inaccessible to measurements. The results are confirmed by simulation under MATLAB∖Simulink∖SimPowerSystems, which show that the proposed regulator is robust with respect to climate changes.

Efficient Model Order Reduction for the Dynamics of Nonlinear Multilayer Sheet Structures with Trial Vector Derivatives

Directory of Open Access Journals (Sweden)

Wolfgang Witteveen

2014-01-01

Full Text Available The mechanical response of multilayer sheet structures, such as leaf springs or car bodies, is largely determined by the nonlinear contact and friction forces between the sheets involved. Conventional computational approaches based on classical reduction techniques or the direct finite element approach have an inefficient balance between computational time and accuracy. In the present contribution, the method of trial vector derivatives is applied and extended in order to obtain a-priori trial vectors for the model reduction which are suitable for determining the nonlinearities in the joints of the reduced system. Findings show that the result quality in terms of displacements and contact forces is comparable to the direct finite element method but the computational effort is extremely low due to the model order reduction. Two numerical studies are presented to underline the method’s accuracy and efficiency. In conclusion, this approach is discussed with respect to the existing body of literature.

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.

Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

Directory of Open Access Journals (Sweden)

Veyis Turut

2013-01-01

Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

Pressure tunable cascaded third order nonlinearity and temporal pulse switching

DEFF Research Database (Denmark)

Eilenberger, Falk; Bache, Morten; Minardi, Stefano

2013-01-01

Effects based on the χ(3)-nonlinearity are arguably the most commonly discussed nonlinear interactions in photonics. In the description of pulse propagation, however, the generation of the third harmonic (TH) is commonly neglected, because it is strongly phase mismatched in most materials...

Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

Directory of Open Access Journals (Sweden)

Omar Abu Arqub

2014-01-01

Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.

Measurements of nonlinear optical properties of PVDF/ZnO using Z-scan technique

Energy Technology Data Exchange (ETDEWEB)

Shanshool, Haider Mohammed, E-mail: haidshan62@gmail.com [Ministry of Science and Technology, Baghdad (Iraq); Yahaya, Muhammad [School of Applied Physics, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Selangor (Malaysia); Yunus, Wan Mahmood Mat [Department of Physics, Faculty of Science, University Putra Malaysia, Serdang (Malaysia); Abdullah, Ibtisam Yahya [Department of Physics, College of Science, University of Mosul, Mosul (Iraq)

2015-10-15

The nonlinear optical properties of ZnO nanoparticles dispersed in poly (vinylidene fluoride) (PVDF) polymer are investigated. PVDF/ZnO nanocomposites were prepared by mixing different concentrations of ZnO nanoparticles, as the filler, with PVDF, as the polymer matrix, using casting method. Acetone was used as a solvent for the polymer. FTIR spectra of the samples were analyzed thus confirming the formation of α and β phases. The absorbance spectra of the samples were obtained, thereby showing high absorption in the UV region. The linear absorption coefficient was calculated. The single-beam Z-scan technique was used to measure the nonlinear refractive index and the nonlinear absorption coefficient of the PVDF/ZnO nanocomposite samples. We observed that the nonlinear refractive index is in the order of 10{sup -13} cm{sup 2}/W with the negative sign, whereas the nonlinear absorption coefficient is in the order of 10{sup -8} cm/W. (author)

A non-linear reduced order methodology applicable to boiling water reactor stability analysis

International Nuclear Information System (INIS)

Prill, Dennis Paul

2013-01-01

Thermal-hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers of boiling water reactor (BWR) stability behavior. High-power low-flow conditions in connection with unfavorable power distributions can lead the BWR system into unstable regions where power oscillations can be triggered. This important threat to operational safety requires careful analysis for proper understanding. Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs), saving computational cost and improving the physical understanding. Presently within reactor dynamics, no general and automatic prediction of high-dimensional ROMs based on detailed BWR models are available. In this thesis a systematic self-contained model order reduction (MOR) technique is derived which is applicable for several classes of dynamical problems, and in particular to BWRs of any degree of details. Expert knowledge can be given by operational, experimental or numerical transient data and is transfered into an optimal basis function representation. The methodology is mostly automated and provides the framework for the reduction of various different systems of any level of complexity. Only little effort is necessary to attain a reduced version within this self-written code which is based on coupling of sophisticated commercial software. The methodology reduces a complex system in a grid-free manner to a small system able to capture even non-linear dynamics. It is based on an optimal choice of basis functions given by the so-called proper orthogonal decomposition (POD). Required steps to achieve reliable and numerical stable ROM are given by a distinct calibration road-map. In validation and verification steps, a wide spectrum of representative test examples is systematically studied regarding a later BWR application. The first example is non-linear and has a dispersive character

Evaluation of polymer based third order nonlinear integrated optics devices

NARCIS (Netherlands)

Driessen, A.; Hoekstra, Hugo; Blom, F.C.; Horst, F.; Horst, F.; Krijnen, Gijsbertus J.M.; van Schoot, J.B.P.; van Schoot, J.B.P.; Lambeck, Paul; Popma, T.J.A.; Diemeer, Mart

Nonlinear polymers are promising materials for high speed active integrated optics devices. In this paper we evaluate the perspectives polymer based nonlinear optical devices can offer. Special attention is directed to the materials aspects. In our experimental work we applied mainly Akzo Nobel DANS

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.

Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

Directory of Open Access Journals (Sweden)

Bin Wang

2016-01-01

Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.

A nanohole in a thin metal film as an efficient nonlinear optical element

International Nuclear Information System (INIS)

Konstantinova, T. V.; Melent’ev, P. N.; Afanas’ev, A. E.; Kuzin, A. A.; Starikov, P. A.; Baturin, A. S.; Tausenev, A. V.; Konyashchenko, A. V.; Balykin, V. I.

2013-01-01

The nonlinear optical properties of single nanoholes and nanoslits fabricated in gold and aluminum nanofilms are studied by third harmonic generation (THG). It is shown that the extremely high third-order optical susceptibility of aluminum and the presence of strong plasmon resonance of a single nanohole in an aluminum film make possible an efficient nanolocalized radiation source at the third harmonic frequency. The THG efficiency for a single nanohole in a thin metal film can be close to unity for an exciting laser radiation intensity on the order of 10 13 W/cm 2

Nonlinear electromagnetic susceptibilities of unmagnetized plasmas

International Nuclear Information System (INIS)

Yoon, Peter H.

2005-01-01

Fully electromagnetic nonlinear susceptibilities of unmagnetized plasmas are analyzed in detail. Concrete expressions of the second-order nonlinear susceptibility are found in various forms in the literature, usually in connection with the discussions of various three-wave decay processes, but the third-order susceptibilities are rarely discussed. The second-order susceptibility is pertinent to nonlinear wave-wave interactions (i.e., the decay/coalescence), whereas the third-order susceptibilities affect nonlinear wave-particle interactions (i.e., the induced scattering). In the present article useful approximate analytical expressions of these nonlinear susceptibilities that can be readily utilized in various situations are derived

Nonlinear Phenomena in the Single-Mode Dynamics in an AFM Cantilever Beam

KAUST Repository

Ruzziconi, Laura

2016-12-05

This study deals with the nonlinear dynamics arising in an atomic force microscope cantilever beam. After analyzing the static behavior, a single degree of freedom Galerkin reduced order model is introduced, which describes the overall scenario of the structure response in a neighborhood of the primary resonance. Extensive numerical simulations are performed when both the forcing amplitude and frequency are varied, ranging from low up to elevated excitations. The coexistence of competing attractors with different characteristics is analyzed. Both the non-resonant and the resonant behavior are observed, as well as ranges of inevitable escape. Versatility of behavior is highlighted, which may be attractive in applications. Special attention is devoted to the effects of the tip-sample separation distance, since this aspect is of fundamental importance to understand the operation of an AFM. We explore the metamorphoses of the multistability region when the tip-sample separation distance is varied. To have a complete description of the AFM response, comprehensive behavior charts are introduced to detect the theoretical boundaries of appearance and disappearance of the main attractors. Also, extensive numerical simulations investigate the AFM response when both the forcing amplitude and the tip-sample separation distance are considered as control parameters. The main features are analyzed in detail and the obtained results are interpreted in terms of oscillations of the cantilever-tip ensemble. However, we note that all the aforementioned results represent the limit when disturbances are absent, which never occurs in practice. Here comes the importance of overcoming local investigations and exploring dynamics from a global perspective, by introducing dynamical integrity concepts. To extend the AFM results to the practical case where disturbances exist, we develop a dynamical integrity analysis. After performing a systematic basin of attraction analysis, integrity

A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations

International Nuclear Information System (INIS)

Ge, Gen; Li, ZePeng

2016-01-01

A modified stochastic averaging method on single-degree-of-freedom (SDOF) oscillators under white noise excitations with strongly nonlinearity was proposed. Considering the existing approach dealing with strongly nonlinear SDOFs derived by Zhu and Huang [14, 15] is quite time consuming in calculating the drift coefficient and diffusion coefficients and the expressions of them are considerable long, the so-called He's energy balance method was applied to overcome the minor defect of the Zhu and Huang's method. The modified method can offer more concise approximate expressions of the drift and diffusion coefficients without weakening the accuracy of predicting the responses of the systems too much by giving an averaged frequency beforehand. Three examples, a cubic and quadratic nonlinearity coexisting oscillator, a quadratic nonlinear oscillator under external white noise excitations and an externally excited Duffing–Rayleigh oscillator, were given to illustrate the approach we proposed. The three examples were excited by the Gaussian white noise and the Gaussian colored noise separately. The stationary responses of probability density of amplitudes and energy, together with joint probability density of displacement and velocity are studied to verify the presented approach. The reliability of the systems were also investigated to offer further support. Digital simulations were carried out and the output of that are coincide with the theoretical approximations well.

On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

Directory of Open Access Journals (Sweden)

Youliang Fu

2016-01-01

Full Text Available This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.

