Localized and periodic exact solutions to the nonlinear Schroedinger equation with spatially modulated parameters: Linear and nonlinear lattices

International Nuclear Information System (INIS)

Belmonte-Beitia, Juan; Konotop, Vladimir V.; Perez-Garcia, Victor M.; Vekslerchik, Vadym E.

2009-01-01

Using similarity transformations we construct explicit solutions of the nonlinear Schroedinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices.

Acoustic nonlinear periodic waves in pair-ion plasmas

Science.gov (United States)

Mahmood, Shahzad; Kaladze, Tamaz; Ur-Rehman, Hafeez

2013-09-01

Electrostatic acoustic nonlinear periodic (cnoidal) waves and solitons are investigated in unmagnetized pair-ion plasmas consisting of same mass and oppositely charged ion species with different temperatures. Using reductive perturbation method and appropriate boundary conditions, the Korteweg-de Vries (KdV) equation is derived. The analytical solutions of both cnoidal wave and soliton solutions are discussed in detail. The phase plane plots of cnoidal and soliton structures are shown. It is found that both compressive and rarefactive cnoidal wave and soliton structures are formed depending on the temperature ratio of positive and negative ions in pair-ion plasmas. In the special case, it is revealed that the amplitude of soliton may become larger than it is allowed by the nonlinear stationary wave theory which is equal to the quantum tunneling by particle through a potential barrier effect. The serious flaws in the earlier published results by Yadav et al., [PRE 52, 3045 (1995)] and Chawla and Misra [Phys. Plasmas 17, 102315 (2010)] of studying ion acoustic nonlinear periodic waves are also pointed out.

ALMOST PERIODIC SOLUTIONS TO SOME NONLINEAR DELAY DIFFERENTIAL EQUATION

Institute of Scientific and Technical Information of China (English)

无

2009-01-01

The existence of an almost periodic solutions to a nonlinear delay diffierential equation is considered in this paper. A set of sufficient conditions for the existence and uniqueness of almost periodic solutions to some delay diffierential equations is obtained.

Sub-nanometer periodic nonlinearity error in absolute distance interferometers

Science.gov (United States)

Yang, Hongxing; Huang, Kaiqi; Hu, Pengcheng; Zhu, Pengfei; Tan, Jiubin; Fan, Zhigang

2015-05-01

Periodic nonlinearity which can result in error in nanometer scale has become a main problem limiting the absolute distance measurement accuracy. In order to eliminate this error, a new integrated interferometer with non-polarizing beam splitter is developed. This leads to disappearing of the frequency and/or polarization mixing. Furthermore, a strict requirement on the laser source polarization is highly reduced. By combining retro-reflector and angel prism, reference and measuring beams can be spatially separated, and therefore, their optical paths are not overlapped. So, the main cause of the periodic nonlinearity error, i.e., the frequency and/or polarization mixing and leakage of beam, is eliminated. Experimental results indicate that the periodic phase error is kept within 0.0018°.

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

DEFF Research Database (Denmark)

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

2009-01-01

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

Effects of weak nonlinearity on dispersion relations and frequency band-gaps of periodic structures

DEFF Research Database (Denmark)

Sorokin, Vladislav; Thomsen, Jon Juel

2015-01-01

of these for nonlinear problems is impossible or cumbersome, since Floquet theory is applicable for linear systems only. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applica-tions may demand effects of nonlinearity on structural response to be accounted for....... The present work deals with analytically predicting dynamic responses for nonlinear continuous elastic periodic structures. Specifically, the effects of weak nonlinearity on the dispersion re-lation and frequency band-gaps of a periodic Bernoulli-Euler beam performing bending os-cillations are analyzed......The analysis of the behaviour of linear periodic structures can be traced back over 300 years, to Sir Isaac Newton, and still attracts much attention. An essential feature of periodic struc-tures is the presence of frequency band-gaps, i.e. frequency ranges in which waves cannot propagate...

Analysis of Nonlinear Periodic and Aperiodic Media: Application to Optical Logic Gates

Science.gov (United States)

Yu, Yisheng

This dissertation is about the analysis of nonlinear periodic and aperiodic media and their application to the design of intensity controlled all optical logic gates: AND, OR, and NOT. A coupled nonlinear differential equation that characterizes the electromagnetic wave propagation in a nonlinear periodic (and aperiodic) medium has been derived from the first principle. The equations are general enough that it reflects the effect of transverse modal fields and can be used to analyze both co-propagating and counter propagating waves. A numerical technique based on the finite differences method and absorbing boundary condition has been developed to solve the coupled differential equations here. The numerical method is simple and accurate. Unlike the method based on characteristics that has been reported in the literature, this method does not involve integration and step sizes of time and space coordinates are decoupled. The decoupling provides independent choice for time and space step sizes. The concept of "gap soliton" has also been re-examined. The dissertation consists of four manuscripts. Manuscript I reports on the design of all optical logic gates: AND, OR, and NOT based on the bistability property of nonlinear periodic and aperiodic waveguiding structures. The functioning of the logic gates has been shown by analysis. The numerical technique that has been developed to solve the nonlinear differential equations are addressed in manuscript II. The effect of transverse modal fields on the bistable property of nonlinear periodic medium is reported in manuscript III. The concept of "gap soliton" that are generated in a nonlinear periodic medium has been re-examined. The details on the finding of the re-examination are discussed in manuscript IV.

Ion-acoustic nonlinear periodic waves in electron-positron-ion plasma

International Nuclear Information System (INIS)

Chawla, J. K.; Mishra, M. K.

2010-01-01

Ion-acoustic nonlinear periodic waves, namely, ion-acoustic cnoidal waves have been studied in electron-positron-ion plasma. Using reductive perturbation method and appropriate boundary condition for nonlinear periodic waves, the Korteweg-de Vries (KdV) equation is derived for the system. The cnoidal wave solution of the KdV equation is discussed in detail. It is found that the frequency of the cnoidal wave is a function of its amplitude. It is also found that the positron concentration modifies the properties of the ion-acoustic cnoidal waves. The existence regions for ion-acoustic cnoidal wave in the parameters space (p,σ), where p and σ are the positron concentration and temperature ratio of electron to positron, are discussed in detail. In the limiting case these ion-acoustic cnoidal waves reduce to the ion-acoustic soliton solutions. The effect of other parameters on the characteristics of the nonlinear periodic waves is also discussed.

Nonlinear dynamics of semiclassical coherent states in periodic potentials

International Nuclear Information System (INIS)

Carles, Rémi; Sparber, Christof

2012-01-01

We consider nonlinear Schrödinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding semiclassical scaling regime, we construct asymptotic solutions, which are concentrated both in space and in frequency around the effective semiclassical phase-space flow induced by Bloch’s spectral problem. The dynamics of these generalized coherent states is governed by a nonlinear Schrödinger model with effective mass. In the case of nonlocal nonlinearities, we establish a novel averaging-type result in the critical case. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

The periodic structure of the natural record, and nonlinear dynamics.

Science.gov (United States)

Shaw, H.R.

1987-01-01

This paper addresses how nonlinear dynamics can contribute to interpretations of the geologic record and evolutionary processes. Background is given to explain why nonlinear concepts are important. A resume of personal research is offered to illustrate why I think nonlinear processes fit with observations on geological and cosmological time series data. The fabric of universal periodicity arrays generated by nonlinear processes is illustrated by means of a simple computer mode. I conclude with implications concerning patterns of evolution, stratigraphic boundary events, and close correlations of major geologically instantaneous events (such as impacts or massive volcanic episodes) with any sharply defined boundary in the geologic column. - from Author

How universal is the period doubling phenomenon in equations with quadratic nonlinearity

International Nuclear Information System (INIS)

Malta, C.P.; Oliveira, C.R. de.

1983-09-01

Varying one parameter, the solution of nonlinear 1 sup(st) order differential equation with time delay tau is Fourier analysed. After the Hopf bifurcation, period-doubling phenomenon always occurs when tau is one of the fixed parameters (both for small and large tau). Varying tau, there are values of the fixed parameters for which no period-doubling occurs. 'Chaos' follows the period-doubling sequence and the rate at which 'chaos' is approached is very close to the universal delta = 4.6692016... characterising the period-doubling sequence to chaos in nonlinear difference equations. (Author) [pt

Periodic solutions for one dimensional wave equation with bounded nonlinearity

Science.gov (United States)

Ji, Shuguan

2018-05-01

This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.

Soliton dynamics in periodic system with different nonlinear media

International Nuclear Information System (INIS)

Zabolotskij, A.A.

2001-01-01

To analyze pulse dynamics in the optical system consisting of periodic sequence of nonlinear media one uses a composition model covering a model of resonance interaction of light ultrashort pulse with energy transition of medium with regard to pumping of the upper level and quasi-integrable model describing propagation of light field in another medium with cubic nonlinearity and dispersion. One additionally takes account of losses and other types of interaction in the from of perturbation members. On the basis of the method of scattering back problem and perturbation theory one developed a simple method to study peculiarities of soliton evolution in such periodic system. Due to its application one managed to describe different modes of soliton evolution in such a system including chaotic dynamics [ru

New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation

International Nuclear Information System (INIS)

Yang Qin; Dai Chaoqing; Zhang Jiefang

2005-01-01

Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.

Five parameters for the evaluation of the soil nonlinearity during the Ms8.0 Wenchuan Earthquake using the HVSR method

Science.gov (United States)

Ren, Yefei; Wen, Ruizhi; Yao, Xinxin; Ji, Kun

2017-08-01

The consideration of soil nonlinearity is important for the accurate estimation of the site response. To evaluate the soil nonlinearity during the 2008 Ms8.0 Wenchuan Earthquake, 33 strong-motion records obtained from the main shock and 890 records from 157 aftershocks were collected for this study. The horizontal-to-vertical spectral ratio (HVSR) method was used to calculate five parameters: the ratio of predominant frequency (RFp), degree of nonlinearity (DNL), absolute degree of nonlinearity (ADNL), frequency of nonlinearity (fNL), and percentage of nonlinearity (PNL). The purpose of this study was to evaluate the soil nonlinearity level of 33 strong-motion stations and to investigate the characteristics, performance, and effective usage of these five parameters. Their correlations with the peak ground acceleration (PGA), peak ground velocity (PGV), average uppermost 30-m shear-wave velocity ( V S30), and maximum amplitude of HVSR ( A max) were investigated. The results showed that all five parameters correlate well with PGA and PGV. The DNL, ADNL, and PNL also show a good correlation with A max, which means that the degree of soil nonlinearity not only depends on the ground-motion amplitude (e.g., PGA and PGV) but also on the site condition. The fNL correlates with PGA and PGV but shows no correlation with either A max or V S30, implying that the frequency width affected by the soil nonlinearity predominantly depends on the ground-motion amplitude rather than the site condition. At 16 of the 33 stations analyzed in this study, the site response showed evident (i.e., strong and medium) nonlinearity during the main shock of the Wenchuan Earthquake, where the ground-motion level was almost beyond the threshold of PGA > 200 cm/s2 or PGV > 15 cm/s. The site response showed weak and no nonlinearity at the other 14 and 3 stations. These results also confirm that RFp, DNL, ADNL, and PNL are effective in identifying the soil nonlinearity behavior. The identification

Low cost metamodel for robust design of periodic nonlinear coupled micro-systems

Directory of Open Access Journals (Sweden)

Chikhaoui K.

2016-01-01

Full Text Available To achieve robust design, in presence of uncertainty, nonlinearity and structural periodicity, a metamodel combining the Latin Hypercube Sampling (LHS method for uncertainty propagation and an enriched Craig-Bampton Component Mode Synthesis approach (CB-CMS for model reduction is proposed. Its application to predict the time responses of a stochastic periodic nonlinear micro-system proves its efficiency in terms of accuracy and reduction of computational cost.

Implications for Primordial Non-Gaussianity ($f_{NL}$) from weak lensing masses of high-z galaxy clusters

CERN Document Server

Jimenez, Raul

2009-01-01

The recent weak lensing measurement of the dark matter mass of the high-redshift galaxy cluster XMMUJ2235.3-2557 of (8.5 +- 1.7) x 10^{14} Msun at z=1.4, indicates that, if the cluster is assumed to be the result of the collapse of dark matter in a primordial gaussian field in the standard LCDM model, then its abundance should be 3-10 if the non-Gaussianity parameter f^local_NL is in the range 150-200. This value is comparable to the limit for f_NL obtained by current constraints from the CMB. We conclude that mass determination of high-redshift, massive clusters can offer a complementary probe of primordial non-gaussianity.

Cross-Kerr nonlinearities in an optically dressed periodic medium

Energy Technology Data Exchange (ETDEWEB)

Slowik, K; Raczynski, A; Zaremba, J [Instytut Fizyki, Uniwersytet Mikolaja Kopernika, ulica Grudziadzka 5, 87-100 Torun (Poland); Zielinska-Kaniasty, S [Instytut Matematyki i Fizyki, Uniwersytet Technologiczno-Przyrodniczy, Aleja Prof. S Kaliskiego 7, 85-789 Bydgoszcz (Poland); Artoni, M [Department of Physics and Chemistry of Materials, CNR-INFM Sensor Lab, Brescia University and European Laboratory for Nonlinear Spectroscopy, Firenze (Italy); La Rocca, G C, E-mail: karolina@fizyka.umk.pl [Scuola Normale Superiore and CNISM, Pisa (Italy)

2011-02-15

Cross-Kerr nonlinearities are analyzed for two light beams propagating in an atomic medium in the tripod configuration, dressed by a strong standing-wave laser field that induces periodic optical properties. The reflection and transmission spectra as well as the phases of both the reflected and transmitted components of the two beams are analyzed theoretically with nonlinearities up to third order being taken into account. Ranges of parameters are sought in which the cross-Kerr effect can be used as the basis of the phase gate.

Non-reciprocal wave propagation in one-dimensional nonlinear periodic structures

Directory of Open Access Journals (Sweden)

Benbiao Luo

2018-01-01

Full Text Available We study a one-dimensional nonlinear periodic structure which contains two different spring stiffness and an identical mass in each period. The linear dispersion relationship we obtain indicates that our periodic structure has obvious advantages compared to other kinds of periodic structures (i.e. those with the same spring stiffness but two different mass, including its increased flexibility for manipulating the band gap. Theoretically, the optical cutoff frequency remains unchanged while the acoustic cutoff frequency shifts to a lower or higher frequency. A numerical simulation verifies the dispersion relationship and the effect of the amplitude-dependent signal filter. Based upon this, we design a device which contains both a linear periodic structure and a nonlinear periodic structure. When incident waves with the same, large amplitude pass through it from opposite directions, the output amplitude of the forward input is one order magnitude larger than that of the reverse input. Our devised, non-reciprocal device can potentially act as an acoustic diode (AD without an electrical circuit and frequency shifting. Our result represents a significant step forwards in the research of non-reciprocal wave manipulation.

Weak-periodic stochastic resonance in a parallel array of static nonlinearities.

Directory of Open Access Journals (Sweden)

Yumei Ma

Full Text Available This paper studies the output-input signal-to-noise ratio (SNR gain of an uncoupled parallel array of static, yet arbitrary, nonlinear elements for transmitting a weak periodic signal in additive white noise. In the small-signal limit, an explicit expression for the SNR gain is derived. It serves to prove that the SNR gain is always a monotonically increasing function of the array size for any given nonlinearity and noisy environment. It also determines the SNR gain maximized by the locally optimal nonlinearity as the upper bound of the SNR gain achieved by an array of static nonlinear elements. With locally optimal nonlinearity, it is demonstrated that stochastic resonance cannot occur, i.e. adding internal noise into the array never improves the SNR gain. However, in an array of suboptimal but easily implemented threshold nonlinearities, we show the feasibility of situations where stochastic resonance occurs, and also the possibility of the SNR gain exceeding unity for a wide range of input noise distributions.

Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

Science.gov (United States)

Issokolo, Remi J. Noumana; Dikandé, Alain M.

2018-05-01

A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

Periodic and solitary wave solutions of cubic–quintic nonlinear ...

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 86; Issue 6. Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients. BHARDWAJ S B SINGH RAM MEHAR SHARMA KUSHAL MISHRA S C. Regular Volume 86 Issue 6 June 2016 pp 1253-1258 ...

Existence of periodic orbits in nonlinear oscillators of Emden–Fowler form

Energy Technology Data Exchange (ETDEWEB)

Mancas, Stefan C., E-mail: mancass@erau.edu [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, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, SLP (Mexico)

2016-01-28

The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden–Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric solution. Through an invariant transformation we find periodic solutions to a certain class of EF equations that pass an integrability condition. We show that this condition is necessary to have periodic solutions and via the ODE analysis we also find the sufficient condition for periodic orbits. EF equations that do not pass integrability conditions can be made integrable via an invariant transformation which also allows us to construct periodic solutions to them. Two other nonlinear equations, a zero-frequency Ermakov equation and a positive power Emden–Fowler equation, are discussed in the same context. - Highlights: • An invariant transformation is used to find periodic solution of EF equations. • Phase plane study of the EF autonomous two-dimensional ODE system is performed. • Three examples are presented from the standpoint of the phase plane analysis.

A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm

International Nuclear Information System (INIS)

Weichert, C; Köchert, P; Köning, R; Flügge, J; Andreas, B; Kuetgens, U; Yacoot, A

2012-01-01

The PTB developed a new optical heterodyne interferometer in the context of the European joint research project ‘Nanotrace’. A new optical concept using plane-parallel plates and spatially separated input beams to minimize the periodic nonlinearities was realized. Furthermore, the interferometer has the resolution of a double-path interferometer, compensates for possible angle variations between the mirrors and the interferometer optics and offers a minimal path difference between the reference and the measurement arm. Additionally, a new heterodyne phase evaluation based on an analogue to digital converter board with embedded field programmable gate arrays was developed, providing a high-resolving capability in the single-digit picometre range. The nonlinearities were characterized by a comparison with an x-ray interferometer, over a measurement range of 2.2 periods of the optical interferometer. Assuming an error-free x-ray interferometer, the nonlinearities are considered to be the deviation of the measured displacement from a best-fit line. For the proposed interferometer, nonlinearities smaller than ±10 pm were observed without any quadrature fringe correction. (paper)

A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm

Science.gov (United States)

Weichert, C.; Köchert, P.; Köning, R.; Flügge, J.; Andreas, B.; Kuetgens, U.; Yacoot, A.

2012-09-01

The PTB developed a new optical heterodyne interferometer in the context of the European joint research project ‘Nanotrace’. A new optical concept using plane-parallel plates and spatially separated input beams to minimize the periodic nonlinearities was realized. Furthermore, the interferometer has the resolution of a double-path interferometer, compensates for possible angle variations between the mirrors and the interferometer optics and offers a minimal path difference between the reference and the measurement arm. Additionally, a new heterodyne phase evaluation based on an analogue to digital converter board with embedded field programmable gate arrays was developed, providing a high-resolving capability in the single-digit picometre range. The nonlinearities were characterized by a comparison with an x-ray interferometer, over a measurement range of 2.2 periods of the optical interferometer. Assuming an error-free x-ray interferometer, the nonlinearities are considered to be the deviation of the measured displacement from a best-fit line. For the proposed interferometer, nonlinearities smaller than ±10 pm were observed without any quadrature fringe correction.

Suppression of period-doubling and nonlinear parametric effects in periodically perturbed systems

International Nuclear Information System (INIS)

Bryant, P.; Wiesenfeld, K.

1986-01-01

We consider the effect on a generic period-doubling bifurcation of a periodic perturbation, whose frequency ω 1 is near the period-doubled frequency ω 0 /2. The perturbation is shown to always suppress the bifurcation, shifting the bifurcation point and stabilizing the behavior at the original bifurcation point. We derive an equation characterizing the response of the system to the perturbation, analysis of which reveals many interesting features of the perturbed bifurcation, including (1) the scaling law relating the shift of the bifurcation point and the amplitude of the perturbation, (2) the characteristics of the system's response as a function of bifurcation parameter, (3) parametric amplification of the perturbation signal including nonlinear effects such as gain saturation and a discontinuity in the response at a critical perturbation amplitude, (4) the effect of the detuning (ω 1 -ω 0 /2) on the bifurcation, and (5) the emergence of a closely spaced set of peaks in the response spectrum. An important application is the use of period-doubling systems as small-signal amplifiers, e.g., the superconducting Josephson parametric amplifier

Nonlinear microscopy of localized field enhancements in fractal shaped periodic metal nanostructures

DEFF Research Database (Denmark)

Beermann, I.; Evlyukhin, A.; Boltasseva, Alexandra

2008-01-01

Fractal shaped periodic nanostructures formed with a 100 nm period square lattice of gold nanoparticles placed on a gold film are characterized using far-field nonlinear scanning optical microscopy, in which two-photon photoluminescence (TPL) excited with a strongly focused femtosecond laser beam...

Perturbation method for periodic solutions of nonlinear jerk equations

International Nuclear Information System (INIS)

Hu, H.

2008-01-01

A Lindstedt-Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton's method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method

A simple predistortion technique for suppression of nonlinear effects in periodic signals generated by nonlinear transducers

Science.gov (United States)

Novak, A.; Simon, L.; Lotton, P.

2018-04-01

Mechanical transducers, such as shakers, loudspeakers and compression drivers that are used as excitation devices to excite acoustical or mechanical nonlinear systems under test are imperfect. Due to their nonlinear behaviour, unwanted contributions appear at their output besides the wanted part of the signal. Since these devices are used to study nonlinear systems, it should be required to measure properly the systems under test by overcoming the influence of the nonlinear excitation device. In this paper, a simple method that corrects distorted output signal of the excitation device by means of predistortion of its input signal is presented. A periodic signal is applied to the input of the excitation device and, from analysing the output signal of the device, the input signal is modified in such a way that the undesirable spectral components in the output of the excitation device are cancelled out after few iterations of real-time processing. The experimental results provided on an electrodynamic shaker show that the spectral purity of the generated acceleration output approaches 100 dB after few iterations (1 s). This output signal, applied to the system under test, is thus cleaned from the undesirable components produced by the excitation device; this is an important condition to ensure a correct measurement of the nonlinear system under test.

Periodic travelling and non-travelling wave solutions of the nonlinear Klein-Gordon equation with imaginary mass

International Nuclear Information System (INIS)

Tang Xiaoyan; Shukla, Padma Kant

2008-01-01

Exact solutions, including the periodic travelling and non-travelling wave solutions, are presented for the nonlinear Klein-Gordon equation with imaginary mass. Some arbitrary functions are permitted in the periodic non-travelling wave solutions, which contribute to various high dimensional nonlinear structures

Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media

International Nuclear Information System (INIS)

Kartashov, Yaroslav V; Egorov, Alexey A; Vysloukh, Victor A; Torner, Lluis

2004-01-01

We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in the appearance of stability (instability) bands in a focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolour periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns

Complexity analyses show two distinct types of nonlinear dynamics in short heart period variability recordings

Science.gov (United States)

Porta, Alberto; Bari, Vlasta; Marchi, Andrea; De Maria, Beatrice; Cysarz, Dirk; Van Leeuwen, Peter; Takahashi, Anielle C. M.; Catai, Aparecida M.; Gnecchi-Ruscone, Tomaso

2015-01-01

Two diverse complexity metrics quantifying time irreversibility and local prediction, in connection with a surrogate data approach, were utilized to detect nonlinear dynamics in short heart period (HP) variability series recorded in fetuses, as a function of the gestational period, and in healthy humans, as a function of the magnitude of the orthostatic challenge. The metrics indicated the presence of two distinct types of nonlinear HP dynamics characterized by diverse ranges of time scales. These findings stress the need to render more specific the analysis of nonlinear components of HP dynamics by accounting for different temporal scales. PMID:25806002

Periodic oscillations in linear continuous media coupled with nonlinear discrete systems

International Nuclear Information System (INIS)

Lupini, R.

1998-01-01

A general derivation of partial differential equations with boundary conditions in the form of ordinary differential equations is obtained using the principle of stationary action for a Lagrangian function composed of continuous plus discrete parts in interaction across the boundaries of a 1-dimensional medium. This approach leads directly to the theorem of energy conservation. For linear continuous medium, homogeneous Dirichlet condition at one boundary, and nonlinear oscillator at the other boundary, the entire differential problem reduces to a nonlinear differential-difference equation of neutral type and of the second order. The lag parameter is τ = l/c, where c is the phase speed, l the length of the continuum. The Author investigate the problem of the occurrence of periodic solutions of period integer multiple of the lag (super harmonic solutions) in the case of zero inertia of the boundary system. The problem for such oscillations is shown to reduce to systems of ordinary differential equations with matching conditions in a phase space of lower dimensionality: Phase-plane techniques are used to determine solutions of period 4τ, 8τ and 6τ

Periodic wavetrains for systems of coupled nonlinear Schrödinger ...

Indian Academy of Sciences (India)

Exact, periodic wavetrains for systems of coupled nonlinear Schrödinger equations are obtained by the Hirota bilinear method and theta functions identities. Both the bright and dark soliton regimes are treated, and the solutions involve products of elliptic functions. The validity of these solutions is verified independently by a ...

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 ...

Spatial Domain Adaptive Control of Nonlinear Rotary Systems Subject to Spatially Periodic Disturbances

Directory of Open Access Journals (Sweden)

Yen-Hsiu Yang

2012-01-01

Full Text Available We propose a generic spatial domain control scheme for a class of nonlinear rotary systems of variable speeds and subject to spatially periodic disturbances. The nonlinear model of the rotary system in time domain is transformed into one in spatial domain employing a coordinate transformation with respect to angular displacement. Under the circumstances that measurement of the system states is not available, a nonlinear state observer is established for providing the estimated states. A two-degree-of-freedom spatial domain control configuration is then proposed to stabilize the system and improve the tracking performance. The first control module applies adaptive backstepping with projected parametric update and concentrates on robust stabilization of the closed-loop system. The second control module introduces an internal model of the periodic disturbances cascaded with a loop-shaping filter, which not only further reduces the tracking error but also improves parametric adaptation. The overall spatial domain output feedback adaptive control system is robust to model uncertainties and state estimated error and capable of rejecting spatially periodic disturbances under varying system speeds. Stability proof of the overall system is given. A design example with simulation demonstrates the applicability of the proposed design.

Synchronizing movements with the metronome: nonlinear error correction and unstable periodic orbits.

Science.gov (United States)

Engbert, Ralf; Krampe, Ralf Th; Kurths, Jürgen; Kliegl, Reinhold

2002-02-01

The control of human hand movements is investigated in a simple synchronization task. We propose and analyze a stochastic model based on nonlinear error correction; a mechanism which implies the existence of unstable periodic orbits. This prediction is tested in an experiment with human subjects. We find that our experimental data are in good agreement with numerical simulations of our theoretical model. These results suggest that feedback control of the human motor systems shows nonlinear behavior. Copyright 2001 Elsevier Science (USA).

A Model for Periodic Nonlinear Electric Field Structures in Space Plasmas

International Nuclear Information System (INIS)

Qureshi, M.N.S.; Shi Jiankui; Liu Zhenxing

2009-01-01

In this study, we present a physical model to explain the generation mechanism of nonlinear periodic waves with a large amplitude electric field structures propagating obliquely and exactly parallel to the magnetic field. The 'Sagdeev potential' from the MHD equations is derived and the nonlinear electric field waveforms are obtained when the Mach number, direction of propagation, and the initial electric field satisfy certain plasma conditions. For the parallel propagation, the amplitude of the electric field waves with ion-acoustic mode increases with the increase of initial electric field and Mach number but its frequency decreases with the increase of Mach number. The amplitude and frequency of the electric field waves with ion-cyclotron mode decrease with the increase of Mach number and become less spiky, and its amplitude increases with the increase of initial electric field. For the oblique propagation, only periodic electric field wave with an ion-cyclotron mode obtained, its amplitude and frequency increase with the increase of Mach number and become spiky. From our model the electric field structures show periodic, spiky, and saw-tooth behaviours corresponding to different plasma conditions.

Squeezed-light generation in a nonlinear planar waveguide with a periodic corrugation

International Nuclear Information System (INIS)

Perina, Jan Jr.; Haderka, Ondrej; Sibilia, Concita; Bertolotti, Mario; Scalora, Michael

2007-01-01

Two-mode nonlinear interaction (second-harmonic and second-subharmonic generation) in a planar waveguide with a small periodic corrugation at the surface is studied. Scattering of the interacting fields on the corrugation leads to constructive interference that enhances the nonlinear process provided that all the interactions are phase matched. Conditions for the overall phase matching are found. Compared with a perfectly quasi-phase-matched waveguide, better values of squeezing as well as higher intensities are reached under these conditions. Procedure for finding optimum values of parameters for squeezed-light generation is described

Sensitive periods in affective development: nonlinear maturation of fear learning.

Science.gov (United States)

Hartley, Catherine A; Lee, Francis S

2015-01-01

At specific maturational stages, neural circuits enter sensitive periods of heightened plasticity, during which the development of both brain and behavior are highly receptive to particular experiential information. A relatively advanced understanding of the regulatory mechanisms governing the initiation, closure, and reinstatement of sensitive period plasticity has emerged from extensive research examining the development of the visual system. In this article, we discuss a large body of work characterizing the pronounced nonlinear changes in fear learning and extinction that occur from childhood through adulthood, and their underlying neural substrates. We draw upon the model of sensitive period regulation within the visual system, and present burgeoning evidence suggesting that parallel mechanisms may regulate the qualitative changes in fear learning across development.

The existence of periodic solutions for nonlinear beam equations on Td by a para-differential method

Science.gov (United States)

Chen, Bochao; Li, Yong; Gao, Yixian

2018-05-01

This paper focuses on the construction of periodic solutions of nonlinear beam equations on the $d$-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a para-differential conjugation. Given the non-resonant conditions on each finite dimensional subspaces, it is shown that the periodic solutions can be constructed for the block diagonal equation by a classical iteration scheme.

Positive solutions for a nonlinear periodic boundary-value problem with a parameter

Directory of Open Access Journals (Sweden)

Jingliang Qiu

2012-08-01

Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$

Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Sun Chengfeng; Gao Hongjun

2009-01-01

The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.

Global attractivity of an almost periodic N-species nonlinear ecological competitive model

Science.gov (United States)

Xia, Yonghui; Han, Maoan; Huang, Zhenkun

2008-01-01

By using comparison theorem and constructing suitable Lyapunov functional, we study the following almost periodic nonlinear N-species competitive Lotka-Volterra model: A set of sufficient conditions is obtained for the existence and global attractivity of a unique positive almost periodic solution of the above model. As applications, some special competition models are studied again, our new results improve and generalize former results. Examples and their simulations show the feasibility of our main results.

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

Nonlinear Phononic Periodic Structures and Granular Crystals

Science.gov (United States)

2012-02-10

and boron-nitride nanotubes, and attributed the rectification to nonlinear processes [21]. Based on these studies, several following works have...nonlinear mass-spring lattices by E. Fermi, J. Pasta , and S. Ulam in 1955 [27], there has been a wealth of interest in the dynamics of nonlinear...lattices. Using one of the first modern computers, Fermi, Pasta , and Ulam (FPU) studied a system where the restoring (spring) force between two adjacent

Nonlinear periodic waves in dusty plasma with variable dust charge

International Nuclear Information System (INIS)

Yadav, Lakhan Lal; Bharuthram, R.

2002-01-01

Using the reductive perturbation method, we present a theory of nonlinear periodic waves, viz. the cnoidal waves, in a dusty plasma consisting of electrons, ions, and cold dust grains with charge fluctuations, which in the limiting case reduce to dust acoustic solitons. It is found that the frequency of the dust acoustic cnoidal wave increases with its amplitude. The dust charge fluctuations are found to affect the characteristics of the cnoidal waves

Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

International Nuclear Information System (INIS)

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-01-01

For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

International Nuclear Information System (INIS)

Chang, Jing; Gao, Yixian; Li, Yong

2015-01-01

Consider the one dimensional nonlinear beam equation u tt + u xxxx + mu + u 3 = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form. 

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

Science.gov (United States)

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-05-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.

Periodic modulations controlling Kuznetsov–Ma soliton formation in nonlinear Schrödinger equations

Energy Technology Data Exchange (ETDEWEB)

Tiofack, C.G.L., E-mail: glatchio@yahoo.fr [Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille (France); Coulibaly, S.; Taki, M. [Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille (France); De Bièvre, S.; Dujardin, G. [Univ. Lille, CNRS, UMR 8524 – Laboratoire Paul Painlevé, F-59000 Lille (France); Équipe-Projet Mephysto, INRIA Lille-Nord Europe (France)

2017-06-28

We analyze the exact Kuznetsov–Ma soliton solution of the one-dimensional nonlinear Schrödinger equation in the presence of periodic modulations satisfying an integrability condition. We show that, in contrast to the case without modulation, the Kuznetsov–Ma soliton develops multiple compression points whose number, shape and position are controlled both by the intensity of the modulation and by its frequency. In addition, when this modulation frequency is a rational multiple of the natural frequency of the Kuznetsov–Ma soliton, a scenario similar to a nonlinear resonance is obtained: in this case the spatial oscillations of the Kuznetsov–Ma soliton's intensity are periodic. When the ratio of the two frequencies is irrational, the soliton's intensity is a quasiperiodic function. A striking and important result of our analysis is the possibility to suppress any component of the output spectrum of the Kuznetsov–Ma soliton by a judicious choice of the amplitude and frequency of the modulation. - Highlights: • Exact Kuznetsov–Ma soliton solution in presence of periodic coefficients is obtained. • The multiple compression points of the solution are studied. • The quasi-periodicity of the solution is discussed. • The possibility to suppress any component of the spectrum is analyzed.