ℋ∞ Adaptive observer for nonlinear fractional-order systems

KAUST Repository

Ndoye, Ibrahima

2016-06-23

In this paper, an adaptive observer is proposed for the joint estimation of states and parameters of a fractional nonlinear system with external perturbations. The convergence of the proposed observer is derived in terms of linear matrix inequalities (LMIs) by using an indirect Lyapunov method.The proposed ℋ∞ adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü\\'s systems. © 2016 John Wiley & Sons, Ltd.

Variation of nonlinearity parameter at low fundamental amplitudes

Science.gov (United States)

Barnard, Daniel J.

1999-04-01

Recent harmonic generation measurements of the nonlinearity parameter β in polycrystalline Cu-Al alloys have shown a transition to lower values at low fundamental amplitude levels. Values for β at high (>10 Å) fundamental levels are in the range predicted by single-crystal second- and third-order elastic constants while lower fundamental levels (alloy by others. The source of the effect is unclear but initial results may require a reexamination of current methods for measurement of third-order elastic constants.

Crystal growth and characterization of a semiorganic nonlinear optical single crystal of gamma glycine

International Nuclear Information System (INIS)

Prakash, J. Thomas Joseph; Kumararaman, S.

2008-01-01

Gamma glycine has been successfully synthesized by taking glycine and potassium chloride and single crystals have been grown by solvent evaporation method for the first time. The grown single crystals have been analyzed with XRD, Fourier transform infrared (FTIR), and thermo gravimetric and differential thermal analyses (TG/DTA) measurements. Its mechanical behavior has been assessed by Vickers microhardness measurements. Its nonlinear optical property has been tested by Kurtz powder technique. Its optical behavior was examined by UV-vis., and found that the crystal is transparent in the region between 240 and 1200 nm. Hence, it may be very much useful for the second harmonic generation (SHG) applications

Nonlinear generalization of the Kallen-Welton formula

International Nuclear Information System (INIS)

Kargin, A.Yu.

1982-01-01

Nonlinear dissipative-fluctuation relations permitting to find spectral correlation functions of (n+1) order for fluctuations of different electrodynamic values in plasma using the given value of tensor of nonlinear response of n order have been obtained for equilibrium plasma. At n=1 the relations obtained transform to the Kallen-Welton dissipative-fluctuation relation. Transformation of the nonlinear dissipative-fluctuation relation for cubical nonlinearity permitting to find nonlinear electric plasma susceptibility from the Known spectral correlation function of fourth order for charge density fluctUations in the absence of particle interaction is considered as an example. A compact expression for tensor of nonlinear plasma response has been obtained for an arbitrary order of nonlinearity

Signatures of nonlinearity in single cell noise-induced oscillations.

Science.gov (United States)

Thomas, Philipp; Straube, Arthur V; Timmer, Jens; Fleck, Christian; Grima, Ramon

2013-10-21

A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power spectrum which measures the dependence of the oscillatory signal's power with frequency. In this paper we derive an approximate closed-form expression for the power spectrum of any monostable biochemical system close to a Hopf bifurcation, where noise-induced oscillations are most pronounced. Unlike the commonly used linear noise approximation which is valid in the macroscopic limit of large volumes, our theory is valid over a wide range of volumes and hence affords a more suitable description of single cell noise-induced oscillations. Our theory predicts that the spectra have three universal features: (i) a dominant peak at some frequency, (ii) a smaller peak at twice the frequency of the dominant peak and (iii) a peak at zero frequency. Of these, the linear noise approximation predicts only the first feature while the remaining two stem from the combination of intrinsic noise and nonlinearity in the law of mass action. The theoretical expressions are shown to accurately match the power spectra determined from stochastic simulations of mitotic and circadian oscillators. Furthermore it is shown how recently acquired single cell rhythmic fibroblast data displays all the features predicted by our theory and that the experimental spectrum is well described by our theory but not by the conventional linear noise approximation. © 2013 Elsevier Ltd. All rights reserved.

Cheap arbitrary high order methods for single integrand SDEs

DEFF Research Database (Denmark)

Debrabant, Kristian; Kværnø, Anne

2017-01-01

For a particular class of Stratonovich SDE problems, here denoted as single integrand SDEs, we prove that by applying a deterministic Runge-Kutta method of order $p_d$ we obtain methods converging in the mean-square and weak sense with order $\\lfloor p_d/2\\rfloor$. The reason is that the B-series...

A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations

Science.gov (United States)

Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi

2016-07-01

We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8], but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free

Unidirectional reflection and invisibility in nonlinear media with an incoherent nonlinearity

Science.gov (United States)

Mostafazadeh, Ali; Oflaz, Neslihan

2017-11-01

We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.

Grey-box state-space identification of nonlinear mechanical vibrations

Science.gov (United States)

Noël, J. P.; Schoukens, J.

2018-05-01

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.

A nonlinear plasmonic resonator for three-state all-optical switching

KAUST Repository

Amin, Muhammad

2014-01-01

A nonlinear plasmonic resonator design is proposed for three-state all-optical switching at frequencies including near infrared and lower red parts of the spectrum. The tri-stable response required for three-state operation is obtained by enhancing nonlinearities of a Kerr medium through multiple (higher order) plasmons excited on resonator\\'s metallic surfaces. Indeed, simulations demonstrate that exploitation of multiple plasmons equips the proposed resonator with a multi-band tri-stable response, which cannot be obtained using existing nonlinear plasmonic devices that make use of single mode Lorentzian resonances. Multi-band three-state optical switching that can be realized using the proposed resonator has potential applications in optical communications and computing. © 2014 Optical Society of America.

A nonlinear plasmonic resonator for three-state all-optical switching

KAUST Repository

Amin, Muhammad; Farhat, Mohamed; Bagci, Hakan

2014-01-01

A nonlinear plasmonic resonator design is proposed for three-state all-optical switching at frequencies including near infrared and lower red parts of the spectrum. The tri-stable response required for three-state operation is obtained by enhancing nonlinearities of a Kerr medium through multiple (higher order) plasmons excited on resonator's metallic surfaces. Indeed, simulations demonstrate that exploitation of multiple plasmons equips the proposed resonator with a multi-band tri-stable response, which cannot be obtained using existing nonlinear plasmonic devices that make use of single mode Lorentzian resonances. Multi-band three-state optical switching that can be realized using the proposed resonator has potential applications in optical communications and computing. © 2014 Optical Society of America.

Nonlinear optics

CERN Document Server

Bloembergen, Nicolaas

1996-01-01

Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe

Magnetic order of Nd5Pb3 single crystals

Science.gov (United States)

Yan, J.-Q.; Ochi, M.; Cao, H. B.; Saparov, B.; Cheng, J.-G.; Uwatoko, Y.; Arita, R.; Sales, B. C.; Mandrus, D. G.

2018-04-01

We report millimeter-sized Nd5Pb3 single crystals grown out of a Nd-Co flux. We experimentally study the magnetic order of Nd5Pb3 single crystals by measuring the anisotropic magnetic properties, electrical resistivity under high pressure up to 8 GPa, specific heat, and neutron single crystal diffraction. Two successive magnetic orders are observed at T N1  =  44 K and T N2  =  8 K. The magnetic cells can be described with a propagation vector k=(0.5, 0, 0) . Cooling below T N1, Nd1 and Nd3 order forming ferromagnetic stripes along the b-axis, and the ferromagnetic stripes are coupled antiferromagnetically along the a-axis for the k=(0.5, 0, 0) magnetic domain. Cooling below T N2, Nd2 orders antiferromagnetically to nearby Nd3 ions. All ordered moments align along the crystallographic c-axis. The magnetic order at T N1 is accompanied by a quick drop of electrical resistivity upon cooling and a lambda-type anomaly in the temperature dependence of specific heat. At T N2, no anomaly was observed in electrical resistivity but there is a weak feature in specific heat. The resistivity measurements under hydrostatic pressures up to 8 GPa suggest a possible phase transition around 6 GPa. Our first-principles band structure calculations show that Nd5Pb3 has the same electronic structure as does Y5Si3 which has been reported to be a one-dimensional electride with anionic electrons that do not belong to any atom. Our study suggests that R 5Pb3 (R  =  rare earth) can be a materials playground for the study of magnetic electrides. This deserves further study after experimental confirmation of the presence of anionic electrons.

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

Science.gov (United States)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

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...

Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics.

Science.gov (United States)

Si, Wenjie; Dong, Xunde; Yang, Feifei

2018-03-01

This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.

Distributed Consensus Tracking for Second-Order Nonlinear Multiagent Systems with a Specified Reference State

Directory of Open Access Journals (Sweden)

Guoguang Wen

2014-01-01

Full Text Available This paper mainly addresses the distributed consensus tracking problem for second-order nonlinear multiagent systems with a specified reference trajectory. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position and velocity information of its neighbors. The consensus reference is taken as a virtual leader, whose output is only its position and velocity information that is available to only a subset of a group of followers. To achieve consensus tracking, a class of nonsmooth control protocols is proposed which reply on the relative information among the neighboring agents. Then some corresponding sufficient conditions are derived. It is shown that if the communication graph associated with the virtual leader and followers is connected at each time instant, the consensus can be achieved at least globally exponentially with the proposed protocol. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Finally, numerical examples are presented to illustrate the theoretical analysis.

Ordered array of CoPc-vacancies filled with single-molecule rotors

Science.gov (United States)

Xie, Zheng-Bo; Wang, Ya-Li; Tao, Min-Long; Sun, Kai; Tu, Yu-Bing; Yuan, Hong-Kuan; Wang, Jun-Zhong

2018-05-01

We report the highly ordered array of CoPc-vacancies and the single-molecule rotors inside the vacancies. When CoPc molecules are deposited on Cd(0001) at low-temperature, three types of molecular vacancies appeared randomly in the CoPc monolayer. Annealing the sample to higher temperature leads to the spontaneous phase separation and self-organized arrangement of the vacancies. Highly ordered arrays of two-molecule vacancies and single-molecule vacancies have been obtained. In particular, there is a rotating CoPc molecule inside each single-molecule vacancy, which constitutes the array of single-molecule rotors. These results provide a new routine to fabricate the nano-machines on a large scale.