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

Energy Technology Data Exchange (ETDEWEB)

Chang, Jing [College of Information Technology, Jilin Agricultural University, Changchun 130118 (China); Gao, Yixian, E-mail: gaoyx643@nenu.edu.cn; Li, Yong [School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024 (China)

2015-05-15

Consider the one dimensional nonlinear beam equation u{sub tt} + u{sub xxxx} + mu + u{sup 3} = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form. .

Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation

International Nuclear Information System (INIS)

Bogolyubov, N.N.; Prikarpatskij, A.K.; AN Ukrainskoj SSR, Lvov. Inst. Prikladnykh Problem Mekhaniki i Matematiki)

1982-01-01

The problem of numerical solution of the Schroedinger nonlinear equation (1) iPSIsub(t) = PSIsub(xx)+-2(PSI)sup(2)PSI. The numerical solution of nonlinear differential equation supposes its discrete approximation is required for the realization of the computer calculation process. Tor the equation (1) there exists the following discrete approximation by variable x(2) iPSIsub(n, t) = (PSIsub(n+1)-2PSIsub(n)+PSIsub(n-1))/(Δx)sup(2)+-(PSIsub(n))sup(2)(PSIsub(n+1)+PSIsub(n-1)), n=0, +-1, +-2... where PSIsub(n)(+) is the corresponding value of PSI(x, t) function in the node and divisions with the equilibrium step Δx. The main problem is obtaining analytically exact solutions of the equations (2). The analysis of the equation system (2) is performed on the base of the discrete analogue of the periodic variant of the inverse scattering problem method developed with the aid of nonlinear equations of the Korteweg-de Vries type. Obtained in explicit form are analytical solutions of the equations system (2). The solutions are expressed through the Riemann THETA-function [ru

Nonlinear analysis of field distribution in electric motor with periodicity conditions

Energy Technology Data Exchange (ETDEWEB)

Stabrowski, M M; Sikora, J

1981-01-01

Numerical analysis of electromagnetic field distribution in linear motion tubular electric motor has been performed with the aid of finite element method. Two Fortran programmes for the solution of DBBF and BF large linear symmetric equation systems have been developed for purposes of this analysis. A new iterative algorithm, taking into account iron nonlinearity and periodicity conditions, has been introduced. Final results of the analysis in the form of induction diagrammes and motor driving force are directly useful for motor designers.

Effects of combined linear and nonlinear periodic training on physical fitness and competition times in finswimmers.

Science.gov (United States)

Yu, Kyung-Hun; Suk, Min-Hwa; Kang, Shin-Woo; Shin, Yun-A

2014-10-01

The purpose of this study was to investigate the effect of combined linear and nonlinear periodic training on physical fitness and competition times in finswimmers. The linear resistance training model (6 days/week) and nonlinear underwater training (4 days/week) were applied to 12 finswimmers (age, 16.08± 1.44 yr; career, 3.78± 1.90 yr) for 12 weeks. Body composition measures included weight, body mass index (BMI), percent fat, and fat-free mass. Physical fitness measures included trunk flexion forward, trunk extension backward, sargent jump, 1-repetition-maximum (1 RM) squat, 1 RM dead lift, knee extension, knee flexion, trunk extension, trunk flexion, and competition times. Body composition and physical fitness were improved after the 12-week periodic training program. Weight, BMI, and percent fat were significantly decreased, and trunk flexion forward, trunk extension backward, sargent jump, 1 RM squat, 1 RM dead lift, and knee extension (right) were significantly increased. The 50- and 100-m times significantly decreased in all 12 athletes. After 12 weeks of training, all finswimmers who participated in this study improved their times in a public competition. These data indicate that combined linear and nonlinear periodic training enhanced the physical fitness and competition times in finswimmers.

Global stability, periodic solutions, and optimal control in a nonlinear differential delay model

Directory of Open Access Journals (Sweden)

Anatoli F. Ivanov

2010-09-01

Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.

On periodic bounded and unbounded solutions of second order nonlinear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander

2017-01-01

Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2017-0009/gmj-2017-0009. xml

On periodic bounded and unbounded solutions of second order nonlinear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander

2017-01-01

Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2017-0009/gmj-2017-0009.xml

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 .

A class of periodic solutions of nonlinear wave and evolution equations

International Nuclear Information System (INIS)

Kashcheev, V.N.

1987-01-01

For the case of 1+1 dimensions a new heuristic method is proposed for deriving dels-similar solutions to nonlinear autonomous differential equations. If the differential function f is a polynomial, then: (i) in the case of even derivatives in f the solution is the ratio of two polynomials from the Weierstrass elliptic functions; (ii) in the case of any order derivatives in f the solution is the ratio of two polynomials from simple exponents. Numerous examples are given constructing such periodic solutions to the wave and evolution equations

Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads

Directory of Open Access Journals (Sweden)

Donald Mark Santee

2006-01-01

Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.

Non-linear vibrational modes in biomolecules: A periodic orbits description

International Nuclear Information System (INIS)

Kampanarakis, Alexandros; Farantos, Stavros C.; Daskalakis, Vangelis; Varotsis, Constantinos

2012-01-01

Graphical abstract: Vibrational frequency shifts in Fe IV = O species of the active site of cytochrome c oxidase are attributed to changes in the surrounding Coulomb field. Periodic orbits analysis assists to find the most anharmonic modes in model biomolecules. Highlights: ► Periodic orbits are extended to multidimensional potentials of biomolecules. ► Highly anharmonic vibrational modes and center-saddle bifurcations are detected. ► Vibrational frequencies shifts in Oxoferryl species of CcO are observed. - Abstract: The vibrational harmonic normal modes of a molecule, which are valid at energies close to an equilibrium point (a minimum, maximum or saddle of the potential energy surface), are extended by periodic orbits to high energies where anharmonicity and coupling of the degrees of freedom are significant. In this way the assignment of the spectra, and thus the extraction of dynamics in highly excited molecules, can be obtained. New vibrational modes emanating from bifurcations of periodic orbits and long living localized trajectories signal the birth and localization of new quantum states. In this article we review and further study non-linear vibrational modes for model biomolecules such as alanine dipeptide and the active site in the oxoferryl oxidation state of the enzyme cytochrome c oxidase. We locate periodic orbits which exhibit high anhamonicity and lead to center-saddle bifurcations. These modes are associated to an isomerization process in alanine dipeptide and to frequency shifts in the oxoferryl observed by modifying the Coulomb field around the Imidazole–Fe IV = O species.

Periodic and solitary wave solutions of cubic–quintic nonlinear ...

Indian Academy of Sciences (India)

Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.

Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay

International Nuclear Information System (INIS)

Ding Yuting; Jiang Weihua; Wang Hongbin

2012-01-01

Highlights: ► We derive the unfolding of a financial system with Hopf-pitchfork bifurcation. ► We show the coexistence of a pair of stable small amplitudes periodic solutions. ► At the same time, also there is a pair of stable large amplitudes periodic solutions. ► Chaos can appear by period-doubling bifurcation far away from Hopf-pitchfork value. ► The study will be useful for interpreting economics phenomena in theory. - Abstract: In this paper, we identify the critical point for a Hopf-pitchfork bifurcation in a nonlinear financial system with delay, and derive the normal form up to third order with their unfolding in original system parameters near the bifurcation point by normal form method and center manifold theory. Furthermore, we analyze its local dynamical behaviors, and show the coexistence of a pair of stable periodic solutions. We also show that there coexist a pair of stable small-amplitude periodic solutions and a pair of stable large-amplitude periodic solutions for different initial values. Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding parameter values are far away from the critical point of the Hopf-pitchfork bifurcation.

Improved harmonic balance approach to periodic solutions of non-linear jerk equations

International Nuclear Information System (INIS)

Wu, B.S.; Lim, C.W.; Sun, W.P.

2006-01-01

An analytical approximate approach for determining periodic solutions of non-linear jerk equations involving third-order time-derivative is presented. This approach incorporates salient features of both Newton's method and the method of harmonic balance. By appropriately imposing the method of harmonic balance to the linearized equation, the approach requires only one or two iterations to predict very accurate analytical approximate solutions for a large range of initial velocity amplitude. One typical example is used to verify and illustrate the usefulness and effectiveness of the proposed approach

Stationary localized modes of the quintic nonlinear Schroedinger equation with a periodic potential

International Nuclear Information System (INIS)

Alfimov, G. L.; Konotop, V. V.; Pacciani, P.

2007-01-01

We consider localized modes (bright solitons) of the one-dimensional quintic nonlinear Schroedinger equation with a periodic potential, describing several mean-field models of low-dimensional condensed gases. In the case of attractive nonlinearity we deduce sufficient conditions for collapse. We show that there exist spatially localized modes with arbitrarily large numbers of particles. We study such solutions in the semi-infinite gap (attractive case) and in the first gap (attractive and repulsive cases), and show that a nonzero minimum value of the number of particles is necessary for a localized mode to be created. In the limit of large negative frequencies (attractive case) we observe quantization of the number of particles of the stationary modes. Such solutions can be interpreted as coupled Townes solitons and appear to be stable. The modes in the first gap have numbers of particles infinitely growing with frequencies approaching one of the gap edges, which is explained by the power decay of the modes. Stability of the localized modes is discussed

Effects of periodic modulation on the nonlinear Landau–Zener tunneling

International Nuclear Information System (INIS)

Li-Hua, Wu; Wen-Shan, Duan

2009-01-01

We study the Landau–Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger. (general)

Spatial solitons in nonlinear photonic crystals

DEFF Research Database (Denmark)

Corney, Joel Frederick; Bang, Ole

2000-01-01

We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero.......We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero....

Numerical tools for musical instruments acoustics: analysing nonlinear physical models using continuation of periodic solutions

OpenAIRE

Karkar , Sami; Vergez , Christophe; Cochelin , Bruno

2012-01-01

International audience; We propose a new approach based on numerical continuation and bifurcation analysis for the study of physical models of instruments that produce self- sustained oscillation. Numerical continuation consists in following how a given solution of a set of equations is modified when one (or several) parameter of these equations are allowed to vary. Several physical models (clarinet, saxophone, and violin) are formulated as nonlinear dynamical systems, whose periodic solution...

Stochastic sensitivity analysis of periodic attractors in non-autonomous nonlinear dynamical systems based on stroboscopic map

Energy Technology Data Exchange (ETDEWEB)

Guo, Kong-Ming, E-mail: kmguo@xidian.edu.cn [School of Electromechanical Engineering, Xidian University, P.O. Box 187, Xi' an 710071 (China); Jiang, Jun, E-mail: jun.jiang@mail.xjtu.edu.cn [State Key Laboratory for Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China)

2014-07-04

To apply stochastic sensitivity function method, which can estimate the probabilistic distribution of stochastic attractors, to non-autonomous dynamical systems, a 1/N-period stroboscopic map for a periodic motion is constructed in order to discretize the continuous cycle into a discrete one. In this way, the sensitivity analysis of a cycle for discrete map can be utilized and a numerical algorithm for the stochastic sensitivity analysis of periodic solutions of non-autonomous nonlinear dynamical systems under stochastic disturbances is devised. An external excited Duffing oscillator and a parametric excited laser system are studied as examples to show the validity of the proposed method. - Highlights: • A method to analyze sensitivity of stochastic periodic attractors in non-autonomous dynamical systems is proposed. • Probabilistic distribution around periodic attractors in an external excited Φ{sup 6} Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined.

Effectiveness of flavour nutrient learning and mere exposure as mechanisms to increase toddler's intake and preference for green vegetables.

Science.gov (United States)

de Wild, Victoire W T; de Graaf, Cees; Jager, Gerry

2013-05-01

Children's consumption of vegetables is still below recommendations. Since preference is the most important predictor of children's intake and most children dislike vegetables, new strategies are needed to increase their preferences for vegetables. Flavour nutrient learning (FNL) could be an effective mechanism to change preferences. Forty healthy toddlers were included in a randomized intervention study. During an intervention period of 7weeks, they consumed vegetable soups (endive and spinach) twice per week. Half of the group received a high-energy variant of one soup (e.g. HE spinach) and a low energy variant of the other (LE endive), whereas for the other half the order was reversed (HE endive, LE spinach). Primary outcome measures were preference and ad libitum consumption (with a maximum of 200g) of both vegetable products (LE), measured before, shortly after the intervention period, and 2 and 6months following conditioning to assess longer-term effects. After completion of the intervention period, 28 children (14 girls and 14 boys, age 35months; SD±8.3) met criteria for FNL to occur, and were included in further data analysis. Results showed a significant increase (~58g) in ad libitum intake for both vegetable soups (stable over time), but irrespective of the energy content. This indicates a robust effect of mere exposure on intake, but no FNL. For preference, however, results showed a significant shift in liking for the vegetable soup consistently paired with high energy, supporting FNL. Copyright © 2013 Elsevier Ltd. All rights reserved.

A variational numerical method based on finite elements for the nonlinear solution characteristics of the periodically forced Chen system

Science.gov (United States)

Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.

2017-09-01

Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.

Nonlinear oscillation system of mass with serial linear and nonlinear springs

DEFF Research Database (Denmark)

Seyedalizadeh Ganji,, S.R; Barari, Amin; Karimpour, S

2013-01-01

In this paper, two powerful methods called Max–Min and parameter expansion have been applied for the determination of the periodic solutions of the nonlinear free vibration of a conservative oscillator with inertia and static type cubic nonlinearities. It is found that these methods introduce two...... alternatives to overcome the difficulty of capturing the periodic behavior of the solution, as the most evident characteristic of oscillators. It can be clearly observed that approximate frequencies and periodic solutions are in excellent agreement with the exact ones. First approximation leads to high...

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

Science.gov (United States)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Nonlinear Magnus-induced dynamics and Shapiro spikes for ac and dc driven skyrmions on periodic quasi-one-dimensional substrates

Science.gov (United States)

Reichhardt, Charles; Reichhardt, Cynthia J. Olson

We numerically examine skyrmions interacting with a periodic quasi-one-dimensional substrate. When we drive the skyrmions perpendicular to the substrate periodicity direction, a rich variety of nonlinear Magnus-induced effects arise, in contrast to an overdamped system that shows only a linear velocity-force curve for this geometry. The skyrmion velocity-force curve is strongly nonlinear and we observe a Magnus-induced speed-up effect when the pinning causes the Magnus velocity response to align with the dissipative response. At higher applied drives these components decouple, resulting in strong negative differential conductivity. For skyrmions under combined ac and dc driving, we find a new class of phase locking phenomena in which the velocity-force curves contain a series of what we call Shapiro spikes, distinct from the Shapiro steps observed in overdamped systems. There are also regimes in which the skyrmion moves in the direction opposite to the applied dc drive to give negative mobility.

Properties of entangled proton pairs generated in periodically poled nonlinear crystals

Czech Academy of Sciences Publication Activity Database

Svozilík, Jiří; Peřina ml., Jan

2009-01-01

Roč. 80, č. 2 (2009), 023819/1-023819/9 ISSN 1050-2947 R&D Projects: GA MŠk(CZ) OC09026; GA AV ČR IAA100100713; GA MŠk(CZ) 1M06002 Institutional research plan: CEZ:AV0Z10100522 Keywords : photon pairs * nonlinear crystals * nonlinear optics * quantum optics Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.866, year: 2009

The nonlinear ambipolar drift and periodic structure of non-self-sustained discharge

International Nuclear Information System (INIS)

Dem'yanov, A.V.; Mazalov, D.A.; Napartovich, A.P.

1995-01-01

Gas discharge is well known to be strongly nonlinear self-organizing system. The diverse nonlinear structures, observed at different conditions (arc, stationary and non-stationary strata, hot spot patterns on the electrodes and so on), are usually explained by the theory taking into account the processes of diffusion and thermoconductivity. In plasma of high pressure discharge these processes become negligible within the characteristic intervals. At these conditions electron drift becomes the main process. Owing to the continuity of full current and plasma quasineutrality there appear effective flows of convective type with the rate depending on the concentration of charged particles. It is this reason that is responsible for the observed structure of the non-moving luminous layers in non-self-sustained discharge in 10%H 2 +Ar mixture under p≥l atm. The present report shows the results of detail experimental and theoretical study of this phenomenon. The experiments have been carried out on the setup with the discharge gap of about 1 cm or of much greater size. Mach-Zender interferometer and an image-converter intensifier operating as a strip or framing camera. The experiments have been carried out under the pressure 1-3 atm. They show that the stationary layers sequentially appear one after another along the direction from the cathode to the anode. Interferometry shows that there is a gas density modulation corresponding to the periodical structure of fringes. The picture of Fig.1 is a typical interferogram, and that of Fig.2 is a gas density distribution restored from it

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

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.

Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

Energy Technology Data Exchange (ETDEWEB)

Garcia Velarde, M

1977-07-01

Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.

Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

International Nuclear Information System (INIS)

Garcia Velarde, M.

1977-01-01

Thermoconvective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Benard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (author) [es

Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

International Nuclear Information System (INIS)

Garcia Velarde, M.

1977-01-01

Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs

Detecting unstable periodic orbits of nonlinear mappings by a novel quantum-behaved particle swarm optimization non-Lyapunov way

International Nuclear Information System (INIS)

Gao Fei; Gao Hongrui; Li Zhuoqiu; Tong Hengqing; Lee, Ju-Jang

2009-01-01

It is well known that set of unstable periodic orbits (UPOs) can be thought of as the skeleton for the dynamics. However, detecting UPOs of nonlinear map is one of the most challenging problems of nonlinear science in both numerical computations and experimental measures. In this paper, a new method is proposed to detect the UPOs in a non-Lyapunov way. Firstly three special techniques are added to quantum-behaved particle swarm optimization (QPSO), a novel mbest particle, contracting the searching space self-adaptively and boundaries restriction (NCB), then the new method NCB-QPSO is proposed. It can maintain an effective search mechanism with fine equilibrium between exploitation and exploration. Secondly, the problems of detecting the UPOs are converted into a non-negative functions' minimization through a proper translation in a non-Lyapunov way. Thirdly the simulations to 6 benchmark optimization problems and different high order UPOs of 5 classic nonlinear maps are done by the proposed method. And the results show that NCB-QPSO is a successful method in detecting the UPOs, and it has the advantages of fast convergence, high precision and robustness.

Period doubling cascades of prey-predator model with nonlinear harvesting and control of over exploitation through taxation

Science.gov (United States)

Gupta, R. P.; Banerjee, Malay; Chandra, Peeyush

2014-07-01

The present study investigates a prey predator type model for conservation of ecological resources through taxation with nonlinear harvesting. The model uses the harvesting function as proposed by Agnew (1979) [1] which accounts for the handling time of the catch and also the competition between standard vessels being utilized for harvesting of resources. In this paper we consider a three dimensional dynamic effort prey-predator model with Holling type-II functional response. The conditions for uniform persistence of the model have been derived. The existence and stability of bifurcating periodic solution through Hopf bifurcation have been examined for a particular set of parameter value. Using numerical examples it is shown that the system admits periodic, quasi-periodic and chaotic solutions. It is observed that the system exhibits periodic doubling route to chaos with respect to tax. Many forms of complexities such as chaotic bands (including periodic windows, period-doubling bifurcations, period-halving bifurcations and attractor crisis) and chaotic attractors have been observed. Sensitivity analysis is carried out and it is observed that the solutions are highly dependent to the initial conditions. Pontryagin's Maximum Principle has been used to obtain optimal tax policy to maximize the monetary social benefit as well as conservation of the ecosystem.

Exact solutions of the two-dimensional discrete nonlinear Schrodinger equation with saturable nonlinearity

DEFF Research Database (Denmark)

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

2010-01-01

We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the e...

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.

Effects of linear and nonlinear time-delayed feedback on the noise-enhanced stability phenomenon in a periodically driven bistable system

International Nuclear Information System (INIS)

Jia, Zheng-Lin; Mei, Dong-Cheng

2011-01-01

We investigate numerically the effects of time delay on the phenomenon of noise-enhanced stability (NES) in a periodically modulated bistable system. Three types of time-delayed feedback, including linear delayed feedback, nonlinear delayed feedback and global delayed feedback, are considered. We find a non-monotonic behaviour of the mean first-passage time (MFPT) as a function of the delay time τ, with a maximum in the case of linear delayed feedback and with a minimum in the case of nonlinear delayed feedback. There are two peculiar values of τ around which the NES phenomenon is enhanced or weakened. For the case of global delayed feedback, the increase of τ always weakens the NES phenomenon. Moreover, we also show that the amplitude A and the frequency Ω of the periodic forcing play an opposite role in the NES phenomenon, i.e. the increase of A weakens the NES effect while the increase of Ω enhances it. These observations demonstrate that the time-delayed feedback can be used as a feasible control scheme for the NES phenomenon

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

Kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations

International Nuclear Information System (INIS)

Davidson, R.C.; Chen, C.

1997-08-01

A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B sol (rvec x) is developed. The analysis is carried out for a thin beam with characteristic beam radius r b much-lt S, and directed axial momentum γ b mβ b c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f b (rvec x,rvec p,t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B z (z) = B 0 = const. and for the case of a periodic solenoidal focusing field B z (z + S) = B z (z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field rvec B sol (rvec x) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria

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

International Nuclear Information System (INIS)

Xu Guiqiong; Li Zhibin

2005-01-01

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

Periodic wavetrains for systems of coupled nonlinear Schrödinger ...

Indian Academy of Sciences (India)

Systems of coupled nonlinear Schrödinger equations (cNLS) have received tremendous ..... The propagation of optical solitons along fibers has played an important role ... To increase the information carrying capacity, it will be desirable and ...

Propagation of a femtosecond laser pulse with duration of several optical oscillation periods in a medium with a quadratic nonlinearity

International Nuclear Information System (INIS)

Akopyan, A A; Oganesyan, D L

1998-01-01

It is shown that the wave equation can be solved by the method of unidirectional waves for a pulse with a duration of several oscillation periods in a medium with a quadratic nonlinearity, such as a group-3m crystal. The wave equation reduces to a system of two equations for waves with different polarisations. (laser applications and other topics in quantum electronics)

Nonlinearity management in higher dimensions

International Nuclear Information System (INIS)

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

2006-01-01

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

Nonlinear Wave Propagation

Science.gov (United States)

2015-05-07

associated with the lattice background; the nonlinearity is derived from the inclusion of cubic nonlinearity. Often the background potential is periodic...dispersion branch we can find discrete evolution equations for the envelope associated with the lattice NLS equation (1) by looking for solutions of...spatial operator in the above NLS equation can be elliptic, hyperbolic or parabolic . We remark that further reduction is possible by going into a moving

Quantitative theory of driven nonlinear brain dynamics.

Science.gov (United States)

Roberts, J A; Robinson, P A

2012-09-01

Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

Assessing non-linear variation of temperature and precipitation for different growth periods of maize and their impacts on phenology in the Midwest of Jilin Province, China

Science.gov (United States)

Guo, Enliang; Zhang, Jiquan; Wang, Yongfang; Alu, Si; Wang, Rui; Li, Danjun; Ha, Si

2018-05-01

In the past two decades, the regional climate in China has undergone significant change, resulting in crop yield reduction and complete failure. The goal of this study is to detect the variation of temperature and precipitation for different growth periods of maize and assess their impact on phenology. The daily meteorological data in the Midwest of Jilin Province during 1960-2014 were used in the study. The ensemble empirical mode decomposition method was adopted to analyze the non-linear trend and fluctuation in temperature and precipitation, and the sensitivity of the length of the maize growth period to temperature and precipitation was analyzed by the wavelet cross-transformation method. The results show that the trends of temperature and precipitation change are non-linear for different growth periods of maize, and the average temperature in the sowing-jointing stage was different from that in the other growth stages, showing a slight decrease trend, while the variation amplitude of maximum temperature is smaller than that of the minimum temperature. This indicates that the temperature difference between day and night shows a gradually decreasing trend. Precipitation in the growth period also showed a decreasing non-linear trend, while the inter-annual variability with period of quasi-3-year and quasi-6-year dominated the variation of temperature and precipitation. The whole growth period was shortened by 10.7 days, and the sowing date was advanced by approximately 11 days. We also found that there was a significant resonance period among temperature, precipitation, and phenology. Overall, a negative correlation between phenology and temperature is evident, while a positive correlation with precipitation is exhibited. The results illustrate that the climate suitability for maize has reduced over the past decades.

On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay

Directory of Open Access Journals (Sweden)

Emmanuel K. Essel

2014-01-01

Full Text Available We prove that the totally nonlinear second-order neutral differential equation \\[\\frac{d^2}{dt^2}x(t+p(t\\frac{d}{dt}x(t+q(th(x(t\\] \\[=\\frac{d}{dt}c(t,x(t-\\tau(t+f(t,\\rho(x(t,g(x(t-\\tau(t\\] has positive periodic solutions by employing the Krasnoselskii-Burton hybrid fixed point theorem.

Linear and nonlinear susceptibilities from diffusion quantum Monte Carlo: application to periodic hydrogen chains.

Science.gov (United States)

Umari, P; Marzari, Nicola

2009-09-07

We calculate the linear and nonlinear susceptibilities of periodic longitudinal chains of hydrogen dimers with different bond-length alternations using a diffusion quantum Monte Carlo approach. These quantities are derived from the changes in electronic polarization as a function of applied finite electric field--an approach we recently introduced and made possible by the use of a Berry-phase, many-body electric-enthalpy functional. Calculated susceptibilities and hypersusceptibilities are found to be in excellent agreement with the best estimates available from quantum chemistry--usually extrapolations to the infinite-chain limit of calculations for chains of finite length. It is found that while exchange effects dominate the proper description of the susceptibilities, second hypersusceptibilities are greatly affected by electronic correlations. We also assess how different approximations to the nodal surface of the many-body wave function affect the accuracy of the calculated susceptibilities.

Nonlinear temporal modulation of pulsar radioemission

International Nuclear Information System (INIS)

Chian, A.C.-L.

1984-01-01

A nonlinear theory is discussed for self-modulation of pulsar radio pulses. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron-positron plasma. The nonlinearities arising from wave intensity induced relativistic particle mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary wave forms may account for the formation of pulsar microstructures. (Author) [pt

Solving Nonlinear Coupled Differential Equations

Science.gov (United States)

Mitchell, L.; David, J.

1986-01-01

Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

Impact of Uncertainties in the Cosmological Parameters on the Measurement of Primordial non-Gaussianity

CERN Document Server

Liguori, M

2008-01-01

We study the impact of cosmological parameters' uncertainties on estimates of the primordial NG parameter f_NL in local and equilateral models of non-Gaussianity. We show that propagating these errors increases the f_NL relative uncertainty by 16% for WMAP and 5 % for Planck in the local case, whereas for equilateral configurations the correction term are 14% and 4%, respectively. If we assume for local f_NL a central value of order 60, according to recent WMAP 5-years estimates, we obtain for Planck a final correction \\Delta f_NL = 3. Although not dramatic, this correction is at the level of the expected estimator uncertainty for Planck, and should then be taken into account when quoting the significance of an eventual future detection. In current estimates of f_NL the cosmological parameters are held fixed at their best-fit values. We finally note that the impact of uncertainties in the cosmological parameters on the final f_NL error bar would become totally negligible if the parameters were allowed to vary...

Solitary waves under the competition of linear and nonlinear periodic potentials

International Nuclear Information System (INIS)

Rapti, Z; Kevrekidis, P G; Konotop, V V; Jones, C K R T

2007-01-01

In this paper, we study the competition of the linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framework, whereby the technique of Hamiltonian perturbation theory can be used to obtain information about the existence of solutions, and the same approach, as well as eigenvalue count considerations, can be used to obtain detailed conditions about their linear stability. We find that the analytical results are in very good agreement with our numerical findings and can also be used to predict features of the dynamical evolution of such solutions. A particularly interesting result of these considerations is the existence of a tunable cancellation effect between the linear and nonlinear lattices that allows for increased mobility of the solitary wave

Nonlinear dynamics between linear and impact limits

CERN Document Server

Pilipchuk, Valery N; Wriggers, Peter

2010-01-01

This book examines nonlinear dynamic analyses based on the existence of strongly nonlinear but simple counterparts to the linear models and tools. Discusses possible application to periodic elastic structures with non-smooth or discontinuous characteristics.

Parametric Identification of Nonlinear Dynamical Systems

Science.gov (United States)

Feeny, Brian

2002-01-01

In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

Periodically poled silicon

Science.gov (United States)

Hon, Nick K.; Tsia, Kevin K.; Solli, Daniel R.; Khurgin, Jacob B.; Jalali, Bahram

2010-02-01

Bulk centrosymmetric silicon lacks second-order optical nonlinearity χ(2) - a foundational component of nonlinear optics. Here, we propose a new class of photonic device which enables χ(2) as well as quasi-phase matching based on periodic stress fields in silicon - periodically-poled silicon (PePSi). This concept adds the periodic poling capability to silicon photonics, and allows the excellent crystal quality and advanced manufacturing capabilities of silicon to be harnessed for devices based on χ(2)) effects. The concept can also be simply achieved by having periodic arrangement of stressed thin films along a silicon waveguide. As an example of the utility, we present simulations showing that mid-wave infrared radiation can be efficiently generated through difference frequency generation from near-infrared with a conversion efficiency of 50% based on χ(2) values measurements for strained silicon reported in the literature [Jacobson et al. Nature 441, 199 (2006)]. The use of PePSi for frequency conversion can also be extended to terahertz generation. With integrated piezoelectric material, dynamically control of χ(2)nonlinearity in PePSi waveguide may also be achieved. The successful realization of PePSi based devices depends on the strength of the stress induced χ(2) in silicon. Presently, there exists a significant discrepancy in the literature between the theoretical and experimentally measured values. We present a simple theoretical model that produces result consistent with prior theoretical works and use this model to identify possible reasons for this discrepancy.

Non-Gaussianity from Broken Symmetries

CERN Document Server

Kolb, Edward W; Vallinotto, A; Kolb, Edward W.; Riotto, Antonio; Vallinotto, Alberto

2006-01-01

Recently we studied inflation models in which the inflaton potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, $f_{NL}$, can be as large as 10^2.

Nonlinear ion-acoustic waves and solitons in a magnetized plasma

International Nuclear Information System (INIS)

Lee, L.C.; Kan, J.R.

1981-01-01

A unified formulation is presented to study the nonlinear low-frequency electrostatic waves in a magnetized low-β plasma. It is found that there exist three types of nonlinear waves; (1) nonlinear ion-cyclotron periodic waves with a wave speed V/sub p/ > C/sub s/ (ion-acoustic velocity); (2) nonlinear ion-acoustic periodic waves with V/sub p/ < C/sub s/ costheta; and (3) ion-acoustic solitons with C/sub s/ costheta < V/sub p/ < C/sub s/, where theta is the angle between the wave vector and the magnetic field

Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schroedinger's equation with Kerr law nonlinearity

International Nuclear Information System (INIS)

Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong

2011-01-01

In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.

A study of discrete nonlinear systems

International Nuclear Information System (INIS)

Dhillon, H.S.

2001-04-01

An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

Design and implementation of novel nonlinear processes in bulk and waveguide periodic structures

Science.gov (United States)

Kajal, Meenu

The telecommunication networks are facing increasing demand to implement all-optical network infrastructure for enabling the wide deployment of new triple play high-speed services (e.g. IPTV, Video On Demand, Voice over IP). One of the challenges with such video broadcasting applications is that these are much more distributed and multi-point in nature unlike the traditional point-to-point communication networks. Currently deployed high-speed electronic components in the optical networks are incapable of handling the unprecedented bandwidth demand for real-time multimedia based broadcasting. The solution essentially lies in increasing the transparency of networks i.e. by replacing high speed signal processing electronics with all-optical signal processors capable of performing signal manipulations such as wavelength switching, time and wavelength division multiplexing, optical pulse compression etc. all in optical domain. This thesis aims at providing an all-optical solution for broadband wavelength conversion and tunable broadcasting, a crucial optical network component, based on quasi-phase-matched wave mixing in nonlinear materials. The quasi phase matching (QPM) technique allows phase matching in long crystal lengths by employing domain-inverted gratings to periodically reverse the sign of nonlinearity, known as periodic poling. This results into new frequency components with high conversion efficiency and has been successfully implemented towards various processes such as second harmonic generation (SHG), sum- and difference- frequency generation (SFG and DFG). Conventionally, the optical networks has an operation window of ˜35 nm centered at 1.55 mum, known as C-band. The wavelength conversion of a signal channel in C-band to an output channel also in the C-band has been demonstrated in periodically poled lithium niobate (PPLN) waveguides via the process of difference frequency mixing, cascaded SHG/DFG and cascaded SFG/DFG. While a DFG process utilized a

Laryngeal ultrasound and vocal fold movement in the pediatric cardiovascular intensive care unit.

Science.gov (United States)

Ongkasuwan, Julina; Ocampo, Elena; Tran, Brandon

2017-01-01

Vocal fold motion impairment (VFMI) is a known sequela of cardiovascular surgery. The gold standard for the evaluation of vocal fold movement is flexible nasolaryngoscopy (FNL). Although safe, FNL does cause measurable physiologic changes. Noxious stimuli in cardiovascular intensive care unit (CVICU) neonates may cause imbalance between the pulmonary and systemic circulations and potentially circulatory collapse. The goals of this project were to determine the accuracy of laryngeal ultrasound (LUS) compared to FNL to identify VFMI in CVICU neonates and compare their physiologic impact. Case control. Prospective case-control study. Forty-six consecutive infants from the CVICU were recruited, 23 with VFMI and 23 without based on FNL findings. They then underwent LUS, which was subsequently reviewed by two pediatric radiologists blinded to the FNL results. Physiologic parameters were recorded before and after the procedures. Data analysis was performed with Cohen's kappa and Wilcoxon signed-rank test. Agreement between LUS and FNL was substantial (κ = 0.78). Laryngeal ultrasound had a sensitivity of 0.84 and specificity of 0.95 for identifying VFMI. In terms of physiologic impact, LUS caused statistically significantly less change in diastolic blood pressure (P = 0.01), pulse (P = 0.001), and O 2 saturation (P = 0.004) compared to FNL. Arytenoid rotation could be seen clearly, and the vocal fold-arytenoid angle in abduction was most predictive of symmetry and movement (P = 0.17). However, it was difficult to determine vocal fold closure patterns with LUS. Laryngeal ultrasound is a comparable to FNL for evaluating vocal fold mobility with less physiologic impact. 3b. Laryngoscope, 127:167-172, 2017. © 2016 The American Laryngological, Rhinological and Otological Society, Inc.

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...

Multiorder nonlinear diffraction in frequency doubling processes

DEFF Research Database (Denmark)

Saltiel, Solomon M.; Neshev, Dragomir N.; Krolikowski, Wieslaw

2009-01-01

We analyze experimentally light scattering from 2 nonlinear gratings and observe two types of second-harmonic frequency-scattering processes. The first process is identified as Raman–Nath type nonlinear diffraction that is explained by applying only transverse phase-matching conditions. The angular...... position of this type of diffraction is defined by the ratio of the second-harmonic wavelength and the grating period. In contrast, the second type of nonlinear scattering process is explained by the longitudinal phase matching only, being insensitive to the nonlinear grating...

Exact solutions for the quintic nonlinear Schroedinger equation with time and space modulated nonlinearities and potentials

International Nuclear Information System (INIS)

Belmonte-Beitia, Juan; Calvo, Gabriel F.

2009-01-01

In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions

Engineering quadratic nonlinear photonic crystals for frequency conversion of lasers

Science.gov (United States)

Chen, Baoqin; Hong, Lihong; Hu, Chenyang; Zhang, Chao; Liu, Rongjuan; Li, Zhiyuan

2018-03-01

Nonlinear frequency conversion offers an effective way to extend the laser wavelength range. Quadratic nonlinear photonic crystals (NPCs) are artificial materials composed of domain-inversion structures whose sign of nonlinear coefficients are modulated with desire to implement quasi-phase matching (QPM) required for nonlinear frequency conversion. These structures can offer various reciprocal lattice vectors (RLVs) to compensate the phase-mismatching during the quadratic nonlinear optical processes, including second-harmonic generation (SHG), sum-frequency generation and the cascaded third-harmonic generation (THG). The modulation pattern of the nonlinear coefficients is flexible, which can be one-dimensional or two-dimensional (2D), be periodic, quasi-periodic, aperiodic, chirped, or super-periodic. As a result, these NPCs offer very flexible QPM scheme to satisfy various nonlinear optics and laser frequency conversion problems via design of the modulation patterns and RLV spectra. In particular, we introduce the electric poling technique for fabricating QPM structures, a simple effective nonlinear coefficient model for efficiently and precisely evaluating the performance of QPM structures, the concept of super-QPM and super-periodically poled lithium niobate for finely tuning nonlinear optical interactions, the design of 2D ellipse QPM NPC structures enabling continuous tunability of SHG in a broad bandwidth by simply changing the transport direction of pump light, and chirped QPM structures that exhibit broadband RLVs and allow for simultaneous radiation of broadband SHG, THG, HHG and thus coherent white laser from a single crystal. All these technical, theoretical, and physical studies on QPM NPCs can help to gain a deeper insight on the mechanisms, approaches, and routes for flexibly controlling the interaction of lasers with various QPM NPCs for high-efficiency frequency conversion and creation of novel lasers.

Oscillations in nonlinear systems

CERN Document Server

Hale, Jack K

2015-01-01

By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa

Degenerate nonlinear diffusion equations

CERN Document Server

Favini, Angelo

2012-01-01

The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

Nonlinear Squeeze Film Dampers without Centralized Springs

Directory of Open Access Journals (Sweden)

Zhu Changsheng

2000-01-01

Full Text Available In this paper, the bifurcation behavior of a flexible rotor supported on nonlinear squeeze film dampers without centralized springs is analyzed numerically by means of rotor trajectories, Poincar maps, bifurcation diagrams and power spectra, based on the short bearing and cavitated film assumptions. It is shown that there also exist two different operations (i.e., socalled bistable operations in some speed regions in the rotor system supported on the nonlinear squeeze film dampers without centralized springs. In the bistable operation speed regions, the rotor system exhibits synchronous, sub-synchronous, sub-super-synchronous and almost-periodic as well as nonperiodic motions. The periodic bifurcation behaviors of the rotor system supported on nonlinear squeeze film dampers without centralized springs are very complex and require further investigations.

Nonlinear optical crystals a complete survey

CERN Document Server

Nikogosyan, David N

2005-01-01

Nonlinear optical crystals are widely used in modern optical science and technology for frequency conversion of laser light, i.e. to generate laser radiation at any specific wavelength in visible, UV or IR spectral regions. This unrivalled reference book contains the most complete and up-to-date information on properties of nonlinear optical crystals. It includes: * Database of 63 common and novel nonlinear optical crystals * Periodically-poled and self-frequency-doubling materials * Full description of linear and nonlinear optical properties * Significant amount of crystallophysical, thermophysical, spectroscopic, electro-optic and magneto-optic information * 7 mini-reviews on novel applications, such as deep-UV light generation, terahertz-wave generation, ultrashort laser pulse compression, photonic band-gap crystals, x3 nonlinearity, etc. * More than 1500 different references with full titles It is a vital source of information for scientists and engineers dealing with modern applications of nonlinear opti...

Experimental chaos in nonlinear vibration isolation system

International Nuclear Information System (INIS)

Lou Jingjun; Zhu Shijian; He Lin; He Qiwei

2009-01-01

The chaotic vibration isolation method was studied thoroughly from an experimental perspective. The nonlinear load-deflection characteristic of the conical coil spring used in the experiment was surveyed. Chaos and subharmonic responses including period-2 and period-6 motions were observed. The line spectrum reduction and the drop of the acceleration vibration level in chaotic state and that in non-chaotic state were compared, respectively. It was concluded from the experiment that the nonlinear vibration isolation system in chaotic state has strong ability in line spectrum reduction.

Double-resonant processes in x.sup.20.sup. nonlinear periodic media

Czech Academy of Sciences Publication Activity Database

Konotop, V. V.; Kuzmiak, Vladimír

2000-01-01

Roč. 17, č. 11 (2000), s. 1874-1883 ISSN 0740-3224 Grant - others:Fundo European de Desenvolvimento Regional and Program PRAXIS XXI(PT) PRAXIS/2/2.1/FIS/176/94 Institutional research plan: CEZ:AV0Z2067918 Keywords : nonlinear media * electromagnetic wave propagation Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.943, year: 2000

Observation of Nonlinear Self-Trapping of Broad Beams in Defocusing Waveguide Arrays

International Nuclear Information System (INIS)

Bennet, Francis H.; Haslinger, Franz; Neshev, Dragomir N.; Kivshar, Yuri S.; Alexander, Tristram J.; Mitchell, Arnan

2011-01-01

We demonstrate experimentally the localization of broad optical beams in periodic arrays of optical waveguides with defocusing nonlinearity. This observation in optics is linked to nonlinear self-trapping of Bose-Einstein-condensed atoms in stationary periodic potentials being associated with the generation of truncated nonlinear Bloch states, existing in the gaps of the linear transmission spectrum. We reveal that unlike gap solitons, these novel localized states can have an arbitrary width defined solely by the size of the input beam while independent of nonlinearity.

Center manifold for nonintegrable nonlinear Schroedinger equations on the line

International Nuclear Information System (INIS)

Weder, R.

2000-01-01

In this paper we study the following nonlinear Schroedinger equation on the line, where f is real-valued, and it satisfies suitable conditions on regularity, on growth as a function of u and on decay as x → ± ∞. The generic potential, V, is real-valued and it is chosen so that the spectrum of H:= -d 2 /dx 2 +V consists of one simple negative eigenvalue and absolutely-continuous spectrum filling (0,∞). The solutions to this equation have, in general, a localized and a dispersive component. The nonlinear bound states, that bifurcate from the zero solution at the energy of the eigenvalue of H, define an invariant center manifold that consists of the orbits of time-periodic localized solutions. We prove that all small solutions approach a particular periodic orbit in the center manifold as t→ ± ∞. In general, the periodic orbits are different for t→ ± ∞. Our result implies also that the nonlinear bound states are asymptotically stable, in the sense that each solution with initial data near a nonlinear bound state is asymptotic as t→ ± ∞ to the periodic orbits of nearby nonlinear bound states that are, in general, different for t→ ± ∞. (orig.)

Quantized gauge invariant periodic TDHF solutions

International Nuclear Information System (INIS)

Kan, K.-K.; Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.

1979-01-01

Time-dependent Hartree-Fock (TDHF) is used to study steady state large amplitude nuclear collective motions, such as vibration and rotation. As is well known the small amplitude TDHF leads to the RPA equation. The analysis of periodicity in TDHF is not trivial because TDHF is a nonlinear theory and it is not known under what circumstances a nonlinear theory can support periodic solutions. It is also unknown whether such periodic solution, if they exist, form a continuous or a discrete set. But, these properties may be important in obtaining the energy spectrum of the collective states from the TDHF description. The periodicity and Gauge Invariant Periodicity of solutions are investigated for that class of models whose TDHF solutions depend on time through two parameters. In such models TDHF supports a continuous family of periodic solutions, but only a discrete subset of these is gauge invariant. These discrete Gauge Invariant Periodic solutions obey the Bohr-Summerfeld quantization rule. The energy spectrum of the Gauge Invariant Periodic solutions is compared with the exact eigenergies in one specific example

Design of advanced materials for linear and nonlinear dynamics

DEFF Research Database (Denmark)

Frandsen, Niels Morten Marslev

to reveal the fundamental dynamic characteristics and thus the relevant design parameters.The thesis is built around the characterization of two one-dimensional, periodic material systems. The first is a nonlinear mass-spring chain with periodically varying material properties, representing a simple......The primary catalyst of this PhD project has been an ambition to design advanced materials and structural systems including, and possibly even exploiting, nonlinear phenomena such as nonlinear modal interaction leading to energy conversion between modes. An important prerequisite for efficient...... but general model of inhomogeneous structural materials with nonlinear material characteristics. The second material system is an “engineered” material in the sense that a classical structural element, a linear elastic and homogeneous rod, is “enhanced” by applying a mechanism on its surface, amplifying...

Spectral theory and nonlinear functional analysis

CERN Document Server

Lopez-Gomez, Julian

2001-01-01

This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.

Periodic flows to chaos in time-delay systems

CERN Document Server

Luo, Albert C J

2017-01-01

This book for the first time examines periodic motions to chaos in time-delay systems, which exist extensively in engineering. For a long time, the stability of time-delay systems at equilibrium has been of great interest from the Lyapunov theory-based methods, where one cannot achieve the ideal results. Thus, time-delay discretization in time-delay systems was used for the stability of these systems. In this volume, Dr. Luo presents an accurate method based on the finite Fourier series to determine periodic motions in nonlinear time-delay systems. The stability and bifurcation of periodic motions are determined by the time-delayed system of coefficients in the Fourier series and the method for nonlinear time-delay systems is equivalent to the Laplace transformation method for linear time-delay systems. Facilitates discovery of analytical solutions of nonlinear time-delay systems; Illustrates bifurcation trees of periodic motions to chaos; Helps readers identify motion complexity and singularity; Explains pro...

Nonlinear silicon photonics

Science.gov (United States)

Tsia, Kevin K.; Jalali, Bahram

2010-05-01

An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.

The reliability of flexible nasolaryngoscopy in the identification of vocal fold movement impairment in young infants.

Science.gov (United States)

Liu, Yi-Chun Carol; McElwee, Tyler; Musso, Mary; Rosenberg, Tara L; Ongkasuwan, Julina

2017-09-01

Flexible nasolaryngoscopy (FNL) is considered the gold standard for evaluation of vocal fold mobility but there has been no data on the reliability of interpretation in the infant population. Visualization may be limited by excessive movement, secretions, or floppy supraglottic structures that prevent accurate diagnosis of vocal fold movement impairment (VFMI). We sought to evaluate the inter- and intra-rater reliability of FNL for the evaluation of VFMI in young infants. Case-control. Twenty infants were identified: 10 with VFMI and 10 normal as seen on FNL. Three pediatric otolaryngologists reviewed the video without sound and rated the presence and/or degree of vocal fold mobility. Twelve videos were repeated to assess intra-rater reliability. There was substantial agreement between the reviewers regarding the identification normal vs. any type of VFMI (kappa = 0.67) but only moderate agreement regarding the degree of vocal fold movement (kappa = 0.49). Intra-rater reliability ranges from moderate to perfect agreement (kappa = 0.48-1). FNL in infants is an extremely challenging procedure. Clinically, physicians frequently use the quality of the cry and the past medical and surgical history to help make a judgment of vocal fold movement when the view is suboptimal. These other factors, however, may bias the interpretation of the FNL. Without sound, there is only moderate inter-rater and variable intra-rater reliability for the identification of degree of movement on FNL. Otolaryngologists must be cognizant of the limitations of FNL when using it as a clinical tool or as a "gold standard" against which other modalities are measured. Copyright © 2017 Elsevier B.V. All rights reserved.

A new analytical approach for limit cycles and quasi-periodic solutions of nonlinear oscillators: the example of the forced Van der Pol Duffing oscillator

International Nuclear Information System (INIS)

Shukla, Anant Kant; Ramamohan, T R; Srinivas, S

2014-01-01

In this paper we propose a technique to obtain limit cycles and quasi-periodic solutions of forced nonlinear oscillators. We apply this technique to the forced Van der Pol oscillator and the forced Van der Pol Duffing oscillator and obtain for the first time their limit cycles (periodic) and quasi-periodic solutions analytically. We introduce a modification of the homotopy analysis method to obtain these solutions. We minimize the square residual error to obtain accurate approximations to these solutions. The obtained analytical solutions are convergent and agree well with numerical solutions even at large times. Time trajectories of the solution, its first derivative and phase plots are presented to confirm the validity of the proposed approach. We also provide rough criteria for the determination of parameter regimes which lead to limit cycle or quasi-periodic behaviour. (papers)

Averaging for solitons with nonlinearity management

International Nuclear Information System (INIS)

Pelinovsky, D.E.; Kevrekidis, P.G.; Frantzeskakis, D.J.

2003-01-01

We develop an averaging method for solitons of the nonlinear Schroedinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

Science.gov (United States)

Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

2018-06-01

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

Nonlinear electrostatic solitary waves in electron-positron plasmas

Science.gov (United States)

Lazarus, I. J.; Bharuthram, R.; Moolla, S.; Singh, S. V.; Lakhina, G. S.

2016-02-01

The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron-positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.

Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.

Science.gov (United States)

El-Shamy, E F

2015-03-01

The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.

Estimates on the minimal period for periodic solutions of nonlinear second order Hamiltonian systems

International Nuclear Information System (INIS)

Yiming Long.

1994-11-01

In this paper, we prove a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition. (author). 20 refs, 1 fig

How useful is slow light in enhancing nonlinear interactions in lossy periodic nanostructures?

DEFF Research Database (Denmark)

Saravi, Sina; Quintero-Bermudez, Rafael; Setzpfandt, Frank

2016-01-01

We investigate analytically, and with nonlinear simulations, the extent of usefulness of slow light for enhancing the efficiency of second harmonic generation in lossy nanostructures, and find that the slower is not always the better....

Discontinuous Spirals of Stable Periodic Oscillations

DEFF Research Database (Denmark)

Sack, Achim; Freire, Joana G.; Lindberg, Erik

2013-01-01

We report the experimental discovery of a remarkable organization of the set of self-generated periodic oscillations in the parameter space of a nonlinear electronic circuit. When control parameters are suitably tuned, the wave pattern complexity of the periodic oscillations is found to increase...

Dynamic behaviors for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a non-Kerr medium

Science.gov (United States)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Liu, De-Yin

2017-04-01

Effects of quantic nonlinearity on the propagation of the ultrashort optical pulses in a non-Kerr medium, like an optical fiber, can be described by a perturbed nonlinear Schrödinger equation with the power law nonlinearity, which is studied in this paper from a planar-dynamic-system view point. We obtain the equivalent two-dimensional planar dynamic system of such an equation, for which, according to the bifurcation theory and qualitative theory, phase portraits are given. Through the analysis of those phase portraits, we present the relations among the Hamiltonian, orbits of the dynamic system and types of the analytic solutions. Analytic expressions of the periodic-wave solutions, kink- and bell-shaped solitary-wave solutions are derived, and we find that the periodic-wave solutions can be reduced to the kink- and bell-shaped solitary-wave solutions.

Halo Mitigation Using Nonlinear Lattices

CERN Document Server

Sonnad, Kiran G

2005-01-01

This work shows that halos in beams with space charge effects can be controlled by combining nonlinear focusing and collimation. The study relies on Particle-in-Cell (PIC) simulations for a one dimensional, continuous focusing model. The PIC simulation results show that nonlinear focusing leads to damping of the beam oscillations thereby reducing the mismatch. It is well established that reduced mismatch leads to reduced halo formation. However, the nonlinear damping is accompanied by emittance growth causing the beam to spread in phase space. As a result, inducing nonlinear damping alone cannot help mitigate the halo. To compensate for this expansion in phase space, the beam is collimated in the simulation and further evolution of the beam shows that the halo is not regenerated. The focusing model used in the PIC is analysed using the Lie Transform perturbation theory showing that by averaging over a lattice period, one can reuduce the focusing force to a form that is identical to that used in the PIC simula...

Two-dimensional linear and nonlinear Talbot effect from rogue waves.

Science.gov (United States)

Zhang, Yiqi; Belić, Milivoj R; Petrović, Milan S; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Lu, Keqing; Zhang, Yanpeng

2015-03-01

We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a π phase shift; no other recurrences are observed. Differing from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue-wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.

A nonlinear filtering algorithm for denoising HR(S)TEM micrographs

International Nuclear Information System (INIS)

Du, Hongchu

2015-01-01

Noise reduction of micrographs is often an essential task in high resolution (scanning) transmission electron microscopy (HR(S)TEM) either for a higher visual quality or for a more accurate quantification. Since HR(S)TEM studies are often aimed at resolving periodic atomistic columns and their non-periodic deviation at defects, it is important to develop a noise reduction algorithm that can simultaneously handle both periodic and non-periodic features properly. In this work, a nonlinear filtering algorithm is developed based on widely used techniques of low-pass filter and Wiener filter, which can efficiently reduce noise without noticeable artifacts even in HR(S)TEM micrographs with contrast of variation of background and defects. The developed nonlinear filtering algorithm is particularly suitable for quantitative electron microscopy, and is also of great interest for beam sensitive samples, in situ analyses, and atomic resolution EFTEM. - Highlights: • A nonlinear filtering algorithm for denoising HR(S)TEM images is developed. • It can simultaneously handle both periodic and non-periodic features properly. • It is particularly suitable for quantitative electron microscopy. • It is of great interest for beam sensitive samples, in situ analyses, and atomic resolution EFTEM

Nonlinear Talbot Effect and Its Applications

Science.gov (United States)

Yang, Zhening

2018-03-01

Talbot effect, a lenless self-imaging phenomenon, was first discovered in 1836 by H.F. Talbot. The conventional Talbott effect has been studied for over a hundred years. Recently, the rapid development of optical superlattices has brought a great breakthrough in Talbot effect research. A nonlinear self-imaging phenomenon was found in the periodically poled LiTaO3 (PPLT) crystals. [1][2][3] This nonlinear Talbot effect has applications not only in optics but also in many other fields. For example, the phenomenon is realized by frequency-doubled beams, which offers people a new way to enhance the spatial resolution of the self-images of periodic objects. And by observing the self-image of the second harmonic (SH) field on the sample surface, people can detect the domain structure in the crystal without damaging the sample. Throughout this review paper, an overview of nonlinear Talbot effect and two applications of this phenomenon is presented. Breakthroughs like achieving a super-focused spot and realizing an acousto-optic tunable SH Talbot illuminator will be introduced as well.

Tuning chaos in network sharing common nonlinearity

Science.gov (United States)

Paul Asir, M.; Jeevarekha, A.; Philominathan, P.

2016-06-01

In this paper, a novel type of network called network sharing common nonlinearity comprising both autonomous and non-autonomous oscillators have been investigated. We propose that these networks are robust for operating at desired modes i.e., chaotic or periodic by altering the v-i characteristics of common nonlinear element alone. The dynamics of these networks were examined through numerical, analytical, experimental and Multisim simulations.

Comparison of stochastic resonance in static and dynamical nonlinearities

International Nuclear Information System (INIS)

Ma, Yumei; Duan, Fabing

2014-01-01

We compare the stochastic resonance (SR) effects in parallel arrays of static and dynamical nonlinearities via the measure of output signal-to-noise ratio (SNR). For a received noisy periodic signal, parallel arrays of both static and dynamical nonlinearities can enhance the output SNR by optimizing the internal noise level. The static nonlinearity is easily implementable, while the dynamical nonlinearity has more parameters to be tuned, at the risk of not exploiting the beneficial role of internal noise components. It is of interest to note that, for an input signal buried in the external Laplacian noise, we show that the dynamical nonlinearity is superior to the static nonlinearity in obtaining a better output SNR. This characteristic is assumed to be closely associated with the kurtosis of noise distribution. - Highlights: • Comparison of SR effects in arrays of both static and dynamical nonlinearities. • Static nonlinearity is easily implementable for the SNR enhancement. • Dynamical nonlinearity yields a better output SNR for external Laplacian noise

The linear and nonlinear response of infinite periodic systems to static and/or dynamic electric fields. Implementation in CRYSTAL code

Energy Technology Data Exchange (ETDEWEB)

Kirtman, Bernard [Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106 (United States); Springborg, Michael [Physical and Theoretical Chemistry, University of Saarland, 66123 Saarbrücken (Germany); Rérat, Michel [Equipe de Chimie Physique, IPREM UMR5254, Université de Pau et des Pays de l' Adour, 64000 Pau (France); Ferrero, Mauro; Lacivita, Valentina; Dovesi, Roberto [Departimeno di Chimica, IFM, Università di Torino and NIS - Nanostructure Interfaces and Surfaces - Centre of Excellence, Via P. Giuria 7, 10125 Torino (Italy); Orlando, Roberto [Departimento di Scienze e Tecnologie Avanzati, Università del Piemonte Orientale, Viale T. Michel 11, 15121 Alessandria (Italy)

2015-01-22

An implementation of the vector potential approach (VPA) for treating the response of infinite periodic systems to static and dynamic electric fields has been initiated within the CRYSTAL code. The VPA method is based on the solution of a time-dependent Hartree-Fock or Kohn-Sham equation for the crystal orbitals wherein the usual scalar potential, that describes interaction with the field, is replaced by the vector potential. This equation may be solved either by perturbation theory or by finite field methods. With some modification all the computational procedures of molecular ab initio quantum chemistry can be adapted for periodic systems. Accessible properties include the linear and nonlinear responses of both the nuclei and the electrons. The programming of static field pure electronic (hyper)polarizabilities has been successfully tested. Dynamic electronic (hyper)polarizabilities, as well as infrared and Raman intensities, are in progress while the addition of finite fields for calculation of vibrational (hyper)polarizabilities, through nuclear relaxation procedures, will begin shortly.

Exact solutions for nonlinear variants of Kadomtsev–Petviashvili (n ...

Indian Academy of Sciences (India)

Studying compactons, solitons, solitary patterns and periodic solutions is important in nonlinear phenomena. In this paper we study nonlinear variants of the Kadomtsev–Petviashvili (KP) and the Korteweg–de Vries (KdV) equations with positive and negative exponents. The functional variable method is used to establish ...

Classification of solutions of the forced periodic nonlinear Schrödinger equation

International Nuclear Information System (INIS)

Shlizerman, Eli; Rom-Kedar, Vered

2010-01-01

The integrable structure of the periodic one-dimensional nonlinear Schrödinger equation is utilized to gain insights regarding the perturbed near-integrable dynamics. After recalling the known results regarding the structure and stability of the unperturbed standing and travelling waves solutions, two new stability results are presented: (1) it is shown numerically that the stability of the 'outer' (cnoidal) unperturbed solutions depends on their power (the L 2 norm): they undergo a finite sequence of Hamiltonian–Hopf bifurcations as their power is increased. (2) another proof that the 'inner'(dnoidal) unperturbed solutions with multiplicity ≥2 are linearly unstable is presented. Then, to study the global phase-space structure, an energy–momentum bifurcation diagram (PDE-EMBD) that consists of projections of the unperturbed standing and travelling waves solutions to the energy–power plane and includes information regarding their linear stability is constructed. The PDE-EMBD helps us to classify the behaviour near the plane wave solutions: the diagram demonstrates that below some known threshold amplitude, precisely three distinct observable chaotic mechanisms arise: homoclinic chaos, homoclinic resonance and, for some parameter values, parabolic-resonance. Moreover, it appears that the dynamics of the PDE chaotic solutions that exhibit the parabolic-resonance instability may be qualitatively predicted: these exhibit the same dynamics as a recently derived parabolic-resonance low-dimensional normal form. In particular, these solutions undergo adiabatic chaos: they follow the level lines of an adiabatic invariant till they reach the separatrix set at which the adiabatic invariant undergoes essentially random jumps

4th International Conference on Structural Nonlinear Dynamics and Diagnosis

CERN Document Server

2018-01-01

This book presents contributions on the most active lines of recent advanced research in the field of nonlinear mechanics and physics selected from the 4th International Conference on Structural Nonlinear Dynamics and Diagnosis. It includes fifteen chapters by outstanding scientists, covering various aspects of applications, including road tanker dynamics and stability, simulation of abrasive wear, energy harvesting, modeling and analysis of flexoelectric nanoactuator, periodic Fermi–Pasta–Ulam problems, nonlinear stability in Hamiltonian systems, nonlinear dynamics of rotating composites, nonlinear vibrations of a shallow arch, extreme pulse dynamics in mode-locked lasers, localized structures in a photonic crystal fiber resonator, nonlinear stochastic dynamics, linearization of nonlinear resonances, treatment of a linear delay differential equation, and fractional nonlinear damping. It appeals to a wide range of experts in the field of structural nonlinear dynamics and offers researchers and engineers a...

Discontinuity and complexity in nonlinear physical systems

CERN Document Server

Baleanu, Dumitru; Luo, Albert

2014-01-01

This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....

Nonlinear Bloch waves in metallic photonic band-gap filaments

International Nuclear Information System (INIS)

Kaso, Artan; John, Sajeev

2007-01-01

We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10-50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell's equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament

Nonlinear Bloch waves in metallic photonic band-gap filaments

Science.gov (United States)

Kaso, Artan; John, Sajeev

2007-11-01

We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10 50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell’s equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament.

Nonlinear tunneling of bright and dark rogue waves in combined nonlinear Schrödinger and Maxwell-Bloch systems

Science.gov (United States)

Raju, Thokala Soloman; Pal, Ritu

2018-05-01

We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.

Modeling of periodic great earthquakes on the San Andreas fault: Effects of nonlinear crustal rheology

Science.gov (United States)

Reches, Ze'ev; Schubert, Gerald; Anderson, Charles

1994-01-01

We analyze the cycle of great earthquakes along the San Andreas fault with a finite element numerical model of deformation in a crust with a nonlinear viscoelastic rheology. The viscous component of deformation has an effective viscosity that depends exponentially on the inverse absolute temperature and nonlinearity on the shear stress; the elastic deformation is linear. Crustal thickness and temperature are constrained by seismic and heat flow data for California. The models are for anti plane strain in a 25-km-thick crustal layer having a very long, vertical strike-slip fault; the crustal block extends 250 km to either side of the fault. During the earthquake cycle that lasts 160 years, a constant plate velocity v(sub p)/2 = 17.5 mm yr is applied to the base of the crust and to the vertical end of the crustal block 250 km away from the fault. The upper half of the fault is locked during the interseismic period, while its lower half slips at the constant plate velocity. The locked part of the fault is moved abruptly 2.8 m every 160 years to simulate great earthquakes. The results are sensitive to crustal rheology. Models with quartzite-like rheology display profound transient stages in the velocity, displacement, and stress fields. The predicted transient zone extends about 3-4 times the crustal thickness on each side of the fault, significantly wider than the zone of deformation in elastic models. Models with diabase-like rheology behave similarly to elastic models and exhibit no transient stages. The model predictions are compared with geodetic observations of fault-parallel velocities in northern and central California and local rates of shear strain along the San Andreas fault. The observations are best fit by models which are 10-100 times less viscous than a quartzite-like rheology. Since the lower crust in California is composed of intermediate to mafic rocks, the present result suggests that the in situ viscosity of the crustal rock is orders of magnitude

Nonlinear resonance in Duffing oscillator with fixed and integrative ...

Indian Academy of Sciences (India)

We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter and the strength of the ...

Nonlinear resonance in Duffing oscillator with fixed and integrative ...

Indian Academy of Sciences (India)

2012-03-02

Mar 2, 2012 ... Abstract. We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter α and the ...

Modeling of Nonlinear Hydrodynamics of the Coastal Areas of the Black Sea by the Chain of the Proprietary and Open Source Models

Science.gov (United States)

Kantardgi, Igor; Zheleznyak, Mark; Demchenko, Raisa; Dykyi, Pavlo; Kivva, Sergei; Kolomiets, Pavlo; Sorokin, Maxim

2014-05-01

The nearshore hydrodynamic fields are produced by the nonlinear interactions of the shoaling waves of different time scales and currents. To simulate the wind wave and swells propagated to the coasts, wave generated near shore currents, nonlinear-dispersive wave transformation and wave diffraction in interaction with coastal and port structure, sediment transport and coastal erosion the chains of the models should be used. The objective of this presentation is to provide an overview of the results of the application of the model chains for the assessment of the wave impacts on new construction designed at the Black Sea coasts and the impacts of these constructions on the coastal erosion/ accretion processes to demonstrate needs for further development of the nonlinear models for the coastal engineering applications. The open source models Wave Watch III and SWAN has been used to simulate wave statistics of the dedicated areas of the Black Sea in high resolution to calculated the statistical parameters of the extreme wave approaching coastal zone construction in accordance with coastal engineering standards. As the main tool for the costal hydrodynamic simulations the modeling system COASTOX-MORPHO has been used, that includes the following models. HWAVE -code based on hyperbolic version of mild slope equations., HWAVE-S - spectral version of HWAVE., BOUSS-FNL - fully nonlinear system of Boussinesq equations for simulation wave nonlinear -dispersive wave transformation in coastal areas. COASTOX-CUR - the code provided the numerical solution of the Nonlinear Shallow Water Equations (NLSWE) by finite-volume methods on the unstructured grid describing the long wave transformation in the coastal zone with the efficient drying -wetting algorithms to simulate the inundation of the coastal areas including tsunami wave runup. Coastox -Cur equations with the radiation stress term calculated via near shore wave fields simulate the wave generated nearhore currents. COASTOX

Topics in nonlinear wave theory with applications

International Nuclear Information System (INIS)

Tracy, E.R.

1984-01-01

Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly

Period multiplication and chaotic phenomena in atmospheric dielectric-barrier glow discharges

International Nuclear Information System (INIS)

Wang, Y. H.; Zhang, Y. T.; Wang, D. Z.; Kong, M. G.

2007-01-01

In this letter, evidence of temporal plasma nonlinearity in which atmospheric dielectric-barrier discharges undergo period multiplication and chaos using a one-dimensional fluid model is reported. Under the conditions conducive for chaotic states, several frequency windows are identified in which period multiplication and secondary bifurcations are observed. Such time-domain nonlinearity is important for controlling instabilities in atmospheric glow discharges

Nonlinear response and avalanche behavior in metallic glasses

Science.gov (United States)

Riechers, B.; Samwer, K.

2017-08-01

The response to different stress amplitudes at temperatures below the glass transition temperature is analyzed by mechanical oscillatory excitation of Pd40Ni40P20 metallic glass samples in single cantilever bending geometry. While low amplitude oscillatory excitations are commonly used in mechanical spectroscopy to probe the relaxation spectrum, in this work the response to comparably high amplitudes is investigated. The strain response of the material is well below the critical yield stress even for highest stress amplitudes, implying the expectation of a linear relation between stress and strain according to Hooke's Law. However, a deviation from the linear behavior is evident, which is analyzed in terms of temperature dependence and influence of the applied stress amplitude by two different approaches of evaluation. The nonlinear approach is based on a nonlinear expansion of the stress-strain-relation, assuming an intrinsic nonlinear character of the shear or elastic modulus. The degree of nonlinearity is extracted by a period-by-period Fourier-analysis and connected to nonlinear coefficients, describing the intensity of nonlinearity at the fundamental and higher harmonic frequencies. The characteristic timescale to adapt to a significant change in stress amplitude in terms of a recovery timescale to a steady state value is connected to the structural relaxation time of the material, suggesting a connection between the observed nonlinearity and primary relaxation processes. The second approach of evaluation is termed the incremental analysis and relates the observed response behavior to avalanches, which occur due to the activation and correlation of local microstructural rearrangements. These rearrangements are connected with shear transformation zones and correspond to localized plastic events, which are superimposed on the linear response behavior of the material.

Nonlinear Response of the Stratosphere and the North Atlantic-European Climate to Global Warming

Science.gov (United States)

Manzini, E.; Karpechko, A. Yu.; Kornblueh, L.