A nanohole in a thin metal film as an efficient nonlinear optical element

Energy Technology Data Exchange (ETDEWEB)

Konstantinova, T. V.; Melent' ev, P. N.; Afanas' ev, A. E. [Russian Academy of Sciences, Institute of Spectroscopy (Russian Federation); Kuzin, A. A.; Starikov, P. A.; Baturin, A. S. [Moscow Institute of Physics and Technology (Russian Federation); Tausenev, A. V.; Konyashchenko, A. V. [OOO Avesta-proekt (Russian Federation); Balykin, V. I., E-mail: balykin@isan.tyroitsk.ru [Russian Academy of Sciences, Institute of Spectroscopy (Russian Federation)

2013-07-15

The nonlinear optical properties of single nanoholes and nanoslits fabricated in gold and aluminum nanofilms are studied by third harmonic generation (THG). It is shown that the extremely high third-order optical susceptibility of aluminum and the presence of strong plasmon resonance of a single nanohole in an aluminum film make possible an efficient nanolocalized radiation source at the third harmonic frequency. The THG efficiency for a single nanohole in a thin metal film can be close to unity for an exciting laser radiation intensity on the order of 10{sup 13} W/cm{sup 2}.

DISPL-1, 2. Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems

International Nuclear Information System (INIS)

Leaf, G.K.; Minkoff, M.

1982-01-01

1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code

Nonlinear optical properties of an electromagnetically induced transparency medium interacting with two quantized fields

CERN Document Server

Kuang-Leman; Wu Yong Shi

2003-01-01

We study linear and nonlinear optical properties of an electromagnetically induced transparency (EIT) medium interacting with two quantized laser fields in the adiabatic EIT case. We show that the EIT medium exhibits normal dispersion. Kerr and higher-order nonlinear refractive index coefficients are also calculated in a completely analytical form. It is indicated that the EIT medium exhibits giant resonantly enhanced nonlinearities. We discuss the response of the EIT medium to nonclassical light fields and find that the polarization vanishes when the probe laser is initially in a nonclassical state of no single-photon coherence.

Analytical study of nonlinear phase shift through stimulated Brillouin scattering in single mode fiber with the pump power recycling technique

International Nuclear Information System (INIS)

Al-Asadi, H A; Mahdi, M A; Bakar, A A A; Adikan, F R Mahamd

2011-01-01

We present a theoretical study of nonlinear phase shift through stimulated Brillouin scattering in single mode optical fiber. Analytical expressions describing the nonlinear phase shift for the pump and Stokes waves in the pump power recycling technique have been derived. The dependence of the nonlinear phase shift on the optical fiber length, the reflectivity of the optical mirror and the frequency detuning coefficient have been analyzed for different input pump power values. We found that with the recycling pump technique, the nonlinear phase shift due to stimulated Brillouin scattering reduced to less than 0.1 rad for 5 km optical fiber length and 0.65 reflectivity of the optical mirror, respectively, at an input pump power equal to 30 mW

Adaptive nonlinear control of single-phase to three-phase UPS system

Directory of Open Access Journals (Sweden)

Kissaoui M.

2014-01-01

Full Text Available This work deals with the problems of uninterruptible power supplies (UPS based on the single-phase to three-phase converters built in two stages: an input bridge rectifier and an output three phase inverter. The two blocks are joined by a continuous intermediate bus. The objective of control is threefold: i power factor correction “PFC”, ii generating a symmetrical three-phase system at the output even if the load is unknown, iii regulating the DC bus voltage. The synthesis of controllers has been reached by two nonlinear techniques that are the sliding mode and adaptive backstepping control. The performances of regulators have been validated by numerical simulation in MATLAB / SIMULINK.

Interaction-induced effects in the nonlinear coherent response of quantum-well excitons

DEFF Research Database (Denmark)

Wagner, Hans Peter; Schätz, A.; Langbein, Wolfgang Werner

1999-01-01

Interaction-induced processes are studied using the third-order nonlinear polarization created in polarization-dependent four-wave-mixing experiments (FWM) on a ZnSe single quantum well. We discuss their influence by a comparison of the experimental FWM with calculations based on extended optical...

Approximate Forward Difference Equations for the Lower Order Non-Stationary Statistics of Geometrically Non-Linear Systems subject to Random Excitation

DEFF Research Database (Denmark)

Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.

Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....

Single-order-parameter description of glass-forming liquids

DEFF Research Database (Denmark)

Ellegaard, Niels Langager; Christensen, Tage Emil; Christiansen, Peder Voetmann

2007-01-01

Thermoviscoelastic linear-response functions are calculated from the master equation describing viscous liquid inherent dynamics. From the imaginary parts of the frequency-dependent isobaric specific heat, isothermal compressibility, and isobaric thermal expansion coefficient, we define a "linear...... dynamic Prigogine-Defay ratio" with the property that if this ratio is unity at one frequency, then it is unity at all frequencies. This happens if and only if there is a single-order-parameter description of the thermoviscoelastic linear responses via an order parameter which may be nonexponential...

The Active Fractional Order Control for Maglev Suspension System

Directory of Open Access Journals (Sweden)

Peichang Yu

2015-01-01

Full Text Available Maglev suspension system is the core part of maglev train. In the practical application, the load uncertainties, inherent nonlinearity, and misalignment between sensors and actuators are the main issues that should be solved carefully. In order to design a suitable controller, the attention is paid to the fractional order controller. Firstly, the mathematical model of a single electromagnetic suspension unit is derived. Then, considering the limitation of the traditional PD controller adaptation, the fractional order controller is developed to obtain more excellent suspension specifications and robust performance. In reality, the nonlinearity affects the structure and the precision of the model after linearization, which will degrade the dynamic performance. So, a fractional order controller is addressed to eliminate the disturbance by adjusting the parameters which are added by the fractional order controller. Furthermore, the controller based on LQR is employed to compare with the fractional order controller. Finally, the performance of them is discussed by simulation. The results illustrated the validity of the fractional order controller.

A third-order asymptotic solution of nonlinear standing water waves in Lagrangian coordinates

International Nuclear Information System (INIS)

Yang-Yih, Chen; Hung-Chu, Hsu

2009-01-01

Asymptotic solutions up to third-order which describe irrotational finite amplitude standing waves are derived in Lagrangian coordinates. The analytical Lagrangian solution that is uniformly valid for large times satisfies the irrotational condition and the pressure p = 0 at the free surface, which is in contrast with the Eulerian solution existing under a residual pressure at the free surface due to Taylor's series expansion. In the third-order Lagrangian approximation, the explicit parametric equation and the Lagrangian wave frequency of water particles could be obtained. In particular, the Lagrangian mean level of a particle motion that is a function of vertical label is found as a part of the solution which is different from that in an Eulerian description. The dynamic properties of nonlinear standing waves in water of a finite depth, including particle trajectory, surface profile and wave pressure are investigated. It is also shown that the Lagrangian solution is superior to an Eulerian solution of the same order for describing the wave shape and the kinematics above the mean water level. (general)

Global format for energy-momentum based time integration in nonlinear dynamics

DEFF Research Database (Denmark)

Krenk, Steen

2014-01-01

A global format is developed for momentum and energy consistent time integration of second‐order dynamic systems with general nonlinear stiffness. The algorithm is formulated by integrating the state‐space equations of motion over the time increment. The internal force is first represented...... of mean value products at the element level or explicit use of a geometric stiffness matrix. An optional monotonic algorithmic damping, increasing with response frequency, is developed in terms of a single damping parameter. In the solution procedure, the velocity is eliminated and the nonlinear...

A HIGH ORDER SOLUTION OF THREE DIMENSIONAL TIME DEPENDENT NONLINEAR CONVECTIVE-DIFFUSIVE PROBLEM USING MODIFIED VARIATIONAL ITERATION METHOD

Directory of Open Access Journals (Sweden)

Pratibha Joshi

2014-12-01

Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.

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

Directory of Open Access Journals (Sweden)

Christer Dalen

2017-10-01

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

Nonlinear optical measurements of conducting copolymers of aniline under CW laser excitation

Science.gov (United States)

Pramodini, S.; Poornesh, P.

2015-08-01

Synthesis and measurements of third-order optical nonlinearity and optical limiting of conducting copolymers of aniline are presented. Single beam z-scan technique was employed for the nonlinear optical studies. Continuous wave He-Ne laser operating at 633 nm was used as the source of excitation. Copolymer samples exhibited reverse saturable absorption (RSA) process. The nonlinear refraction studies depict that the copolymers exhibit self-defocusing property. The estimated values of βeff, n2 and χ(3) were found to be of the order of 10-2 cm/W, 10-5 esu and 10-7 esu respectively. Self-diffraction rings were observed due to refractive index change when exposed to the laser beam. A good optical limiting and clamping of power of ∼0.9 mW and ∼0.05 mW was observed. Therefore, copolymers of aniline emerge as a potential candidate for photonic device applications.

Light-induced second-order nonlinear optical properties of molecular materials

International Nuclear Information System (INIS)

Fiorini, Celine

1995-01-01

We present a theoretical and experimental study of all-optical orientation. The work focusses more particularly on the realization of poled polymers for quadratic nonlinear optics. It is shown that the coherent superposition of two beams at fundamental and second harmonic frequencies results in the breaking of the former centro-symmetry of the material. The source is a Neodymium-YAG laser delivering 25 ps pulses at 1064 nm. The incident second-harmonic beam is obtained by frequency doubling in a KDP crystal. Using a phase conjugation configuration based on six-wave mixing interactions, we have Investigated in detail the mechanism of photo-induced second-harmonic generation in initially centrosymmetric materials. It is shown that the light-induced non-centro-symmetry is due to an orientational hole burning of the molecules. The process involves interference effects between one and two photon absorptions. Experiments are performed in various solutions of an azo-dye molecule (Disperse Red One). The possibility of inducing quasi-permanent second-order susceptibility in a PMMA polymer matrix doped with the azo-dye molecule of Disperse Red One is also demonstrated. The method of all-optical poling consists in a seeding type process with alternate writing and probing phases. Permanent orientation of the molecules can be described in terms of photo-isomerization processes. It leads to a poling of the molecules with a spatial modulation which is phase-matched for frequency doubling. Relevant parameters leading to an efficient polarisation of the sample are identified. A theoretical modelling of the different phenomena observed is proposed. Last part of the study is devoted to an enlarged study of the potentialities offered by this dual-frequency holography technique: orientation of octupolar molecules, polarisation of highly transparent materials. We also show that the new techniques developed during this work can also reveal to be complementary methods for nonlinear

Application of power series to the solution of the boundary value problem for a second order nonlinear differential equation

International Nuclear Information System (INIS)

Semenova, V.N.

2016-01-01

A boundary value problem for a nonlinear second order differential equation has been considered. A numerical method has been proposed to solve this problem using power series. Results of numerical experiments have been presented in the paper [ru

Fourth-order perturbative extension of the single-double excitation coupled-cluster method

International Nuclear Information System (INIS)

Derevianko, Andrei; Emmons, Erik D.

2002-01-01

Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wave function. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulas are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e., contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed

Vectorial control of nonlinear emission via chiral butterfly nanoantennas: generation of pure high order nonlinear vortex beams.

Science.gov (United States)

Lesina, Antonino Cala'; Berini, Pierre; Ramunno, Lora

2017-02-06

We report on a chiral gap-nanostructure, which we term a "butterfly nanoantenna," that offers full vectorial control over nonlinear emission. The field enhancement in its gap occurs for only one circular polarization but for every incident linear polarization. As the polarization, phase and amplitude of the linear field in the gap are highly controlled, the linear field can drive nonlinear emitters within the gap, which behave as an idealized Huygens source. A general framework is thereby proposed wherein the butterfly nanoantennas can be arranged in a metasurface, and the nonlinear Huygens sources exploited to produce a highly structured far-field optical beam. Nonlinearity allows us to shape the light at shorter wavelengths, not accessible by linear plasmonics, and resulting in high purity beams. The chirality of the butterfly allows us to create orbital angular momentum states using a linearly polarized excitation. A third harmonic Laguerre-Gauss beam carrying an optical orbital angular momentum of 41 is demonstrated as an example, through large-scale simulations on a high-performance computing platform of the full plasmonic metasurface with an area large enough to contain up to 3600 nanoantennas.

Linear and ultrafast nonlinear plasmonics of single nano-objects

Science.gov (United States)

Crut, Aurélien; Maioli, Paolo; Vallée, Fabrice; Del Fatti, Natalia

2017-03-01

Single-particle optical investigations have greatly improved our understanding of the fundamental properties of nano-objects, avoiding the spurious inhomogeneous effects that affect ensemble experiments. Correlation with high-resolution imaging techniques providing morphological information (e.g. electron microscopy) allows a quantitative interpretation of the optical measurements by means of analytical models and numerical simulations. In this topical review, we first briefly recall the principles underlying some of the most commonly used single-particle optical techniques: near-field, dark-field, spatial modulation and photothermal microscopies/spectroscopies. We then focus on the quantitative investigation of the surface plasmon resonance (SPR) of metallic nano-objects using linear and ultrafast optical techniques. While measured SPR positions and spectral areas are found in good agreement with predictions based on Maxwell’s equations, SPR widths are strongly influenced by quantum confinement (or, from a classical standpoint, surface-induced electron scattering) and, for small nano-objects, cannot be reproduced using the dielectric functions of bulk materials. Linear measurements on single nano-objects (silver nanospheres and gold nanorods) allow a quantification of the size and geometry dependences of these effects in confined metals. Addressing the ultrafast response of an individual nano-object is also a powerful tool to elucidate the physical mechanisms at the origin of their optical nonlinearities, and their electronic, vibrational and thermal relaxation processes. Experimental investigations of the dynamical response of gold nanorods are shown to be quantitatively modeled in terms of modifications of the metal dielectric function enhanced by plasmonic effects. Ultrafast spectroscopy can also be exploited to unveil hidden physical properties of more complex nanosystems. In this context, two-color femtosecond pump-probe experiments performed on individual

Multi-photon absorption limits to heralded single photon sources

Science.gov (United States)

Husko, Chad A.; Clark, Alex S.; Collins, Matthew J.; De Rossi, Alfredo; Combrié, Sylvain; Lehoucq, Gaëlle; Rey, Isabella H.; Krauss, Thomas F.; Xiong, Chunle; Eggleton, Benjamin J.

2013-01-01

Single photons are of paramount importance to future quantum technologies, including quantum communication and computation. Nonlinear photonic devices using parametric processes offer a straightforward route to generating photons, however additional nonlinear processes may come into play and interfere with these sources. Here we analyse spontaneous four-wave mixing (SFWM) sources in the presence of multi-photon processes. We conduct experiments in silicon and gallium indium phosphide photonic crystal waveguides which display inherently different nonlinear absorption processes, namely two-photon (TPA) and three-photon absorption (ThPA), respectively. We develop a novel model capturing these diverse effects which is in excellent quantitative agreement with measurements of brightness, coincidence-to-accidental ratio (CAR) and second-order correlation function g(2)(0), showing that TPA imposes an intrinsic limit on heralded single photon sources. We build on these observations to devise a new metric, the quantum utility (QMU), enabling further optimisation of single photon sources. PMID:24186400

A single-vendor and a single-buyer integrated inventory model with ordering cost reduction dependent on lead time

Science.gov (United States)

Vijayashree, M.; Uthayakumar, R.

2017-09-01

Lead time is one of the major limits that affect planning at every stage of the supply chain system. In this paper, we study a continuous review inventory model. This paper investigates the ordering cost reductions are dependent on lead time. This study addressed two-echelon supply chain problem consisting of a single vendor and a single buyer. The main contribution of this study is that the integrated total cost of the single vendor and the single buyer integrated system is analyzed by adopting two different (linear and logarithmic) types ordering cost reductions act dependent on lead time. In both cases, we develop effective solution procedures for finding the optimal solution and then illustrative numerical examples are given to illustrate the results. The solution procedure is to determine the optimal solutions of order quantity, ordering cost, lead time and the number of deliveries from the single vendor and the single buyer in one production run, so that the integrated total cost incurred has the minimum value. Ordering cost reduction is the main aspect of the proposed model. A numerical example is given to validate the model. Numerical example solved by using Matlab software. The mathematical model is solved analytically by minimizing the integrated total cost. Furthermore, the sensitivity analysis is included and the numerical examples are given to illustrate the results. The results obtained in this paper are illustrated with the help of numerical examples. The sensitivity of the proposed model has been checked with respect to the various major parameters of the system. Results reveal that the proposed integrated inventory model is more applicable for the supply chain manufacturing system. For each case, an algorithm procedure of finding the optimal solution is developed. Finally, the graphical representation is presented to illustrate the proposed model and also include the computer flowchart in each model.

Nonlinear Dynamic Model of Power Plants with Single-Phase Coolant Reactors

International Nuclear Information System (INIS)

Vollmer, H.

1968-12-01

The traditional way of developing dynamic models for a specific nuclear power plant and for specific purpose seems rather uneconomical, as much of the information often can not be utilized if the plant design or the required accuracy of the calculation is desired to be changed. It is therefore suggested that the model development may be made more systematic, general and flexible by - applying the 'box of bricks' system, where the main components of a nuclear power plant are treated separately and combined afterwards according to a given flow scheme, - a dynamic determination of the components which is as general as possible without taking into account those details which have a minor influence on the overall dynamics, - providing approximations of the more rigorous solution sufficient to meet the user s requirements on accuracy, - proper use of computers. A dynamic model for single-phase coolant reactor plants is established along these lines. By separation of the nonlinear and linear parts of the system, application of Laplace transformation and proper approximations, and the use of a hybrid computer it seems possible to determine the (nonlinear) dynamic behaviour of such a plant for perturbations which are not so large that phase changes of physical parameters occur, e. g. fuel does not melt. The model is applied to a steam cooled fast reactor power plant

Nonlinear Dynamic Model of Power Plants with Single-Phase Coolant Reactors

Energy Technology Data Exchange (ETDEWEB)

Vollmer, H

1968-12-15

The traditional way of developing dynamic models for a specific nuclear power plant and for specific purpose seems rather uneconomical, as much of the information often can not be utilized if the plant design or the required accuracy of the calculation is desired to be changed. It is therefore suggested that the model development may be made more systematic, general and flexible by - applying the 'box of bricks' system, where the main components of a nuclear power plant are treated separately and combined afterwards according to a given flow scheme, - a dynamic determination of the components which is as general as possible without taking into account those details which have a minor influence on the overall dynamics, - providing approximations of the more rigorous solution sufficient to meet the user s requirements on accuracy, - proper use of computers. A dynamic model for single-phase coolant reactor plants is established along these lines. By separation of the nonlinear and linear parts of the system, application of Laplace transformation and proper approximations, and the use of a hybrid computer it seems possible to determine the (nonlinear) dynamic behaviour of such a plant for perturbations which are not so large that phase changes of physical parameters occur, e. g. fuel does not melt. The model is applied to a steam cooled fast reactor power plant.