2018-05-01

The response of the northern winter atmospheric circulation for two consecutive global warming periods of 2 K is examined in a grand ensemble (68 members) of idealized CO2 increase experiments performed with the same climate model. The comparison of the atmospheric responses for the two periods shows remarkable differences, indicating the nonlinearity of the response. The nonlinear signature of the atmospheric and surface responses is reminiscent of the positive phase of the annular mode of variability. The stratospheric vortex response shifts from an easterly wind change for the first 2 K to a westerly wind change for the second 2 K. The North Atlantic storm track shifts poleward only in the second period. A weaker November Arctic amplification during the second period suggests that differences in Arctic sea ice changes can act to trigger the atmospheric nonlinear response. Stratosphere-troposphere coupling thereafter can provide for the persistence of this nonlinearity throughout the winter.

Nonlinear extraordinary wave in dense plasma

Energy Technology Data Exchange (ETDEWEB)

Krasovitskiy, V. B., E-mail: krasovit@mail.ru [Russian Academy of Sciences, Keldysh Institute of Applied Mathematics (Russian Federation); Turikov, V. A. [Russian University of Peoples’ Friendship (Russian Federation)

2013-10-15

Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.

The halo bispectrum in N-body simulations with non-Gaussian initial conditions

Science.gov (United States)

Sefusatti, E.; Crocce, M.; Desjacques, V.

2012-10-01

We present measurements of the bispectrum of dark matter haloes in numerical simulations with non-Gaussian initial conditions of local type. We show, in the first place, that the overall effect of primordial non-Gaussianity on the halo bispectrum is larger than on the halo power spectrum when all measurable configurations are taken into account. We then compare our measurements with a tree-level perturbative prediction, finding good agreement at large scales when the constant Gaussian bias parameter, both linear and quadratic, and their constant non-Gaussian corrections are fitted for. The best-fitting values of the Gaussian bias factors and their non-Gaussian, scale-independent corrections are in qualitative agreement with the peak-background split expectations. In particular, we show that the effect of non-Gaussian initial conditions on squeezed configurations is fairly large (up to 30 per cent for fNL = 100 at redshift z = 0.5) and results from contributions of similar amplitude induced by the initial matter bispectrum, scale-dependent bias corrections as well as from non-linear matter bispectrum corrections. We show, in addition, that effects at second order in fNL are irrelevant for the range of values allowed by cosmic microwave background and galaxy power spectrum measurements, at least on the scales probed by our simulations (k > 0.01 h Mpc-1). Finally, we present a Fisher matrix analysis to assess the possibility of constraining primordial non-Gaussianity with future measurements of the galaxy bispectrum. We find that a survey with a volume of about 10 h-3 Gpc3 at mean redshift z ≃ 1 could provide an error on fNL of the order of a few. This shows the relevance of a joint analysis of galaxy power spectrum and bispectrum in future redshift surveys.

Nonlinear shear wave in a non Newtonian visco-elastic medium

Energy Technology Data Exchange (ETDEWEB)

Banerjee, D.; Janaki, M. S.; Chakrabarti, N. [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700 064 (India); Chaudhuri, M. [Max-Planck-Institut fuer extraterrestrische Physik, 85741 Garching (Germany)

2012-06-15

An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.

Controllable behaviours of rogue wave triplets in the nonautonomous nonlinear and dispersive system

International Nuclear Information System (INIS)

Dai Chaoqing; Tian Qing; Zhu Shiqun

2012-01-01

A similarity transformation connecting the variable coefficient nonlinear Schrödinger equation with the standard nonlinear Schrödinger equation is constructed. The self-similar rogue wave triplet solutions (rational solutions) are analytically obtained for the nonautonomous nonlinear and dispersive system. The controllable behaviours of rogue wave triplets in two typical soliton management systems are discussed. In the exponential dispersion decreasing fibre, three kinds of rogue wave triplets with controllable behaviours are analysed. In the periodic distributed system, the rogue wave triplets recur periodically in the form of a cluster. (paper)

Some non-linear physics in crystallographic structures

International Nuclear Information System (INIS)

Aubry, S.

1977-10-01

A summary of studies on simple but strongly nonlinear crystallographic models that make use of some methods in stochasticity is presented. Two one-dimensional models are described; one has been studied to understand some aspects of the nonlinear dynamics in crystals when close to the transition temperature, the other is for commensurability and incommensurability problems. Periodic orbits and the dynamics of a one-dimensional coupled double-well chain are considered, along with lattice locking and stochasticity

Forecasting with nonlinear time series models

DEFF Research Database (Denmark)

Kock, Anders Bredahl; Teräsvirta, Timo

In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econo- metrics are presented and some of their properties discussed. This in- cludes two models based on universal approximators: the Kolmogorov- Gabor polynomial model...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...... and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...

Linear and nonlinear stability of periodic orbits in annular billiards

Science.gov (United States)

Dettmann, Carl P.; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Global Transcriptomic and Proteomic Responses of Dehalococcoides ethenogenes Strain 195 to Fixed Nitrogen Limitation

Energy Technology Data Exchange (ETDEWEB)

Lee, Patrick K. H. [University of California, Berkeley; Dill, Brian [ORNL; Louie, Tiffany S. [University of California, Berkeley; Shah, Manesh B [ORNL; Verberkmoes, Nathan C [ORNL; Andersen, Gary L. [Lawrence Berkeley National Laboratory (LBNL); Zinder, Stephen H. [Cornell University; Alvarez-Cohen, Lisa [Lawrence Berkeley National Laboratory (LBNL)

2012-01-01

Bacteria of the genus Dehalococcoides play an important role in the reductive dechlorination of chlorinated ethenes. A systems level approach was taken in this study to examine the global transcriptomic and proteomic responses of exponentially growing D. ethenogenes strain 195 to fixed nitrogen limitation (FNL) as dechlorination activity and cell yield both decrease during FNL. As expected, the nitrogen-fixing (nif) genes were differentially up-regulated in the transcriptome and proteome of strain 195 during FNL. Aside from the nif operon, a putative methylglyoxal synthase-encoding gene (DET1576), the product of which is predicted to catalyze the formation of the toxic electrophile methylglyoxal and implicated in the uncoupling of anabolism from catabolism in bacteria, was strongly up-regulated in the transcriptome and could potentially play a role in the observed growth inhibition during FNL. Carbon catabolism genes were generally down regulated in response to FNL and a number of transporters were differentially regulated in response to nitrogen limitation, with some playing apparent roles in nitrogen acquisition while others were associated with general stress responses. A number of genes related to the functions of nucleotide synthesis, replication, transcription, translation, and post-translational modifications were also differentially expressed. One gene coding for a putative reductive dehalogenase (DET1545) and a number coding for oxidoreductases, which have implications in energy generation and redox reactions, were also differentially regulated. Interestingly, most of the genes within the multiple integrated elements were not differentially expressed. Overall, this study elucidates the molecular responses of strain 195 to FNL and identifies differentially expressed genes that are potential biomarkers to evaluate environmental cellular nitrogen status.

Exact solutions of a nonpolynomially nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Parwani, R.; Tan, H.S.

2007-01-01

A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics

Oscillating solitons in nonlinear optics

Indian Academy of Sciences (India)

The study of solitons in those physical systems reveals some exciting .... With the following power series expansions for g(z,t) and f(z,t): g(z,t) = εg1(z,t) + ... If nonlinearity γ (z) is also taken as a function in figure 1b, the periodic and oscillation.

Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory

Science.gov (United States)

Bridges, Thomas J.; Ratliff, Daniel J.

2018-04-01

The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Model-free inference of direct network interactions from nonlinear collective dynamics.

Science.gov (United States)

Casadiego, Jose; Nitzan, Mor; Hallerberg, Sarah; Timme, Marc

2017-12-19

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

Science.gov (United States)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Nonlinear effects in modulated quantum optomechanics

Science.gov (United States)

Yin, Tai-Shuang; Lü, Xin-You; Zheng, Li-Li; Wang, Mei; Li, Sha; Wu, Ying

2017-05-01

The nonlinear quantum regime is crucial for implementing interesting quantum effects, which have wide applications in modern quantum science. Here we propose an effective method to reach the nonlinear quantum regime in a modulated optomechanical system (OMS), which is originally in the weak-coupling regime. The mechanical spring constant and optomechanical interaction are modulated periodically. This leads to the result that the resonant optomechanical interaction can be effectively enhanced into the single-photon strong-coupling regime by the modulation-induced mechanical parametric amplification. Moreover, the amplified phonon noise can be suppressed completely by introducing a squeezed vacuum reservoir, which ultimately leads to the realization of photon blockade in a weakly coupled OMS. The reached nonlinear quantum regime also allows us to engineer the nonclassical states (e.g., Schrödinger cat states) of the cavity field, which are robust against the phonon noise. This work offers an alternative approach to enhance the quantum nonlinearity of an OMS, which should expand the applications of cavity optomechanics in the quantum realm.

Nonlinear response and bistability of driven ion acoustic waves

Science.gov (United States)

Akbari-Moghanjoughi, M.

2017-08-01

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

Unveiling Quasiperiodicity through Nonlinear Wave Mixing in Periodic Media

International Nuclear Information System (INIS)

Bahabad, Alon; Arie, Ady; Voloch, Noa; Bruner, Ariel; Eger, David

2007-01-01

Quasiperiodicity is the concept of order without translation symmetry. The discovery of quasiperiodic order in natural materials transformed the way scientists examine and define ordered structure. We show and verify experimentally that quasiperiodicity can be observed by scattering processes from a periodic structure, provided the interaction area is of finite width. This is made through a momentum conservation condition, physically realizing a geometrical method used to model quasiperiodic structures by projecting a periodic structure of a higher dimension

Hofstadter butterflies in nonlinear Harper lattices, and their optical realizations

International Nuclear Information System (INIS)

Manela, Ofer; Segev, Mordechai; Christodoulides, Demetrios N; Kip, Detlef

2010-01-01

The ubiquitous Hofstadter butterfly describes a variety of systems characterized by incommensurable periodicities, ranging from Bloch electrons in magnetic fields and the quantum Hall effect to cold atoms in optical lattices and more. Here, we introduce nonlinearity into the underlying (Harper) model and study the nonlinear spectra and the corresponding extended eigenmodes of nonlinear quasiperiodic systems. We show that the spectra of the nonlinear eigenmodes form deformed versions of the Hofstadter butterfly and demonstrate that the modes can be classified into two families: nonlinear modes that are a 'continuation' of the linear modes of the system and new nonlinear modes that have no counterparts in the linear spectrum. Finally, we propose an optical realization of the linear and nonlinear Harper models in transversely modulated waveguide arrays, where these Hofstadter butterflies can be observed. This work is relevant to a variety of other branches of physics beyond optics, such as disorder-induced localization in ultracold bosonic gases, localization transition processes in disordered lattices, and more.

Hofstadter butterflies in nonlinear Harper lattices, and their optical realizations

Energy Technology Data Exchange (ETDEWEB)

Manela, Ofer; Segev, Mordechai [Department of Physics and Solid State Institute, Technion, Haifa 32000 (Israel); Christodoulides, Demetrios N [College of Optics/CREOL, University of Central Florida, FL 32816-2700 (United States); Kip, Detlef, E-mail: msegev@tx.technion.ac.i [Department of Electrical Engineering, Helmut Schmidt University, 22043 Hamburg (Germany)

2010-05-15

The ubiquitous Hofstadter butterfly describes a variety of systems characterized by incommensurable periodicities, ranging from Bloch electrons in magnetic fields and the quantum Hall effect to cold atoms in optical lattices and more. Here, we introduce nonlinearity into the underlying (Harper) model and study the nonlinear spectra and the corresponding extended eigenmodes of nonlinear quasiperiodic systems. We show that the spectra of the nonlinear eigenmodes form deformed versions of the Hofstadter butterfly and demonstrate that the modes can be classified into two families: nonlinear modes that are a 'continuation' of the linear modes of the system and new nonlinear modes that have no counterparts in the linear spectrum. Finally, we propose an optical realization of the linear and nonlinear Harper models in transversely modulated waveguide arrays, where these Hofstadter butterflies can be observed. This work is relevant to a variety of other branches of physics beyond optics, such as disorder-induced localization in ultracold bosonic gases, localization transition processes in disordered lattices, and more.

Photonic microwave carrier recovery using period-one nonlinear dynamics of semiconductor lasers for OFDM-RoF coherent detection.

Science.gov (United States)

Hung, Yu-Han; Yan, Jhih-Heng; Feng, Kai-Ming; Hwang, Sheng-Kwang

2017-06-15

This study investigates an all-optical scheme based on period-one (P1) nonlinear dynamics of semiconductor lasers, which regenerates the microwave carrier of an orthogonal frequency division multiplexing radio-over-fiber (OFDM-RoF) signal and uses it as a microwave local oscillator for coherent detection. Through the injection locking established between the OFDM-RoF signal and the P1 dynamics, frequency synchronization with highly preserved phase quality is inherently achieved between the recovered microwave carrier and the microwave carrier of the OFDM-RoF signal. A bit-error ratio down to 1.9×10-9 is achieved accordingly using the proposed scheme for coherent detection of a 32-GHz OFDM-RoF signal carrying 4  Gb/s 16-quadrature amplitude modulation data. No electronic microwave generators or electronic phase-locked loops are thus required. The proposed system can be operated up to at least 100 GHz and can be self-adapted to certain changes in the operating microwave frequency.

The non-linear response of the magnetosphere: 30 October 1978

International Nuclear Information System (INIS)

Price, C.P.; Prichard, D.

1993-01-01

The authors address the question of whether the response of the earth magnetosphere to the solar wind can be viewed as a nonlinear phenomena, rather than a linear response. The difficulty in answering this question is that the driving function, namely the solar wind, is very aperiodic, and it is difficult to argue that the system has time to go to any sort of a steady state in response to the driving force, prior to its making another random change. The application of nonlinear analysis methods in the face of this type of system is very limited. The authors pick a particular day, namely October 30, 1978, when the solar wind was very uniform for an extended period of time, and there is the possibility the system could converge to some type of strange attractor state within this period. They look at the auroral electrojet as a measure of the potential nonlinear response of the magnetosphere, and apply both nonlinear and linear analysis procedures to the data to try to determine if the data would support a nonlinear response of the magnetosphere to the solar wind driver, taken as the product of the solar wind speed v, and the southward component of the interplanetary magnetic field B s

Strongly nonlinear theory of rapid solidification near absolute stability

Science.gov (United States)

Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the

Nonlinear dynamic effects in a two-wave CO2 laser

International Nuclear Information System (INIS)

Gorobets, V A; Kozlov, K V; Kuntsevich, B F; Petukhov, V O

1999-01-01

Theoretical and experimental investigations were made of nonlinear dynamic regimes of the operation of a two-wave CO 2 laser with cw excitation in an electric discharge and loss modulation in one of the channels. Nonlinear amplitude - frequency characteristics of each of the laser channels have two low-frequency resonance spikes, associated with forced linear oscillations of two coupled oscillators, and high-frequency spikes, corresponding to doubling of the period of the output radiation oscillations. At low loss-modulation frequencies the intensity oscillations of the output radiation in the coupled channels are in antiphase, whereas at high modulation frequencies the dynamics is cophasal. Nonlinear dynamic effects, such as doubling of the period and of the repetition frequency of the pulses and chaotic oscillations of the output radiation intensity, are observed for certain system parameters. (control of laser radiation parameters)

Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

Indian Academy of Sciences (India)

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...

Solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere

International Nuclear Information System (INIS)

Li Ziliang

2008-01-01

By introducing a new transformation, a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system, which extends Fan's direct algebraic method to the case when r > 4. The solutions of a first-order nonlinear ordinary differential equation with a higher degree nonlinear term and Fan's direct algebraic method of obtaining exact solutions to nonlinear partial differential equations are applied to the combined KdV-mKdV-GKdV equation, which is derived from a simple incompressible non-hydrostatic Boussinesq equation with the influence of thermal forcing and is applied to investigate internal gravity waves in the atmosphere. As a result, by taking advantage of the new first-order nonlinear ordinary differential equation with a fifth-degree nonlinear term and an eighth-degree nonlinear term, periodic wave solutions associated with the Jacobin elliptic function and the bell and kink profile solitary wave solutions are obtained under the effect of thermal forcing. Most importantly, the mechanism of propagation and generation of the periodic waves and the solitary waves is analysed in detail according to the values of the heating parameter, which show that the effect of heating in atmosphere helps to excite westerly or easterly propagating periodic internal gravity waves and internal solitary waves in atmosphere, which are affected by the local excitation structures in atmosphere. In addition, as an illustrative sample, the properties of the solitary wave solution and Jacobin periodic solution are shown by some figures under the consideration of heating interaction

Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems

DEFF Research Database (Denmark)

Bayat, M.; Shahidi, M.; Barari, Amin

2011-01-01

approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...

Nonlinear behavior in the time domain in argon atmospheric dielectric-barrier discharges

International Nuclear Information System (INIS)

Shi Hong; Wang Yanhui; Wang Dezhen

2008-01-01

A vast majority of nonlinear behavior in atmospheric pressure discharges has so far been studied in the space domain, and their time-domain characters are often believed to exact the periodicity of the externally applied voltage. In this paper, based on one-dimensional fluid mode, we study complex nonlinear behavior in the time domain in argon atmospheric dielectric-barrier discharges at very broad frequency range from kilohertz to megahertz. Under certain conditions, the discharge not only can be driven to chaos from time-periodic state through period-doubling bifurcation, but also can return stable periodic motion from chaotic state through an inverse period-doubling bifurcation sequence. Upon changing the parameter the discharge undergoes alternatively chaotic and periodic behavior. Some periodic windows embedded in chaos, as well as the secondary bifurcation occurring in the periodic windows can also be observed. The corresponding discharge characteristics are investigated.

Experimental and numerical investigations of temporally and spatially periodic modulated wave trains

Science.gov (United States)

Houtani, H.; Waseda, T.; Tanizawa, K.

2018-03-01

A number of studies on steep nonlinear waves were conducted experimentally with the temporally periodic and spatially evolving (TPSE) wave trains and numerically with the spatially periodic and temporally evolving (SPTE) ones. The present study revealed that, in the vicinity of their maximum crest height, the wave profiles of TPSE and SPTE modulated wave trains resemble each other. From the investigation of the Akhmediev-breather solution of the nonlinear Schrödinger equation (NLSE), it is revealed that the dispersion relation deviated from the quadratic dependence of frequency on wavenumber and became linearly dependent instead. Accordingly, the wave profiles of TPSE and SPTE breathers agree. The range of this agreement is within the order of one wave group of the maximum crest height and persists during the long-term evolution. The findings extend well beyond the NLSE regime and can be applied to modulated wave trains that are highly nonlinear and broad-banded. This was demonstrated from the numerical wave tank simulations with a fully nonlinear potential flow solver based on the boundary element method, in combination with the nonlinear wave generation method based on the prior simulation with the higher-order spectral model. The numerical wave tank results were confirmed experimentally in a physical wave tank. The findings of this study unravel the fundamental nature of the nonlinear wave evolution. The deviation of the dispersion relation of the modulated wave trains occurs because of the nonlinear phase variation due to quasi-resonant interaction, and consequently, the wave geometry of temporally and spatially periodic modulated wave trains coincides.

Nonlinear saturation of the Rayleigh endash Taylor instability

International Nuclear Information System (INIS)

Das, A.; Mahajan, S.; Kaw, P.; Sen, A.; Benkadda, S.; Verga, A.

1997-01-01

A detailed numerical simulation of the nonlinear state of the Rayleigh endash Taylor instability has been carried out. There are three distinct phases of evolution where it is governed by the (i) linear effects, (ii) effects arising from the conventional nonlinear terms and (iii) subtle nonlinear effects arising through the coupling terms. During the third phase of evolution, there is a self-consistent generation of shear flow which saturates the Rayleigh endash Taylor instability even in situations (with periodic boundaries) where, in principle, an infinite amount of gravitational energy can be tapped. The Galerkin approximation is presented to provide an understanding of our numerical findings. Last, there is an attempt to provide a comprehensive understanding of the nonlinear state of the Rayleigh endash Taylor instability by comparing and contrasting this work with earlier studies. copyright 1997 American Institute of Physics

The application of nonlinear dynamics in the study of ferroelectric materials

International Nuclear Information System (INIS)

Blochwitz, S.; Habel, R.; Diestelhorst, M.; Beige, H.

1996-01-01

It is well known that the structural phase transitions in ferroelectric materials are connected with strong nonlinear properties. So we can expect all features of nonlinear dynamical systems such as period-doubling cascades and chaos in a dynamical system that contains ferroelectric materials. Therefore we can apply nonlinear dynamics to these ferroelectric materials and we are doing it in two directions: (i) We study the structural phase transitions by analyzing the large signal behaviour with means of nonlinear dynamics. (ii) We control the chaotic behaviour of the system with the method proposed by Ott, Grebogi and Yorke. (authors)

Nonlinear dynamic analysis of 2-DOF nonlinear vibration isolation floating raft systems with feedback control

International Nuclear Information System (INIS)

Li Yingli; Xu Daolin; Fu Yiming; Zhou Jiaxi

2012-01-01

In this paper, the average method is adopted to analysis dynamic characteristics of nonlinear vibration isolation floating raft system with feedback control. The analytic results show that the purposes of reducing amplitude of oscillation and complicating the motion can be achieved by adjusting properly the system parameters, exciting frequency and control gain. The conclusions can provide some available evidences for the design and improvement of both the passive and active control of the vibration isolation systems. By altering the exciting frequency and control gain, complex motion of the system can be obtained. Numerical simulations show the system exhibits period vibration, double period vibration and quasi-period motion.

Nonlinear analysis of a closed-loop tractor-semitrailer vehicle system with time delay

Science.gov (United States)

Liu, Zhaoheng; Hu, Kun; Chung, Kwok-wai

2016-08-01

In this paper, a nonlinear analysis is performed on a closed-loop system of articulated heavy vehicles with driver steering control. The nonlinearity arises from the nonlinear cubic tire force model. An integration method is employed to derive an analytical periodic solution of the system in the neighbourhood of the critical speed. The results show that excellent accuracy can be achieved for the calculation of periodic solutions arising from Hopf bifurcation of the vehicle motion. A criterion is obtained for detecting the Bautin bifurcation which separates branches of supercritical and subcritical Hopf bifurcations. The integration method is compared to the incremental harmonic balance method in both supercritical and subcritical scenarios.

Laser acceleration and nonlinear beam dynamics

International Nuclear Information System (INIS)

Pellegrini, C.

1991-01-01

This research contract covers the period April 1990, September 1991. The work to be done under the contract was theoretical research in the areas of nonlinear beam dynamics and laser acceleration. In this final report we will discuss the motivation for this work and the results obtained

Energy flow theory of nonlinear dynamical systems with applications

CERN Document Server

Xing, Jing Tang

2015-01-01

This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...

Resonant driving of a nonlinear Hamiltonian system

International Nuclear Information System (INIS)

Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro

2013-01-01

As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.

Periodicity in Age-Resolved Populations

Science.gov (United States)

Esipov, Sergei

We discuss the interplay between the non-linear diffusion and age-resolved population dynamics. Depending on the age properties of collective migration the system may exhibit continuous joint expansion of all ages or continuous expansion with age segregation. Between these two obvious limiting regimes there is an interesting window of periodic expansion, which has been previously used by us in modeling bacterial colonies of Proteus mirabilis. In order to test whether the age-dependent collective migration leads to periodicity in other systems we performed a Fourier analysis of historical data on ethnic expansions and found multiple co-existing periods of activity.

Period doubling phenomenon in a class of time delay equations

International Nuclear Information System (INIS)

Oliveira, C.R. de; Malta, C.P.

1985-01-01

The properties of the solution of a nonlinear time delayed differential equation (infinite dimension) as function of two parameters: the time delay tau and another parameter A (nonlinearity) are investigated. After a Hopf bifurcation period doubling may occur and is characterized by Feigenbaum's delta. A strange atractor is obtained after the period doubling cascade and the largest Lyapunov exponent is calculated indicating that the attractor has low dimension. The behaviour of this Liapunov exponent as function of tau is different from its behaviour as function of A. (Author) [pt

Asymmetric bistable reflection and polarization switching in a magnetic nonlinear multilayer structure

DEFF Research Database (Denmark)

Tuz, Vladimir R.; Novitsky, Denis V.; Prosvirnin, Sergey L.

2014-01-01

Optical properties of one-dimensional photonic structures consisting of Kerr-type nonlinear and magnetic layers under the action of an external static magnetic field in the Faraday geometry are investigated. The structure is a periodic arrangement of alternating nonlinear and magnetic layers (a o...

Are Current Accounts of Asian Economies Mean-reverting?: Nonlinear Unit Root Test Approach

Directory of Open Access Journals (Sweden)

Bonghan Kim

2005-12-01

Full Text Available This paper tests the mean reverting property of current account in the financial crisis-affected 5 counties of southeast Asia using nonlinear unit root tests of Park and shintani(2004. Our approach is based on the idea that a conventional unit root test has lower power in detecting the nonlinear mean reverting behavior if the current account follows a nonlinear mean reversion process. We obtained following empirical results. First, for the pre-crisis period (1981Q1-1996Q4, the current accounts of Indonesia, Malaysia and Philippines are mean-reverting but those of Korea and Thailand are not mean-reverting. Second, for the full sample period (1981Q1-2003Q4, the ADF test fails to reject the unit root of the current account in all countries except Philippines. However, unit root is rejected in favor of nonlinear mean reversion except Thailand. This nonlinear unit root test result implies that crisis-affected Asian countries except Thailand have sustainable paths of current accounts. Third, when the current accounts of East Asian countries are nonlinear mean-reverting, the mean reverting process can be well described by the ESTAR model, instead of the DTAR or DLSTAR model. The nonlinear unit root test results imply smooth nonlinear mean-reversion behaviors of East Asian current accounts. Finally, the shape of estimated impulse response functions becomes steeper as the size of shock increases, which is the very characteristic of the nonlinear process.

Analysis of Nonlinear Dynamics by Square Matrix Method

Energy Technology Data Exchange (ETDEWEB)

Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II

2016-07-25

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.

Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser

International Nuclear Information System (INIS)

Li Xiaofeng; Pan Wei; Luo Bin; Ma Dong; Wang Yong; Li Nuohan

2006-01-01

Nonlinear dynamics of a vertical-cavity surface-emitting laser (VCSEL) with external optical injection are studied numerically. We consider a master-slave configuration where the dynamic characteristics of the slave are affected by the optical injection from the master, and we also establish the corresponding Simulink model. The period-doubling route as well as the period-halving route is observed, where the regular, double-periodic, and chaotic pulsings are found. By adjusting the injection strength properly, the laser can be controlled to work at a given state. The effects of frequency detuning on the nonlinear behaviors are also investigated in terms of the bifurcation diagrams of photon density with the frequency detuning. For weak injection case, the nonlinear dynamics shown by the laser are quite different when the value of frequency detuning varies contrarily (positive and negative direction). If the optical injection is strong enough, the slave can be locked by the master even though the frequency detuning is relatively large

Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

Directory of Open Access Journals (Sweden)

Haitao Liao

2013-01-01

Full Text Available In order to calculate the limit cycle oscillations and bifurcations of nonlinear aeroelastic system, the problem of finding periodic solutions with maximum vibration amplitude is transformed into a nonlinear optimization problem. An algebraic system of equations obtained by the harmonic balance method and the stability condition derived from the Floquet theory are used to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated, and the effects of structural parameter uncertainty on the limit cycle oscillations and bifurcations of an airfoil with multiple nonlinearities are studied. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

Gap solitons under competing local and nonlocal nonlinearities

International Nuclear Information System (INIS)

Kuo, Kuan-Hsien; Lin Yuanyao; Lee, Ray-Kuang; Malomed, Boris A.

2011-01-01

We analyze the existence, bifurcations, and shape transformations of one-dimensional gap solitons (GSs) in the first finite band gap induced by a periodic potential built into materials with local self-focusing and nonlocal self-defocusing nonlinearities. Originally stable on-site GS modes become unstable near the upper edge of the band gap with the introduction of the nonlocal self-defocusing nonlinearity with a small nonlocality radius. Unstable off-site GSs bifurcate into a new branch featuring single-humped, double-humped, and flat-top modes due to the competition between local and nonlocal nonlinearities. The mechanism underlying the complex bifurcation pattern and cutoff effects (termination of some bifurcation branches) is illustrated in terms of the shape transformation under the action of the varying degree of the nonlocality. The results of this work suggest a possibility of optical-signal processing by means of the competing nonlocal and local nonlinearities.

The Changing Nonlinear Relationship between Income and Terrorism

Science.gov (United States)

Enders, Walter; Hoover, Gary A.

2014-01-01

This article reinvestigates the relationship between real per capita gross domestic product (GDP) and terrorism. We devise a terrorism Lorenz curve to show that domestic and transnational terrorist attacks are each more concentrated in middle-income countries, thereby suggesting a nonlinear income–terrorism relationship. Moreover, this point of concentration shifted to lower income countries after the rising influence of the religious fundamentalist and nationalist/separatist terrorists in the early 1990s. For transnational terrorist attacks, this shift characterized not only the attack venue but also the perpetrators’ nationality. The article then uses nonlinear smooth transition regressions to establish the relationship between real per capita GDP and terrorism for eight alternative terrorism samples, accounting for venue, perpetrators’ nationality, terrorism type, and the period. Our nonlinear estimates are shown to be favored over estimates using linear or quadratic income determinants of terrorism. These nonlinear estimates are robust to additional controls. PMID:28579636

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

Science.gov (United States)

Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

2017-04-01

This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

Controller Synthesis for Periodically Forced Chaotic Systems

Science.gov (United States)

Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo

Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.

Period doubling induced by thermal noise amplification in genetic circuits

KAUST Repository

Ruocco, G.

2014-11-18

Rhythms of life are dictated by oscillations, which take place in a wide rage of biological scales. In bacteria, for example, oscillations have been proven to control many fundamental processes, ranging from gene expression to cell divisions. In genetic circuits, oscillations originate from elemental block such as autorepressors and toggle switches, which produce robust and noise-free cycles with well defined frequency. In some circumstances, the oscillation period of biological functions may double, thus generating bistable behaviors whose ultimate origin is at the basis of intense investigations. Motivated by brain studies, we here study an “elemental” genetic circuit, where a simple nonlinear process interacts with a noisy environment. In the proposed system, nonlinearity naturally arises from the mechanism of cooperative stability, which regulates the concentration of a protein produced during a transcription process. In this elemental model, bistability results from the coherent amplification of environmental fluctuations due to a stochastic resonance of nonlinear origin. This suggests that the period doubling observed in many biological functions might result from the intrinsic interplay between nonlinearity and thermal noise.

PERIOD ESTIMATION FOR SPARSELY SAMPLED QUASI-PERIODIC LIGHT CURVES APPLIED TO MIRAS

Energy Technology Data Exchange (ETDEWEB)

He, Shiyuan; Huang, Jianhua Z.; Long, James [Department of Statistics, Texas A and M University, College Station, TX (United States); Yuan, Wenlong; Macri, Lucas M., E-mail: lmacri@tamu.edu [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Department of Physics and Astronomy, Texas A and M University, College Station, TX (United States)

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequency parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period–luminosity relations.

Nonlinear stability of source defects in the complex Ginzburg–Landau equation

International Nuclear Information System (INIS)

Beck, Margaret; Nguyen, Toan T; Sandstede, Björn; Zumbrun, Kevin

2014-01-01

In an appropriate moving coordinate frame, source defects are time-periodic solutions to reaction–diffusion equations that are spatially asymptotic to spatially periodic wave trains whose group velocities point away from the core of the defect. In this paper, we rigorously establish nonlinear stability of spectrally stable source defects in the complex Ginzburg–Landau equation. Due to the outward transport at the far field, localized perturbations may lead to a highly non-localized response even on the linear level. To overcome this, we first investigate in detail the dynamics of the solution to the linearized equation. This allows us to determine an approximate solution that satisfies the full equation up to and including quadratic terms in the nonlinearity. This approximation utilizes the fact that the non-localized phase response, resulting from the embedded zero eigenvalues, can be captured, to leading order, by the nonlinear Burgers equation. The analysis is completed by obtaining detailed estimates for the resolvent kernel and pointwise estimates for Green's function, which allow one to close a nonlinear iteration scheme. (paper)

Rogue periodic waves of the modified KdV equation

Science.gov (United States)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-05-01

Rogue periodic waves stand for rogue waves on a periodic background. Two families of travelling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and two-fold Darboux transformations of the travelling periodic waves, we construct new explicit solutions for the mKdV equation. Since the dn-periodic wave is modulationally stable with respect to long-wave perturbations, the new solution constructed from the dn-periodic wave is a nonlinear superposition of an algebraically decaying soliton and the dn-periodic wave. On the other hand, since the cn-periodic wave is modulationally unstable with respect to long-wave perturbations, the new solution constructed from the cn-periodic wave is a rogue wave on the cn-periodic background, which generalizes the classical rogue wave (the so-called Peregrine’s breather) of the nonlinear Schrödinger equation. We compute the magnification factor for the rogue cn-periodic wave of the mKdV equation and show that it remains constant for all amplitudes. As a by-product of our work, we find explicit expressions for the periodic eigenfunctions of the spectral problem associated with the dn and cn periodic waves of the mKdV equation.

Quadratic soliton self-reflection at a quadratically nonlinear interface

Science.gov (United States)

Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

2003-11-01

The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

Chaotic synchronization of two complex nonlinear oscillators

International Nuclear Information System (INIS)

Mahmoud, Gamal M.; Mahmoud, Emad E.; Farghaly, Ahmed A.; Aly, Shaban A.

2009-01-01

Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

Seasonality Effects on Nonlinear Properties of Hydrometeorological Records: A New Method of Data Analysis

Science.gov (United States)

Livina, V. N.; Ashkenazy, Y.; Bunde, A.; Havlin, S.

2007-12-01

Climatic time series in general, and hydrological time series in particular, exhibit pronounced annual periodicity. This periodicity and its corresponding harmonics affect the nonlinear properties of the relevant time series (i.e., the long-range volatility correlations and width of multifractal spectrum) and thus have to be filtered out before studying fractal and volatility properties. We compare several filtering techniques (one of them proposed here) and find that in order to eliminate the periodicity effect on the nonlinear properties of the time series (i.e., the volatility and multifractal properties) it is necessary to filter out the seasonal standard deviation in addition to the filtering of the seasonal mean. The obtained results indicate weak volatility correlations (weak nonlinearity) in the river data, and this can be seen using different filterings approaches. [1] Livina~V.~N., Y.~Ashkenazy, A.~Bunde, and S.~Havlin, Seasonality effects on nonlinear properties of hydrometeorological records, in Extremes, Trends, and Correlations in Hydrology and Climate (ed. by J.P.Kropp & H.-J.Schellnhuber), Springer, Berlin, submitted.

An introduction to geometric theory of fully nonlinear parabolic equations

International Nuclear Information System (INIS)

Lunardi, A.

1991-01-01

We study a class of nonlinear evolution equations in general Banach space being an abstract version of fully nonlinear parabolic equations. In addition to results of existence, uniqueness and continuous dependence on the data, we give some qualitative results about stability of the stationary solutions, existence and stability of the periodic orbits. We apply such results to some parabolic problems arising from combustion theory. (author). 24 refs

Nonlinear damping based semi-active building isolation system

Science.gov (United States)

Ho, Carmen; Zhu, Yunpeng; Lang, Zi-Qiang; Billings, Stephen A.; Kohiyama, Masayuki; Wakayama, Shizuka

2018-06-01

Many buildings in Japan currently have a base-isolation system with a low stiffness that is designed to shift the natural frequency of the building below the frequencies of the ground motion due to earthquakes. However, the ground motion observed during the 2011 Tohoku earthquake contained strong long-period waves that lasted for a record length of 3 min. To provide a novel and better solution against the long-period waves while maintaining the performance of the standard isolation range, the exploitation of the characteristics of nonlinear damping is proposed in this paper. This is motivated by previous studies of the authors, which have demonstrated that nonlinear damping can achieve desired performance over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Simulation results have shown strong vibration isolation performance on a building model with identified parameters and have indicated that nonlinear damping can achieve low acceleration transmissibilities round the structural natural frequency as well as the higher ground motion frequencies that have been frequently observed during most earthquakes in Japan. In addition, physical building model based laboratory experiments are also conducted, The results demonstrate the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. In comparison with the tuned-mass damper and other active control methods, the proposed solution offers a more pragmatic, low-cost, robust and effective alternative that can be readily installed into the base-isolation system of most buildings.

Nonlinear dynamics and cavity cooling of levitated nanoparticles

Science.gov (United States)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-09-01

We investigate a dynamic nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. Through the rich sideband structure displayed by the cavity output we can observe cooling of the linear and non-linear particle's motion. Here we present an experimental setup which allows full control over the cavity resonant frequencies, and shows cooling of the particle's motion as a function of the detuning. This work paves the way to strong-coupled quantum dynamics between a cavity and a mesoscopic object largely decoupled from its environment.

Dynamics of Solid Body in Magnetic Suspension under Periodic Excitation

Directory of Open Access Journals (Sweden)

A. M. Gouskov

2017-01-01

Full Text Available The article studies dynamics of ferromagnetic body in hybrid magnetic suspension (HMS. The body is supposed to have one degree of freedom and a nonlinear magnetic force dependence on the current and displacement. The magnetic force induced in the HMS is divided into a passive component and an active one. Specifying the law of current variation in the coil allows us to generate nonlinear oscillations under electromagnet action. To provide periodic excitation the appropriate law of the current variation in the electromagnet coil is proposed. The mathematical model includes external periodic step-excitation. The equation of motion is formed. The scales of similarity are highlighted in the system, and the equation of motion is reduced to dimensionless form.The motion dynamics is studied numerically. The relaxation method was used to determine the periodic motions at different values of dimensionless frequency of the electromagnet excitation as well as to estimate the influence of other dimensionless parameters on the system dynamics. The amplitude-frequency curve analysis allows us to come to conclusion that the nature of system nonlinearity is rigid. Adding the external periodic step-excitation leads to the qualitative change in the nature of movement. This points to the occurrence of bifurcation.

Spatially localized, temporally quasiperiodic, discrete nonlinear excitations

International Nuclear Information System (INIS)

Cai, D.; Bishop, A.R.; Gronbech-Jensen, N.

1995-01-01

In contrast to the commonly discussed discrete breather, which is a spatially localized, time-periodic solution, we present an exact solution of a discrete nonlinear Schroedinger breather which is a spatially localized, temporally quasiperiodic nonlinear coherent excitation. This breather is a multiple-soliton solution in the sense of the inverse scattering transform. A discrete breather of multiple frequencies is conceptually important in studies of nonlinear lattice systems. We point out that, for this breather, the incommensurability of its frequencies is a discrete lattice effect and these frequencies become commensurate in the continuum limit. To understand the dynamical properties of the breather, we also discuss its stability and its behavior in the presence of an external potential. Finally, we indicate how to obtain an exact N-soliton breather as a discrete generalization of the continuum multiple-soliton solution

Two simple ansaetze for obtaining exact solutions of high dispersive nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Palacios, Sergio L.

2004-01-01

We propose two simple ansaetze that allow us to obtain different analytical solutions of the high dispersive cubic and cubic-quintic nonlinear Schroedinger equations. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

Science.gov (United States)

Fonseca, P Z G; Aranas, E B; Millen, J; Monteiro, T S; Barker, P F

2016-10-21

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

Science.gov (United States)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-10-01

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Self-guiding light in layered nonlinear media

DEFF Research Database (Denmark)

Bergé, L.; Mezentsev, V. K.; Juul Rasmussen, Jens

2000-01-01

We study the propagation of intense optical beams in layered Kerr media. With appropriate shapes, beams with a power close to the self-focusing threshold are shown to propagate over long distances as quasistationary waveguides in cubic media supporting a periodic nonlinear refractive index. (C...

First constraints on the running of non-Gaussianity.

Science.gov (United States)

Becker, Adam; Huterer, Dragan

2012-09-21

We use data from the Wilkinson Microwave Anisotropy probe temperature maps to constrain a scale-dependent generalization of the popular "local" model for primordial non-Gaussianity. In the model where the parameter f(NL) is allowed to run with scale k, f(NL)(k) = f*(NL) (k/k(piv))(n)(fNL), we constrain the running to be n(f)(NL) = 0.30(-1.2)(+1.9) at 95% confidence, marginalized over the amplitude f*(NL). The constraints depend somewhat on the prior probabilities assigned to the two parameters. In the near future, constraints from a combination of Planck and large-scale structure surveys are expected to improve this limit by about an order of magnitude and usefully constrain classes of inflationary models.

Enhancement of current commensurate with mutual noise-noise correlation in a symmetric periodic substrate: The benefits of noise and nonlinearity

Energy Technology Data Exchange (ETDEWEB)

Ghosh, Pradipta [Department of Chemistry and Biochemistry, Presidency University, Kolkata 700073 (India); Chattopadhyay, Sudip, E-mail: sudip_chattopadhyay@rediffmail.com [Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103 (India); Chaudhuri, Jyotipratim Ray, E-mail: jprc_8@yahoo.com [Department of Physics, Katwa College, Katwa, Burdwan 713130 (India)

2012-06-19

Highlights: Black-Right-Pointing-Pointer Exploration of directed transport in stochastic systems with embedded nonlinearity. Black-Right-Pointing-Pointer Formalism is valid for open system in the presence of arbitrary periodic potential. Black-Right-Pointing-Pointer Effective temperature depends on correlation time and extent of correlation. Black-Right-Pointing-Pointer Study of the directed motion in presence of external cross-correlated noises. Black-Right-Pointing-Pointer Steady state current increases with increase in the extent of correlation. - Abstract: Starting from a Langevin description of a particle submerged in a heat bath that offers a state dependent dissipation, we examine the noise-induced transport of a Brownian particle in the presence of two external, mutually correlated noises and envisage that in a symmetric periodic potential, the steady state current increases with an increase in the extent of correlation. The study of inhomogeneous diffusion in the presence of colored noise makes the present development formally interesting since this brings in a direct implication that exercising control on the degree of correlation can enhance the current in a properly designed experiment. As an offshoot of this development, we also envisage an effective temperature that depends on the correlation time and the extent of correlation.

Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers.

Science.gov (United States)

Conforti, Matteo; Mas Arabi, Carlos; Mussot, Arnaud; Kudlinski, Alexandre

2017-10-01

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists of a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.

Nonlinear streak computation using boundary region equations

Energy Technology Data Exchange (ETDEWEB)

Martin, J A; Martel, C, E-mail: juanangel.martin@upm.es, E-mail: carlos.martel@upm.es [Depto. de Fundamentos Matematicos, E.T.S.I Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid (Spain)

2012-08-01

The boundary region equations (BREs) are applied for the simulation of the nonlinear evolution of a spanwise periodic array of streaks in a flat plate boundary layer. The well-known BRE formulation is obtained from the complete Navier-Stokes equations in the high Reynolds number limit, and provides the correct asymptotic description of three-dimensional boundary layer streaks. In this paper, a fast and robust streamwise marching scheme is introduced to perform their numerical integration. Typical streak computations present in the literature correspond to linear streaks or to small-amplitude nonlinear streaks computed using direct numerical simulation (DNS) or the nonlinear parabolized stability equations (PSEs). We use the BREs to numerically compute high-amplitude streaks, a method which requires much lower computational effort than DNS and does not have the consistency and convergence problems of the PSE. It is found that the flow configuration changes substantially as the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, which end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results. (paper)

On modulated complex non-linear dynamical systems

International Nuclear Information System (INIS)

Mahmoud, G.M.; Mohamed, A.A.; Rauh, A.

1999-01-01

This paper is concerned with the development of an approximate analytical method to investigate periodic solutions and their stability in the case of modulated non-linear dynamical systems whose equation of motion is describe. Such differential equations appear, for example, in problems of colliding particle beams in high-energy accelerators or one-mass systems with two or more degrees of freedom, e.g. rotors. The significance of periodic solutions lies on the fact that all non-periodic responses, if convergent, would approach to periodic solutions at the steady-state conditions. The example shows a good agreement between numerical and analytical results for small values of ε. The effect of the periodic modulation on the stability of the 2π-periodic solutions is discussed

Coupling of reciprocal vectors and corresponding degeneracy effect in a dual-periodic optical superlattice

International Nuclear Information System (INIS)

Qin Yiqiang

2006-01-01

A dual-periodic structure for quasi-phase matching cascaded optical parametric interactions is proposed. Due to the coupling of reciprocal vectors between the original and imposed periodic sequence, the reciprocal vectors and the corresponding effective nonlinear coefficients is no longer the simple combination of two periodic structures. The new analytical expression of the effective nonlinear coefficients is deduced and given. The degeneracy phenomena and the novel extinction rule resulting from the coupling of reciprocal vectors are found and investigated. The corresponding physical nature is also discussed

Separation of variables for the nonlinear wave equation in polar coordinates

International Nuclear Information System (INIS)

Shermenev, Alexander

2004-01-01

Some classical types of nonlinear wave motion in polar coordinates are studied within quadratic approximation. When the nonlinear quadratic terms in the wave equation are arbitrary, the usual perturbation techniques used in polar coordinates leads to overdetermined systems of linear algebraic equations for the unknown coefficients. However, we show that these overdetermined systems are compatible with the special case of the nonlinear shallow water equation and express explicitly the coefficients of the first two harmonics as polynomials of the Bessel functions of radius and of the trigonometric functions of angle. It gives a series of solutions to the nonlinear shallow water equation that are periodic in time and found with the same accuracy as the equation is derived

Nonlinearity and fractional integration in the US dollar/euro exchange rate

Directory of Open Access Journals (Sweden)

Kiran Burcu

2012-01-01

Full Text Available This paper examines the nonlinear behavior and the fractional integration property of the US dollar/euro exchange rate over the period from January 1999 to August 2010 by extending the procedure of Peter M. Robinson (1994 to the case of nonlinearity. First, using the approach developed by Mehmet Caner and Bruce E. Hansen (2001, we investigate the possible presence of nonlinearity in the series through the estimation of a two-regime threshold autoregressive model. After finding nonlinearity, we also allow for disturbances to be fractionally integrated based on the different versions of Robinson (1994 tests. The findings show that the US dollar/euro exchange rate follows a stationary process with a weak evidence for long memory.

Nonlinear dynamical phenomena in liquid crystals

International Nuclear Information System (INIS)

Wang, X.Y.; Sun, Z.M.

1988-09-01

Because of the existence of the orientational order and anisotropy in liquid crystals, strong nonlinear phenomena and singular behaviors, such as solitary wave, transient periodic structure, chaos, fractal and viscous fingering, can be excited by a very small disturbance. These phenomena and behaviors are in connection with physics, biology and mathematics. 12 refs, 6 figs

Non-linear adjustment to purchasing power parity: an analysis using Fourier approximations

OpenAIRE

Juan-Ángel Jiménez-Martín; M. Dolores Robles Fernández

2005-01-01

This paper estimates the dynamics of adjustment to long run purchasing power parity (PPP) using data for 18 mayor bilateral US dollar exchange rates, over the post-Bretton Woods period, in a non-linear framework. We use new unit root and cointegration tests that do not assume a specific non-linear adjustment process. Using a first-order Fourier approximation, we find evidence of non-linear mean reversion in deviations from both absolute and relative PPP. This first-order Fourier approximation...

Evaluation of stratospheric temperature simulation results by the global GRAPES model

Science.gov (United States)

Liu, Ningwei; Wang, Yangfeng; Ma, Xiaogang; Zhang, Yunhai

2017-12-01

Global final analysis (FNL) products and the general circulation spectral model (ECHAM) were used to evaluate the simulation of stratospheric temperature by the global assimilation and prediction system (GRAPES). Through a series of comparisons, it was shown that the temperature variations at 50 hPa simulated by GRAPES were significantly elevated in the southern hemisphere, whereas simulations by ECHAM and FNL varied little over time. The regional warming predicted by GRAPES seemed to be too distinct and uncontrolled to be reasonable. The temperature difference between GRAPES and FNL (GRAPES minus FNL) was small at the start time on the global scale. Over time, the positive values became larger in more locations, especially in parts of the southern hemisphere, where the warming predicted by GRAPES was dominant, with a maximal value larger than 24 K. To determine the reasons for the stratospheric warming, we considered the model initial conditions and ozone data to be possible factors; however, a comparison and sensitivity test indicated that the errors produced by GRAPES were not significantly related to either factor. Further research focusing on the impact of factors such as vapor, heating rate, and the temperature tendency on GRAPES simulations will be conducted.

Geometric phases for nonlinear coherent and squeezed states

International Nuclear Information System (INIS)

Yang Dabao; Chen Ying; Chen Jingling; Zhang Fulin

2011-01-01

The geometric phases for standard coherent states which are widely used in quantum optics have attracted considerable attention. Nevertheless, few physicists consider the counterparts of nonlinear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated, respectively. Moreover, some of their common properties are discussed, such as gauge invariance, non-locality and nonlinear effects. The nonlinear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have an application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r → ∞, the limiting value of the geometric phase is also determined by a nonlinear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states may be regarded as a geometric criterion.

Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow.

Science.gov (United States)

Ryzhov, Eugene A

2017-11-01

The nonlinear dynamics of an elliptic vortex subjected to a time-periodic linear external shear flow is studied numerically. Making use of the ideas from the theory of nonlinear resonance overlaps, the study focuses on the appearance of chaotic regimes in the ellipse dynamics. When the superimposed flow is stationary, two general types of the steady-state phase portrait are considered: one that features a homoclinic separatrix delineating bounded and unbounded phase trajectories and one without a separatrix (all the phase trajectories are bounded in a periodic domain). When the external flow is time-periodic, the ensuing nonlinear dynamics differs significantly in both cases. For the case with a separatrix and two distinct types of phase trajectories: bounded and unbounded, the effect of the most influential nonlinear resonance with the winding number of 1:1 is analyzed in detail. Namely, the process of occupying the central stability region associated with the steady-state elliptic critical point by the stability region associated with the nonlinear resonance of 1:1 as the perturbation frequency gradually varies is investigated. A stark increase in the persistence of the central regular dynamics region against perturbation when the resonance of 1:1 associated stability region occupies the region associated with the steady-state elliptic critical point is observed. An analogous persistence of the regular motion occurs for higher perturbation frequencies when the corresponding stability islands reach the central stability region associated with the steady-state elliptic point. An analysis for the case with the resonance of 1:2 is presented. For the second case with only bounded phase trajectories and, therefore, no separatrix, the appearance of much bigger stability islands associated with nonlinear resonances compared with the case with a separatrix is reported.

Nonlinear dynamics of boiling water reactors

International Nuclear Information System (INIS)

March-Leuba, J.; Cacuci, D.G.; Perez, R.B.

1983-01-01

Recent stability tests in Boiling Water Reactors (BWRs) have indicated that these reactors can exhibit the special nonlinear behavior of following a closed trajectory called limit cycle. The existence of a limit cycle corresponds to an oscillation of fixed amplitude and period. During these tests, such oscillations had their amplitudes limited to about +- 15% of the operating power. Since limit cycles are fairly insensitive to parameter variations, it is possible to operate a BWR under conditions that sustain a limit cycle (of fixed amplitude and period) over a finite range of reactor parameters

Nonlinear dynamical analysis of an aeroelastic system with multi-segmented moment in the pitch degree-of-freedom

Science.gov (United States)

Vasconcellos, Rui; Abdelkefi, Abdessattar

2015-01-01

The effects of a multi-segmented nonlinearity in the pitch degree of freedom on the behavior of a two-degree of freedom aeroelastic system are investigated. The aeroelastic system is free to plunge and pitch and is supported by linear translational and nonlinear torsional springs and is subjected to an incoming flow. The unsteady representation based on the Duhamel formulation is used to model the aerodynamic loads. Using modern method of nonlinear dynamics, a nonlinear characterization is performed to identify the system's response when increasing the wind speed. It is demonstrated that four sudden transitions take place with a change in the system's response. It is shown that, in the first transition, the system's response changes from simply periodic (only main oscillating frequency) to two periods (having the main oscillating frequency and its superharmonic of order 2). In the second transition, the response of the system changes from two periods (having the main oscillating frequency and its superharmonic of order 2) to a period-1. The results also show that the third transition is accompanied by a change in the system's response from simply periodic to two periods (having the main oscillating frequency and its superharmonic of order 3). After this transition, chaotic responses take place and then the fourth transition is accompanied by a sudden change in the system's response from chaotic to two periods (having the main oscillating frequency and its superharmonic of order 3). The results show that these transitions are caused by the tangential contact between the trajectory and the multi-segmented nonlinearity boundaries and with a zero-pitch speed incidence. This observation is associated with the definition of grazing bifurcation.

NONLINEAR TIDES IN CLOSE BINARY SYSTEMS

International Nuclear Information System (INIS)

Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh

2012-01-01

We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' ∼> 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P ∼ 3 [P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P ∼< a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing

Wind - Ceiling - Visibility Data at Selected Airports. Volume VIII. Northwest Region.

Science.gov (United States)

1981-06-01

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Nonlinear robust hierarchical control for nonlinear uncertain systems

Directory of Open Access Journals (Sweden)

Leonessa Alexander

1999-01-01

Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.

Nonlinear dynamics in integrated coupled DFB lasers with ultra-short delay.

Science.gov (United States)

Liu, Dong; Sun, Changzheng; Xiong, Bing; Luo, Yi

2014-03-10

We report rich nonlinear dynamics in integrated coupled lasers with ultra-short coupling delay. Mutually stable locking, period-1 oscillation, frequency locking, quasi-periodicity and chaos are observed experimentally. The dynamic behaviors are reproduced numerically by solving coupled delay differential equations that take the variation of both frequency detuning and coupling phase into account. Moreover, it is pointed out that the round-trip frequency is not involved in the above nonlinear dynamical behaviors. Instead, the relationship between the frequency detuning Δν and the relaxation oscillation frequency νr under mutual injection are found to be critical for the various observed dynamics in mutually coupled lasers with very short delay.

Exact periodic solutions of the sixth-order generalized Boussinesq equation

International Nuclear Information System (INIS)

Kamenov, O Y

2009-01-01

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u tt = u xx + 3(u 2 ) xx + u xxxx + αu xxxxxx , α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

Detection method of nonlinearity errors by statistical signal analysis in heterodyne Michelson interferometer.

Science.gov (United States)

Hu, Juju; Hu, Haijiang; Ji, Yinghua

2010-03-15

Periodic nonlinearity that ranges from tens of nanometers to a few nanometers in heterodyne interferometer limits its use in high accuracy measurement. A novel method is studied to detect the nonlinearity errors based on the electrical subdivision and the analysis method of statistical signal in heterodyne Michelson interferometer. Under the movement of micropositioning platform with the uniform velocity, the method can detect the nonlinearity errors by using the regression analysis and Jackknife estimation. Based on the analysis of the simulations, the method can estimate the influence of nonlinearity errors and other noises for the dimensions measurement in heterodyne Michelson interferometer.

The relationship between crude oil spot and futures prices: Cointegration, linear and nonlinear causality

International Nuclear Information System (INIS)

Bekiros, Stelios D.; Diks, Cees G.H.

2008-01-01

The present study investigates the linear and nonlinear causal linkages between daily spot and futures prices for maturities of one, two, three and four months of West Texas Intermediate (WTI) crude oil. The data cover two periods October 1991-October 1999 and November 1999-October 2007, with the latter being significantly more turbulent. Apart from the conventional linear Granger test we apply a new nonparametric test for nonlinear causality by Diks and Panchenko after controlling for cointegration. In addition to the traditional pairwise analysis, we test for causality while correcting for the effects of the other variables. To check if any of the observed causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of VECM filtered residuals. Finally, we investigate the hypothesis of nonlinear non-causality after controlling for conditional heteroskedasticity in the data using a GARCH-BEKK model. Whilst the linear causal relationships disappear after VECM cointegration filtering, nonlinear causal linkages in some cases persist even after GARCH filtering in both periods. This indicates that spot and futures returns may exhibit asymmetric GARCH effects and/or statistically significant higher order conditional moments. Moreover, the results imply that if nonlinear effects are accounted for, neither market leads or lags the other consistently, videlicet the pattern of leads and lags changes over time. (author)

Nonlinear Dynamics Analysis of the Semiactive Suspension System with Magneto-Rheological Damper

Directory of Open Access Journals (Sweden)

Hailong Zhang

2015-01-01

Full Text Available This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The magneto-rheological (MR suspension system has been established, by employing the modified Bouc-Wen force-velocity (F-v model of magneto-rheological damper (MRD. The possibility of chaotic motions in MR suspension is discovered by employing the method of nonlinear stability analysis. With the bifurcation diagrams and corresponding Lyapunov exponent (LE spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasiperiodic oscillations, and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolutions to chaos through period-doubling bifurcations, saddle-node bifurcations, and reverse period-doubling bifurcations.

Dynamics of elliptic breathers in saturable nonlinear media with linear anisotropy

International Nuclear Information System (INIS)

Liang, Guo; Guo, Qi; Shou, Qian; Ren, Zhanmei

2014-01-01

We have introduced a class of dynamic elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behavior for the dynamic breathers, rotations and molecule-like librations, are both predicted by the variational approach, and confirmed in numerical simulations. The dynamic elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). As the media are linear anisotropic, OAM is no longer conserved, and hence the angular velocity is not constant but a periodic function of the propagation distance. When the linear anisotropy is large enough, the dynamic elliptic breathers librate like molecules. The dynamic elliptic breathers are present in media with not only saturable nonlinearity but also nonlocal nonlinearity; indeed, they are universal in nonlinear media with linear anisotropy. (paper)

Attractors of the periodically forced Rayleigh system

Directory of Open Access Journals (Sweden)

Petre Bazavan

2011-07-01

Full Text Available The autonomous second order nonlinear ordinary differential equation(ODE introduced in 1883 by Lord Rayleigh, is the equation whichappears to be the closest to the ODE of the harmonic oscillator withdumping.In this paper we present a numerical study of the periodic andchaotic attractors in the dynamical system associated with the generalized Rayleigh equation. Transition between periodic and quasiperiodic motion is also studied. Numerical results describe the system dynamics changes (in particular bifurcations, when the forcing frequency is varied and thus, periodic, quasiperiodic or chaotic behaviour regions are predicted.

Periodic solutions of nonautonomous differential systems modeling obesity population

International Nuclear Information System (INIS)

Arenas, Abraham J.; Gonzalez-Parra, Gilberto; Jodar, Lucas

2009-01-01

In this paper we study the periodic behaviour of the solutions of a nonautonomous model for obesity population. The mathematical model represented by a nonautonomous system of nonlinear ordinary differential equations is used to model the dynamics of obese populations. Numerical simulations suggest periodic behaviour of subpopulations solutions. Sufficient conditions which guarantee the existence of a periodic positive solution are obtained using a continuation theorem based on coincidence degree theory.

Periodic solutions of nonautonomous differential systems modeling obesity population

Energy Technology Data Exchange (ETDEWEB)

Arenas, Abraham J. [Departamento de Matematicas y Estadistica, Universidad de Cordoba Monteria (Colombia)], E-mail: aarenas@sinu.unicordoba.edu.co; Gonzalez-Parra, Gilberto [Departamento de Calculo, Universidad de los Andes, Merida (Venezuela, Bolivarian Republic of)], E-mail: gcarlos@ula.ve; Jodar, Lucas [Instituto de Matematica Multidisciplinar, Universidad Politecnica de Valencia Edificio 8G, 2o, 46022 Valencia (Spain)], E-mail: ljodar@imm.upv.es

2009-10-30

In this paper we study the periodic behaviour of the solutions of a nonautonomous model for obesity population. The mathematical model represented by a nonautonomous system of nonlinear ordinary differential equations is used to model the dynamics of obese populations. Numerical simulations suggest periodic behaviour of subpopulations solutions. Sufficient conditions which guarantee the existence of a periodic positive solution are obtained using a continuation theorem based on coincidence degree theory.

q Breathers in Finite Lattices: Nonlinearity and Weak Disorder

Science.gov (United States)

Ivanchenko, M. V.

2009-05-01

Nonlinearity and disorder are the recognized ingredients of the lattice vibrational dynamics, the factors that could be diminished, but never excluded. We generalize the concept of q breathers—periodic orbits in nonlinear lattices, exponentially localized in the linear mode space—to the case of weak disorder, taking the Fermi-Pasta-Ulan chain as an example. We show that these nonlinear vibrational modes remain exponentially localized near the central mode and stable, provided the disorder is sufficiently small. The instability threshold depends sensitively on a particular realization of disorder and can be modified by specifically designed impurities. Based on this sensitivity, an approach to controlling the energy flow between the modes is proposed. The relevance to other model lattices and experimental miniature arrays is discussed.

Nonlinear Recurrent Dynamics and Long-Term Nonstationarities in EEG Alpha Cortical Activity: Implications for Choosing Adequate Segment Length in Nonlinear EEG Analyses.

Science.gov (United States)

Cerquera, Alexander; Vollebregt, Madelon A; Arns, Martijn

2018-03-01

Nonlinear analysis of EEG recordings allows detection of characteristics that would probably be neglected by linear methods. This study aimed to determine a suitable epoch length for nonlinear analysis of EEG data based on its recurrence rate in EEG alpha activity (electrodes Fz, Oz, and Pz) from 28 healthy and 64 major depressive disorder subjects. Two nonlinear metrics, Lempel-Ziv complexity and scaling index, were applied in sliding windows of 20 seconds shifted every 1 second and in nonoverlapping windows of 1 minute. In addition, linear spectral analysis was carried out for comparison with the nonlinear results. The analysis with sliding windows showed that the cortical dynamics underlying alpha activity had a recurrence period of around 40 seconds in both groups. In the analysis with nonoverlapping windows, long-term nonstationarities entailed changes over time in the nonlinear dynamics that became significantly different between epochs across time, which was not detected with the linear spectral analysis. Findings suggest that epoch lengths shorter than 40 seconds neglect information in EEG nonlinear studies. In turn, linear analysis did not detect characteristics from long-term nonstationarities in EEG alpha waves of control subjects and patients with major depressive disorder patients. We recommend that application of nonlinear metrics in EEG time series, particularly of alpha activity, should be carried out with epochs around 60 seconds. In addition, this study aimed to demonstrate that long-term nonlinearities are inherent to the cortical brain dynamics regardless of the presence or absence of a mental disorder.

Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models

International Nuclear Information System (INIS)

Zhang Hao; Ma Xikui; Xue Bianling; Liu Weizeng

2005-01-01

This paper mainly deals with nonlinear phenomena like intermittent bifurcations and chaos in boost PFC converters under peak-current control mode. Two nonlinear models in the form of discrete maps are derived to describe precisely the nonlinear dynamics of boost PFC converters from two points of view, i.e., low- and high-frequency regimes. Based on the presented discrete models, both the evolution of intermittent behavior and the periodicity of intermittency are investigated in detail from the fast and slow-scale aspects, respectively. Numerical results show that the occurrence of intermittent bifurcations and chaos with half one line period is one of the most distinguished dynamical characteristics. Finally, we make some instructive conclusions, which prove to be helpful in improving the performances of practical circuits

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

The inherent complexity in nonlinear business cycle model in resonance

International Nuclear Information System (INIS)

Ma Junhai; Sun Tao; Liu Lixia

2008-01-01

Based on Abraham C.-L. Chian's research, we applied nonlinear dynamic system theory to study the first-order and second-order approximate solutions to one category of the nonlinear business cycle model in resonance condition. We have also analyzed the relation between amplitude and phase of second-order approximate solutions as well as the relation between outer excitements' amplitude, frequency approximate solutions, and system bifurcation parameters. Then we studied the system quasi-periodical solutions, annulus periodical solutions and the path leading to system bifurcation and chaotic state with different parameter combinations. Finally, we conducted some numerical simulations for various complicated circumstances. Therefore this research will lay solid foundation for detecting the complexity of business cycles and systems in the future

Breathers and rogue waves: Demonstration with coupled nonlinear ...

Indian Academy of Sciences (India)

It has been found that the rational solution of nonlinear Schrödinger (NLS) ..... Figures 3a and 3b illustrate the behaviour of this solution, which is periodic both ... peaks increases or decreases and if the direction gets changed or not when the ...

Near-Integrability of Low-Dimensional Periodic Klein-Gordon Lattices

Directory of Open Access Journals (Sweden)

Ognyan Christov

2018-01-01

Full Text Available The low-dimensional periodic Klein-Gordon lattices are studied for integrability. We prove that the periodic lattice with two particles and certain nonlinear potential is nonintegrable. However, in the cases of up to six particles, we prove that their Birkhoff-Gustavson normal forms are integrable, which allows us to apply KAM theory in most cases.

Diffractons: Solitary Waves Created by Diffraction in Periodic Media

KAUST Repository

Ketcheson, David I.

2015-03-31

A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. These solitary waves depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the sound speed of the medium. A high-order homogenized model confirms this effective dispersive behavior, and its solutions agree well with those obtained by direct simulation of the variable-coefficient system. These waves are observed to be long-time stable, globally attracting solutions that arise in general as solutions to nonlinear wave problems with periodically varying sound speed. They share some properties with known classes of solitary waves but possess important differences as well.

Superposition of elliptic functions as solutions for a large number of nonlinear equations

International Nuclear Information System (INIS)

Khare, Avinash; Saxena, Avadh

2014-01-01

For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ 4 , the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn 2 (x, m), it also admits solutions in terms of dn 2 (x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

Science.gov (United States)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Intracavity quasi-phase-matched self-frequency conversion in a periodically poled Nd:Mg:LiNbO3 crystal

International Nuclear Information System (INIS)

Laptev, G D; Novikov, Aleksei A

2001-01-01

The theory of intracavity quasi-phase-matched self-frequency conversion in an active nonlinear periodically poled structure is developed. The processes of quasi-phase-matched self-frequency doubling, self-halving and mixing using the pump wave in a periodically poled Nd:Mg:LiNbO 3 crystal are studied. The dependences of the efficiency of nonlinear optical conversion in these processes on the reflection coefficient of the output mirror and on linear losses in the medium are investigated. (nonlinear optical phenomena)

Analysis of factors influencing fire damage to concrete using nonlinear resonance vibration method

Energy Technology Data Exchange (ETDEWEB)

Park, Gang Kyu; Park, Sun Jong; Kwak, Hyo Gyoung [Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, KAIST, Daejeon (Korea, Republic of); Yim, Hong Jae [Dept. of Construction and Disaster Prevention Engineering, Kyungpook National University, Sangju (Korea, Republic of)

2015-04-15

In this study, the effects of different mix proportions and fire scenarios (exposure temperatures and post-fire-curing periods) on fire-damaged concrete were analyzed using a nonlinear resonance vibration method based on nonlinear acoustics. The hysteretic nonlinearity parameter was obtained, which can sensitively reflect the damage level of fire-damaged concrete. In addition, a splitting tensile strength test was performed on each fire-damaged specimen to evaluate the residual property. Using the results, a prediction model for estimating the residual strength of fire-damaged concrete was proposed on the basis of the correlation between the hysteretic nonlinearity parameter and the ratio of splitting tensile strength.