Stability of a nonlinear second order equation under parametric bounded noise excitation

International Nuclear Information System (INIS)

Wiebe, Richard; Xie, Wei-Chau

2016-01-01

The motivation for the following work is a structural column under dynamic axial loads with both deterministic (harmonic transmitted forces from the surrounding structure) and random (wind and/or earthquake) loading components. The bounded noise used herein is a sinusoid with an argument composed of a random (Wiener) process deviation about a mean frequency. By this approach, a noise parameter may be used to investigate the behavior through the spectrum from simple harmonic forcing, to a bounded random process with very little harmonic content. The stability of both the trivial and non-trivial stationary solutions of an axially-loaded column (which is modeled as a second order nonlinear equation) under parametric bounded noise excitation is investigated by use of Lyapunov exponents. Specifically the effect of noise magnitude, amplitude of the forcing, and damping on stability of a column is investigated. First order averaging is employed to obtain analytical approximations of the Lyapunov exponents of the trivial solution. For the non-trivial stationary solution however, the Lyapunov exponents are obtained via Monte Carlo simulation as the stability equations become analytically intractable. (paper)

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

Science.gov (United States)

Owolabi, Kolade M.

2017-03-01

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

Growth, spectral, linear and nonlinear optical characteristics of an efficient semiorganic acentric crystal: L-valinium L-valine chloride

Energy Technology Data Exchange (ETDEWEB)

Nageshwari, M.; Jayaprakash, P.; Kumari, C. Rathika Thaya [PG & Research Department of Physics, Arignar Anna Govt. Arts College, Cheyyar 604407, Tamil Nadu (India); Vinitha, G. [Department of Physics, School of Advanced Sciences, VIT Chennai, 600127 Tamil Nadu (India); Caroline, M. Lydia, E-mail: lydiacaroline2006@yahoo.co.in [PG & Research Department of Physics, Arignar Anna Govt. Arts College, Cheyyar 604407, Tamil Nadu (India)

2017-04-15

An efficient nonlinear optical semiorganic material L-valinium L-valine chloride (LVVCl) was synthesized and grown-up by means of slow evaporation process. Single crystal XRD evince that LVVCl corresponds to monoclinic system having acentric space group P2{sub 1}. The diverse functional groups existing in LVVCl were discovered with FTIR spectral investigation. The UV-Visible and photoluminescence spectrum discloses the optical and electronic properties respectively for the grown crystal. Several optical properties specifically extinction coefficient, reflectance, linear refractive index, electrical and optical conductivity were also determined. The SEM analysis was also carried out and it portrayed the surface morphology of LVVCl. The calculated value of laser damage threshold was 2.59 GW/cm{sup 2}. The mechanical and dielectric property of LVVCl was investigated employing microhardness and dielectric studies. The second and third order nonlinear optical characteristics of LVVCl was characterized utilizing Kurtz Perry and Z scan technique respectively clearly suggest its suitability in the domain of optics and photonics. - Graphical abstract: Good quality transparent single crystals of L-valinium L-valine chloride single crystal was grown by slow evaporation technique. The grown crystals were analyzed using different instrumentation methods to check its usefulness for the device fabrication. The determination of nonlinear refractive index (n{sub 2}), absorption coefficient (β) and third order nonlinear susceptibility was determined by Z scan technique, highlighted that LVVCl can serve as a promising candidate for opto electronic and nonlinear optical applications.

Linking structure and activity in nonlinear spiking networks.

Directory of Open Access Journals (Sweden)

Gabriel Koch Ocker

2017-06-01

Full Text Available Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities-including those of different cell types-combine with connectivity to shape population activity and function.

Linking structure and activity in nonlinear spiking networks.

Science.gov (United States)

Ocker, Gabriel Koch; Josić, Krešimir; Shea-Brown, Eric; Buice, Michael A

2017-06-01

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities-including those of different cell types-combine with connectivity to shape population activity and function.

Uniqueness of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations

International Nuclear Information System (INIS)

Tran Duc Van

1994-01-01

The notion of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations is presented, some uniqueness theorems and a stability result are established by the method based on the theory of differential inclusions. In particular, the answer to an open problem of S.N. Kruzhkov is given. (author). 10 refs, 1 fig

Preparation and third-order nonlinear optical property of poly(urethane-imide containing dispersed red chromophore

Directory of Open Access Journals (Sweden)

2008-11-01

Full Text Available A novel poly(urethane-imide (PUI containing dispersed red chromophore was synthesized. The PUI was characterized by FT-IR, UV-Vis, DSC and TGA. The results of DSC and TGA indicated that the PUI exhibited high thermal stability up to its glass-transition temperature (Tg of 196°C and 5% heat weight loss temperature of 229°C. According to UV-Vis spectrum and working curve, the maximum molar absorption coefficient and absorption wavelength were measured. They were used to calculate the third-order nonlinear optical coefficient χ(3. At the same time, the chromophore density of PUI, nonlinear refractive index coefficient and molecular hyperpolarizability of PUI were obtained. The fluorescence spectra of PUI and model compound DR-19 were determined at excitation wavelength 300 nm. The electron donor and acceptor in polymer formed the exciplex through the transfer of the electric charges. The results show that the poly(urethane-imide is a promising candidate for application in optical devices.

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

Order and chaos in polarized nonlinear optics

International Nuclear Information System (INIS)

Holm, D.D.

1990-01-01

Methods for investigating temporal complexity in Hamiltonian systems are applied to the dynamics of a polarized optical laser beam propagating as a travelling wave in a medium with cubically nonlinear polarizability (i.e., a Kerr medium). The theory of Hamiltonian systems with symmetry is used to study the geometry of phase space for the optical problem, transforming from C 2 to S 2 x (J,θ), where (J,θ) is a symplectic action-angle pair. The bifurcations of the phase portraits of the Hamiltonian motion on S 2 are classified and shown graphically. These bifurcations create various saddle connections on S 2 as either J (the beam intensity), or the optical parameters of the medium are varied. After this bifurcation analysis, the Melnikov method is used to demonstrate analytically that the saddle connections break and intersect transversely in a Poincare map under spatially periodic perturbations of the optical parameters of the medium. These transverse intersections in the Poincare map imply intermittent polarization switching with extreme sensitivity to initial conditions characterized by a Smale horseshoe construction for the travelling waves of a polarized optical laser pulse. The resulting chaotic behavior in the form of sensitive dependence on initial conditions may have implications for the control and predictability of nonlinear optical polarization switching in birefringent media. 19 refs., 2 figs., 1 tab

Persistent Charge-Density-Wave Order in Single-Layer TaSe2.

Science.gov (United States)

Ryu, Hyejin; Chen, Yi; Kim, Heejung; Tsai, Hsin-Zon; Tang, Shujie; Jiang, Juan; Liou, Franklin; Kahn, Salman; Jia, Caihong; Omrani, Arash A; Shim, Ji Hoon; Hussain, Zahid; Shen, Zhi-Xun; Kim, Kyoo; Min, Byung Il; Hwang, Choongyu; Crommie, Michael F; Mo, Sung-Kwan

2018-02-14

We present the electronic characterization of single-layer 1H-TaSe 2 grown by molecular beam epitaxy using a combined angle-resolved photoemission spectroscopy, scanning tunneling microscopy/spectroscopy, and density functional theory calculations. We demonstrate that 3 × 3 charge-density-wave (CDW) order persists despite distinct changes in the low energy electronic structure highlighted by the reduction in the number of bands crossing the Fermi energy and the corresponding modification of Fermi surface topology. Enhanced spin-orbit coupling and lattice distortion in the single-layer play a crucial role in the formation of CDW order. Our findings provide a deeper understanding of the nature of CDW order in the two-dimensional limit.

New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs

Science.gov (United States)

Venturi, D.; Karniadakis, G. E.

2012-08-01

By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs). The theory is presented for both fully nonlinear and for quasilinear scalar PDEs subject to random boundary conditions, random initial conditions or random forcing terms. Particular applications are discussed for the classical linear and nonlinear advection equations and for the advection-reaction equation. By using a Fourier-Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations. These numerical solutions are compared against those obtained by using more conventional statistical approaches such as probabilistic collocation and multi-element probabilistic collocation methods. It is found that the response-excitation approach yields accurate predictions of the statistical properties of the system. In addition, it allows to directly ascertain the tails of probabilistic distributions, thus facilitating the assessment of rare events and associated risks. The computational cost of the response-excitation method is order magnitudes smaller than the one of more conventional statistical approaches if the PDE is subject to high-dimensional random boundary or initial conditions. The question of high-dimensionality for evolution equations involving multidimensional joint response-excitation PDFs is also addressed.

Synthesis, characterization and theoretical investigations of the structure, electronic properties and third-order nonlinearity optics (NLO) of M(DPIP)2

Science.gov (United States)

Li, Kang; Tang, Guodong; Kou, ShanShan; Culnane, Lance F.; Zhang, Yu; Song, Yinglin; Li, Rongqing; Wei, Changmei

2015-03-01

Three complexes of M(DPIP)2 (M = Cu, Co, Zn as 1, 2, 3) were synthesized and characterized by elemental analysis, IR, UV-Vis, thermogravimetry, and X-ray diffraction. Their nonlinear optical properties were measured by the Z-scan technique and yielded a normalized transmittance of about 70% for complex 1 (45 μJ pulse), and 93% for complex 3 (68 μJ pulse at the focus point). The nonlinear absorption coefficient, β, is 1.4 × 10-11 m/W for 1 and 5.6 × 10-13 m/W for 3, and the third-order nonlinear refraction index, n2, is 1.0 × 10-18 m2/W for 3. Complex 1 shows self-defocusing property, while complex 3 exhibits self-focusing property. The thermogravimetric results show that the frame structure of compounds 1-3 begin to collapse at 400, 250 and 280 °C, respectively, which suggests that they elicit excellent thermal stability. This research aims to provide better understanding of these compounds, and offer preliminary explanations for the significant differences between compounds 1-3, in order to potentially help in the designing of future novel materials with NLO properties.

Microstructure evolution to reach the single variant in an ordered Fe–55at.%Pd alloy

International Nuclear Information System (INIS)

Farjami, Sahar; Fukuda, Takashi; Kakeshita, Tomoyuki

2013-01-01

Highlights: ► We confirmed formation of the single variant in Fe–55at.%Pd by XRD measurement and TEM observation. ► The size of each ordered domain is about 2 nm at the early stage of ordering. ► High density of antiphase boundaries has been observed after formation of the single variant. -- Abstract: Recently, we reported single variant formation in an Fe–55at.%Pd is certainly realized from a disordered fcc-phase to an ordered L1 0 -phase by heat-treatment under magnetic field. In the present study, we have investigated microstructure evolution during the process of the single variant formation by an X-ray diffraction and an electron microscopy observation. As a result, followings are obtained: size of the ordered particles at the early stage of ordering is about 2 nm and the nucleation ratio of preferable variant, whose easy axis lies in the field direction, is higher than that of other variants. Each of the ordered preferable variant grows by consuming the order variants and finally come together to become a single variant. Based on the observation, a model is proposed for the single variant formation of the ordered L1 0 -phase under magnetic field

Third-order nonlinearities and structural features in Langmuir-Blodgett films of 1-benzyl-9-hydrofullerene-60

International Nuclear Information System (INIS)

Shihong Ma; Liying Liu; Xingze Lu

1995-01-01

Third-order nonlinear susceptibilities χ xxxx (3) (-3ω; ω, ω, ω) have been deduced by measuring third-harmonic generation in Langmuir-Blodgett (LB) films of 1-benzyl-9-hydrofullerene-60 (C 60 -Be). The structural features of the condensed layer at the air-water interface and LB films of the C 60 -Be were investigated by small angle x-ray diffraction (SAXD) and optical measurements. The third-order nonlinear susceptibilities (χ (3) ) were obtained by measuring the THG intensities in LB films of C 60 -Be and comparing with that of CS 2 used as the reference. The value of χ xxxx (3) (2.1 x 10 -11 esu) was deduced at a 65 nm thick films. The χ (3) is attributed to a three-photon near resonance at the energy level of 29410 cm -1 . A new-type of two-chain amphiphilic molecule 1,10-bistearyl-4,6,13, 15-tetra-18-nitrogencrown-6 (NC) was used as insert material to construct mixed C 60 -Be/NC LB films. Our π-A, UV-visible absorption and SAXD measurements showed that the structural improvement in the mixed C 60 -Be/NC LB films was realized by insertion of the C 60 -Be molecules between the two hydrophobic chains of the NC molecules

Investigation on the behavioral difference in third order nonlinearity and optical limiting of Mn0.55Cu0.45Fe2O4 nanoparticles annealed at different temperatures

Science.gov (United States)

Yuvaraj, S.; Manikandan, N.; Vinitha, G.

2017-11-01

Mn0.55Cu0.45Fe2O4 nanoparticles were synthesized by wet chemical co-precipitation method. The obtained samples were annealed at different temperatures (500 °C to 1250 °C). All annealed samples were characterized for their structural, magnetic, linear and non-linear optical properties. XRD results confirm single phase cubic spinel structure only for samples annealed at 800 °C and 1250 °C. The average crystallite sizes of the samples are in the range of 11-37 nm. HR-SEM image of the sample annealed at 800 °C exposed spherical morphology. The quantitative analysis of EDX results is close to the expected values. Bandgaps were evaluated from UV-DRS. The FTIR spectrum showing the essential peaks around 452.1 and 567.2 cm-1 prove the formation of spinel nanoparticles. In PL spectrum, a broad emission peak is attained in visible region at 485 nm. The saturation magnetization (M s), coercivity (H c) and remanence magnetization (M r) are obtained from the hysteresis curve. Nonlinear absorption coefficients (10-4 cm W-1), nonlinear indices of refraction (10-8 cm2 W-1) and the third order nonlinear susceptibilities (10-6 esu) are determined using Z-scan experiment. CW laser beam is utilized to study the optical limiting characteristics and the results prove these materials to be a potential candidate for device applications like optical switches and power limiters.

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

Second-Order Nonlinear Optical Dendrimers and Dendronized Hyperbranched Polymers.

Science.gov (United States)

Tang, Runli; Li, Zhen

2017-01-01

Second-order nonlinear optical (NLO) dendrimers with a special topological structure were regarded as the most promising candidates for practical applications in the field of optoelectronic materials. Dendronized hyperbranched polymers (DHPs), a new type of polymers with dendritic structures, proposed and named by us recently, demonstrated interesting properties and some advantages over other polymers. Some of our work concerning these two types of polymers are presented herein, especially focusing on the design idea and structure-property relationship. To enhance their comprehensive NLO performance, dendrimers were designed and synthesized by adjusting their isolation mode, increasing the number of the dendritic generation, modifying their topological structure, introducing isolation chromophores, and utilizing the Ar-Ar F self-assembly effect. To make full use of the advantages of both the structural integrity of dendrimers and the convenient one-pot synthesis of hyperbranched polymers, DHPs were explored by utilizing low-generation dendrons as big monomers to construct hyperbranched polymers. These selected works could provide valuable information to deeply understand the relationship between the structure and properties of functional polymers with dendritic structures, but not only limited to the NLO ones, and might contribute much to the further development of functional polymers with rational design. © 2017 The Chemical Society of Japan & Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Distributed Adaptive Neural Network Output Tracking of Leader-Following High-Order Stochastic Nonlinear Multiagent Systems With Unknown Dead-Zone Input.

Science.gov (United States)

Hua, Changchun; Zhang, Liuliu; Guan, Xinping

2017-01-01

This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.

Structural characterizations, Hirshfeld surface analyses, and third-order nonlinear optical properties of two novel chalcone derivatives

Science.gov (United States)

Maidur, Shivaraj R.; Jahagirdar, Jitendra R.; Patil, Parutagouda Shankaragouda; Chia, Tze Shyang; Quah, Ching Kheng

2018-01-01

We report synthesis, characterizations, structure-property relationships, and third-order nonlinear optical studies for two new chalcone derivatives, (2E)-1-(anthracen-9-yl)-3-(4-bromophenyl)prop-2-en-1-one (Br-ANC) and (2E)-1-(anthracen-9-yl)-3-(4-chlorophenyl)prop-2-en-1-one (Cl-ANC). These derivatives were crystallized in the centrosymmetric monoclinic P21/c crystal structure. The intermolecular interactions of both the crystals were visualized by Hirshfeld surface analyses (HSA). The crystals are thermally stable up to their melting points (180.82 and 191.16 °C for Cl-ANC and Br-ANC, respectively). The geometry optimizations, FT-IR spectra, 1H and 13C NMR spectra, electronic absorption spectra, electronic transitions, and HOMO-LUMO energy gaps were studied by Density Functional Theory (DFT) at B3LYP/6-311+G(d, p) level. The theoretical results provide excellent agreement with experimental findings. The electric dipole moments, static polarizabilities, molecular electrostatic potentials (MEP) and global chemical reactivity descriptors (GCRD) were also theoretically computed. The materials exhibited good nonlinear absorption (NLA), nonlinear refraction (NLR) and optical limiting (OL) behavior under diode-pumped solid-state (DPSS) continuous wave (CW) laser excitation (532 nm and 200 mW). The NLO parameters such as NLA coefficient (β∼10-5 cmW-1), NLR index (n2∼10-10 cm2 W-1) and third-order NLO susceptibilities (χ(3) ∼10-7 esu) were measured. Further, we estimated one-photon and two-photon figures of merit, which satisfy the demands (W > 1 and T < 1) for all-optical switching. Thus, the present chalcone derivatives with anthracene moiety are potential materials for OL and optical switching applications.

Single Particle Linear and Nonlinear Dynamics

International Nuclear Information System (INIS)

Cai, Y

2004-01-01

I will give a comprehensive review of existing particle tracking tools to assess long-term particle stability for small and large accelerators in the presence of realistic magnetic imperfections and machine misalignments. The emphasis will be on the tracking and analysis tools based upon the differential algebra, Lie operator, and ''polymorphism''. Using these tools, a uniform linear and non-linear analysis will be outlined as an application of the normal form

The second-order interference of two independent single-mode He-Ne lasers

Science.gov (United States)

Liu, Jianbin; Le, Mingnan; Bai, Bin; Wang, Wentao; Chen, Hui; Zhou, Yu; Li, Fu-li; Xu, Zhuo

2015-09-01

The second-order spatial and temporal interference patterns with two independent single-mode continuous-wave He-Ne lasers are observed when these two lasers are incident to two adjacent input ports of a 1:1 non-polarizing beam splitter, respectively. Two-photon interference based on the superposition principle in Feynman's path integral theory is employed to interpret the experimental results. The conditions to observe the second-order interference pattern with two independent single-mode continuous-wave lasers are discussed. It is concluded that frequency stability is important to observe the second-order interference pattern with two independent light beams.

Effects of magnetic non-linearities on a stored proton beam and their implications for superconducting storage rings

International Nuclear Information System (INIS)

Cornacchia, M.; Evans, L.

1985-06-01

A nonlinear lens may be used to study the effect of high-order multipolar field imperfections on a stored proton beam. Such a nonlinear lens is particulary suitable to simulate field imperfections of the types encountered in coil dominated superconducting magnets. We have studied experimentally at the SPS the effect of high order (5th and 8th) single isolated resonances driven by the nonlinear lens. The width of these resonances is of the order one expects to be caused by field errors in superconducting magnets of the SSC type. The experiment shows that, in absence of tune modulation, these resonances are harmless. Slow crossings of the resonance, on the other hand, have destructive effects on the beam, much more so than fast crossings caused by synchrotron oscillations. In the design of future storage rings, sources of low-frequency tune modulation should be avoided as a way to reduce the harmful effects of high order multipolar field imperfection

Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

Directory of Open Access Journals (Sweden)

Zhonghai Guo

2012-01-01

Full Text Available We study the following second order mixed nonlinear impulsive differential equations with delay (r(tΦα(x′(t′+p0(tΦα(x(t+∑i=1npi(tΦβi(x(t-σ=e(t, t≥t0, t≠τk,x(τk+=akx(τk, x'(τk+=bkx'(τk, k=1,2,…, where Φ*(u=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.

Subharmonic response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random excitation.