Alfven wave resonances and flow induced by nonlinear Alfven waves in a stratified atmosphere

International Nuclear Information System (INIS)

Stark, B. A.; Musielak, Z. E.; Suess, S. T.

1996-01-01

A nonlinear, time-dependent, ideal MHD code has been developed and used to compute the flow induced by nonlinear Alfven waves propagating in an isothermal, stratified, plane-parallel atmosphere. The code is based on characteristic equations solved in a Lagrangian frame. Results show that resonance behavior of Alfven waves exists in the presence of a continuous density gradient and that the waves with periods corresponding to resonant peaks exert considerably more force on the medium than off-resonance periods. If only off-peak periods are considered, the relationship between the wave period and induced longitudinal velocity shows that short period WKB waves push more on the background medium than longer period, non-WKB, waves. The results also show the development of the longitudinal waves induced by finite amplitude Alfven waves. Wave energy transferred to the longitudinal mode may provide a source of localized heating

Nonlinear Vibration of Oscillation Systems using Frequency-Amplitude Formulation

Directory of Open Access Journals (Sweden)

A. Fereidoon

2012-01-01

Full Text Available In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF.The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.

Nonlinear Coupled Dynamics of a Rod Fastening Rotor under Rub-Impact and Initial Permanent Deflection

Directory of Open Access Journals (Sweden)

Liang Hu

2016-10-01

Full Text Available A nonlinear coupled dynamic model of a rod fastening rotor under rub-impact and initial permanent deflection was developed in this paper. The governing motion equation was derived by the D’Alembert principle considering the contact characteristic between disks, nonlinear oil-film force, rub-impact force, unbalance mass, etc. The contact effects between disks was modeled as a flexural spring with cubical nonlinear stiffness. The coupled nonlinear dynamic phenomena of the rub-impact rod fastening rotor bearing system with initial permanent deflection were investigated by the fourth-order Runge-Kutta method. Bifurcation diagram, vibration waveform, frequency spectrum, shaft orbit and Poincaré map are used to illustrate the rich diversity of the system response with complicated dynamics. The studies indicate that the coupled dynamic responses of the rod fastening rotor bearing system under rub-impact and initial permanent deflection exhibit a rich nonlinear dynamic diversity, synchronous periodic-1 motion, multiple periodic motion, quasi-periodic motion and chaotic motion can be observed under certain conditions. Larger radial stiffness of the stator will simplify the system motion and make the oil whirl weaker or even disappear at a certain rotating speed. With the increase of initial permanent deflection length, the instability speed of the system gradually rises, and the chaotic motion region gets smaller and smaller. The corresponding results can provide guidance for the fault diagnosis of a rub-impact rod fastening rotor with initial permanent deflection and contribute to the further understanding of the nonlinear dynamic characteristics of the rod fastening rotor bearing system.

Punchets: nonlinear transport in Hamiltonian pump-ratchet hybrids

Science.gov (United States)

Dittrich, Thomas; Medina Sánchez, Nicolás

2018-02-01

‘Punchets’ are hybrids between ratchets and pumps, combining a spatially periodic static potential, typically asymmetric under space inversion, with a local driving that breaks time-reversal invariance, and are intended to model metal or semiconductor surfaces irradiated by a collimated laser beam. Their crucial feature is irregular driven scattering between asymptotic regions supporting periodic (as opposed to free) motion. With all binary spatio-temporal symmetries broken, scattering in punchets typically generates directed currents. We here study the underlying nonlinear transport mechanisms, from chaotic scattering to the parameter dependence of the currents, in three types of Hamiltonian models, (i) with spatially periodic potentials where only in the driven scattering region, spatial and temporal symmetries are broken, and (ii), spatially asymmetric (ratchet) potentials with a driving that only breaks time-reversal invariance. As more realistic models of laser-irradiated surfaces, we consider (iii), a driving in the form of a running wave confined to a compact region by a static envelope. In this case, the induced current can even run against the direction of wave propagation, drastically evidencing its nonlinear nature. Quantizing punchets is indicated as a viable research perspective.

Quantum osp-invariant non-linear Schroedinger equation

International Nuclear Information System (INIS)

Kulish, P.P.

1985-04-01

The generalizations of the non-linear Schroedinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the wholeline in the case of a finite number of excitations. (author)

Classical Yang-Mills mechanics. Nonlinear colour oscillations

International Nuclear Information System (INIS)

Matinyan, S.G.; Savvidi, G.K.; Ter-Arutyunyan-Savvidi, N.G.

1981-01-01

A novel class of solutions of the classical Yang-Mills equations in the Minkowsky space which leads to nonlinear colour oscillations is studied. The system discribing these oscillations is apparently stochastic. Periodic trajectories corresponding to the solutions are found and studied and it is demonstrated that they constitute at least an enumerable set [ru

Effect of primordial non-Gaussianities on galaxy clusters scaling relations

Science.gov (United States)

Trindade, A. M. M.; da Silva, Antonio

2017-07-01

Galaxy clusters are a valuable source of cosmological information. Their formation and evolution depends on the underlying cosmology and on the statistical nature of the primordial density fluctuations. Here we investigate the impact of primordial non-Gaussianities (PNG) on the scaling properties of galaxy clusters. We performed a series of hydrodynamic N-body simulations featuring adiabatic gas physics and different levels of non-Gaussianity within the Λ cold dark matter framework. We focus on the T-M, S-M, Y-M and YX-M scalings relating the total cluster mass with temperature, entropy and Sunyaev-Zeld'ovich integrated pressure that reflect the thermodynamic state of the intracluster medium. Our results show that PNG have an impact on cluster scalings laws. The scalings mass power-law indexes are almost unaffected by the existence of PNG, but the amplitude and redshift evolution of their normalizations are clearly affected. Changes in the Y-M and YX-M normalizations are as high as 22 per cent and 16 per cent when fNL varies from -500 to 500, respectively. Results are consistent with the view that positive/negative fNL affect cluster profiles due to an increase/decrease of cluster concentrations. At low values of fNL, as suggested by present Planck constraints on a scale invariant fNL, the impact on the scaling normalizations is only a few per cent. However, if fNL varies with scale, PNG may have larger amplitudes at clusters scales; thus, our results suggest that PNG should be taken into account when cluster data are used to infer or forecast cosmological parameters from existing or future cluster surveys.

Determination of Periodic Solution for Tapered Beams with Modified Iteration Perturbation Method

Directory of Open Access Journals (Sweden)

Mohammad Mehdi Mashinchi Joubari

2015-01-01

Full Text Available In this paper, we implemented the Modified Iteration Perturbation Method (MIPM for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need to complicated calculations. Comparing the results of the MIPM with the exact solution shows that this method is effective and convenient. Also, it is predicated that MIPM can be potentially used in the analysis of strongly nonlinear oscillation problems accurately.

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....

Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity

Science.gov (United States)

Paul Asir, M.; Jeevarekha, A.; Philominathan, P.

This paper deals with the generation of chaotic beats in a system of two forced dissipative LCR oscillators sharing a nonlinear element. The presence of two external periodic excitations and a common nonlinear element in the chosen system enables the facile generation of chaotic beats. Thus rendered chaotic beats were characterized in both time domain and phase space. Lyapunov exponents and envelope of the beats were computed to diagnose the chaotic nature of the signals. The role of common nonlinearity on the complexity of the generated beats is discussed. Real-time experimental hardware implementation has also been done to confirm the subsistence of the phenomenon, for the first time. Extensive Multisim simulations were carried out to understand, a bit more about the shrinkage and revivals of state variables in phase space.

Exact periodic solutions of the sixth-order generalized Boussinesq equation

Energy Technology Data Exchange (ETDEWEB)

Kamenov, O Y [Department of Applied Mathematics and Informatics, Technical University of Sofia, PO Box 384, 1000 Sofia (Bulgaria)], E-mail: okam@abv.bg

2009-09-18

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u{sub tt} = u{sub xx} + 3(u{sup 2}){sub xx} + u{sub xxxx} + {alpha}u{sub xxxxxx}, {alpha} in R, depending on the positive parameter {alpha}. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices

International Nuclear Information System (INIS)

Testa, J.; Perez, J.; Jeffries, C.

1982-01-01

Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos

Tracing the transition of a macro electron shuttle into nonlinear response

Energy Technology Data Exchange (ETDEWEB)

Kim, Chulki [Sensor System Research Center, Korea Institute of Science and Technology, Seoul 136791 (Korea, Republic of); Prada, Marta [I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstr. 9, Hamburg 20355 (Germany); Qin, Hua [Key Laboratory of Nanodevices, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, 398 Ruoshui Road, Industrial Park, Suzhou City, Jiangsu 215123 (China); Kim, Hyun-Seok [Division of Electronics and Electrical Engineering, Dongguk University-Seoul, 100715 Seoul (Korea, Republic of); Blick, Robert H., E-mail: rblick@physnet.uni-hamburg.de [Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin-53706 (United States); Center for Hybrid Nanostructures, Universität Hamburg, Jungiusstr. 11c, Hamburg 20355 (Germany); Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 1415 Engineering Dr. Madison, Wisconsin-53706 (United States)

2015-02-09

We present a study on a macroscopic electron shuttle in the transition from linear to nonlinear response. The shuttle consists of a classical mechanical pendulum situated between two capacitor plates. The metallic pendulum enables mechanical transfer of electrons between the plates, hence allowing to directly trace electron shuttling in the time domain. By applying a high voltage to the plates, we drive the system into a controlled nonlinear response, where we observe period doubling.

Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation

International Nuclear Information System (INIS)

Ji, J.C.; Hansen, Colin H.

2005-01-01

The trivial equilibrium of a nonlinear autonomous system with time delay may become unstable via a Hopf bifurcation of multiplicity two, as the time delay reaches a critical value. This loss of stability of the equilibrium is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. The resultant dynamic behaviour of the corresponding nonlinear non-autonomous system in the neighbourhood of the Hopf bifurcation is investigated based on the reduction of the infinite-dimensional problem to a four-dimensional centre manifold. As a result of the interaction between the Hopf bifurcating periodic solutions and the external periodic excitation, a primary resonance can occur in the forced response of the system when the forcing frequency is close to the Hopf bifurcating periodic frequency. The method of multiple scales is used to obtain four first-order ordinary differential equations that determine the amplitudes and phases of the phase-locked periodic solutions. The first-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration of the delay-differential equation. It is also found that the steady state solutions of the nonlinear non-autonomous system may lose their stability via either a pitchfork or Hopf bifurcation. It is shown that the primary resonance response may exhibit symmetric and asymmetric phase-locked periodic motions, quasi-periodic motions, chaotic motions, and coexistence of two stable motions

Domain decomposition solvers for nonlinear multiharmonic finite element equations

KAUST Repository

Copeland, D. M.; Langer, U.

2010-01-01

of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series

Nonlinear optics

International Nuclear Information System (INIS)

Boyd, R.W.

1992-01-01

Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics

Nonlinear identification and control a neural network approach

CERN Document Server

Liu, G P

2001-01-01

The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies . . . , new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series otTers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. The time for nonlinear control to enter routine application seems to be approaching. Nonlinear control has had a long gestation period but much ofthe past has been concerned with methods that involve formal nonlinear functional model representations. It seems more likely that the breakthough will come through the use of other more flexible and ame...

Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

DEFF Research Database (Denmark)

Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole

2001-01-01

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...... the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site....

Nonlinear Science

CERN Document Server

Yoshida, Zensho

2010-01-01

This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl

Nonlinear generation of non-acoustic modes by low-frequency sound in a vibrationally relaxing gas

International Nuclear Information System (INIS)

Perelomova, A.

2010-01-01

Two dynamic equations referring to a weakly nonlinear and weakly dispersive flow of a gas in which molecular vibrational relaxation takes place, are derived. The first one governs an excess temperature associated with the thermal mode, and the second one describes variations in vibrational energy. Both quantities refer to non-wave types of gas motion. These variations are caused by the nonlinear transfer of acoustic energy into thermal mode and internal vibrational degrees of freedom of a relaxing gas. The final dynamic equations are instantaneous; they include a quadratic nonlinear acoustic source, reflecting the nonlinear character of interaction of low-frequency acoustic and non-acoustic motions of the fluid. All types of sound, periodic or aperiodic, may serve as an acoustic source of both phenomena. The low-frequency sound is considered in this study. Some conclusions about temporal behavior of non-acoustic modes caused by periodic and aperiodic sound are made. Under certain conditions, acoustic cooling takes place instead of heating. (author)

Nonlinear spin wave coupling in adjacent magnonic crystals

Energy Technology Data Exchange (ETDEWEB)

Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)

2016-07-25

We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.

Nonlinear spin wave coupling in adjacent magnonic crystals

International Nuclear Information System (INIS)

Sadovnikov, A. V.; Nikitov, S. A.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.

2016-01-01

We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.

Nonlinear dynamics in cardiac conduction

Science.gov (United States)

Kaplan, D. T.; Smith, J. M.; Saxberg, B. E.; Cohen, R. J.

1988-01-01

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.

Statistical properties of nonlinear one-dimensional wave fields

Directory of Open Access Journals (Sweden)

D. Chalikov

2005-01-01

Full Text Available A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

Statistical properties of nonlinear one-dimensional wave fields

Science.gov (United States)

Chalikov, D.

2005-06-01

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

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

Extreme control of impulse transmission by cylinder-based nonlinear phononic crystals

Science.gov (United States)

Chaunsali, Rajesh; Toles, Matthew; Yang, Jinkyu; Kim, Eunho

2017-10-01

We present a novel device that can offer two extremes of elastic wave propagation - nearly complete transmission and strong attenuation under impulse excitation. The mechanism of this highly tunable device relies on intermixing effects of dispersion and nonlinearity. The device consists of identical cylinders arranged in a chain, which interact with each other as per nonlinear Hertz contact law. For a 'dimer' configuration, i.e., two different contact angles alternating in the chain, we analytically, numerically, and experimentally show that impulse excitation can either propagate as a localized wave, or it can travel as a highly dispersive wave. Remarkably, these extremes can be achieved in this periodic arrangement simply by in-situ control of contact angles between cylinders. We close the discussion by highlighting the key characteristics of the mechanisms that facilitate strong attenuation of incident impulse. These include low-to-high frequency scattering, and turbulence-like cascading in a periodic system. We thus envision that these adaptive, cylinder-based nonlinear phononic crystals, in conjunction with conventional impact mitigation mechanisms, could be used to design highly tunable and efficient impact manipulation devices.

Engineering of spatial solitons in two-period QPM structures

DEFF Research Database (Denmark)

Johansen, Steffen Kjær; Carrasco, Silvia; Torner, Lluis

2002-01-01

We report on a scheme which might make it practically possible to engineer the effective competing nonlinearities that on average govern the light propagation in quasi-phase-matching (QPM) gratings. Modulation of the QPM period with a second longer period, introduces an extra degree of freedom...... relative lengths of the two periods and we consider the effect on solitons and the bandwidth for their generation. We derive an expression for the bandwidth of multicolor soliton generation in two-period QPM samples and we predict and confirm numerically that the bandwidth is broader in the two-period QPM...

Bifurcation analysis of delay-induced periodic oscillations

NARCIS (Netherlands)

Green, K.

2010-01-01

In this paper we consider a generic differential equation with a cubic nonlinearity and delay. This system, in the absence of delay, is known to undergo an oscillatory instability. The addition of the delay is shown to result in the creation of a number of periodic solutions with constant amplitude

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

Domain decomposition solvers for nonlinear multiharmonic finite element equations

KAUST Repository

Copeland, D. M.

2010-01-01

In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

Science.gov (United States)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

Temporal nonlinear beam dynamics in infiltrated photonic crystal fibers

DEFF Research Database (Denmark)

Bennet, Francis; Rosberg, Christian Romer; Neshev, Dragomir N.

Liquid-infiltrated photonic crystal fibers (PCFs) offer a new way of studying light propagation in periodic and discrete systems. A wide range of available fiber structures combined with the ease of infiltration opens up a range of novel experimental opportunities for optical detection and bio...... the evolution of the fiber output beam in the few micro or milliseconds after the beam is turned on. The characterization of the temporal behavior of the thermal nonlinear response provides important information about the nonlocality associated with heat diffusion inside the fiber, thus enabling studies of long...... and technological potential of liquid-infiltrated PCFs it is important to understand the temporal dynamics of nonlinear beam propagation in such structures. In this work we consider thermally induced spatial nonlinear effects in infiltrated photonic crystal fibers. We experimentally study the temporal dynamics...

Nonlinear dynamics of the relativistic standard map

International Nuclear Information System (INIS)

Nomura, Y.; Ichikawa, Y.H.; Horton, W.

1991-01-01

Heating and acceleration of charged particles by RF fields have been extensively investigated by the standard map (ST). Thus, it is natural to pose the question asking how the relativistic effects change the nonlinear dynamical behavior described by the classical ST map. The authors show that the speed of light limits the rate of advance of the phase in the relativistic standard map (RST) and introduces KAM surfaces persisting in the high momentum region. The RST map is a two parameter (k, β = ω/kc) family of dynamics reducing to the ST map when β → 0. For β ≠ 0 the relativity suppresses the onset of stochasticity. Chernikov et al. has also reported this effect. They have carried out extensive studies of nonlinear dynamics of the RST map and found very intricate structure of mixing of the higher order periodic orbits and chaotic orbits. They have shown that no matter how its gets chaotic the symmetry properties of the RST map determines its nonlinear dynamical behavior. 1 ref

Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives

Science.gov (United States)

Yao, Jianyong

2018-06-01

Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.

An ansatz for solving nonlinear partial differential equations in mathematical physics.

Science.gov (United States)

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

Study of possible chaotic, quasi-periodic and periodic structures in quantum dusty plasma

International Nuclear Information System (INIS)

Ghosh, Uday Narayan; Chatterjee, Prasanta; Roychoudhury, Rajkumar

2014-01-01

Existence of chaotic, quasi-periodic, and periodic structures of dust-ion acoustic waves is studied in quantum dusty plasmas through dynamical system approach. A system of coupled differential equations is derived from the fluid model and subsequently, variational matrix is obtained. The characteristic equation is obtained at the equilibrium point, and the behavior of nonlinear waves is studied numerically using Runge-Kutta method. The behavior of the dynamical system changes significantly when any of plasma parameters, such as the dust concentration parameter, temperature ratio, or the quantum diffraction parameter, is varied. The change of the characteristic of solution of the system is extensively studied. It is found that the system changes its behavior from chaotic pattern to limit cycle behavior

NONLINEAR DYNAMO IN A ROTATING ELECTRICALLY CONDUCTING FLUID

Directory of Open Access Journals (Sweden)

M. I. Kopp

2017-05-01

Full Text Available We found a new large-scale instability, which arises in the rotating conductive fluid with small-scale turbulence. Turbulence is generated by small-scale external force with a low Reynolds number. The theory is built simply by the method of multiscale asymptotic expansions. Nonlinear equations for vortex and magnetic perturbations obtained in the third order for small Reynolds number. It is shown that the combined effects of the Coriolis force and the small external forces in a rotating conducting fluid possible large-scale instability. The large-scale increments of the instability, correspond to generation as the vortex and magnetic disturbances. This type of instability is classified as hydrodynamic and MHD alpha-effect. We studied the stationary regimes of nonlinear equations of magneto-vortex dynamo. In the limit of weakly conducting fluid found stationary solutions in the form of helical kinks. In the limit of high conductivity fluid was obtained stationary solutions in the form of nonlinear periodic waves and kinks.

Tunable ultraviolet radiation by second-harmonic generation in periodically poled lithium tantalate.

Science.gov (United States)

Meyn, J P; Fejer, M M

1997-08-15

We describe electric-field poling of fine-pitch ferroelectric domain gratings in lithium tantalate and characterization of nonlinear-optical properties by single-pass quasi-phase-matched second-harmonic generation (QPM SHG). With a 7.5-microm-period grating, the observed effective nonlinear coefficient for first-order QPM SHG of 532-nm radiation is 9 pm/V, whereas for a grating with a 2.625-microm period, 2.6 pm/V was observed for second-order QPM SHG of 325-nm radiation. These values are 100% and 55% of the theoretically expected values, respectively. We derive a temperature-dependent Sellmeier equation for lithium tantalate that is valid deeper into the UV than currently available results, based on temperature-tuning experiments at different QPM grating periods combined with refractive-index data in the literature.

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

Science.gov (United States)

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Nonlinear graphene plasmonics

Science.gov (United States)

Ooi, Kelvin J. A.; Tan, Dawn T. H.

2017-10-01

The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.

Non-linear Vibration of Oscillation Systems using Frequency-Amplitude Formulation

DEFF Research Database (Denmark)

Fereidoon, A.; Ghadimi, M.; Barari, Amin

2012-01-01

In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifthorder nonlinearity for two examples using He’s Frequency Amplitude Formulation (HFAF).The effectiveness and convenience of the method is illustrated in these examples. It will be shown that t...... that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems....

Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

International Nuclear Information System (INIS)

Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.

2007-01-01

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves

Analysis of highly nonlinear oscillation systems using He's max–min ...

Indian Academy of Sciences (India)

Min–max method; nonlinear oscillation; duffing equation; homo- .... where c and ε are the linear and cubic stiffness which do not need to be small in the ..... an easy and direct procedure for determining approximations to the periodic solutions.

Exact solutions for the cubic-quintic nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Zhu Jiamin; Ma Zhengyi

2007-01-01

In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions

Nonlinear systems

CERN Document Server

Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús

2018-01-01

This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many  new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...

Nonlinear dynamics near resonances of a rotor-active magnetic bearings system with 16-pole legs and time varying stiffness

Science.gov (United States)

Wu, R. Q.; Zhang, W.; Yao, M. H.

2018-02-01

In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing equation of motion for rotor-active magnetic bearings is derived by using the Newton's second law. The resulting dimensionless equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.

Nonlinear asteroseismology: insight from amplitude and frequency modulations of oscillation modes in compact pulsators from Kepler photometry

Directory of Open Access Journals (Sweden)

Zong Weikai

2017-01-01

Full Text Available Nonlinear mode interactions are difficult to observe from ground-based telescopes as the typical periods of the modulations induced by those nonlinear phenomena are on timescales of weeks, months, even years. The launch of space telescopes, e.g., Kepler, has tremendously changed the situation and shredded new light on this research field. We present results from Kepler photometry showing evidence that nonlinear interactions between modes occur in the two compact pulsators KIC 8626021, a DB white dwarf, and KIC 10139564, a short period hot B subdwarf. KIC 8626021 and KIC 10139564 had been monitored by Kepler in short-cadence for nearly two years and more than three years without interruption, respectively. By analyzing these high-quality photometric data, we found that the modes within the triplets induced by rotation clearly reveal different behaviors: their frequencies and amplitudes may exhibit either periodic or irregular modulations, or remain constant. These various behaviors of the amplitude and of the frequency modulations of the oscillation modes observed in these two stars are in good agreement with those predicted within the amplitude equation formalism in the case of the nonlinear resonant mode coupling mechanism.

Measurement of picometre non-linearity in an optical grating encoder using x-ray interferometry

Science.gov (United States)

Yacoot, Andrew; Cross, Nigel

2003-01-01

X-ray interferometry has been used to characterize the non-linearity in an optical encoder displacement measuring system. Traceable measurements of the non-linearity have been made and an estimation of the uncertainty associated with the measurements is given. Cyclic errors with a magnitude of up to 50 pm and periodicity of the encoder system (128 nm) have been recorded.

Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam system with impacts

International Nuclear Information System (INIS)

Emans, Joseph; Wiercigroch, Marian; Krivtsov, Anton M.

2005-01-01

The nonlinear analysis of a common beam system was performed, and the method for such, outlined and presented. Nonlinear terms for the governing dynamic equations were extracted and the behaviour of the system was investigated. The analysis was carried out with and without physically realistic parameters, to show the characteristics of the system, and the physically realistic responses. Also, the response as part of a more complex system was considered, in order to investigate the cumulative effects of nonlinearities. Chaos, as well as periodic motion was found readily for the physically unrealistic parameters. In addition, nonlinear behaviour such as co-existence of attractors was found even at modest oscillation levels during investigations with realistic parameters. When considered as part of a more complex system with further nonlinearities, comparisons with linear beam theory show the classical approach to be lacking in accuracy of qualitative predictions, even at weak oscillations

Coupled large earthquakes in the Baikal rift system: Response to bifurcations in nonlinear resonance hysteresis

Directory of Open Access Journals (Sweden)

Anatoly V. Klyuchevskii

2013-11-01

Full Text Available The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation. The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures (RAS. The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes, proximal in time but distant in space, may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors. The space-time distribution of coupled MLH > 5.5 events has been stable for the period of instrumental seismicity, with the largest events occurring in pairs, one shortly after another, on two ends of the rift system and with couples of smaller events in the central part of the rift. The event couples appear as peaks of earthquake ‘migration’ rate with an approximately decadal periodicity. Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation. The new knowledge, with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis, may be of theoretical and practical value for earthquake prediction issues. Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region, i.e., there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.

Complex motion in nonlinear-map model of elevators in energy-saving traffic

International Nuclear Information System (INIS)

Nagatani, Takashi

2011-01-01

We have studied the dynamic behavior and dynamic transitions of elevators in a system for reducing energy consumption. We present a nonlinear-map model for the dynamics of M elevators. The motion of elevators depends on the loading parameter and their number M. The dependence of the fixed points on the loading parameter is derived. The dynamic transitions occur at 2(M-1) stages with increasing the value of loading parameter. At the dynamic transition point, the motion of elevators changes from a stable state to an unstable state and vice versa. The elevators display periodic motions with various periods in the unstable state. In the unstable state, the number of riding passengers fluctuates in a complex manner over various trips. - Highlights: → We propose the nonlinear-map model in energy-saving traffic of elevators. → We study the dynamical behavior and dynamical transitions in the system of elevators. → We derive the fixed point of the nonlinear map analytically. → We clarify the dependence of the motion on the loading parameter and the number.

Complex motion in nonlinear-map model of elevators in energy-saving traffic

Energy Technology Data Exchange (ETDEWEB)

Nagatani, Takashi, E-mail: tmtnaga@ipc.shizuoka.ac.j [Department of Mechanical Engineering, Division of Thermal Science, Shizuoka University, Hamamatsu 432-8561 (Japan)

2011-05-16

We have studied the dynamic behavior and dynamic transitions of elevators in a system for reducing energy consumption. We present a nonlinear-map model for the dynamics of M elevators. The motion of elevators depends on the loading parameter and their number M. The dependence of the fixed points on the loading parameter is derived. The dynamic transitions occur at 2(M-1) stages with increasing the value of loading parameter. At the dynamic transition point, the motion of elevators changes from a stable state to an unstable state and vice versa. The elevators display periodic motions with various periods in the unstable state. In the unstable state, the number of riding passengers fluctuates in a complex manner over various trips. - Highlights: We propose the nonlinear-map model in energy-saving traffic of elevators. We study the dynamical behavior and dynamical transitions in the system of elevators. We derive the fixed point of the nonlinear map analytically. We clarify the dependence of the motion on the loading parameter and the number.

Nonlinear Dirac Equations

Directory of Open Access Journals (Sweden)

Wei Khim Ng

2009-02-01

Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

Predicting seizures in untreated temporal lobe epilepsy using point-process nonlinear models of heartbeat dynamics.

Science.gov (United States)

Valenza, G; Romigi, A; Citi, L; Placidi, F; Izzi, F; Albanese, M; Scilingo, E P; Marciani, M G; Duggento, A; Guerrisi, M; Toschi, N; Barbieri, R

2016-08-01

Symptoms of temporal lobe epilepsy (TLE) are frequently associated with autonomic dysregulation, whose underlying biological processes are thought to strongly contribute to sudden unexpected death in epilepsy (SUDEP). While abnormal cardiovascular patterns commonly occur during ictal events, putative patterns of autonomic cardiac effects during pre-ictal (PRE) periods (i.e. periods preceding seizures) are still unknown. In this study, we investigated TLE-related heart rate variability (HRV) through instantaneous, nonlinear estimates of cardiovascular oscillations during inter-ictal (INT) and PRE periods. ECG recordings from 12 patients with TLE were processed to extract standard HRV indices, as well as indices of instantaneous HRV complexity (dominant Lyapunov exponent and entropy) and higher-order statistics (bispectra) obtained through definition of inhomogeneous point-process nonlinear models, employing Volterra-Laguerre expansions of linear, quadratic, and cubic kernels. Experimental results demonstrate that the best INT vs. PRE classification performance (balanced accuracy: 73.91%) was achieved only when retaining the time-varying, nonlinear, and non-stationary structure of heartbeat dynamical features. The proposed approach opens novel important avenues in predicting ictal events using information gathered from cardiovascular signals exclusively.

Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

Directory of Open Access Journals (Sweden)

Y. N. Pavlov

2015-01-01

Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

Exact optical solitons in (n + 1)-dimensions with anti-cubic nonlinearity

Science.gov (United States)

Younis, Muhammad; Shahid, Iram; Anbreen, Sumaira; Rizvi, Syed Tahir Raza

2018-02-01

The paper studies the propagation of optical solitons in (n + 1)-dimensions under anti-cubic law of nonlinearity. The bright, dark and singular optical solitons are extracted using the extended trial equation method. The constraint conditions, for the existence of these solitons, are also listed. Additionally, a couple of other solutions known as singular periodic and Jacobi elliptic solutions, fall out as a by-product of this scheme. The obtained results are new and reported first time in (n + 1)-dimensions with anti-cubic law of nonlinearity.

Bifurcation of forced periodic oscillations for equations with Preisach hysteresis

International Nuclear Information System (INIS)

Krasnosel'skii, A; Rachinskii, D

2005-01-01

We study oscillations in resonant systems under periodic forcing. The systems depend on a scalar parameter and have the form of simple pendulum type equations with ferromagnetic friction represented by the Preisach hysteresis nonlinearity. If for some parameter value the period of free oscillations of the principal linear part of the system coincides with the period of the forcing term, then one may expect the existence of unbounded branches of periodic solutions for nearby parameter values. We present conditions for the existence and nonexistence of such branches and estimates of their number

Nonlinear analysis of piezoelectric nanocomposite energy harvesting plates

International Nuclear Information System (INIS)

Rafiee, M; He, X Q; Liew, K M

2014-01-01

This paper investigates the nonlinear analysis of energy harvesting from piezoelectric functionally graded carbon nanotube reinforced composite plates under combined thermal and mechanical loadings. The excitation, which derives from harmonically varying mechanical in-plane loading, results in parametric excitation. The governing equations of the piezoelectric functionally graded carbon nanotube reinforced composite plates are derived based on classical plate theory and von Kármán geometric nonlinearity. The material properties of the nanocomposite plate are assumed to be graded in the thickness direction. The single-walled carbon nanotubes (SWCNTs) are assumed to be aligned, straight and have a uniform layout. The linear buckling and vibration behavior of the nanocomposite plates is obtained in the first step. Then, Galerkin’s method is employed to derive the nonlinear governing equations of the problem with cubic nonlinearities associated with mid-plane stretching. Periodic solutions are determined by using the Poincaré–Lindstedt perturbation scheme with movable simply supported boundary conditions. The effects of temperature change, the volume fraction and the distribution pattern of the SWCNTs on the parametric resonance, in particular the amplitude of vibration and the average harvested power of the smart functionally graded carbon nanotube reinforced composite plates, are investigated through a detailed parametric study. (paper)

Linear and nonlinear market correlations: Characterizing financial crises and portfolio optimization

Science.gov (United States)

Haluszczynski, Alexander; Laut, Ingo; Modest, Heike; Räth, Christoph

2017-12-01

Pearson correlation and mutual information-based complex networks of the day-to-day returns of U.S. S&P500 stocks between 1985 and 2015 have been constructed to investigate the mutual dependencies of the stocks and their nature. We show that both networks detect qualitative differences especially during (recent) turbulent market periods, thus indicating strongly fluctuating interconnections between the stocks of different companies in changing economic environments. A measure for the strength of nonlinear dependencies is derived using surrogate data and leads to interesting observations during periods of financial market crises. In contrast to the expectation that dependencies reduce mainly to linear correlations during crises, we show that (at least in the 2008 crisis) nonlinear effects are significantly increasing. It turns out that the concept of centrality within a network could potentially be used as some kind of an early warning indicator for abnormal market behavior as we demonstrate with the example of the 2008 subprime mortgage crisis. Finally, we apply a Markowitz mean variance portfolio optimization and integrate the measure of nonlinear dependencies to scale the investment exposure. This leads to significant outperformance as compared to a fully invested portfolio.

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.

Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations

International Nuclear Information System (INIS)

Chen, Jin

2009-01-01

Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

Quantum Nonlinear Optics

CERN Document Server

Hanamura, Eiichi; Yamanaka, Akio

2007-01-01

This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.

NONLINEAR ASTEROSEISMOLOGY OF RR LYRAE

Energy Technology Data Exchange (ETDEWEB)

Molnar, L.; Kollath, Z.; Szabo, R. [Konkoly Observatory, MTA CSFK, H-1121 Budapest, Konkoly Thege Miklos ut 15-17 (Hungary); Bryson, S.; Mullally, F.; Thompson, S. E. [NASA Ames Research Center, MS 244-30, Moffet Field, CA 94035 (United States); Kolenberg, K., E-mail: molnar.laszlo@csfk.mta.hu [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge MA 02138 (United States)

2012-09-20

The observations of the Kepler Space Telescope revealed that fundamental-mode RR Lyrae stars may show various radial overtones. The presence of multiple radial modes may allow us to conduct nonlinear asteroseismology: comparison of mode amplitudes and frequency shifts between observations and models. Here we report the detection of three radial modes in the star RR Lyr, the eponym of the class, using the Kepler short cadence data: besides the fundamental mode, both the first and the ninth overtones can be derived from the data set. RR Lyrae shows period doubling, but switches occasionally to a state where a pattern of six pulsation cycles repeats instead of two. We found hydrodynamic models that show the same three modes and the period-six state, allowing for comparison with the observations.