Science.gov (United States)

Haiwu, Rong; Wang, Xiangdong; Xu, Wei; Fang, Tong

2009-08-01

The subharmonic response of single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to narrow-band random excitation is investigated. The narrow-band random excitation used here is a filtered Gaussian white noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the applications of asymptotic averaging over the "fast" variables. The averaged stochastic equations are solved exactly by the method of moments for the mean-square response amplitude for the case of linear system with zero offset. A perturbation-based moment closure scheme is proposed and the formula of the mean-square amplitude is obtained approximately for the case of linear system with nonzero offset. The perturbation-based moment closure scheme is used once again to obtain the algebra equation of the mean-square amplitude of the response for the case of nonlinear system. The effects of damping, detuning, nonlinear intensity, bandwidth, and magnitudes of random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak amplitudes may be strongly reduced at large detunings or large nonlinear intensity.

Nonlinear photonic metasurfaces

Science.gov (United States)

Li, Guixin; Zhang, Shuang; Zentgraf, Thomas

2017-03-01

Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the 'meta-atoms'), enable the manipulation of light-matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing.

ℋ∞ Adaptive observer for nonlinear fractional-order systems

KAUST Repository

Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed; Voos, Holger

2016-01-01

inequalities (LMIs) by using an indirect Lyapunov method.The proposed ℋ∞ adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü

Optimal Decision-Making in Fuzzy Economic Order Quantity (EOQ Model under Restricted Space: A Non-Linear Programming Approach

Directory of Open Access Journals (Sweden)

M. Pattnaik

2013-08-01

Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.

Single Particle Linear and Nonlinear Dynamics

Energy Technology Data Exchange (ETDEWEB)

Cai, Y

2004-06-25

I will give a comprehensive review of existing particle tracking tools to assess long-term particle stability for small and large accelerators in the presence of realistic magnetic imperfections and machine misalignments. The emphasis will be on the tracking and analysis tools based upon the differential algebra, Lie operator, and ''polymorphism''. Using these tools, a uniform linear and non-linear analysis will be outlined as an application of the normal form.

Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

International Nuclear Information System (INIS)

Batou, A.; Soize, C.; Brie, N.

2013-01-01

Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading

Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

Energy Technology Data Exchange (ETDEWEB)

Batou, A., E-mail: anas.batou@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Brie, N., E-mail: nicolas.brie@edf.fr [EDF R and D, Département AMA, 1 avenue du général De Gaulle, 92140 Clamart (France)

2013-09-15

Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading.

Synthesis, growth, structure and characterization of 1-Ethyl-2-(2-p-tolyl-vinyl)-pyridinium iodide (TASI) – An efficient material for third-order nonlinear optical applications

Energy Technology Data Exchange (ETDEWEB)

Nivetha, K. [Centre for Crystal Growth, School of Advanced Sciences, VIT University, Vellore 632 014 (India); Kalainathan, S., E-mail: kalainathan@yahoo.com [Centre for Crystal Growth, School of Advanced Sciences, VIT University, Vellore 632 014 (India); Yamada, M. [Research Center for Engineering Science, Graduate School of Engineering Science, Akita University, 1-1 Tegatagakuen-machi, Akita 010-8502 (Japan); Kondo, Y. [Department of Life Science, Graduate School of Engineering Science, Akita University, 1-1 Tegatagakuen-machi, Akita 010-8502 (Japan); Hamada, F. [Department of Applied Chemistry, Graduate School of Engineering Science, Akita University, 1-1 Tegatagakuen-machi, Akita 010-8502 (Japan)

2017-02-15

A new organic stilbazolium derivative, 1-Ethyl-2-(2-p-tolyl-vinyl)-pyridinium iodide (TASI), was grown from methanol:acetonitrile (1:3) mixed solvent by slow evaporation technique. Single crystal X-ray diffraction analysis revealed that TASI crystallizes in triclinic system with a centrosymmetric space group P-1. The molecular structure and the presence of expected functional groups of TASI were confirmed by {sup 1}H NMR and FT-IR spectroscopic studies. The HOMO and LUMO energies influence the charge transfer takes place within the molecule. The grown crystal was thermally stable up to 210 °C as determined by TG/DTA analysis. UV-Vis-NIR spectral study showed that the grown crystal was transparent in the wavelength range of 438–1100 nm. Mechanical behaviour and surface laser damage threshold were studied to find the suitability of the grown crystal for device fabrication. Studies of its third-order nonlinear optical properties using a Z-scan technique demonstrates that TASI crystal is capable of exhibiting reverse saturable absorption and self-focusing performance with the second-order molecular hyperpolarizability (γ) 4.983 × 10{sup −34} esu. The third-order nonlinear susceptibility of TASI was found to be 8.931 × 10{sup −6} esu, which is higher than a few other stilbazolium derivative crystals. - Highlights: • TASI is a new organic stilbazolium derivative and was grown by slow evaporation technique. • HOMO-LUMO analysis helps to explain charge transfer interaction within the molecule. • The grown crystal has 80% transmittance in the visible and near-IR spectral range. • Thermally, electrically and mechanically efficient for NLO applications. • Z-scan measurements reveal the aptness of the grown crystal for third order NLO applications.

Growth and spectroscopic, thermodynamic and nonlinear optical studies of L-threonine phthalate crystal

Science.gov (United States)

Theras, J. Elberin Mary; Kalaivani, D.; Jayaraman, D.; Joseph, V.

2015-10-01

L-threonine phthalate (LTP) single crystal has been grown using a solution growth technique at room temperature. Single crystal X-ray diffraction analysis reveals that LTP crystallizes in monoclinic crystal system with space group C2/c. The optical absorption studies show that the crystal is transparent in the entire visible region with a cut-off wavelength 309 nm. The optical band gap is found to be 4.05 eV. The functional groups of the synthesized compound have been identified by FTIR spectral analysis. The functional groups present in the material were also confirmed by FT-RAMAN spectroscopy. Surface morphology and the presence of various elements were studied by SEM-EDAX analysis. The thermal stability of LTP single crystal has been analyzed by TGA/DTA studies. The thermodynamic parameters such as activation energy, entropy, enthalpy and Gibbs free energy were determined for the grown material using TG data and Coats-Redfern relation. Since the grown crystal is centrosymmetric, Z-Scan studies were carried out for analyzing the third order nonlinear optical property. The nonlinear absorption coefficient, nonlinear refractive index and susceptibility have been measured using Z-Scan technique.

Nonlinear dynamics and anisotropic structure of rotating sheared turbulence.

Science.gov (United States)

Salhi, A; Jacobitz, F G; Schneider, K; Cambon, C

2014-01-01

Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations.

Numerical Simulation of Freak Waves Based on the Four-Order Nonlinear Schr(o)dinger Equation

Institute of Scientific and Technical Information of China (English)

ZHANG Yun-qiu; ZHANG Ning-chuan; PEI Yu-guo

2007-01-01

A numerical wave model based on the modified four-order nonlinear Schrodinger (NLS) equation in deep water is developed to simulate freak waves. A standard split-step, pseudo-spectral method is used to solve NLS equation. The validation of the model is firstly verified, and then the simulation of freak waves is performed by changing sideband conditions. Results show that freak waves entirely consistent with the definition in the evolution of wave trains are obtained. The possible occurrence mechanism of freak waves is discussed and the relevant characteristics are also analyzed.

Synthesis, characterization and theoretical investigations of the structure, electronic properties and third-order nonlinearity optics (NLO) of M(DPIP)₂.

Science.gov (United States)

Li, Kang; Tang, Guodong; Kou, ShanShan; Culnane, Lance F; Zhang, Yu; Song, Yinglin; Li, Rongqing; Wei, Changmei

2015-03-15

Three complexes of M(DPIP)2 (M=Cu, Co, Zn as 1, 2, 3) were synthesized and characterized by elemental analysis, IR, UV-Vis, thermogravimetry, and X-ray diffraction. Their nonlinear optical properties were measured by the Z-scan technique and yielded a normalized transmittance of about 70% for complex 1 (45 μJ pulse), and 93% for complex 3 (68 μJ pulse at the focus point). The nonlinear absorption coefficient, β, is 1.4×10(-11) m/W for 1 and 5.6×10(-13) m/W for 3, and the third-order nonlinear refraction index, n2, is 1.0×10(-18) m(2)/W for 3. Complex 1 shows self-defocusing property, while complex 3 exhibits self-focusing property. The thermogravimetric results show that the frame structure of compounds 1-3 begin to collapse at 400, 250 and 280°C, respectively, which suggests that they elicit excellent thermal stability. This research aims to provide better understanding of these compounds, and offer preliminary explanations for the significant differences between compounds 1-3, in order to potentially help in the designing of future novel materials with NLO properties. Copyright © 2014 Elsevier B.V. All rights reserved.

Evaluation of Advanced Nonlinear Static Procedure

Directory of Open Access Journals (Sweden)

Mohsen Ali Shayanfar

2015-03-01

Full Text Available Having very simplicity, nonlinear static procedures (NSPs are the most popular tools for estimation of structural capacity. These approaches construct a graphic display of the overall structural response via a pushover curve. The overall response of the system provides a direct simulation of the building as single degree of freedom (SDOF system that simplifies the design and evaluation of the structure. In this research, the first step in any nonlinear static analysis or in other words perform a pushover analysis has been studied. Applied lateral load to the structural model not only affects the overall responses of the structure through structural capacity curve, but also directly affects the local responses of the structure. In order to evaluate these lateral loads, steel buckling restrained braced frame structures are examined by advanced modal pushovers. Next, the results of these pushover analyses will be compared with nonlinear time history analysis as the most accurate method. Finally, the most efficient method in this particular structure is introduced. The analysis conducted in these structures shows that the lateral load pattern based on story shears offers a good prediction of the maximum response of the concentrically buckling restrained braced frame buildings.

Computational studies of third-order nonlinear optical properties of ...