Estimation of non-linear effective permeability of magnetic materials with fine structure

International Nuclear Information System (INIS)

Waki, H.; Igarashi, H.; Honma, T.

2006-01-01

This paper describes a homogenization method for magnetic materials with fine structure. In this method, the structures of the magnetic materials are assumed to be periodic, and the unit cell is defined. The effective permeability is determined on the basis of magnetic energy balance in the unit cell. This method can be applied not only for linear problems but also for non-linear ones. In this paper, estimation of the effective permeability of non-linear magnetic materials by using the homogenization method is described in detail, and then the validity for the non-liner problems is tested for two-dimensional problems. It is shown that this homogenization method gives accurate non-linear effective permeability

Symbolic-computation study of the perturbed nonlinear Schrodinger model in inhomogeneous optical fibers

International Nuclear Information System (INIS)

Tian Bo; Gao Yitian

2005-01-01

A realistic, inhomogeneous fiber in the optical communication systems can be described by the perturbed nonlinear Schrodinger model (also named as the normalized nonlinear Schrodinger model with periodically varying coefficients, dispersion managed nonlinear Schrodinger model or nonlinear Schrodinger model with variable coefficients). Hereby, we extend to this model a direct method, perform symbolic computation and obtain two families of the exact, analytic bright-solitonic solutions, with or without the chirp respectively. The parameters addressed include the shape of the bright soliton, soliton amplitude, inverse width of the soliton, chirp, frequency, center of the soliton and center of the phase of the soliton. Of optical and physical interests, we discuss some previously-published special cases of our solutions. Those solutions could help the future studies on the optical communication systems. ms

The convergence of psychology and neurobiology in flavor-nutrient learning.

Science.gov (United States)

Myers, Kevin P

2018-03-01

Flavor evaluation is influenced by learning from experience with foods. One main influence is flavor-nutrient learning (FNL), a Pavlovian process whereby a flavor acts as a conditioned stimulus (CS) that becomes associated with the postingestive effects of ingested nutrients (the US). As a result that flavor becomes preferred and intake typically increases. This learning powerfully influences food choice and meal patterning. This paper summarizes how research elucidating the physiological and neural substrates of FNL has progressed in parallel with work characterizing how FNL affects perception, motivation, and behavior. The picture that emerges from this work is of a robust system of appetition (a term coined by Sclafani in contrast to the better-understood satiation signals) whereby ingested nutrients sensed in the gut evoke positive motivational responses. Appetition signals act within a meal to promote continued intake in immediate response to gut feedback, and act in the longer term to steer preference towards sensory cues that predict nutritional consequences. Copyright © 2017 Elsevier Ltd. All rights reserved.

Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media

Science.gov (United States)

Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai

2018-01-01

Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.

Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions

Science.gov (United States)

Qian, Ying-Jing; Yang, Xiao-Dong; Zhai, Guan-Qiao; Zhang, Wei

2017-08-01

Innovated by the nonlinear modes concept in the vibrational dynamics, the vertical periodic orbits around the triangular libration points are revisited for the Circular Restricted Three-body Problem. The ζ -component motion is treated as the dominant motion and the ξ and η -component motions are treated as the slave motions. The slave motions are in nature related to the dominant motion through the approximate nonlinear polynomial expansions with respect to the ζ -position and ζ -velocity during the one of the periodic orbital motions. By employing the relations among the three directions, the three-dimensional system can be transferred into one-dimensional problem. Then the approximate three-dimensional vertical periodic solution can be analytically obtained by solving the dominant motion only on ζ -direction. To demonstrate the effectiveness of the proposed method, an accuracy study was carried out to validate the polynomial expansion (PE) method. As one of the applications, the invariant nonlinear relations in polynomial expansion form are used as constraints to obtain numerical solutions by differential correction. The nonlinear relations among the directions provide an alternative point of view to explore the overall dynamics of periodic orbits around libration points with general rules.

Distributed nonlinear optical response

DEFF Research Database (Denmark)

Nikolov, Nikola Ivanov

2005-01-01

of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....

Inheritance of Cell-Cycle Duration in the Presence of Periodic Forcing

Science.gov (United States)

Mosheiff, Noga; Martins, Bruno M. C.; Pearl-Mizrahi, Sivan; Grünberger, Alexander; Helfrich, Stefan; Mihalcescu, Irina; Kohlheyer, Dietrich; Locke, James C. W.; Glass, Leon; Balaban, Nathalie Q.

2018-04-01

Periodic forcing of nonlinear oscillators leads to a large number of dynamic behaviors. The coupling of the cell cycle to the circadian clock provides a biological realization of such forcing. A previous model of forcing leads to nontrivial relations between correlations along cell lineages. Here, we present a simplified two-dimensional nonlinear map for the periodic forcing of the cell cycle. Using high-throughput single-cell microscopy, we have studied the correlations between cell-cycle duration in discrete lineages of several different organisms, including those with known coupling to a circadian clock and those without known coupling to a circadian clock. The model reproduces the paradoxical correlations and predicts new features that can be compared with the experimental data. By fitting the model to the data, we extract the important parameters that govern the dynamics. Interestingly, the model reproduces bimodal distributions for cell-cycle duration, as well as the gating of cell division by the phase of the clock, without having been explicitly fed into the model. In addition, the model predicts that circadian coupling may increase cell-to-cell variability in a clonal population of cells. In agreement with this prediction, deletion of the circadian clock reduces variability. Our results show that simple correlations can identify systems under periodic forcing and that studies of nonlinear coupling of biological oscillators provide insight into basic cellular processes of growth.

Nonlinear MHD Waves in a Prominence Foot

Science.gov (United States)

Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.

2015-11-01

We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ˜ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5-11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is ˜20 km s-1, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.

NONLINEAR MHD WAVES IN A PROMINENCE FOOT

Energy Technology Data Exchange (ETDEWEB)

Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)

2015-11-10

We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.

Nonlinear Transient Growth and Boundary Layer Transition

Science.gov (United States)

Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

2016-01-01

Parabolized stability equations (PSE) are used in a variational approach to study the optimal, non-modal disturbance growth in a Mach 3 at plate boundary layer and a Mach 6 circular cone boundary layer. As noted in previous works, the optimal initial disturbances correspond to steady counter-rotating streamwise vortices, which subsequently lead to the formation of streamwise-elongated structures, i.e., streaks, via a lift-up effect. The nonlinear evolution of the linearly optimal stationary perturbations is computed using the nonlinear plane-marching PSE for stationary perturbations. A fully implicit marching technique is used to facilitate the computation of nonlinear streaks with large amplitudes. To assess the effect of the finite-amplitude streaks on transition, the linear form of plane- marching PSE is used to investigate the instability of the boundary layer flow modified by spanwise periodic streaks. The onset of bypass transition is estimated by using an N- factor criterion based on the amplification of the streak instabilities. Results show that, for both flow configurations of interest, streaks of sufficiently large amplitude can lead to significantly earlier onset of transition than that in an unperturbed boundary layer without any streaks.

TWIN POSITIVE PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

In this paper, the author studies a class of nonlinear functional differential equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of twin positive periodic solutions.

Nonlinear and Asymmetric Adjustment to Purchasing Power Parity in East-Asian Countries

OpenAIRE

Wen-Chi Liu

2014-01-01

This study applies a simple and powerful nonlinear unit root test to test the validity of long-run purchasing power parity (PPP) in a sample of 10 East-Asian countries (i.e., China, Hong Kong, Indonesia, Japan, Korea, Malaysia, Philippines, Singapore, Taiwan and Thailand) over the period of March 1985 to September 2008. The empirical results indicate that PPP holds true for half of these 10 East-Asian countries under study, and the adjustment toward PPP is found to be nonlinear and in ...

Nonlinear dynamic analysis of piping systems using the pseudo force method

International Nuclear Information System (INIS)

Prachuktam, S.; Bezler, P.; Hartzman, M.

1979-01-01

Simple piping systems are composed of linear elastic elements and can be analyzed using conventional linear methods. The introduction of constraint springs separated from the pipe with clearance gaps to such systems to cope with the pipe whip or other extreme excitation conditions introduces nonlinearities to the system, the nonlinearities being associated with the gaps. Since these spring-damper constraints are usually limited in number, descretely located, and produce only weak nonlinearities, the analysis of linear systems including these nonlinearities can be carried out by using modified linear methods. In particular, the application of pseudo force methods wherein the nonlinearities are treated as displacement dependent forcing functions acting on the linear system were investigated. The nonlinearities induced by the constraints are taken into account as generalized pseudo forces on the right-hand side of the governing dynamic equilibrium equations. Then an existing linear elastic finite element piping code, EPIPE, was modified to permit application of the procedure. This option was inserted such that the analyses could be performed using either the direct integration method or via a modal superposition method, the Newmark-Beta integration procedure being employed in both methods. The modified code was proof tested against several problems taken from the literature or developed with the nonlinear dynamics code OSCIL. The problems included a simple pipe loop, cantilever beam, and lumped mass system subjected to pulsed and periodic forcing functions. The problems were selected to gage the overall accuracy of the method and to insure that it properly predicted the jump phenomena associated with nonlinear systems. (orig.)

The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes

Science.gov (United States)

Grinevich, P. G.; Santini, P. M.

2018-04-01

The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, the main physical mechanism for the generation of rogue (anomalous) waves (RWs) in Nature. In this paper we investigate the x-periodic Cauchy problem for NLS for a generic periodic initial perturbation of the unstable constant background solution, in the case of N = 1 , 2 unstable modes. We use matched asymptotic expansion techniques to show that the solution of this problem describes an exact deterministic alternate recurrence of linear and nonlinear stages of MI, and that the nonlinear RW stages are described by the N-breather solution of Akhmediev type, whose parameters, different at each RW appearance, are always given in terms of the initial data through elementary functions. This paper is motivated by a preceding work of the authors in which a different approach, the finite gap method, was used to investigate periodic Cauchy problems giving rise to RW recurrence.

Symbolic computation of exact solutions for a nonlinear evolution equation

International Nuclear Information System (INIS)

Liu Yinping; Li Zhibin; Wang Kuncheng

2007-01-01

In this paper, by means of the Jacobi elliptic function method, exact double periodic wave solutions and solitary wave solutions of a nonlinear evolution equation are presented. It can be shown that not only the obtained solitary wave solutions have the property of loop-shaped, cusp-shaped and hump-shaped for different values of parameters, but also different types of double periodic wave solutions are possible, namely periodic loop-shaped wave solutions, periodic hump-shaped wave solutions or periodic cusp-shaped wave solutions. Furthermore, periodic loop-shaped wave solutions will be degenerated to loop-shaped solitary wave solutions for the same values of parameters. So do cusp-shaped solutions and hump-shaped solutions. All these solutions are new and first reported here

Nonlinear dynamics, chaos and complex cardiac arrhythmias

Science.gov (United States)

Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.

1987-01-01

Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.

Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities

DEFF Research Database (Denmark)

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

2006-01-01

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

Solar-cycle period-amplitude relation as evidence of hysteresis of the solar-cycle nonlinear magnetic oscillation and the long-term (55 year) cyclic modulation

International Nuclear Information System (INIS)

Yoshimura, H.

1979-01-01

A new dynamical model of the solar cycle has predicted that the cycle should have a hysteretic nature: the behavior of each 11 year cycle should depend on previous cycles. In the light of this new understanding of the dynamical mechanism of the solar cycle, Waldmeier's (hypothetical) law was examined as a yet unexplained characteristic of the cycle by studying the observed sunspot frequency curve. Contrary to this hypothetical law, however, it was found that sunspot cycle curves did not form a single-parameter family characterized by the maximum amplitude of the cycle. The evolutionary trajectories in period-amplitude phase space verified the hysteretic nature of the observed cycle and revealed long-term (55 year instead of the previously claimed 80 year) periodic modulations, called here 55 year grand cycles. Each 55 year grand cycle forms a loop in the phase space, and the characteristics of each 11 year cycle depend on its position in the ascending or descending phase of the grand cycle. This new law was analyzed by the nonlinear multiple-period dynamo oscillation model which has predicted the hysteretic nature. The era from cycle 11 to cycle 15 turned out to be an anomalous one characterized by alternating amplitudes for odd and even cycles. Cycles 16--20 seem to constitute one grand cycle. If this is true, cycle 21 would be the beginning of another grand maximum and the model predicts that its duration would be short

Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ-Expansion Method Implementation

Directory of Open Access Journals (Sweden)

Nur Alam

2016-02-01

Full Text Available In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs describing microtubules, by implementing the exp(−Φ(ξ-Expansion Method. The considered models, describing highly nonlinear dynamics of microtubules, can be reduced to nonlinear ordinary differential equations. While the first PDE describes the longitudinal model of nonlinear dynamics of microtubules, the second one describes the nonlinear model of dynamics of radial dislocations in microtubules. The acquired solutions are then graphically presented, and their distinct properties are enumerated in respect to the corresponding dynamic behavior of the microtubules they model. Various patterns, including but not limited to regular, singular kink-like, as well as periodicity exhibiting ones, are detected. Being the method of choice herein, the exp(−Φ(ξ-Expansion Method not disappointing in the least, is found and declared highly efficient.

Nonlinear evolution equations

CERN Document Server

Uraltseva, N N

1995-01-01

This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

Period doubling in a model of magnetoconvection with Ohmic heating

International Nuclear Information System (INIS)

Osman, M. B. H.

2000-01-01

In this work it has been studied an idealized model of rotating nonlinear magneto convection to investigate the effects of Ohmic heating. In the over stable region it was found that Ohmic heating can lead to a period-doubling sequence

Nonlinear optics

CERN Document Server

Boyd, Robert W

2013-01-01

Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

Science.gov (United States)

Bache, Morten; Lavrinenko, Andrei V.

2017-09-01

Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.

Pulsation properties of Mira long period variables

International Nuclear Information System (INIS)

Cahn, J.H.

1980-01-01

A matter of great interest to variable star students concerns the mode of pulsation of Mira long period variables. In this report we first give observational evidence for the pulsation constant Q. We then compare the observations with calculations. Next, we review two interesting groups of papers dealing with hydrodynamic properties of long period variables. In the first, a fully dynamic nonlinear calculation maps out the Mira instability domain. In the second, special attention is paid to shock propagation beyond the photosphere which in large measure accounts for the complex spectra from this region. (orig./WL)

Few-cycle nonlinear mid-IR pulse generated with cascaded quadratic nonlinearities

DEFF Research Database (Denmark)

Bache, Morten; Liu, Xing; Zhou, Binbin

Generating few-cycle energetic and broadband mid-IR pulses is an urgent current challenge in nonlinear optics. Cascaded second-harmonic generation (SHG) gives access to an ultrafast and octave-spanning self-defocusing nonlinearity: when ΔkL >> 2π the pump experiences a Kerr-like nonlinear index...

Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers

International Nuclear Information System (INIS)

Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.

2005-01-01

The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules

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

International Nuclear Information System (INIS)

Abdou, M.A.

2008-01-01

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

Self-Organized Biological Dynamics and Nonlinear Control

Science.gov (United States)

Walleczek, Jan

2006-04-01

The frontiers and challenges of biodynamics research Jan Walleczek; Part I. Nonlinear Dynamics in Biology and Response to Stimuli: 1. External signals and internal oscillation dynamics - principal aspects and response of stimulated rhythmic processes Friedemann Kaiser; 2. Nonlinear dynamics in biochemical and biophysical systems: from enzyme kinetics to epilepsy Raima Larter, Robert Worth and Brent Speelman; 3. Fractal mechanisms in neural control: human heartbeat and gait dynamics in health and disease Chung-Kang Peng, Jeffrey M. Hausdorff and Ary L. Goldberger; 4. Self-organising dynamics in human coordination and perception Mingzhou Ding, Yanqing Chen, J. A. Scott Kelso and Betty Tuller; 5. Signal processing in biochemical reaction networks Adam P. Arkin; Part II. Nonlinear Sensitivity of Biological Systems to Electromagnetic Stimuli: 6. Electrical signal detection and noise in systems with long-range coherence Paul C. Gailey; 7. Oscillatory signals in migrating neutrophils: effects of time-varying chemical and electrical fields Howard R. Petty; 8. Enzyme kinetics and nonlinear biochemical amplification in response to static and oscillating magnetic fields Jan Walleczek and Clemens F. Eichwald; 9. Magnetic field sensitivity in the hippocampus Stefan Engström, Suzanne Bawin and W. Ross Adey; Part III. Stochastic Noise-Induced Dynamics and Transport in Biological Systems: 10. Stochastic resonance: looking forward Frank Moss; 11. Stochastic resonance and small-amplitude signal transduction in voltage-gated ion channels Sergey M. Bezrukov and Igor Vodyanoy; 12. Ratchets, rectifiers and demons: the constructive role of noise in free energy and signal transduction R. Dean Astumian; 13. Cellular transduction of periodic and stochastic energy signals by electroconformational coupling Tian Y. Tsong; Part IV. Nonlinear Control of Biological and Other Excitable Systems: 14. Controlling chaos in dynamical systems Kenneth Showalter; 15. Electromagnetic fields and biological

Method of asymptotic expansions and qualitative analysis of finite-dimensional models in the nonlinear field theory

International Nuclear Information System (INIS)

Eleonskij, V.M.; Kulagin, N.E.; Novozhilova, N.S.; Silin, V.P.

1984-01-01

The reasons which prevent the existence of periodic in time and self-localised in space solutions of the nonlinear wave equation u=F (u) are determined by the methods of qualitative theory of dynamical systems. The correspondence between the qualitative behaviour of special (separatrix) trajectories in the phase space and asymptotic solutions of the nonlinear wave equation is analysed

Nonlinear crack mechanics

International Nuclear Information System (INIS)

Khoroshun, L.P.

1995-01-01

The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero

Increase in speed of Wilkinson-type ADC and improvement of differential non-linearity

Energy Technology Data Exchange (ETDEWEB)

Kinbara, S [Japan Atomic Energy Research Inst., Tokai, Ibaraki. Tokai Research Establishment

1977-06-01

It is shown that the differential non-linearity of a Wilkinson-type analog-to-digital converter (ADC) is dominated by the unbalance of even-numbered periods caused by the action of interference resulting from operation of a channel scaler. To improve this situation, new methods were tested which allow such action of interference to be dispersed. Measurements show that a differential non-linearity value of +- 0.043% is attainable for a clock rate of 300 MHz.

Nonlinear electrorheological instability of two Rivlin-Ericksen elastico-viscous fluids

CERN Document Server

El-Dib, Y O

2003-01-01

The behaviour of surface waves propagating between two Rivlin-Ericksen elastico-viscous fluids is examined. The investigation is made in the presence of a vertical electric field and a relative horizontal constant velocity. The influence of both surface tension and gravity force is taken into account. Due to the inclusion of streaming flow a mathematical simplification is considered. The viscoelastic contribution is demonstrated in the boundary conditions. From this point of view the approximation equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement and having damping terms with complex coefficients. This equation is accomplished by utilizing the cubic nonlinearity. The use of the Gardner-Morikawa transformation yields a simplified linear dispersion relation so that the periodic solution for the linear form is utilized. The ...

Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations

Energy Technology Data Exchange (ETDEWEB)

Jin Chen

2009-12-07

Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

Chaotic Dynamics-Based Analysis of Broadband Piezoelectric Vibration Energy Harvesting Enhanced by Using Nonlinearity

Directory of Open Access Journals (Sweden)

Zhongsheng Chen

2016-01-01

Full Text Available Nonlinear magnetic forces are always used to enlarge resonant bandwidth of vibration energy harvesting systems with piezoelectric cantilever beams. However, how to determine properly the distance between two magnets is one of the key engineering problems. In this paper, the Melnikov theory is introduced to overcome it. Firstly, the Melnikov state-space model of the nonlinear piezoelectric vibration energy harvesting (PVEH system is built. Based on it, chaotic dynamics mechanisms of achieving broadband PVEH by nonlinearity are exposed by potential function of the unperturbed nonlinear PVEH system. Then the corresponding Melnikov function of the nonlinear PVEH system is defined, based on which two Melnikov necessary conditions of determining the distance are obtained. Finally, numerical simulations are done to testify the theoretic results. The results demonstrate that the distance is closely related to the excitation amplitude and frequency once geometric and material parameters are fixed. Under a single-frequency excitation, the nonlinear PVEH system can generate a periodic vibration around a stable point, a large-amplitude vibration around two stable points, or a chaotic vibration. The proposed method is very valuable for optimally designing and utilizing nonlinear broadband PVEH devices in engineering applications.

Nonlinear dynamics and complexity

CERN Document Server

Luo, Albert; Fu, Xilin

2014-01-01

This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

Waves and Structures in Nonlinear Nondispersive Media General Theory and Applications to Nonlinear Acoustics

CERN Document Server

Gurbatov, S N; Saichev, A I

2012-01-01

"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...

Nonlinear effects in the radiation force generated by amplitude-modulated focused beams

Science.gov (United States)

González, Nuria; Jiménez, Noé; Redondo, Javier; Roig, Bernardino; Picó, Rubén; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.; Camarena, Francisco

2012-10-01

Harmonic Motion Imaging (HMI) uses an amplitude-modulated (AM) beam to induce an oscillatory radiation force before, during and after ablation. In this paper, the findings from a numerical analysis of the effects related with the nonlinear propagation of AM focused ultrasonic beams in water on the radiation force and the location of its maxima will be presented. The numerical modeling is performed using the KZK nonlinear parabolic equation. The radiation force is generated by a focused transducer with a gain of 18, a carrier frequency of 1 MHz and a modulation frequency of 25 kHz. The modulated excitation generates a spatially-invariant force proportional to the intensity. Regarding the nonlinear wave propagation, the force is no longer proportional to the intensity, reaching a factor of eight between the nonlinear and linear estimations. Also, a 9 mm shift in the on-axis force peak occurs when the initial pressure increased from 1 to 300 kPa. This spatial shift, due to the nonlinear effects, becomes dynamic in AM focused beams, as the different signal periods have different amplitudes. This study shows that both the value and the spatial position of the force peak are affected by the nonlinear propagation of the ultrasonic waves.

Long-Period Solar Variability

Energy Technology Data Exchange (ETDEWEB)

GAUTHIER,JOHN H.

2000-07-20

Terrestrial climate records and historical observations of the Sun suggest that the Sun undergoes aperiodic oscillations in radiative output and size over time periods of centuries and millenia. Such behavior can be explained by the solar convective zone acting as a nonlinear oscillator, forced at the sunspot-cycle frequency by variations in heliomagnetic field strength. A forced variant of the Lorenz equations can generate a time series with the same characteristics as the solar and climate records. The timescales and magnitudes of oscillations that could be caused by this mechanism are consistent with what is known about the Sun and terrestrial climate.

Almost periodic solutions to systems of parabolic equations

Directory of Open Access Journals (Sweden)

Janpou Nee

1994-01-01

Full Text Available In this paper we show that the second-order differential solution is 2-almost periodic, provided it is 2-bounded, and the growth of the components of a non-linear function of a system of parabolic equation is bounded by any pair of con-secutive eigenvalues of the associated Dirichlet boundary value problems.

Nonlinear Approaches in Engineering Applications

CERN Document Server

Jazar, Reza

2012-01-01

Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...

Nonlinear modelling of polymer electrolyte membrane fuel cell stack using nonlinear cancellation technique

Energy Technology Data Exchange (ETDEWEB)

Barus, R. P. P., E-mail: rismawan.ppb@gmail.com [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung and Centre for Material and Technical Product, Jalan Sangkuriang No. 14 Bandung (Indonesia); Tjokronegoro, H. A.; Leksono, E. [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia); Ismunandar [Chemistry Study, Faculty of Mathematics and Science, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia)

2014-09-25

Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.

Nonlinear modelling of polymer electrolyte membrane fuel cell stack using nonlinear cancellation technique

International Nuclear Information System (INIS)

Barus, R. P. P.; Tjokronegoro, H. A.; Leksono, E.; Ismunandar

2014-01-01

Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range

Periodic solutions to singular second order differential equations: the repulsive case

Czech Academy of Sciences Publication Activity Database

Hakl, Robert; Torres, P.J.; Zamora, M.

2012-01-01

Roč. 39, č. 2 (2012), s. 199-220 ISSN 1230-3429 Institutional support: RVO:67985840 Keywords : singular nonlinear boundary value problem * positive solutions * periodic solutions Subject RIV: BA - General Mathematics Impact factor: 1.099, year: 2012

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...

Nonlinear dynamics and predictability in the atmospheric sciences

Science.gov (United States)

Ghil, M.; Kimoto, M.; Neelin, J. D.

1991-01-01

Systematic applications of nonlinear dynamics to studies of the atmosphere and climate are reviewed for the period 1987-1990. Problems discussed include paleoclimatic applications, low-frequency atmospheric variability, and interannual variability of the ocean-atmosphere system. Emphasis is placed on applications of the successive bifurcation approach and the ergodic theory of dynamical systems to understanding and prediction of intraseasonal, interannual, and Quaternary climate changes.

Reactivity estimation using digital nonlinear H∞ estimator for VHTRC experiment

International Nuclear Information System (INIS)

Suzuki, Katsuo; Nabeshima, Kunihiko; Yamane, Tsuyoshi

2003-01-01

On-line and real-time estimation of time-varying reactivity in a nuclear reactor in necessary for early detection of reactivity anomaly and safe operation. Using a digital nonlinear H ∞ estimator, an experiment of real-time dynamic reactivity estimation was carried out in the Very High Temperature Reactor Critical Assembly (VHTRC) of Japan Atomic Energy Research Institute. Some technical issues of the experiment are described, such as reactivity insertion, data sampling frequency, anti-aliasing filter, experimental circuit and digitalising nonlinear H ∞ reactivity estimator, and so on. Then, we discussed the experimental results obtained by the digital nonlinear H ∞ estimator with sampled data of the nuclear instrumentation signal for the power responses under various reactivity insertions. Good performances of estimated reactivity were observed, with almost no delay to the true reactivity and sufficient accuracy between 0.05 cent and 0.1 cent. The experiment shows that real-time reactivity for data sampling period of 10 ms can be certainly realized. From the results of the experiment, it is concluded that the digital nonlinear H ∞ reactivity estimator can be applied as on-line real-time reactivity meter for actual nuclear plants. (author)

Nonlinear dynamics analysis of a modified optically injected semiconductor lasers model

International Nuclear Information System (INIS)

Chu Yandong; Li Xianfeng; Zhang Jiangang; Chang Yingxiang

2009-01-01

In this paper, a new nonlinear autonomous system that was introduced by Chlouverakis and Sprott is studied further, to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or numerically, such as Poincare mapping, Lyapunov exponents, fractal dimension, continuous power spectrum and so forth. Furthermore, the coexistence of different attractors is discovered on the Poincare maps. Meanwhile, chaotic oscillation of this system is converted into a stable periodic orbit with the method of time-delayed feedback, which demonstrated by numerical simulations and the robustness of this method is proved.

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

Science.gov (United States)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

On the dynamic buckling of a weakly damped nonlinear elastic ...

African Journals Online (AJOL)

In this paper we determine the dynamic buckling load of a strictly nonlinear but weakly damped elastic oscillatory model structure subjected to small perturbations The loading history is explicitly time dependent and varies slowly with time over a natural period of oscillation of the structure. A multiple timing regular ...

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.

Note on nonlinear seismic response of reinforced concrete structures with low initial periods

International Nuclear Information System (INIS)

Sozen, M.A.

1985-01-01

This note was prepared to illustrate by specific examples an opinion on the seismic response of reinforced concrete structures with low initial periods. The object is to point out what the writer considers to be important in relation to the behavior of such structures at levels of ground shaking higher than indicated by design criteria. Structures of concern are assumed to have low initial periods. A structure with a low initial period is assumed to have both of two attributes: (a) its flexural stiffness is high so that its total overall lateral deformation is not dominated by flexural deformation and (b) its calculated period is below the one at which the calculated response spectrum may be idealized to change from the nearly-constant acceleration to the nearly-constant velocity response range

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

Science.gov (United States)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Time history nonlinear earthquake response analysis considering materials and geometrical nonlinearity

International Nuclear Information System (INIS)

Kobayashi, T.; Yoshikawa, K.; Takaoka, E.; Nakazawa, M.; Shikama, Y.

2002-01-01

A time history nonlinear earthquake response analysis method was proposed and applied to earthquake response prediction analysis for a Large Scale Seismic Test (LSST) Program in Hualien, Taiwan, in which a 1/4 scale model of a nuclear reactor containment structure was constructed on sandy gravel layer. In the analysis both of strain-dependent material nonlinearity, and geometrical nonlinearity by base mat uplift, were considered. The 'Lattice Model' for the soil-structure interaction model was employed. An earthquake record on soil surface at the site was used as control motion, and deconvoluted to the input motion of the analysis model at GL-52 m with 300 Gal of maximum acceleration. The following two analyses were considered: (A) time history nonlinear, (B) equivalent linear, and the advantage of time history nonlinear earthquake response analysis method is discussed

Geometrically Nonlinear Transient Response of Laminated Plates with Nonlinear Elastic Restraints

Directory of Open Access Journals (Sweden)

Shaochong Yang

2017-01-01

Full Text Available To investigate the dynamic behavior of laminated plates with nonlinear elastic restraints, a varied constraint force model and a systematic numerical procedure are presented in this work. Several kinds of typical relationships of force-displacement for spring are established to simulate the nonlinear elastic restraints. In addition, considering the restraining moments of flexible pads, the pads are modeled by translational and rotational springs. The displacement- dependent constraint forces are added to the right-hand side of equations of motion and treated as additional applied loads. These loads can be explicitly defined, via an independent set of nonlinear load functions. The time histories of transverse displacements at typical points of the laminated plate are obtained through the transient analysis. Numerical examples show that the present method can effectively treat the geometrically nonlinear transient response of plates with nonlinear elastic restraints.

Nonlinear optical systems

CERN Document Server

Lugiato, Luigi; Brambilla, Massimo

2015-01-01

Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.

Nonlinear dynamic analysis of D α signals for type I edge localized modes characterization on JET with a carbon wall

Science.gov (United States)

Cannas, Barbara; Fanni, Alessandra; Murari, Andrea; Pisano, Fabio; Contributors, JET

2018-02-01

In this paper, the dynamic characteristics of type-I ELM time-series from the JET tokamak, the world’s largest magnetic confinement plasma physics experiment, have been investigated. The dynamic analysis has been focused on the detection of nonlinear structure in D α radiation time series. Firstly, the method of surrogate data has been applied to evaluate the statistical significance of the null hypothesis of static nonlinear distortion of an underlying Gaussian linear process. Several nonlinear statistics have been evaluated, such us the time delayed mutual information, the correlation dimension and the maximal Lyapunov exponent. The obtained results allow us to reject the null hypothesis, giving evidence of underlying nonlinear dynamics. Moreover, no evidence of low-dimensional chaos has been found; indeed, the analysed time series are better characterized by the power law sensitivity to initial conditions which can suggest a motion at the ‘edge of chaos’, at the border between chaotic and regular non-chaotic dynamics. This uncertainty makes it necessary to further investigate about the nature of the nonlinear dynamics. For this purpose, a second surrogate test to distinguish chaotic orbits from pseudo-periodic orbits has been applied. In this case, we cannot reject the null hypothesis which means that the ELM time series is possibly pseudo-periodic. In order to reproduce pseudo-periodic dynamical properties, a periodic state-of-the-art model, proposed to reproduce the ELM cycle, has been corrupted by a dynamical noise, obtaining time series qualitatively in agreement with experimental time series.

Mechanics of inter-modal tunneling in nonlinear waveguides

Science.gov (United States)

Jiao, Weijian; Gonella, Stefano

2018-02-01

In this article, we investigate the mechanics of nonlinearly induced inter-modal energy tunneling between flexurally-dominated and axially-dominated modes in phononic waveguides. Special attention is devoted to elucidating the role played by the coupling between axial and flexural degrees of freedom in the determination of the available mode hopping conditions and the associated mechanisms of deformation. Waveguides offer an ideal test bed to investigate the mechanics of nonlinear energy tunneling, due to the fact that they naturally feature, even at low frequencies, families of modes (flexural and axial) that are intrinsically characterized by extreme complementarity. Moreover, thanks to their geometric simplicity, their behavior can be explained by resorting to intuitive structural mechanics models that effectively capture the dichotomy and interplay between flexural and axial mechanisms. After having delineated the fundamental mechanics of flexural-to-axial hopping using the benchmark example of a homogeneous structure, we adapt the analysis to the case of periodic waveguides, in which the complex dispersive behavior due to periodicity results in additional richness of mode hopping mechanisms. We finally extend the analysis to periodic waveguides with internal resonators, in which the availability of locally-resonant bandgaps implies the possibility to activate the resonators even at relatively low frequencies, thus increasing the degree of modal complementarity that is available in the acoustic range. In this context, inter-modal tunneling provides an unprecedented mechanism to transfer conspicuous packets of energy to the resonating microstructure.

Nonlinear elastic waves in materials

CERN Document Server

Rushchitsky, Jeremiah J

2014-01-01

The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...

On the Stability of Periodic Mercury-type Rotations

Science.gov (United States)

Churkina, Tatyana E.; Stepanov, Sergey Y.

2017-12-01

We consider the stability of planar periodic Mercury-type rotations of a rigid body around its center of mass in an elliptical orbit in a central Newtonian field of forces. Mercurytype rotations mean that the body makes 3 turns around its center of mass during 2 revolutions of the center of mass in its orbit (resonance 3:2). These rotations can be 1) symmetrical 2π- periodic, 2) symmetrical 4π-periodic and 3) asymmetrical 4π-periodic. The stability of rotations of type 1) was investigated by A.P.Markeev. In our paper we present a nonlinear stability analysis for some rotations of types 2) and 3) in 3rd- and 4th-order resonant cases, in the nonresonant case and at the boundaries of regions of linear stability.

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.

Time-periodic solution of a 2D fourth-order nonlinear parabolic ...

Indian Academy of Sciences (India)

appropriate function space for the initial boundary value problem. ... time discretizations which allow much larger time steps than those of a standard implicit– explicit approach. ... set of ω-periodic X-valued measurable functions on R such that.

On Helmholtz Problem for Plane Periodical Structures

International Nuclear Information System (INIS)

Akishin, P.G.; Vinitskij, S.I.

1994-01-01

The plane Helmholtz problem of the periodical disc structures with the phase shifts conditions of the solutions along the basis lattice vectors and the Dirichlet conditions on the basic boundaries is considered. The Green function satisfying the quasi periodical conditions on the lattice is constructed. The Helmholtz problem is reduced to the boundary integral equations for the simple layer potentials of this Green function. The methods of the discretization of the arising integral equations are proposed. The procedures of calculation of the matrix elements are discussed. The reality of the spectral parameter of the nonlinear continuous and discretized problems is shown. 8 refs., 2 figs

On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations

International Nuclear Information System (INIS)

Valat, J.

1960-12-01

Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [fr

Asymptotic inverse periods of reflected reactors above prompt critical

International Nuclear Information System (INIS)

Spriggs, G.D.; Busch, R.D.

1995-01-01

It is commonly assumed that the kinetic behavior of reflected and unreflected reactors is identical. In particular, it is often accepted that a given reactivity change in either type of system will result in an identical asymptotic inverse period. This is generally true for reactivities below prompt critical. For reactivities above prompt critical, however, the asymptotic inverse period can vary in a highly nonlinear fashion with system reactivity depending on the reflector return fraction, the neutron lifetime in the core, and the neutron lifetime in the reflector

New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa-Holm equations

International Nuclear Information System (INIS)

Tian Lixin; Yin Jiuli

2004-01-01

In this paper, we introduce the fully nonlinear generalized Camassa-Holm equation C(m,n,p) and by using four direct ansatzs, we obtain abundant solutions: compactons (solutions with the absence of infinite wings), solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions and obtain kink compacton solutions and nonsymmetry compacton solutions. We also study other forms of fully nonlinear generalized Camassa-Holm equation, and their compacton solutions are governed by linear equations

Fiber Nonlinearity Post-Compensation by Optical Phase Conjugation for 40Gb/s CO-OFDM Systems

International Nuclear Information System (INIS)

Qiao Yao-Jun; Liu Xue-Jun; Ji Yue-Feng

2011-01-01

Fiber nonlinearity impairments in a 40-Gb/s coherent optical orthogonal frequency division multiplexing (COOFDM) system are post-compensated for by a new method of fiber nonlinearity post-compensation (FNPC). The FNPC located before the CO-OFDM receiver includes an optical phase conjugation (OPC) unit and a subsequent 80-km-high nonlinear fiber (HNLF) as a fiber nonlinearity compensator. The OPC unit is based on a four wave mixing effect in a semiconductor optical amplifier. The fiber nonlinearity impairments in the transmission link are post-compensated for after OPC by transmission through the HNLF with a large nonlinearity coefficient. Simulation results show that the nonlinear threshold (NLT) (for Q > 10 dB) can be increased by about 2.5 dB and the maximum Q factor is increased by about 1.2 dB for the single-channel 40-Gb/s CO-OFDM system with periodic dispersion maps. In the 50-GHz channel spacing wavelength-division-multiplexing system, the NLT increases by 1.1 dB, equating to a 0.7 dB improvement for the maximum Q factor. (fundamental areas of phenomenology(including applications))

The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems

International Nuclear Information System (INIS)

Di Dong; Yiming Long.

1994-10-01

In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous periodic and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems. (author). 40 refs

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

Nonlinear dynamics analysis of the spur gear system for railway locomotive

Science.gov (United States)

Wang, Junguo; He, Guangyue; Zhang, Jie; Zhao, Yongxiang; Yao, Yuan

2017-02-01

Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincaré maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions

Science.gov (United States)

Khajehtourian, Romik

Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The

Investigating the Nonlinear Dynamics of Emerging and Developed Stock Markets

Directory of Open Access Journals (Sweden)

K. Guhathakurta

2015-01-01

Full Text Available Financial time-series has been of interest of many statisticians and financial experts. Understanding the characteristic features of a financial-time series has posed some difficulties because of its quasi-periodic nature. Linear statistics can be applied to a periodic time series, but since financial time series is non-linear and non-stationary, analysis of its quasi periodic characteristics is not entirely possible with linear statistics. Thus, the study of financial series of stock market still remains a complex task having its specific requirements. In this paper keeping in mind the recent trends and developments in financial time series studies, we want to establish if there is any significant relationship existing between trading behavior of developing and developed markets. The study is conducted to draw conclusions on similarity or differences between developing economies, developed economies, developing-developed economy pairs. We take the leading stock market indices dataset for the past 15 years in those markets to conduct the study. First we have drawn probability distribution of the dataset to see if any graphical similarity exists. Then we perform quantitative techniques to test certain hypotheses. Then we proceed to implement the Ensemble Empirical Mode Distribution technique to draw out amplitude and phase of movement of index value each data set to compare at granular level of detail. Our findings lead us to conclude that the nonlinear dynamics of emerging markets and developed markets are not significantly different. This could mean that increasing cross market trading and involvement of global investment has resulted in narrowing the gap between emerging and developed markets. From nonlinear dynamics perspective we find no reason to distinguish markets into emerging and developed any more.

A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

International Nuclear Information System (INIS)

Yan Zhenya

2005-01-01

A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer-Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations

Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses.

Science.gov (United States)

Kim, Kihong; Phung, D K; Rotermund, F; Lim, H

2008-01-21

We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.

Nonlinear dynamics and stability of boiling water reactors: qualitative and quantitative analyses

International Nuclear Information System (INIS)

March-Leuba, J.; Cacuci, D.G.; Perez, R.B.

1985-01-01

A phenomenological model has been developed to simulate the qualitative behavior of boiling water reactors (BWRs) in the nonlinear regime under deterministic and stochastic excitations. After the linear stability threshold is crossed, limit cycle oscillations appear due to interactions between two unstable equilibrium points and the phase-space trajectories. This limit cycle becomes unstable when the feedback gain exceeds a certain critical value. Subsequent limit cycle instabilities produce a cascade of period-doubling bifurcations that leads to a periodic pulsed behavior. Under stochastic excitations, BWRs exhibit a single characteristic resonance, at approx.0.5 Hz, in the linear regime. By contrast, this work shows that harmonics of this characteristic frequency appear in the nonlinear regime. Furthermore, this work also demonstrates that amplitudes of the limit cycle oscillations do not depend on the variance of the stochastic excitation and remain bounded at all times. A physical model of nonlinear BWR dynamics has also been developed and employed to calculate the amplitude of limit cycle oscillations and their effects on fuel integrity over a wide range of operating conditions in the Vermont Yankee reactor. These calculations have confirmed that, beyond the threshold for linear stability, the reactor's state variable undergo limit cycle oscillations

Periodic Forcing of Inhibition-Stabilized Networks: Nonlinear Resonances and Phase-Amplitude Coupling

Science.gov (United States)

Veltz, Romain; Sejnowski, Terrence J.

2016-01-01

Inhibition-stabilized networks (ISNs) are neural architectures with strong positive feedback among pyramidal neurons balanced by strong negative feedback from inhibitory interneurons, a circuit element found in the hippocampus and the primary visual cortex. In their working regime, ISNs produce damped oscillations in the γ-range in response to inputs to the inhibitory population. In order to understand the properties of interconnected ISNs, we investigated periodic forcing of ISNs. We show that ISNs can be excited over a range of frequencies and derive properties of the resonance peaks. In particular, we studied the phase-locked solutions, the torus solutions, and the resonance peaks. Periodically forced ISNs respond with (possibly multistable) phase-locked activity, whereas networks with sustained intrinsic oscillations respond more dynamically to periodic inputs with tori. Hence, the dynamics are surprisingly rich, and phase effects alone do not adequately describe the network response. This strengthens the importance of phaseamplitude coupling as opposed to phase-phase coupling in providing multiple frequencies for multiplexing and routing information. PMID:26496044

Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

Science.gov (United States)

Agarwal, S.; Wettlaufer, J. S.

2014-12-01

We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report

International Nuclear Information System (INIS)

Tataronis, J. A.

2004-01-01

This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfven continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named ''accumulation continuum'' and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory

A study of 2014 record drought in India with CFSv2 model: role of water vapor transport

KAUST Repository

Ramakrishna, S. S. V. S.; Brahmananda Rao, V.; Srinivasa Rao, B. R.; Hari Prasad, D.; Nanaji Rao, N.; Panda, Roshmitha

2016-01-01

The Indian summer monsoon season of 2014 was erratic and ended up with a seasonal rainfall deficit of 12 % and a record drought in June. In this study we analyze the moisture transport characteristics for the monsoon season of 2014 using both NCEP FNL reanalysis (FNL) and CFSv2 (CFS) model data. In FNL, in June 2014 there was a large area of divergence of moisture flux. In other months also there was lesser flux. This probably is the cause of 2014 drought. The CFS model overestimated the drought and it reproduces poorly the observed rainfall over central India (65E–95E; 5N–35N). The correlation coefficient (CC) between the IMD observed rainfall and CFS model rainfall is only 0.1 while the CC between rainfall and moisture flux convergence in CFS model is only 0.20 and with FNL data −0.78. This clearly shows that the CFS model has serious difficulty in reproducing the moisture flux convergence and rainfall. We found that the rainfall variations are strongly related to the moisture convergence or divergence. The hypothesis of Krishnamurti et al. (J Atmos Sci 67:3423–3441, 2010) namely the intrusion of west African desert air and the associated low convective available potential energy inhibiting convection and rainfall shows some promise to explain dry spells in Indian summer monsoon. However, the rainfall or lack of it is mainly explained by convergence or divergence of moisture flux. © 2016 Springer-Verlag Berlin Heidelberg

A study of 2014 record drought in India with CFSv2 model: role of water vapor transport

KAUST Repository

Ramakrishna, S. S. V. S.

2016-09-16

The Indian summer monsoon season of 2014 was erratic and ended up with a seasonal rainfall deficit of 12 % and a record drought in June. In this study we analyze the moisture transport characteristics for the monsoon season of 2014 using both NCEP FNL reanalysis (FNL) and CFSv2 (CFS) model data. In FNL, in June 2014 there was a large area of divergence of moisture flux. In other months also there was lesser flux. This probably is the cause of 2014 drought. The CFS model overestimated the drought and it reproduces poorly the observed rainfall over central India (65E–95E; 5N–35N). The correlation coefficient (CC) between the IMD observed rainfall and CFS model rainfall is only 0.1 while the CC between rainfall and moisture flux convergence in CFS model is only 0.20 and with FNL data −0.78. This clearly shows that the CFS model has serious difficulty in reproducing the moisture flux convergence and rainfall. We found that the rainfall variations are strongly related to the moisture convergence or divergence. The hypothesis of Krishnamurti et al. (J Atmos Sci 67:3423–3441, 2010) namely the intrusion of west African desert air and the associated low convective available potential energy inhibiting convection and rainfall shows some promise to explain dry spells in Indian summer monsoon. However, the rainfall or lack of it is mainly explained by convergence or divergence of moisture flux. © 2016 Springer-Verlag Berlin Heidelberg

Nonlinear optical behaviour of absorbing CdSxSe1-x interference filters

International Nuclear Information System (INIS)

Ferencz, K.; Szipoecs, R.

1988-01-01

First experimental results of nonlinear, thin film interference filter wedges with mixed CdS x Se 1-x as spacer material at the 633 nm wavelength of He-Ne laser are reported. Optical bistability is observed with less than 7.5 mW of optical power in single-cavity structures. The change in refractive index is found to be positive which is in accordance with the thermal mechanism of nonlinearity. Producing a double-cavity structure a device is obtained which works as an optical astable multivibrator having periodical change of transmission as the function of time. (author)

Fundamentals of nonlinear optical materials

Indian Academy of Sciences (India)

Nonlinear optics; nonlinear polarization; optical fiber communication; optical switch- ing. PACS Nos 42.65Tg; ... The importance of nonlinear optics is to understand the nonlinear behavior in the induced polarization and to ..... but much work in material development and characterization remains to be done. 16. Conclusion.

On nonlinear dynamics and control of a robotic arm with chaos

Directory of Open Access Journals (Sweden)

Felix J. L. P.

2014-01-01

Full Text Available In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified, for a wide range of parameters. Controlling of the chaotic behaviour of the system, were implemented using, two control techniques, the nonlinear saturation control (NSC and the optimal linear feedback control (OLFC. The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The nonlinear saturation control (NSC is based in the order second differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The optimal linear feedback control (OLFC involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and control a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.

3-D nonlinear calculations of resistive tearing modes

International Nuclear Information System (INIS)

Hicks, H.R.; Holmes, J.A.; Lee, D.K.; Carreras, B.; Waddell, B.V.

1981-03-01

Recent numerical calculations of the evolution of resistive tearing modes have been central to the understanding of magnetohydrodynamic activity and disruptions in tokamaks. The nonlinear, 3-D, initial-value computer code RSF has provided many of these results. This code assumes cylindrical geometry with a Fourier series representation in the two periodic coordinates and a finite-difference representation in the radial direction. This choice makes RSF considerably more accurate and efficient than previous codes

Automatic Target Recognition Using Nonlinear Autoregressive Neural Networks

Science.gov (United States)

2014-03-27

series. Chakraborty et al. (1992) modeled flour prices over an eight year period for the cities of Buffalo, Minneapolis and Kansas City via a neural...on stock and commodity market prices (Kaastra & Boyd, 1996) with a goal of discovering non-linear relationships via ANNs which might provide an...Time Series A vector of past observations from a specific time interval is an example of a time series. For example, monthly stock prices from 2000

Ultrasonic nonlinearity of AISI316 austenitic steel subjected to long-term isothermal aging

Energy Technology Data Exchange (ETDEWEB)

Gong, Won Sik; Kim, Chung Seok [Dept. of Materials Science and Engineering, Chosun University, Gwangju (Korea, Republic of)

2014-06-15

This study presents the ultrasonic nonlinearity of AISI316 austenitic stainless steels subjected to longterm isothermal aging. These steels are attractive materials for use in industrial mechanical structures because of their strength at high-temperatures and their chemical stability. The test materials were subjected to accelerated heat-treatment in an electrical furnace for a predetermined aging duration. The variations in the ultrasonic nonlinearity and microstructural damage were carefully evaluated through observation of the microstructure. The ultrasonic nonlinearity stiffly dropped after aging for up to 1000 h and, then, monotonously decreased. The polygonal shape of the initial grain structures changed to circular, especially as the annealing twins in the grains dissolved and disappeared. The delta ferrite on the grain boundaries could not be observed at 1000 h of aging, and these continuously transformed into their sigma phases. Consequently, in the intial aging period, the rapid decrease in the ultrasonic nonlinearity was caused by voids, dislocations, and twin annihilation. The continuous monotonic decrease in the ultrasonic nonlinearity after the first drop resulted from the generation of Cr{sub 23}C{sub 6} precipitates and σ phases.

On the pressure field of nonlinear standing water waves

Science.gov (United States)

Schwartz, L. W.

1980-01-01

The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.

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)

Plain and oscillatory solitons of the cubic complex Ginzburg-Landau equation with nonlinear gradient terms

Science.gov (United States)

Facão, M.; Carvalho, M. I.

2017-10-01

In this work, we present parameter regions for the existence of stable plain solitons of the cubic complex Ginzburg-Landau equation (CGLE) with higher-order terms associated with a fourth-order expansion. Using a perturbation approach around the nonlinear Schrödinger equation soliton and a full numerical analysis that solves an ordinary differential equation for the soliton profiles and using the Evans method in the search for unstable eigenvalues, we have found that the minimum equation allowing these stable solitons is the cubic CGLE plus a term known in optics as Raman-delayed response, which is responsible for the redshift of the spectrum. The other favorable term for the occurrence of stable solitons is a term that represents the increase of nonlinear gain with higher frequencies. At the stability boundary, a bifurcation occurs giving rise to stable oscillatory solitons for higher values of the nonlinear gain. These oscillations can have very high amplitudes, with the pulse energy changing more than two orders of magnitude in a period, and they can even exhibit more complex dynamics such as period-doubling.

Quantum revivals in periodically driven systems close to nonlinear resonances

International Nuclear Information System (INIS)

Saif, Farhan; Fortunato, Mauro

2002-01-01

We calculate the quantum revival time for a wave packet initially well localized in a one-dimensional potential in the presence of an external periodic modulating field. The dependence of the revival time on various parameters of the driven system is shown analytically. As an example of an application of our approach, we compare the analytically obtained values of the revival time for various modulation strengths with the numerically computed ones in the case of a driven gravitational cavity. We show that they are in very good agreement

Nonlinear Optics and Applications

Science.gov (United States)

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

2007-01-01

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

Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains

Energy Technology Data Exchange (ETDEWEB)

Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M., E-mail: D.J.Pascoe@warwick.ac.uk [Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)

2017-10-01

Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra.

Effect of Loss on Slow-light-enhanced Second Harmonic Generation in Periodic Nanostructures

DEFF Research Database (Denmark)

Saravi, Sina; Quintero-Bermudez, Rafael; Setzpfandt, Frank

2016-01-01

We analyze, analytically and through nonlinear simulations, the dependence of SHG efficiency on the group index in lossy periodic structures, and find that the optimal efficiency is reached for finite values of the group index....

Approximations for Large Deflection of a Cantilever Beam under a Terminal Follower Force and Nonlinear Pendulum

Directory of Open Access Journals (Sweden)

H. Vázquez-Leal

2013-01-01

Full Text Available In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to 179.99999999∘ yielding a relative error of 0.01222747.

Local and global nonlinear dynamics of a parametrically excited rectangular symmetric cross-ply laminated composite plate

International Nuclear Information System (INIS)

Ye Min; Lu Jing; Zhang Wei; Ding Qian

2005-01-01

The present investigation deals with nonlinear dynamic behavior of a parametrically excited simply supported rectangular symmetric cross-ply laminated composite thin plate for the first time. The governing equation of motion for rectangular symmetric cross-ply laminated composite thin plate is derived by using von Karman equation. The geometric nonlinearity and nonlinear damping are included in the governing equations of motion. The Galerkin approach is used to obtain a two-degree-of-freedom nonlinear system under parametric excitation. The method of multiple scales is utilized to transform the second-order non-autonomous differential equations to the first-order averaged equations. Using numerical method, the averaged equations are analyzed to obtain the steady state bifurcation responses. The analysis of stability for steady state bifurcation responses in laminated composite thin plate is also given. Under certain conditions laminated composite thin plate may have two or multiple steady state bifurcation solutions. Jumping phenomenon occurs in the steady state bifurcation solutions. The chaotic motions of rectangular symmetric cross-ply laminated composite thin plate are also found by using numerical simulation. The results obtained here demonstrate that the periodic, quasi-periodic and chaotic motions coexist for a parametrically excited fore-edge simply supported rectangular symmetric cross-ply laminated composite thin plate under certain conditions

Collapse of nonlinear Langmuir waves

International Nuclear Information System (INIS)

Malkin, V.M.

1986-01-01

The dispersion of sufficiently intensive Langmuir waves is determined by intrinsic (electron) nonlinearity. During Langmuir collapse the wave energy density required for the appearance of electron nonlinearity is attained, generally speaking, prior to the development of dissipative processes. Up to now, the effect of electron nonlinearity on the collapse dynamics and spectrum of strong Langmuir turbulence ( which may be very appreciable ) has not been studied extensively because of the difficulty of describing nonlinear Langmuir waves. In the present paper the positive determinacy of the electron nonlinear hamiltonian is proven, the increment of modulation instability of a nonlinear Langmuir wave cluster localized in a cavity is calculated, and the universal law of their collapse is found

Nonlinear sausage-wave propagation in a magnetic slab in an incompressible fluid

International Nuclear Information System (INIS)

Ruderman, M.S.

1993-01-01

Long nonlinear sausage-wave propagation in a magnetic slab in an incompressible plasma is considered. The governing equation is derived with the aid of the reductive perturbation method. The solutions of this equation in the form of periodic waves of permanent shape are found numerically. (Author)

Chaotic synchronization of symbolic information in the discrete nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Pando L, C.L.

2003-08-01

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

Empirical Site Amplification Factors Incorporating Soil Nonlinearity in Taiwan

Science.gov (United States)

Kuo, C. H.; Chung, C. H.; Che-Min, L.; Huang, J. Y.; Wen, K. L.

2017-12-01

Characteristics of site amplifications caused by both crustal and subduction earthquakes are important in Taiwan. For example, seismic waves were amplified and led to significant building damages in the Taipei Basin by the 1986 Hualien offshore (subduction interface) and the 1999 Chi-Chi earthquakes (crustal), for which the epicentral distances were about 100 km. To understand local site amplifications in Taiwan, empirical site amplification factors for horizontal ground motions are studied using recently constructed strong motion and site databases for the free-field TSMIP stations in Taiwan. Records of large magnitude earthquakes of ML larger than six from 1994 to 2014 were selected for this study. Site amplification factors at site conditions with Vs30 of 120 m/s to 1500 m/s and base accelerations up to 0.7g were inferred from intensity ratios of station pairs within specific distances. The reference site condition is assumed as Vs30 of 760 m/s (B/C boundary). Preliminary results indicate: 1. Soil nonlinearity is more obviously at short periods (PGA, Sa0.3) than long periods (PGV, Sa1.0). 2. Soil nonlinearity is significant for stations belong to site classes of B, C, D, and E in Taiwan. 3. Effect of station-pair distance is seen at short periods (PGA and Sa0.3). 4. No significant different is found in site amplifications of crustal and subduction earthquakes. The result could be a reference for the Fa and Fv in Taiwan's building code.

Pescara benchmarks: nonlinear identification

Science.gov (United States)

Gandino, E.; Garibaldi, L.; Marchesiello, S.

2011-07-01

Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled "Monitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing", financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.

Pescara benchmarks: nonlinear identification

International Nuclear Information System (INIS)

Gandino, E; Garibaldi, L; Marchesiello, S

2011-01-01

Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled M onitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing , financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.

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.

Characterising non-linear dynamics in nocturnal breathing patterns of healthy infants using recurrence quantification analysis.

Science.gov (United States)

Terrill, Philip I; Wilson, Stephen J; Suresh, Sadasivam; Cooper, David M; Dakin, Carolyn

2013-05-01

Breathing dynamics vary between infant sleep states, and are likely to exhibit non-linear behaviour. This study applied the non-linear analytical tool recurrence quantification analysis (RQA) to 400 breath interval periods of REM and N-REM sleep, and then using an overlapping moving window. The RQA variables were different between sleep states, with REM radius 150% greater than N-REM radius, and REM laminarity 79% greater than N-REM laminarity. RQA allowed the observation of temporal variations in non-linear breathing dynamics across a night's sleep at 30s resolution, and provides a basis for quantifying changes in complex breathing dynamics with physiology and pathology. Copyright © 2013 Elsevier Ltd. All rights reserved.

Cascaded nonlinearities for ultrafast nonlinear optical science and applications

DEFF Research Database (Denmark)

Bache, Morten

the cascading nonlinearity is investigated in detail, especially with focus on femtosecond energetic laser pulses being subjected to this nonlinear response. Analytical, numerical and experimental results are used to understand the cascading interaction and applications are demonstrated. The defocusing soliton...... observations with analogies in fiber optics are observed numerically and experimentally, including soliton self-compression, soliton-induced resonant radiation, supercontinuum generation, optical wavebreaking and shock-front formation. All this happens despite no waveguide being present, thanks...... is of particular interest here, since it is quite unique and provides the solution to a number of standing challenges in the ultrafast nonlinear optics community. It solves the problem of catastrophic focusing and formation of a filaments in bulk glasses, which even under controlled circumstances is limited...

Existence of extremal periodic solutions for quasilinear parabolic equations

Directory of Open Access Journals (Sweden)

Siegfried Carl

1997-01-01

bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately defined upper and lower solutions. The main tools used in the proof of our result are recently obtained abstract results on nonlinear evolution equations, comparison and truncation techniques and suitably constructed special testfunction.

The forced nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Kaup, D.J.; Hansen, P.J.

1985-01-01

The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

Blow-Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity

Directory of Open Access Journals (Sweden)

Hee Chul Pak

2012-01-01

Full Text Available A blow-up time for nonlinear heat equations with transcendental nonlinearity is investigated. An upper bound of the first blow-up time is presented. It is pointed out that the upper bound of the first blow-up time depends on the support of the initial datum.

Simplified Methods Applied to Nonlinear Motion of Spar Platforms

Energy Technology Data Exchange (ETDEWEB)

Haslum, Herbjoern Alf

2000-07-01

Simplified methods for prediction of motion response of spar platforms are presented. The methods are based on first and second order potential theory. Nonlinear drag loads and the effect of the pumping motion in a moon-pool are also considered. Large amplitude pitch motions coupled to extreme amplitude heave motions may arise when spar platforms are exposed to long period swell. The phenomenon is investigated theoretically and explained as a Mathieu instability. It is caused by nonlinear coupling effects between heave, surge, and pitch. It is shown that for a critical wave period, the envelope of the heave motion makes the pitch motion unstable. For the same wave period, a higher order pitch/heave coupling excites resonant heave response. This mutual interaction largely amplifies both the pitch and the heave response. As a result, the pitch/heave instability revealed in this work is more critical than the previously well known Mathieu's instability in pitch which occurs if the wave period (or the natural heave period) is half the natural pitch period. The Mathieu instability is demonstrated both by numerical simulations with a newly developed calculation tool and in model experiments. In order to learn more about the conditions for this instability to occur and also how it may be controlled, different damping configurations (heave damping disks and pitch/surge damping fins) are evaluated both in model experiments and by numerical simulations. With increased drag damping, larger wave amplitudes and more time are needed to trigger the instability. The pitch/heave instability is a low probability of occurrence phenomenon. Extreme wave periods are needed for the instability to be triggered, about 20 seconds for a typical 200m draft spar. However, it may be important to consider the phenomenon in design since the pitch/heave instability is very critical. It is also seen that when classical spar platforms (constant cylindrical cross section and about 200m draft

Nonlocal and nonlinear dispersion in a nonlinear Schrodinger-type equation: exotic solitons and short-wavelength instabilities

DEFF Research Database (Denmark)

Oster, Michael; Gaididei, Yuri B.; Johansson, Magnus

2004-01-01

We study the continuum limit of a nonlinear Schrodinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose-Einstein condensates. The resulting continuum nonlinear Schrodinger-type equation includes both nonlocal and nonlinear...

Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane

Science.gov (United States)

Zhang, Zhen; Manevitch, Leonid I.; Smirnov, Valeri; Bergman, Lawrence A.; Vakakis, Alexander F.

2018-01-01

We study the in-plane damped oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Strong nonlinearity in this system is generated by geometric effects due to the in-plane stretching of the coupling spring elements. The lattice has a finite number of nonlinear transverse standing waves (termed nonlinear normal modes - NNMs), and an equal number of axial linear modes which are nonlinearly coupled to the transverse ones. Nonlinear interactions between the transverse and axial modes under harmonic excitation give rise to unexpected and extreme nonlinear energy exchanges in the lattice. In particular, we directly excite a transverse NNM by harmonic forcing (causing simulataneous indirect excitation of a corresponding axial linear mode due to nonlinear coupling), and identify three energy transfer mechanisms in the lattice. First, we detect the stable response of the directly excited transverse NNM (despite its instability in the absence of forcing), with simultaneous stability of the indirectly excited axial linear mode. Second, by changing the system and forcing parameters we report extreme nonlinear "energy explosions," whereby, after an initial regime of stability, the directly excited transverse NNM loses stability, leading to abrupt excitation of all transverse and axial modes of the lattice, at all possible wave numbers. This strong instability is triggered by the parametric instability of an indirectly excited axial mode which builds energy until the explosion. This is proved through theoretical analysis. Finally, in other parameter ranges we report intermittent, intense energy transfers from the directly excited transverse NNM to a small set of transverse NNMs with smaller wavelengths, and from the indirectly excited axial mode to a small set of axial modes, but with larger wavelengths. These intermittent energy transfers resemble energy cascades occurring in turbulent flows. Our results show that

C-type period-doubling transition in nephron autoregulation

DEFF Research Database (Denmark)

Laugesen, Jakob Lund; Mosekilde, Erik; Holstein-Rathlou, Niels-Henrik

2011-01-01

The functional units of the kidney, called nephrons, utilize mechanisms that allow the individual nephron to regulate the incoming blood flow in response to fluctuations in the arterial pressure. This regulation tends to be unstable and to generate self-sustained oscillations, period-doubling bif......The functional units of the kidney, called nephrons, utilize mechanisms that allow the individual nephron to regulate the incoming blood flow in response to fluctuations in the arterial pressure. This regulation tends to be unstable and to generate self-sustained oscillations, period......-doubling bifurcations, mode-locking and other nonlinear dynamic phenomena in the tubular pressures and flows. Using a simplified nephron model, the paper examines how the regulatory mechanisms react to an external periodic variation in arterial pressure near a region of resonance with one of the internally generated...

An unusual nonlinear system in the magnetosphere: A possible driver for auroral pulsations

International Nuclear Information System (INIS)

Davidson, G.T.; Chiu, Y.T.

1991-01-01

Many aspects of the relation between spatial and temporal structures in morningside aurorae can be explained with the aid of a nonlinear model that describes the interactions between energetic electrons and VLF waves. The simplest form of the model consists of three differential equations, with time derivatives generated in reference frames moving with either the energetic electrons, the cold plasma; or the VLF waves that interact with the energetic electrons. Although unstable solutions that could explain the origin of spatial structures are not found, the existence of spatial structures having sufficiently fine scales can provide a repetitive perturbation that maintains the temporal variations. An analysis of the behavior of solutions of the nonlinear system reveals that a strange attractor does not occur in the autonomous system; but when the repetitive perturbations are regarded as external periodic forcing terms, unusual forms of nonlinear behavior are revealed. If the frequencies of the forcing terms are not commensurate with the natural periods of the system, the solutions present some of the characteristics of deterministic chaos. The nearest analogy is a driven nonlinear oscillator with asymmetric damping. However, because of the stiffness of the system, even those solutions that are not truly chaotic (in the commonly accepted usage) will be indistinguishable from chaos over tens to hundreds of pulsation cycles. In certain cases, when damping terms are reduced to zero, the system displays a form of behavior with many of the important characteristics of chaos, but the phase trajectories do not appear to be bounded

Nonlinear analysis of EEGs of patients with major depression during different emotional states.

Science.gov (United States)

Akdemir Akar, Saime; Kara, Sadık; Agambayev, Sümeyra; Bilgiç, Vedat

2015-12-01

Although patients with major depressive disorder (MDD) have dysfunctions in cognitive behaviors and the regulation of emotions, the underlying brain dynamics of the pathophysiology are unclear. Therefore, nonlinear techniques can be used to understand the dynamic behavior of the EEG signals of MDD patients. To investigate and clarify the dynamics of MDD patients׳ brains during different emotional states, EEG recordings were analyzed using nonlinear techniques. The purpose of the present study was to assess whether there are different EEG complexities that discriminate between MDD patients and healthy controls during emotional processing. Therefore, nonlinear parameters, such as Katz fractal dimension (KFD), Higuchi fractal dimension (HFD), Shannon entropy (ShEn), Lempel-Ziv complexity (LZC) and Kolmogorov complexity (KC), were computed from the EEG signals of two groups under different experimental states: noise (negative emotional content) and music (positive emotional content) periods. First, higher complexity values were generated by MDD patients relative to controls. Significant differences were obtained in the frontal and parietal scalp locations using KFD (pemotional bias was demonstrated by their higher brain complexities during the noise period than the music stimulus. Additionally, we found that the KFD, HFD and LZC values were more sensitive in discriminating between patients and controls than the ShEn and KC measures, according to the results of ANOVA and ROC calculations. It can be concluded that the nonlinear analysis may be a useful and discriminative tool in investigating the neuro-dynamic properties of the brain in patients with MDD during emotional stimulation. Copyright © 2015 Elsevier Ltd. All rights reserved.

Non-linear model predictive supervisory controller for building, air handling unit with recuperator and refrigeration system with heat waste recovery

DEFF Research Database (Denmark)

Minko, Tomasz; Wisniewski, Rafal; Bendtsen, Jan Dimon

2016-01-01

. The retrieved heat excess can be stored in the water tank. For this purpose the charging and the discharging water loops has been designed. We present the non-linear model of the above described system and a non-linear model predictive supervisory controller that according to the received price signal......, occupancy information and ambient temperature minimizes the operation cost of the whole system and distributes set points to local controllers of supermarkets subsystems. We find that when reliable information about the high price period is available, it is profitable to use the refrigeration system...... to generate heat during the low price period, store it and use it to substitute the conventional heater during the high price period....

Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion

Directory of Open Access Journals (Sweden)

Jun Wang

2013-01-01

Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.

Tuning the dielectric properties of thiourea analog crystals for efficient nonlinear optical applications