Indian Academy of Sciences (India)

Anuj Kumar

2017-06-20

Jun 20, 2017 ... Department of Physics, Jaypee University of Engineering and Technology, Raghogarh,. Guna 473 226, India. ∗ ... properties and other molecular properties of the organic nonlinear optical crystal 2-aminopyridinium p- toluenesulphonate ... nal processing, optical limiting, optical logic gates, laser radiation ...

Nonlinear dynamics aspects of modern storage rings

International Nuclear Information System (INIS)

Helleman, R.H.G.; Kheifets, S.A.

1986-01-01

It is argued that the nonlinearity of storage rings becomes an essential problem as the design parameters of each new machine are pushed further and further. Yet the familiar methods of classical mechanics do not allow determination of single particle orbits over reasonable lengths of time. It is also argued that the single particle dynamics of a storage ring is possibly one of the cleanest and simplest nonlinear dynamical systems available with very few degrees of freedom. Hence, reasons are found for accelerator physicists to be interested in nonlinear dynamics and for researchers in nonlinear dynamics to be interested in modern storage rings. The more familiar methods of treating nonlinear systems routinely used in acclerator theory are discussed, pointing out some of their limitations and pitfalls. 39 refs., 1 fig

A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions

Nonlinear drift tearing mode

International Nuclear Information System (INIS)

Zelenyj, L.M.; Kuznetsova, M.M.

1989-01-01

Nonlinear study of magnetic perturbation development under single-mode conditions in collision-free plasma in configurations with the magnetic field shear is investigated. Results are obtained with regard of transverse component of electrical field and its effect on ion dynamics within wide range of ion Larmor radius value and values of magnetic field shear. Increments of nonlinear drift tearing mode are obtained and it is shown that excitation drastic conditions of even linearly stable modes are possible. Mechanism of instability nonlinear stabilization is considered and the value of magnetic island at the saturation threshold is estimeted. Energy of nonlinear drift tearing mode is discussed

50 years of nonlinear optics

International Nuclear Information System (INIS)

Shen Yuanrang

2011-01-01

This article presents a brief introduction to the birth and early investigations of nonlinear optics, such as second harmonic generation,sum and difference frequency generation, stimulated Raman scattering,and self-action of light etc. Several important research achievements and applications of nonlinear optics are presented as well, including nonlinear optical spectroscopy, phase conjugation and adaptive optics, coherent nonlinear optics, and high-order harmonic generation. In the end, current and future research topics in nonlinear optics are summarized. (authors)

Correlation between ultrasonic nonlinearity and elastic nonlinearity in heat-treated aluminum alloy

Energy Technology Data Exchange (ETDEWEB)

Kim, Jong Beom; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)

2017-04-15

The nonlinear ultrasonic technique is a potential nondestructive method to evaluate material degradation, in which the ultrasonic nonlinearity parameter is usually measured. The ultrasonic nonlinearity parameter is defined by the elastic nonlinearity coefficients of the nonlinear Hooke’s equation. Therefore, even though the ultrasonic nonlinearity parameter is not equal to the elastic nonlinearity parameter, they have a close relationship. However, there has been no experimental verification of the relationship between the ultrasonic and elastic nonlinearity parameters. In this study, the relationship is experimentally verified for a heat-treated aluminum alloy. Specimens of the aluminum alloy were heat-treated at 300°C for different periods of time (0, 1, 2, 5, 10, 20, and 50 h). The relative ultrasonic nonlinearity parameter of each specimen was then measured, and the elastic nonlinearity parameter was determined by fitting the stress-strain curve obtained from a tensile test to the 5th-order-polynomial nonlinear Hooke’s equation. The results showed that the variations in these parameters were in good agreement with each other.

Single-step emulation of nonlinear fiber-optic link with gaussian mixture model

DEFF Research Database (Denmark)

Borkowski, Robert; Doberstein, Andy; Haisch, Hansjörg

2015-01-01

We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission.......We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission....

On nonlinear reduced order modeling

International Nuclear Information System (INIS)

Abdel-Khalik, Hany S.

2011-01-01

When applied to a model that receives n input parameters and predicts m output responses, a reduced order model estimates the variations in the m outputs of the original model resulting from variations in its n inputs. While direct execution of the forward model could provide these variations, reduced order modeling plays an indispensable role for most real-world complex models. This follows because the solutions of complex models are expensive in terms of required computational overhead, thus rendering their repeated execution computationally infeasible. To overcome this problem, reduced order modeling determines a relationship (often referred to as a surrogate model) between the input and output variations that is much cheaper to evaluate than the original model. While it is desirable to seek highly accurate surrogates, the computational overhead becomes quickly intractable especially for high dimensional model, n ≫ 10. In this manuscript, we demonstrate a novel reduced order modeling method for building a surrogate model that employs only 'local first-order' derivatives and a new tensor-free expansion to efficiently identify all the important features of the original model to reach a predetermined level of accuracy. This is achieved via a hybrid approach in which local first-order derivatives (i.e., gradient) of a pseudo response (a pseudo response represents a random linear combination of original model’s responses) are randomly sampled utilizing a tensor-free expansion around some reference point, with the resulting gradient information aggregated in a subspace (denoted by the active subspace) of dimension much less than the dimension of the input parameters space. The active subspace is then sampled employing the state-of-the-art techniques for global sampling methods. The proposed method hybridizes the use of global sampling methods for uncertainty quantification and local variational methods for sensitivity analysis. In a similar manner to

Reduced order dynamic model for polysaccharides molecule attached to an atomic force microscope

International Nuclear Information System (INIS)

Tang Deman; Li Aiqin; Attar, Peter; Dowell, Earl H.

2004-01-01

A dynamic analysis and numerical simulation has been conducted of a polysaccharides molecular structure (a ten (10) single-α-D-glucose molecule chain) connected to a moving atomic force microscope (AFM). Sinusoidal base excitation of the AFM cantilevered beam is considered. First a linearized perturbation model is constructed for the complex polysaccharides molecular structure. Then reduced order (dynamic) models based upon a proper orthogonal decomposition (POD) technique are constructed using global modes for both the linearized perturbation model and for the full nonlinear model. The agreement between the original and reduced order models (ROM/POD) is very good even when only a few global modes are included in the ROM for either the linear case or for the nonlinear case. The computational advantage of the reduced order model is clear from the results presented

Nonlinear Ritz approximation for Fredholm functionals

Directory of Open Access Journals (Sweden)

Mudhir A. Abdul Hussain

2015-11-01

Full Text Available In this article we use the modify Lyapunov-Schmidt reduction to find nonlinear Ritz approximation for a Fredholm functional. This functional corresponds to a nonlinear Fredholm operator defined by a nonlinear fourth-order differential equation.

ONIOM Investigation of the Second-Order Nonlinear Optical Responses of Fluorescent Proteins.

Science.gov (United States)

de Wergifosse, Marc; Botek, Edith; De Meulenaere, Evelien; Clays, Koen; Champagne, Benoît

2018-05-17

The first hyperpolarizability (β) of six fluorescent proteins (FPs), namely, enhanced green fluorescent protein, enhanced yellow fluorescent protein, SHardonnay, ZsYellow, DsRed, and mCherry, has been calculated to unravel the structure-property relationships on their second-order nonlinear optical properties, owing to their potential for multidimensional biomedical imaging. The ONIOM scheme has been employed and several of its refinements have been addressed to incorporate efficiently the effects of the microenvironment on the nonlinear optical responses of the FP chromophore that is embedded in a protective β-barrel protein cage. In the ONIOM scheme, the system is decomposed into several layers (here two) treated at different levels of approximation (method1/method2), from the most elaborated method (method1) for its core (called the high layer) to the most approximate one (method2) for the outer surrounding (called the low layer). We observe that a small high layer can already account for the variations of β as a function of the nature of the FP, provided the low layer is treated at an ab initio level to describe properly the effects of key H-bonds. Then, for semiquantitative reproduction of the experimental values obtained from hyper-Rayleigh scattering experiments, it is necessary to incorporate electron correlation as described at the second-order Møller-Plesset perturbation theory (MP2) level as well as implicit solvent effects accounted for using the polarizable continuum model (PCM). This led us to define the MP2/6-31+G(d):HF/6-31+G(d)/IEFPCM scheme as an efficient ONIOM approach and the MP2/6-31+G(d):HF/6-31G(d)/IEFPCM as a better compromise between accuracy and computational needs. Using these methods, we demonstrate that many parameters play a role on the β response of FPs, including the length of the π-conjugated segment, the variation of the bond length alternation, and the presence of π-stacking interactions. Then, noticing the small diversity

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.

Few-photon Non-linearities in Nanophotonic Devices for Quantum Information Technology

DEFF Research Database (Denmark)

Nysteen, Anders

In this thesis we investigate few-photon non-linearities in all-optical, on-chip circuits, and we discuss their possible applications in devices of interest for quantum information technology, such as conditional two-photon gates and single-photon sources. In order to propose efficient devices...... the scattered photons. Even though the non-linearity also alters the pulse spectrum due to a four-wave mixing process, we demonstrate that input pulses with a Gaussian spectrum can be mapped to the output with up to 80 % fidelity. Using two identical two-level emitters, we propose a setup for a deterministic...... by the capturing process. Semiconductor quantum dots (QDs) are promising for realizing few-photon non-linearities in solid-state implementations, although coupling to phonon modes in the surrounding lattice have significant influence on the dynamics. By accounting for the commonly neglected asymmetry between...

Nonlinear perturbations of differential operators with nontrivial kernel and applications to third order periodic boundary value problems

International Nuclear Information System (INIS)

Afuwape, A.U.; Omari, P.

1987-11-01

This paper deals with the solvability of the nonlinear operator equations in normed spaces Lx=EGx+f, where L is a linear map with possible nontrivial kernel. Applications are given to the existence of periodic solutions for the third order scalar differential equation x'''+ax''+bx'+cx+g(t,x)=p(t), under various conditions on the interaction of g(t,x)/x with spectral configurations of a, b and c. (author). 48 refs

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions