Imaging Lithium Atoms at Sub-Angstrom Resolution

Energy Technology Data Exchange (ETDEWEB)

O' Keefe, Michael A.; Shao-Horn, Yang

2005-01-03

John Cowley and his group at ASU were pioneers in the use of transmission electron microscopy (TEM) for high-resolution imaging. Three decades ago they achieved images showing the crystal unit cell content at better than 4A resolution. Over the years, this achievement has inspired improvements in resolution that have enabled researchers to pinpoint the positions of heavy atom columns within the cell. More recently, this ability has been extended to light atoms as resolution has improved. Sub-Angstrom resolution has enabled researchers to image the columns of light atoms (carbon, oxygen and nitrogen) that are present in many complex structures. By using sub-Angstrom focal-series reconstruction of the specimen exit surface wave to image columns of cobalt, oxygen, and lithium atoms in a transition metal oxide structure commonly used as positive electrodes in lithium rechargeable batteries, we show that the range of detectable light atoms extends to lithium. HRTEM at sub-Angstrom resolution will provide the essential role of experimental verification for the emergent nanotech revolution. Our results foreshadow those to be expected from next-generation TEMs with CS-corrected lenses and monochromated electron beams.

Variations of aerosol optical depth and Angstrom parameters at a ...

Indian Academy of Sciences (India)

In this paper, aerosol optical properties including aerosol optical depth (AOD), Angstrom exponent () and Angstrom turbidity coefficient () have been investigated during December 2009 to October 2010, in a suburban area of Zanjan (36°N, 43°E, 1700 m), in the north–west of Iran, using meteorological and sun ...

Gap solitons in periodic Schrodinger lattice system with nonlinear hopping

Directory of Open Access Journals (Sweden)

Ming Cheng

2016-10-01

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

Nonlinear periodic space-charge waves in plasma

International Nuclear Information System (INIS)

Kovalev, V. A.

2009-01-01

A solution is obtained in the form of coupled nonlinear periodic space-charge waves propagating in a magnetoactive plasma. The wave spectrum in the vicinity of the critical point, where the number of harmonics increases substantially, is found to fall with harmonic number as ∝ s -1/3 . Periodic space-charge waves are invoked to explain the zebra pattern in the radio emission from solar flares.

Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

International Nuclear Information System (INIS)

Geng Xianguo; Su Ting

2007-01-01

A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

Black Carbon, Aerosol optical depth and Angstrom Exponent in São Paulo, Brazil

Science.gov (United States)

Miranda, R. M.; Perez-Martinez, P. J.; Andrade, M. D. F.

2017-12-01

Black carbon (BC) is a major absorber of solar radiation, and its impact on the radiative balance is therefore considered important. Fossil fuel combustion processes and biomass burning result in the emission of BC. Black carbon is being monitored since 2014 with a Multi-Angle Absorption Photometer-MAAP (5012; Thermo Scientific) in the East Zone of São Paulo, Brazil. São Paulo Metropolitan Area with more than 19 million inhabitants, 7 million vehicles, has high concentrations of air pollutants, especially in the winter. Vehicles can be considered the principal source of particles emitted to the atmosphere. Concentration of the pollutant had an average of 1.95 ug.m-3 ± 2.06 and a maximum value of 19.93 ug.m-3. These large variations were due to meteorological effects and to the influence of anthropogenic activities, since samples were collected close to important highways. Winds coming from the East part predominate. Higher concentrations were found in the winter months (June, July and August). Optical data from AERONET (Aerosol Optical Depth-AOD 550 nm and Angstrom Exponent 440-675 nm) were related to BC concentrations for the period from August, 2016. Average values of AOD at 500 nm and Angstrom Parameter (440-675nm) were 0.16±0.11 and 1.44±0.23, respectively. Higher BC concentrations were related to lower Angstrom values.

Periodic Solutions for Highly Nonlinear Oscillation Systems

DEFF Research Database (Denmark)

Ghadimi, M; Barari, Amin; Kaliji, H.D

2012-01-01

In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...

Weakly nonlinear dispersion and stop-band effects for periodic structures

DEFF Research Database (Denmark)

Sorokin, Vladislav; Thomsen, Jon Juel

of frequency band-gaps, i.e. frequency ranges in which elastic waves cannot propagate. Most existing analytical methods in the field are based on Floquet theory [1]; e.g. this holds for the classical Hill’s method of infinite determinants [1,2], and themethod of space-harmonics [3]. However, application...... of these methods for studying nonlinear problems isimpossible or cumbersome, since Floquet theory is applicable only for linear systems. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applications may demand effects of nonlinearity on structural response...... to be accounted for.The paper deals with analytically predicting dynamic response for nonlinear elastic structures with a continuous periodic variation in structural properties. Specifically, for a Bernoulli-Euler beam with aspatially continuous modulation of structural properties in the axial direction...

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°.

Sub-Angstrom Atomic-Resolution Imaging of Heavy Atoms to Light Atoms

Energy Technology Data Exchange (ETDEWEB)

O' Keefe, Michael A.; Shao-Horn, Yang

2003-05-23

Three decades ago John Cowley and his group at ASU achieved high-resolution electron microscope images showing the crystal unit cell contents at better than 4Angstrom resolution. Over the years, this achievement has inspired improvements in resolution that have enabled researchers to pinpoint the positions of heavy atom columns within the cell. More recently, this ability has been extended to light atoms as resolution has improved. Sub-Angstrom resolution has enabled researchers to image the columns of light atoms (carbon, oxygen and nitrogen) that are present in many complex structures. By using sub-Angstrom focal-series reconstruction of the specimen exit surface wave to image columns of cobalt, oxygen, and lithium atoms in a transition metal oxide structure commonly used as positive electrodes in lithium rechargeable batteries, we show that the range of detectable light atoms extends to lithium. HRTEM at sub-Angstrom resolution will provide the essential role of experimental verification for the emergent nanotech revolution. Our results foreshadow those to be expected from next-generation TEMs with Cs-corrected lenses and monochromated electron beams.

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.

Observation of melting in 30 angstrom diameter CdS nanocrystals

International Nuclear Information System (INIS)

Goldstein, A.N.; Colvin, V.L.; Alivisatos, A.P.

1991-01-01

In this paper temperature dependent electron diffraction studies on 30 Angstrom diameter CdS nanocrystals are described. The linear thermal expansion coefficient of the nanocrystals is 2.75 * 10 -5 Angstrom/K, and the melting point is 575 K. These data are in contrast to bulk CdS which has a melting point of 1750 K and a linear expansion coefficient of 5.5 * 10 -6 Angstrom/K. The observed depression in the melting point of these semiconductor clusters is similar to effects observed in metals and molecular crystals, indicating that the phenomenon of reduced melting point in small systems is a general one regardless of the type of material. The observation of melting point depression in these clusters also has far reaching implications for the preparation of highly crystalline clusters of CdS, as well as for the use of these nanocrystals as precursors to thin films

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)

Spectra in the 60 /angstrom/ to 345 /angstrom/ wavelength region of elements injected into the PLT tokamak

International Nuclear Information System (INIS)

Wouters, A.; Schwob, J.L.; Suckewer, S.; Seely, J.F.; Feldman, U.; Dave, J.H.

1988-03-01

High resolution spectra of the elements Fe, Ni, Zn, Ge, Se, and Mo injected into the PLT tokamak were recorded by the 2-meter Schwob-Fraenkel soft X-ray multichannel spectrometer (SOXMOS). Spectra were recorded every 50 ms during the time before and after injection. The spectral lines of the injected element were very strong in the spectrum recorded immedately after injection, and the transition in the injected element were easily distinguished from the transitions in te intrinsic elements (C, O, Ti, Cr, Fe, and Ni). An accurate wavelength scale was established using well-known reference transitions in the intrinsic elements. The spectra recorded just prior to injection were substracted from the spectra recorded after injection, and the resulting spectrum was composed almost entirely of transitions from the injected element. A large number of Δn + 0 transitions between the ground and the first excited configurations in the Li I through K I isoelectronic sequences of the injected elements were identified in the wavelength region 60 /angstrom/ to 345 /angstrom/. 33 refs., 5 figs., 1 tab

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)

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.

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.

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.

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

Sub-Angstrom microscopy through incoherent imaging and image reconstruction

International Nuclear Information System (INIS)

Pennycook, S.J.; Jesson, D.E.; Chisholm, M.F.; Ferridge, A.G.; Seddon, M.J.

1992-03-01

Z-contrast scanning transmission electron microscopy (STEM) with a high-angle annular detector breaks the coherence of the imaging process, and provides an incoherent image of a crystal projection. Even in the presence of strong dynamical diffraction, the image can be accurately described as a convolution between an object function, sharply peaked at the projected atomic sites, and the probe intensity profile. Such an image can be inverted intuitively without the need for model structures, and therefore provides the important capability to reveal unanticipated interfacial arrangements. It represents a direct image of the crystal projection, revealing the location of the atomic columns and their relative high-angle scattering power. Since no phase is associated with a peak in the object function or the contrast transfer function, extension to higher resolution is also straightforward. Image restoration techniques such as maximum entropy, in conjunction with the 1.3 Angstrom probe anticipated for a 300 kV STEM, appear to provide a simple and robust route to the achievement of sub-Angstrom resolution electron microscopy

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

Modeling the 6,300-angstrom low-latitude nightglow

International Nuclear Information System (INIS)

Fesen, C.G.; Abreu, V.J.

1987-01-01

Observations of the 6,300-angstrom nightglow form the Visible Airglow Experiment (VAE) instrument on AE-E are presented for spring equinox, solar cycle maximum conditions. The data comprise altitude profiles and integrated column brightness maps from ∼1,800 to 0400 LT and within ±30 degrees of the dip equator. The data clearly show near-midnight enhancements of the 6,300-angstrom emission. Attempts to model the column brightness maps indicated that these enhancements are due to tidal effects: the enhancements were only reproduced in the theoretical calculations which included upward propagating tidal components in the neutral winds. Further, low equatorial intensities were observed by the VCAE which could only be simulated by assuming that the phase of the E x B drift by shifted 1 hour LT; i.e., upward drift persists until 2,000 LT instead of 1,900 LT. The VAE observations could be reasonably simulated with the phase shift in the E x B drift and with the dip and geographic equators offset. The major discrepancy is in the magnitude of the nightglow maxima: the calculated intensities are a maximum of 2 times too large. Possible sources are uncertainties in the neutral densities, chemistry, and rate coefficients and in the neutral winds

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).

Diffraction patterns from 7-Angstroms tubular halloysite

International Nuclear Information System (INIS)

Eggleton, T.

1998-01-01

Full text: The diffraction patterns from 7-Angstroms tubular halloysite are superficially like those from kaolinite. Diffraction from a tubular aggregate of atoms, however, differs from that from a crystal because there is no linear repetition in two of the three conventional crystallographic directions. In tubular halloysite, the tube axis is [010] or [110] and in this direction the unit cell repeats in the normal linear fashion. The x-axis, by contrast, changes direction tangentially around the tube circumference, and there can be no true z-axis, because unit cells in the radial direction do not superimpose, since each successive tubular layer has a larger radius than its predecessor and therefore must contain more unit cells than its predecessor. Because tubular 'crystals' do not have a lattice repeat, use of Bragg 'hkl' indices is not appropriate. In the xy plane, a small area of the structure approximates a flat layer silicate, and hk indices may been used to label diffraction maxima. Similarly, successive 1:1 layers tangential to the tube walls yield a series of apparent 001 diffraction maxima. Measurement of these shows that the d-spacings do not form an exact integral series. The reason for this lies in the curvature of the structure. Calculated electron and powder X-ray diffraction patterns, based on a model of concentric 1:1 layers with no regular relation between them other than the 7.2 Angstroms spacing, closely simulate the observed data. Evidence for the 2-layer structure that is generally accepted may need to be reassessed in the light of these results

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.

THE Na 8200 Angstrom-Sign DOUBLET AS AN AGE INDICATOR IN LOW-MASS STARS

Energy Technology Data Exchange (ETDEWEB)

Schlieder, Joshua E.; Simon, Michal [Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794 (United States); Lepine, Sebastien; Rice, Emily [Department of Astrophysics, American Museum of Natural History, Central Park West at 79th Street, New York, NY 10024 (United States); Fielding, Drummond [Department of Physics and Astronomy, Johns Hopkins University, 366 Bloomberg Center, 3400 North Charles Street, Baltimore, MD 21218 (United States); Tomasino, Rachael, E-mail: michal.simon@stonybrook.edu, E-mail: schlieder@mpia-hd.mpg.de, E-mail: lepine@amnh.org, E-mail: erice@amnh.org, E-mail: dfieldi1@jhu.edu, E-mail: tomas1r@cmich.edu [Department of Physics, Central Michigan University, Mount Pleasant, MI 48859 (United States)

2012-05-15

We investigate the use of the gravity sensitive neutral sodium (Na I) doublet at 8183 Angstrom-Sign and 8195 Angstrom-Sign (Na 8200 Angstrom-Sign doublet) as an age indicator for M dwarfs. We measured the Na doublet equivalent width (EW) in giants, old dwarfs, young dwarfs, and candidate members of the {beta} Pic moving group using medium-resolution spectra. Our Na 8200 A doublet EW analysis shows that the feature is useful as an approximate age indicator in M-type dwarfs with (V - K{sub s}) {>=} 5.0, reliably distinguishing stars older and younger than 100 Myr. A simple derivation of the dependence of the Na EW on temperature and gravity supports the observational results. An analysis of the effects of metallicity shows that this youth indicator is best used on samples with similar metallicity. The age estimation technique presented here becomes useful in a mass regime where traditional youth indicators are increasingly less reliable, is applicable to other alkali lines, and will help identify new low-mass members in other young clusters and associations.

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, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$

1D goes 2D: A Berezinskii-Kosterlitz-Thouless transition in superconducting arrays of 4-Angstrom carbon nanotubes

KAUST Repository

Wang, Zhe

2010-10-01

We report superconducting resistive transition characteristics for array(s) of coupled 4-Angstrom single wall carbon nanotubes embedded in aluminophosphate-five zeolite. The transition was observed to initiate at 15 K with a slow resistance decrease switching to a sharp, order of magnitude drop between 7.5 and 6.0 K with strong (anisotropic) magnetic field dependence. Both the sharp resistance drop and its attendant nonlinear IV characteristics are consistent with the manifestations of a Berezinskii-Kosterlitz-Thouless transition that establishes quasi long range order in the plane transverse to the c-axis of the nanotubes, leading to an inhomogeneous system comprising 3D superconducting regions connected by weak links. Global coherence is established at below 5 K with the appearance of a well-defined supercurrent gap/low resistance region at 2 K. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Angstrom-Resolution Magnetic Resonance Imaging of Single Molecules via Wave-Function Fingerprints of Nuclear Spins

Science.gov (United States)

Ma, Wen-Long; Liu, Ren-Bao

2016-08-01

Single-molecule sensitivity of nuclear magnetic resonance (NMR) and angstrom resolution of magnetic resonance imaging (MRI) are the highest challenges in magnetic microscopy. Recent development in dynamical-decoupling- (DD) enhanced diamond quantum sensing has enabled single-nucleus NMR and nanoscale NMR. Similar to conventional NMR and MRI, current DD-based quantum sensing utilizes the "frequency fingerprints" of target nuclear spins. The frequency fingerprints by their nature cannot resolve different nuclear spins that have the same noise frequency or differentiate different types of correlations in nuclear-spin clusters, which limit the resolution of single-molecule MRI. Here we show that this limitation can be overcome by using "wave-function fingerprints" of target nuclear spins, which is much more sensitive than the frequency fingerprints to the weak hyperfine interaction between the targets and a sensor under resonant DD control. We demonstrate a scheme of angstrom-resolution MRI that is capable of counting and individually localizing single nuclear spins of the same frequency and characterizing the correlations in nuclear-spin clusters. A nitrogen-vacancy-center spin sensor near a diamond surface, provided that the coherence time is improved by surface engineering in the near future, may be employed to determine with angstrom resolution the positions and conformation of single molecules that are isotope labeled. The scheme in this work offers an approach to breaking the resolution limit set by the "frequency gradients" in conventional MRI and to reaching the angstrom-scale resolution.

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

Crystal Structure of VC0702 at 2.0 Angstrom: Conserved Hypothetical Protein from Vibrio Cholerae

International Nuclear Information System (INIS)

Ni, S.; Forouhar, F.; Bussiere, D.; Robinson, H.; Kennedy, M.

2006-01-01

VC0702, a conserved hypothetical protein of unknown function from Vibrio cholerae, resides in a three-gene operon containing the MbaA gene that encodes for a GGDEF and EAL domain-containing protein which is involved in regulating formation of the extracellular matrix of biofilms in Vibrio cholerae. The VC0702 crystal structure has been determined at 2.0 Angstroms and refined to R work = 22.8% and R free = 26.3%. VC0702 crystallized in an orthorhombic crystal lattice in the C2221 space group with dimensions of a = 66.61 Angstroms, b = 88.118 Angstroms, and c = 118.35 Angstroms with a homodimer in the asymmetric unit. VC0702, which forms a mixed α + β three-layered αβα sandwich, belongs to the Pfam DUF84 and COG1986 families of proteins. Sequence conservation within the DUF84 and COG1986 families was used to identify a conserved patch of surface residues that define a cleft and potential substrate-binding site in VC0702. The three-dimensional structure of VC0702 is similar to that of Mj0226 from Methanococcus janeschii, which has been identified as a novel NTPase that binds NTP in a deep cleft similarly located to the conserved patch of surface residues that define an analogous cleft in VC0702. Collectively, the data suggest that VC0702 may have a biochemical function that involves NTP binding and phosphatase activity of some kind, and is likely involved in regulation of the signaling pathway that controls biofilm formation and maintenance in Vibrio cholerae

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

Angstrom analysis with dynamic in-situ aberration corrected electron microscopy

International Nuclear Information System (INIS)

Gai, P L; Boyes, E D

2010-01-01

Following the pioneering development of atomic resolution in-situ environmental TEM (ETEM) for direct probing of gas-solid reactions, recent developments are presented of dynamic real time in-situ studies at the Angstrom level in an aberration corrected electron microscope. The in-situ data from Pt-Pd nanoparticles on carbon with the corresponding FFT/optical diffractogram (OD) illustrate an achieved resolution of 0 C and higher, in a double aberration corrected JEOL 2200 FS TEM/STEM employing a wider gap objective pole piece and gas tolerant TMP column pumping system. Direct observations of dynamic biofuel catalysts under controlled calcinations conditions and quantified with catalytic reactivity and physico-chemical studies show the benefits in-situ aberration correction in unveiling the evolution of surface active sites necessary for the development efficient heterogeneous catalysts. The new results open up opportunities for dynamic studies of materials in an aberration corrected environment and direct future development activities.

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. .

Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

International Nuclear Information System (INIS)

Zhang Zhijie; Jiang Dongguang; Wang Wei

2011-01-01

Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)

Research and development toward a 4.5-1.5{angstrom} linac coherent light source (LCLS) at SLAC

Energy Technology Data Exchange (ETDEWEB)

Tatchyn, R.; Arthur, J.; Baltay, M. [Stanford Univ., CA (United States)] [and others

1995-12-31

In recent years significant studies have been initiated on the theoretical and technical feasibility of utilizing a portion of the 3km S-band accelerator at the Stanford Linear Accelerator Center (SLAC) to drive a short wavelength (4.5-1.5 {Angstrom}) Linac Coherent Light Source (LCLS), a Free-Electron Laser (FEL) operating in the Self-Amplified Spontaneous Emission (SASE) regime. Electron beam requirements for single-pass saturation include: (1) a peak current in the 3-7 kA range, (2) a relative energy spread of <0.05%, ad (3) a transverse emittance, {epsilon}{le}{lambda}/4{pi}, where {lambda}[m] is the output wavelength. Requirements on the insertion device include field error levels of 0.1-0.2% for keeping the electron bunch centered on and in phase with the amplified photons, and a focusing beta of 4-8 m for inhibiting the dilution of its transverse density. Although much progress techniques necessary for LCLS operation down to {approximately}20 {angstrom}, a substantial amount of research and development is still required in a number of theoretical and experimental areas leading to the construction and operation of a 4.5-1.5 {angstrom} LCLS. In this paper we report on a research and development program underway and in planning at SLAC for addressing critical questions in these areas. These include the construction and operation of a linac test stand for developing laser-driven photocathode rf guns with normalized emittances approaching 1 mm-mr; development of advanced beam compression, stability, an emittance control techniques at multi-GeV energies; the construction and operation of a FEL Amplifier Test Experiment (FATE) for theoretical and experimental studies of SASE at IR wavelengths; an undulator development program to investigate superconducting, hybrid/permanent magnet (hybrid/PM), and pulsed-Cu technologies; theoretical and computational studies of high-gain FEL physics and LCLS component designs.

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

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.

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

Science.gov (United States)

Kowligy, Abijith S.

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

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.

Non-linear interactions of multi-level atoms with a near-resonant standing wave

International Nuclear Information System (INIS)

O'Kane, T.J.; Scholten, R.E.; Walkiewicz, M.R.; Farrell, P.M.

1998-01-01

Using a semiclassical density matrix formalism we have calculated the behavior of multi-level atoms interacting with a standing wave field, and show how complex non-linear phenomena, including multi-photon effects, combine to produce saturation spectra as observed in experiments. We consider both 20-level sodium and 24-level rubidium models, contrasting these with a simple 2-level case. The influence of parameters such as atomic trajectory and the time the atom remains in the beam are shown to have a critical effect on the lineshape of these resonances and the emission/absorption processes. Stable oscillations in the excited state populations for both the two-level and multi-level cases are shown to be limit cycles. These limit cycles undergo period doubling as the system evolves into chaos. Finally, using a Monte Carlo treatment, these processes average to produce saturated absorption spectra complete with power and Doppler broadening effects consistent with experiment. (authors)

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.

Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels.

Science.gov (United States)

Steinacher, Arno; Bates, Declan G; Akman, Ozgur E; Soyer, Orkun S

2016-01-01

Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for

Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels.

Directory of Open Access Journals (Sweden)

Arno Steinacher

Full Text Available Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest

Towards sub-{Angstrom} resolution through incoherent imaging

Energy Technology Data Exchange (ETDEWEB)

Pennycook, S.J.; Chisholm, M.F. [Oak Ridge National Lab., TN (United States); Nellist, P.D. [Cavendish Lab., Cambridge, (United Kingdom)

1997-04-01

As first pointed out by Lord Rayleigh a century ago, incoherent imaging offers a substantial resolution enhancement compared to coherent imaging, together with freedom from phase contrast interference effects and contrast oscillations. In the STEM configuration, with a high angle annular detector to provide the transverse incoherence, the image also shows strong Z-contrast, sufficient in the case of a 300 kV STEM to image single Pt and Rh atoms on a {gamma}-alumina support. The annular detector provides complementarity to a bright field detector of the same size. For weakly scattering specimens, it shows greater contrast than the incoherent bright field image, and also facilitates EELS analysis at atomic resolution, using the Z-contrast image to locate the probe with sub-{angstrom} precision. The inner radius of the annular detector can be chosen to reduce the transverse coherence length to well below the spacings needed to resolve the object, a significant advantage compared to light microscopy.

Electromagnetic Saturation of Angstrom-Sized Quantum Barriers at Terahertz Frequencies

Science.gov (United States)

Bahk, Young-Mi; Kang, Bong Joo; Kim, Yong Seung; Kim, Joon-Yeon; Kim, Won Tae; Kim, Tae Yun; Kang, Taehee; Rhie, Jiyeah; Han, Sanghoon; Park, Cheol-Hwan; Rotermund, Fabian; Kim, Dai-Sik

2015-09-01

Metal-graphene-metal hybrid structures allow angstrom-scale van der Waals gaps, across which electron tunneling occurs. We squeeze terahertz electromagnetic waves through these λ /10 000 000 gaps, accompanied by giant field enhancements. Unprecedented transmission reduction of 97% is achieved with the transient voltage across the gap saturating at 5 V. Electron tunneling facilitated by the transient electric field strongly modifies the gap index, starting a self-limiting process related to the barrier height. Our work enables greater interplay between classical optics and quantum tunneling, and provides optical indices to the van der Waals gaps.

Electromagnetic Saturation of Angstrom-Sized Quantum Barriers at Terahertz Frequencies.

Science.gov (United States)

Bahk, Young-Mi; Kang, Bong Joo; Kim, Yong Seung; Kim, Joon-Yeon; Kim, Won Tae; Kim, Tae Yun; Kang, Taehee; Rhie, Jiyeah; Han, Sanghoon; Park, Cheol-Hwan; Rotermund, Fabian; Kim, Dai-Sik

2015-09-18

Metal-graphene-metal hybrid structures allow angstrom-scale van der Waals gaps, across which electron tunneling occurs. We squeeze terahertz electromagnetic waves through these λ/10 000 000 gaps, accompanied by giant field enhancements. Unprecedented transmission reduction of 97% is achieved with the transient voltage across the gap saturating at 5 V. Electron tunneling facilitated by the transient electric field strongly modifies the gap index, starting a self-limiting process related to the barrier height. Our work enables greater interplay between classical optics and quantum tunneling, and provides optical indices to the van der Waals gaps.

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

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.

Identification of Nonlinear Micron-Level Mechanics for a Precision Deployable Joint

Science.gov (United States)

Bullock, S. J.; Peterson, L. D.

1994-01-01

The experimental identification of micron-level nonlinear joint mechanics and dynamics for a pin-clevis joint used in a precision, adaptive, deployable space structure are investigated. The force-state mapping method is used to identify the behavior of the joint under a preload. The results of applying a single tension-compression cycle to the joint under a tensile preload are presented. The observed micron-level behavior is highly nonlinear and involves all six rigid body motion degrees-of-freedom of the joint. it is also suggests that at micron levels of motion modelling of the joint mechanics and dynamics must include the interactions between all internal components, such as the pin, bushings, and the joint node.

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

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.

X-ray study of the structure of polyethylene at the scale of 100-200 Angstrom; Etude par rayons X dela structure du polyethylene a l'echelle de 100-200 Angstrom

Energy Technology Data Exchange (ETDEWEB)

Belbeoch nee Goldsztein, B [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1958-06-15

Information on the structure of polyethylene is deduced from a comparison of the results obtained by central diffusion and by other X-ray methods. The structure depends on the thermal and mechanical treatment to which the samples are subjected, as well as on the observation temperature. The central diffusion due to the heterogeneity of the material at the scale of 100-200 Angstrom is bound up with the presence of both the amorphous and crystalline phases. Stretched polythene shows a more or less regular succession of orderly and disorderly regions. When released it has a structure of recrystallisation preceded by 'amorphization'. (author) [French] Les informations sur la structure du polyethylene sont deduites de la confrontation des resultats obtenus par la diffusion centrale et par d'autres methodes de rayons X. La structure depend des traitements thermiques et mecaniques subis par les echantillons ainsi que la temperature d'observation. La diffusion centrale due a l'existence d'heterogeneites de la matiere a l'echelle 100-200 Angstrom est lie a la presence des deux phases amorphe et cristallisee. Le polyethylene etire comporte une succession plus ou moins reguliere de domaines ordonnes et desordonnes. Le polyethylene relaxe a une structure de recristallisation precedee d'une 'amorphisation'. (auteur)

LID: Computer code for identifying atomic and ionic lines below 3500 Angstroms

International Nuclear Information System (INIS)

Peek, J.M.; Dukart, R.J.

1987-08-01

An interactive computer code has been written to search a data base containing information useful for identifying lines in experimentally-observed spectra or for designing experiments. The data base was the basis for the Kelly and Palumbo critical review of well-resolved lines below 2000 Angstroms, includes lines below 3500 Angstroms for atoms and ions of hydrogen through krypton, and was obtained from R.L. Kelly. This code allows the user to search the data base for a user-specified wavelength region, with this search either limited to atoms or ions of the user's choice for all atoms and ions contained in the data base. The line information found in the search is stored in a local file for later reference. A plotting capability is provided to graphically display the lines resulting from the search. Several options are available to control the nature of these graphs. It is also possible to bring in data from another source, such as an experimental spectra, for display along with the lines from the data-base search. Options for manipulating the experimental spectra's background intensity and wavelength scale are also available to the user. The intensities for the lines from each ion found in the data-base search can be scaled by a multiplicative constant to better simulate the observed spectrum

Nonlinear Jaynes–Cummings model for two interacting two-level atoms

International Nuclear Information System (INIS)

Santos-Sánchez, O de los; González-Gutiérrez, C; Récamier, J

2016-01-01

In this work we examine a nonlinear version of the Jaynes–Cummings model for two identical two-level atoms allowing for Ising-like and dipole–dipole interplays between them. The model is said to be nonlinear in the sense that it can incorporate both a general intensity-dependent interaction between the atomic system and the cavity field and/or the presence of a nonlinear medium inside the cavity. As an example, we consider a particular type of atom-field coupling based upon the so-called Buck–Sukumar model and a lossless Kerr-like cavity. We describe the possible effects of such features on the evolution of some quantities of current interest, such as atomic excitation, purity, concurrence, the entropy of the field and the evolution of the latter in phase space. (paper)

A nonlinear bi-level programming approach for product portfolio management.

Science.gov (United States)

Ma, Shuang

2016-01-01

Product portfolio management (PPM) is a critical decision-making for companies across various industries in today's competitive environment. Traditional studies on PPM problem have been motivated toward engineering feasibilities and marketing which relatively pay less attention to other competitors' actions and the competitive relations, especially in mathematical optimization domain. The key challenge lies in that how to construct a mathematical optimization model to describe this Stackelberg game-based leader-follower PPM problem and the competitive relations between them. The primary work of this paper is the representation of a decision framework and the optimization model to leverage the PPM problem of leader and follower. A nonlinear, integer bi-level programming model is developed based on the decision framework. Furthermore, a bi-level nested genetic algorithm is put forward to solve this nonlinear bi-level programming model for leader-follower PPM problem. A case study of notebook computer product portfolio optimization is reported. Results and analyses reveal that the leader-follower bi-level optimization model is robust and can empower product portfolio optimization.

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

Achieving high permeability and enhanced selectivity for Angstrom-scale separations using artificial water channel membranes.

Science.gov (United States)

Shen, Yue-Xiao; Song, Woochul C; Barden, D Ryan; Ren, Tingwei; Lang, Chao; Feroz, Hasin; Henderson, Codey B; Saboe, Patrick O; Tsai, Daniel; Yan, Hengjing; Butler, Peter J; Bazan, Guillermo C; Phillip, William A; Hickey, Robert J; Cremer, Paul S; Vashisth, Harish; Kumar, Manish

2018-06-12

Synthetic polymer membranes, critical to diverse energy-efficient separations, are subject to permeability-selectivity trade-offs that decrease their overall efficacy. These trade-offs are due to structural variations (e.g., broad pore size distributions) in both nonporous membranes used for Angstrom-scale separations and porous membranes used for nano to micron-scale separations. Biological membranes utilize well-defined Angstrom-scale pores to provide exceptional transport properties and can be used as inspiration to overcome this trade-off. Here, we present a comprehensive demonstration of such a bioinspired approach based on pillar[5]arene artificial water channels, resulting in artificial water channel-based block copolymer membranes. These membranes have a sharp selectivity profile with a molecular weight cutoff of ~ 500 Da, a size range challenging to achieve with current membranes, while achieving a large improvement in permeability (~65 L m -2  h -1  bar -1  compared with 4-7 L m -2  h -1  bar -1 ) over similarly rated commercial membranes.

Atomic Scale coexistence of Periodic and quasiperiodic order in a2-fold A1-Ni-Co decagonal quasicrystal surface

Energy Technology Data Exchange (ETDEWEB)

Park, Jeong Young; Ogletree, D. Frank; Salmeron, Miquel; Ribeiro,R.A.; Canfield, P.C.; Jenks, C.J.; Thiel, P.A.

2005-11-14

Decagonal quasicrystals are made of pairs of atomic planes with pentagonal symmetry periodically stacked along a 10-fold axis. We have investigated the atomic structure of the 2-fold surface of a decagonal Al-Ni-Co quasicrystal using scanning tunneling microscopy (STM). The surface consists of terraces separated by steps of heights 1.9, 4.7, 7.8, and 12.6{angstrom} containing rows of atoms parallel to the 10-fold direction with an internal periodicity of 4{angstrom}. The rows are arranged aperiodically, with separations that follow a Fibonacci sequence and inflation symmetry. The results indicate that the surfaces are preferentially Al-terminated and in general agreement with bulk models.

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....

Strong nonlinearity-induced correlations for counterpropagating photons scattering on a two-level emitter

DEFF Research Database (Denmark)

Nysteen, Anders; McCutcheon, Dara; Mørk, Jesper

2015-01-01

We analytically treat the scattering of two counterpropagating photons on a two-level emitter embedded in an optical waveguide. We find that the nonlinearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could be quanti......We analytically treat the scattering of two counterpropagating photons on a two-level emitter embedded in an optical waveguide. We find that the nonlinearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could...

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.

Noise level estimation in weakly nonlinear slowly time-varying systems

International Nuclear Information System (INIS)

Aerts, J R M; Dirckx, J J J; Lataire, J; Pintelon, R

2008-01-01

Recently, a method using multisine excitation was proposed for estimating the frequency response, the nonlinear distortions and the disturbing noise of weakly nonlinear time-invariant systems. This method has been demonstrated on the measurement of nonlinear distortions in the vibration of acoustically driven systems such as a latex membrane, which is a good example of a time-invariant system [1]. However, not all systems are perfectly time invariant, e.g. biomechanical systems. This time variation can be misinterpreted as an elevated noise floor, and the classical noise estimation method gives a wrong result. Two improved methods to retrieve the correct noise information from the measurements are presented. Both of them make use of multisine excitations. First, it is demonstrated that the improved methods give the same result as the classical noise estimation method when applied to a time-invariant system (high-quality microphone membrane). Next, it is demonstrated that the new methods clearly give an improved estimate of the noise level on time-varying systems. As an application example results for the vibration response of an eardrum are shown

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.

Acoustic characterization of a nonlinear vibroacoustic absorber at low frequencies and high sound levels

Science.gov (United States)

Chauvin, A.; Monteil, M.; Bellizzi, S.; Côte, R.; Herzog, Ph.; Pachebat, M.

2018-03-01

A nonlinear vibroacoustic absorber (Nonlinear Energy Sink: NES), involving a clamped thin membrane made in Latex, is assessed in the acoustic domain. This NES is here considered as an one-port acoustic system, analyzed at low frequencies and for increasing excitation levels. This dynamic and frequency range requires a suitable experimental technique, which is presented first. It involves a specific impedance tube able to deal with samples of sufficient size, and reaching high sound levels with a guaranteed linear response thank's to a specific acoustic source. The identification method presented here requires a single pressure measurement, and is calibrated from a set of known acoustic loads. The NES reflection coefficient is then estimated at increasing source levels, showing its strong level dependency. This is presented as a mean to understand energy dissipation. The results of the experimental tests are first compared to a nonlinear viscoelastic model of the membrane absorber. In a second step, a family of one degree of freedom models, treated as equivalent Helmholtz resonators is identified from the measurements, allowing a parametric description of the NES behavior over a wide range of levels.

Soliton Trains Induced by Adaptive Shaping with Periodic Traps in Four-Level Ultracold Atom Systems

International Nuclear Information System (INIS)

Djouom Tchenkoue, M. L.; Welakuh Mbangheku, D.; Dikandé, Alain M.

2017-01-01

It is well known that an optical trap can be imprinted by a light field in an ultracold-atom system embedded in an optical cavity, and driven by three different coherent fields. Of the three fields coexisting in the optical cavity there is an intense control field that induces a giant Kerr nonlinearity via electromagnetically-induced transparency, and another field that creates a periodic optical grating of strength proportional to the square of the associated Rabi frequency. In this work elliptic-soliton solutions to the nonlinear equation governing the propagation of the probe field are considered, with emphasis on the possible generation of optical soliton trains forming a discrete spectrum with well defined quantum numbers. The problem is treated assuming two distinct types of periodic optical gratings and taking into account the negative and positive signs of detunings (detuning above or below resonance). Results predict that the competition between the self-phase and cross-phase modulation nonlinearities gives rise to a rich family of temporal soliton train modes characterized by distinct quantum numbers. (paper)

Soliton Trains Induced by Adaptive Shaping with Periodic Traps in Four-Level Ultracold Atom Systems

Science.gov (United States)

Djouom Tchenkoue, M. L.; Welakuh Mbangheku, D.; Dikandé, Alain M.

2017-06-01

It is well known that an optical trap can be imprinted by a light field in an ultracold-atom system embedded in an optical cavity, and driven by three different coherent fields. Of the three fields coexisting in the optical cavity there is an intense control field that induces a giant Kerr nonlinearity via electromagnetically-induced transparency, and another field that creates a periodic optical grating of strength proportional to the square of the associated Rabi frequency. In this work elliptic-soliton solutions to the nonlinear equation governing the propagation of the probe field are considered, with emphasis on the possible generation of optical soliton trains forming a discrete spectrum with well defined quantum numbers. The problem is treated assuming two distinct types of periodic optical gratings and taking into account the negative and positive signs of detunings (detuning above or below resonance). Results predict that the competition between the self-phase and cross-phase modulation nonlinearities gives rise to a rich family of temporal soliton train modes characterized by distinct quantum numbers.

Power-level regulation and simulation of nonlinear pressurized water reactor core with xenon oscillation using H-infinity loop shaping control

Directory of Open Access Journals (Sweden)

Li Gang

2016-01-01

Full Text Available This investigation is to solve the power-level control issue of a nonlinear pressurized water reactor core with xenon oscillations. A nonlinear pressurized water reactor core is modeled using the lumped parameter method, and a linear model of the core is then obtained through the small perturbation linearization way. The H∞loop shapingcontrolis utilized to design a robust controller of the linearized core model.The calculated H∞loop shaping controller is applied to the nonlinear core model. The nonlinear core model and the H∞ loop shaping controller build the nonlinear core power-level H∞loop shaping control system.Finally, the nonlinear core power-level H∞loop shaping control system is simulatedconsidering two typical load processes that are a step load maneuver and a ramp load maneuver, and simulation results show that the nonlinear control system is effective.

A comparison of the Angstrom-type correlations and the estimation of monthly average daily global irradiation

International Nuclear Information System (INIS)

Jain, S.; Jain, P.C.

1985-12-01

Linear regression analysis of the monthly average daily global irradiation and the sunshine duration data of 8 Zambian locations has been performed using the least square technique. Good correlation (r>0.95) is obtained in all the cases showing that the Angstrom equation is valid for Zambian locations. The values of the correlation parameters thus obtained show substantial unsystematic scatter. The analysis was repeated after incorporating the effects of (i) multiple reflections of radiation between the ground and the atmosphere, and (ii) not burning of the sunshine recorder chart, into the Angstrom equation. The surface albedo measurements at Lusaka were used. The scatter in the correlation parameters was investigated by graphical representation, by regression analysis of the data of the individual stations as well as the combined data of the 8 stations. The results show that the incorporation of none of the two effects reduces the scatter significantly. A single linear equation obtained from the regression analysis of the combined data of the 8 stations is found to be appropriate for estimating the global irradiation over Zambian locations with reasonable accuracy from the sunshine duration data. (author)

Nonlinear Stochastic Models for Water Level Dynamics in Closed Lakes

OpenAIRE

Mishchenko, A.S.; Zelikin, M.I.; Zelikina, L.F.

1995-01-01

This paper presents the results of investigation of nonlinear mathematical models of the behavior of closed lakes using the example of the Caspian Sea. Forecasting the level of the Caspian Sea is crucial both for the economy of the region and for the region's environment. The Caspian Sea is a closed reservoir; it is well known that its level changes considerably due to a variety of factors including global climate change. A series of forecasts exists based on different methods and taking...

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

Cascaded two-photon nonlinearity in a one-dimensional waveguide with multiple two-level emitters

Science.gov (United States)

Roy, Dibyendu

2013-01-01

We propose and theoretically investigate a model to realize cascaded optical nonlinearity with few atoms and photons in one-dimension (1D). The optical nonlinearity in our system is mediated by resonant interactions of photons with two-level emitters, such as atoms or quantum dots in a 1D photonic waveguide. Multi-photon transmission in the waveguide is nonreciprocal when the emitters have different transition energies. Our theory provides a clear physical understanding of the origin of nonreciprocity in the presence of cascaded nonlinearity. We show how various two-photon nonlinear effects including spatial attraction and repulsion between photons, background fluorescence can be tuned by changing the number of emitters and the coupling between emitters (controlled by the separation). PMID:23948782

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...

Calcium binding in α-amylases: An X-ray diffraction study at 2.1-angstrom resolution of two enzymes from Aspergillus

International Nuclear Information System (INIS)

Boel, E.; Jensen, V.J.; Petersen, S.B.; Thim, L.; Woldike, H.F.; Brady, L.; Brzozowski, AM.; Derewenda, Z.; Dodson, G.G.; Swift, H.

1990-01-01

X-ray diffraction analysis (at 2.1-angstrom resolution) of an acid alpha-amylase from Aspergillus niger allowed a detailed description of the stereochemistry of the calcium-binding sites. The primary site (which is essential in maintaining proper folding around the active site) contains a tightly bound Ca 2+ with an unusually high number of eight ligands. A secondary binding site was identified at the bottom of the substrate binding cleft; it involves the residues presumed to play a catalytic role (Asp206 and Glu230). This explains the inhibitory effect of calcium observed at higher concentrations. Neutral Aspergillus oryzae (TAKA) α-amylase was also refined in a new crystal at 2.1-angstrom resolution. The structure of this homologous (over 80%) enzyme and addition kinetic studies support all the structural conclusions regarding both calcium-binding sites

Discrete Nonlinear Schrödinger Equation and Polygonal Solitons with Applications to Collapsed Proteins

Science.gov (United States)

Molkenthin, Nora; Hu, Shuangwei; Niemi, Antti J.

2011-02-01

We introduce a novel generalization of the discrete nonlinear Schrödinger equation. It supports solitons that we utilize to model chiral polymers in the collapsed phase and, in particular, proteins in their native state. As an example we consider the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. We use its backbone as a template to explicitly construct a two-soliton configuration. Each of the two solitons describe well over 7.000 supersecondary structures of folded proteins in the Protein Data Bank with sub-angstrom accuracy suggesting that these solitons are common in nature.

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.

A nonlinear wavelet method for data smoothing of low-level gamma-ray spectra

International Nuclear Information System (INIS)

Gang Xiao; Li Deng; Benai Zhang; Jianshi Zhu

2004-01-01

A nonlinear wavelet method was designed for smoothing low-level gamma-ray spectra. The spectra of a 60 Co graduated radioactive source and a mixed soil sample were smoothed respectively according to this method and a 5 point smoothing method. The FWHM of 1,332 keV peak of 60 Co source and the absolute activities of 238 U of soil sample were calculated. The results show that the nonlinear wavelet method is better than the traditional method, with less loss of spectral peak and a more complete reduction of statistical fluctuation. (author)

Interference pattern period measurement at picometer level

Science.gov (United States)

Xiang, Xiansong; Wei, Chunlong; Jia, Wei; Zhou, Changhe; Li, Minkang; Lu, Yancong

2016-10-01

To produce large scale gratings by Scanning Beam Interference Lithography (SBIL), a light spot containing grating pattern is generated by two beams interfering, and a scanning stage is used to drive the substrate moving under the light spot. In order to locate the stage at the proper exposure positions, the period of the Interference pattern must be measured accurately. We developed a set of process to obtain the period value of two interfering beams at picometer level. The process includes data acquisition and data analysis. The data is received from a photodiode and a laser interferometer with sub-nanometer resolution. Data analysis differs from conventional analyzing methods like counting wave peaks or using Fourier transform to get the signal period, after a preprocess of filtering and envelope removing, the mean square error is calculated between the received signal and ideal sinusoid waves to find the best-fit frequency, thus an accuracy period value is acquired, this method has a low sensitivity to amplitude noise and a high resolution of frequency. With 405nm laser beams interfering, a pattern period value around 562nm is acquired by employing this process, fitting diagram of the result shows the accuracy of the period value reaches picometer level, which is much higher than the results of conventional methods.

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

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

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.

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

Demonstration of resonant photopumping of Mo VII by Mo XII for a VUV laser near 600 Angstrom

International Nuclear Information System (INIS)

Ilcisin, K.J.; Aumayr, F.; Schwob, J.L.; Suckewer, S.

1993-09-01

We present data of experiments on the resonant photopumping of Mo VII by Mo XII as a method of generating a coherent VUV source near 600 angstrom. The experiment is based on a scheme proposed by Feldman and Reader in which the 4p 6 -- 4p 5 6s transition in Mo VII in resonantly photopumped by the 5s 2 S 1/2 -- 4p 2 P 1/2 transition in Mo XII. Results of the laser produced plasma experiments show the successful enhancement of the population of the Mo VII 4p 5 6s upper lasing level when pumped by an adjacent Mo VII plasma. No enhancement was seen in a control experiment where the Mo VII plasma was pumped by a Zr X plasma. Improvements of the intensity of the Mo XII pump source, achieved using an additional pump laser, lead to the generation of a population inversion for the VUV transition

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

Nonlinear optics at the single-photon level inside a hollow core fiber

DEFF Research Database (Denmark)

Hofferberth, Sebastian; Peyronel, Thibault; Liang, Qiyu

2011-01-01

Cold atoms inside a hollow core fiber provide an unique system for studying optical nonlinearities at the few-photon level. Confinement of both atoms and photons inside the fiber core to a diameter of just a few wavelengths results in high electric field intensity per photon and large optical...

Development of XUV-interferometry (155 angstrom) using a soft x-ray laser

International Nuclear Information System (INIS)

Da Silva, L.B.; Barbee, T.W.; Cauble, R.

1995-01-01

Over the past several years the authors have developed a variety of techniques for probing plasmas with x-ray lasers. These have included direct high resolution plasma imaging to quantify laser produced plasma uniformities and moire deflectometry to measure electron density profiles in one-dimension. Although these techniques have been valuable, a need existed for direct two dimensional measurements of electron densities in large high density plasmas. For this reason the authors have worked on developing a xuv interferometer compatible with the harsh environment of laser produced plasmas. This paper describes the design and presents some results showing excellent fringe visibility using the neon-like yttrium x-ray laser operating at 155 angstrom. The coherence properties of this x-ray laser source were measured using interferometry and are also discussed

CRYSTAL-STRUCTURE OF DEOXYGENATED LIMULUS-POLYPHEMUS SUBUNIT-II HEMOCYANIN AT 2.18-ANGSTROM RESOLUTION - CLUES FOR A MECHANISM FOR ALLOSTERIC REGULATION

NARCIS (Netherlands)

HAZES, B; MAGNUS, KA; BONAVENTURA, C; BONAVENTURA, J; DAUTER, Z; KALK, KH; HOL, WGJ

The crystal structure of Limulus polyphemus subunit type II hemocyanin in the deoxygenated state has been determined to a resolution of 2.18 angstrom. Phase information for this first structure of a cheliceratan hemocyanin was obtained by molecular replacement using the crustacean hemocyanin

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.

The effect of cochlear nonlinearities on binaural masking level differences

DEFF Research Database (Denmark)

Le Goff, Nicolas; Kohlrausch, Armin

Background The binaural masking level difference (BMLD) has been shown to be constant (10−15dB) for masker spectrum levels from 70dB/Hz down to 30−40dB/Hz and to gradually decrease with lower levels (McFadden, 1968; Hall and Harvey, 1984). The decrease at low levels was larger in an asymmetric...... on the BMLD was investigated using an equalization−cancelation (EC) based binaural model framework. Methods The BMLD was measured for 500−Hz target tones presented in 3−kHz−wide maskers. BMLDs were obtained as a function of masker level in one symmetric and two asymmetric masker conditions: (i) No...... of 20dB/Hz in the non−attenuated ear. An EC based binaural model with a frontend including nonlinear peripheral processing (Jepsen et al., 2011) was used to predict these results. Results The BMLD obtained in the No′Sπ′50 condition was smaller than that obtained in the NoSπ condition at all masker...

Estimation of monthly solar exposure on horizontal surface by Angstrom-type regression equation

International Nuclear Information System (INIS)

Ravanshid, S.H.

1981-01-01

To obtain solar flux intensity, solar radiation measuring instruments are the best. In the absence of instrumental data there are other meteorological measurements which are related to solar energy and also it is possible to use empirical relationships to estimate solar flux intensit. One of these empirical relationships to estimate monthly averages of total solar radiation on a horizontal surface is the modified angstrom-type regression equation which has been employed in this report in order to estimate the solar flux intensity on a horizontal surface for Tehran. By comparing the results of this equation with four years measured valued by Tehran's meteorological weather station the values of meteorological constants (a,b) in the equation were obtained for Tehran. (author)

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...

X-ray study of the structure of polyethylene at the scale of 100-200 Angstrom

International Nuclear Information System (INIS)

Belbeoch nee Goldsztein, B.

1958-06-01

Information on the structure of polyethylene is deduced from a comparison of the results obtained by central diffusion and by other X-ray methods. The structure depends on the thermal and mechanical treatment to which the samples are subjected, as well as on the observation temperature. The central diffusion due to the heterogeneity of the material at the scale of 100-200 Angstrom is bound up with the presence of both the amorphous and crystalline phases. Stretched polythene shows a more or less regular succession of orderly and disorderly regions. When released it has a structure of recrystallisation preceded by 'amorphization'. (author) [fr

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

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

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)

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.

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

EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening

International Nuclear Information System (INIS)

Dinh Xuan Khoa; Le Van Doai; Pham Van Trong; Tran Manh Cuong; Vu Ngoc Sau; Nguyen Huy Bang; Le Nguyen Mai Anh

2014-01-01

Using density-matrix theory, an analytical expression of the self-Kerr nonlinear coefficient of a three-level lambda EIT medium for a weak probe light is derived. Influences of the coupling light and Doppler broadening on the self-Kerr coefficient are investigated and compared to experimental observation with a good agreement. The self-Kerr nonlinearity of the medium is modified and greatly enhanced in the spectral region of EIT window. Furthermore, sign, slope, and magnitude of the self-Kerr coefficient can be controlled with frequency and intensity of the coupling light and temperature of the medium. Specially, for a given set of fixed values of the parameters of coupling and probe lights, it could be able to choose an optimized temperature to have largest magnitude of the self-Kerr coefficient. Such controllable Kerr nonlinearity can find interesting applications in optoelectronic devices working with low-light intensity at various temperature conditions. (author)

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

Láser de monóxido de carbono : Estudio espectroscópico del sistema Angstrom

OpenAIRE

Schinca, Daniel Carlos

1985-01-01

En el presente trabajo se intenta resumir la labor desarrollada en láseres gaseosos de moléculas diatómicas de excitación pulsada, particularmente en lo que respecta a láseres de monóxido de carbono de geometría axial. De esta manera, se realiza un detallado análisis espectroscópico tanto de la salida láser de las bandas de emisión del Sistema Angstrom como de la emisión espontánea de las mismas bajo diferentes condiciones experimentales. Es sabido que la molécula de monóxido de car...

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

Crystallization of Mitochondrial Respiratory Complex II fromChicken Heart: A Membrane-Protein Complex Diffracting to 2.0Angstrom

Energy Technology Data Exchange (ETDEWEB)

Huang, Li-shar; Borders, Toni M.; Shen, John T.; Wang, Chung-Jen; Berry, Edward A.

2004-12-17

Procedure is presented for preparation of diffraction-quality crystals of a vertebrate mitochondrial respiratory Complex II. The crystals have the potential to diffract to at least 2.0 Angstrom with optimization of post-crystal-growth treatment and cryoprotection. This should allow determination of the structure of this important and medically relevant membrane protein complex at near-atomic resolution and provide great detail of the mode of binding of substrates and inhibitors at the two substrate-binding sites.

EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening

International Nuclear Information System (INIS)

Doai, Le Van; Khoa, Dinh Xuan; Bang, Nguyen Huy

2015-01-01

Using density-matrix theory, an analytical expression of the self-Kerr nonlinear coefficient of a three-level lambda EIT medium for a weak probe light is derived. Influences of the coupling light and Doppler broadening on the self-Kerr coefficient are investigated and compared to experimental observation with a good agreement. The self-Kerr nonlinearity of the medium is modified and greatly enhanced in the spectral region of EIT window. Furthermore, sign, slope, and magnitude of the self-Kerr coefficient can be controlled with frequency and intensity of the coupling light and temperature of the medium. In particular, for a given set of fixed values of the parameter coupling and probe lights, it is possible to choose an optimized temperature with which to obtain the largest magnitude of the self-Kerr coefficient. Such a controllable Kerr nonlinearity can find interesting applications in optoelectronic devices working with low-light intensity at various temperature conditions. (paper)

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.

Minimax terminal approach problem in two-level hierarchical nonlinear discrete-time dynamical system

Energy Technology Data Exchange (ETDEWEB)

Shorikov, A. F., E-mail: afshorikov@mail.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)

2015-11-30

We consider a discrete–time dynamical system consisting of three controllable objects. The motions of all objects are given by the corresponding vector nonlinear or linear discrete–time recurrent vector relations, and control system for its has two levels: basic (first or I level) that is dominating and subordinate level (second or II level) and both have different criterions of functioning and united a priori by determined informational and control connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistep problem of two-level hierarchical minimax program control over the terminal approach process with incomplete information and give a general scheme for its solving.

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.

Aerosol optical depth (AOD) and Angstrom exponent of aerosols observed by the Chinese Sun Hazemeter Network from August 2004 to September 2005

Science.gov (United States)

Jinyuan Xin; Yuesi Wang; Zhanqing Li; Pucai Wang; Wei Min Hao; Bryce L. Nordgren; Shigong Wang; Guangren Lui; Lili Wang; Tianxue Wen; Yang Sun; Bo Hu

2007-01-01

To reduce uncertainties in the quantitative assessment of aerosol effects on regional climate and environmental changes, extensive measurements of aerosol optical properties were made with handheld Sun photometers in the Chinese Sun Hazemeter Network (CSHNET) starting in August 2004. Regional characteristics of the aerosol optical depth (AOD) at 500 nm and Angstrom...

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

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.

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.

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

Entanglement Dynamics of Linear and Nonlinear Interaction of Two Two-Level Atoms with a Quantized Phase-Damped Field in the Dispersive Regime

Science.gov (United States)

Tavassoly, M. K.; Daneshmand, R.; Rustaee, N.

2018-06-01

In this paper we study the linear and nonlinear (intensity-dependent) interactions of two two-level atoms with a single-mode quantized field far from resonance, while the phase-damping effect is also taken into account. To find the analytical solution of the atom-field state vector corresponding to the considered model, after deducing the effective Hamiltonian we evaluate the time-dependent elements of the density operator using the master equation approach and superoperator method. Consequently, we are able to study the influences of the special nonlinearity function f (n) = √ {n}, the intensity of the initial coherent state field and the phase-damping parameter on the degree of entanglement of the whole system as well as the field and atom. It is shown that in the presence of damping, by passing time, the amount of entanglement of each subsystem with the rest of system, asymptotically reaches to its stationary and maximum value. Also, the nonlinear interaction does not have any effect on the entanglement of one of the atoms with the rest of system, but it changes the amplitude and time period of entanglement oscillations of the field and the other atom. Moreover, this may cause that, the degree of entanglement which may be low (high) at some moments of time becomes high (low) by entering the intensity-dependent function in the atom-field coupling.

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.

Achieving nonlinear optical modulation via four-wave mixing in a four-level atomic system

Science.gov (United States)

Li, Hai-Chao; Ge, Guo-Qin; Zubairy, M. Suhail

2018-05-01

We propose an accessible scheme for implementing tunable nonlinear optical amplification and attenuation via a synergetic mechanism of four-wave mixing (FWM) and optical interference in a four-level ladder-type atomic system. By constructing a cyclic atom-field interaction, we show that two reverse FWM processes can coexist via optical transitions in different branches. In the suitable input-field conditions, strong interference effects between the input fields and the generated FWM fields can be induced and result in large amplification and deep attenuation of the output fields. Moreover, such an optical modulation from enhancement to suppression can be controlled by tuning the relative phase. The quantum system can be served as a switchable optical modulator with potential applications in quantum nonlinear optics.

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.

The 2.3 {angstrom} crystal structure of cholera toxin B subunit pentamer: Choleragenoid

Energy Technology Data Exchange (ETDEWEB)

Zhang, Rong-Guang; Westbrook, M.L. [Argonne National Lab., IL (United States); Maulik, P.R.; Reed, R.A.; Shipley, G. [Boston Univ., MA (United States). School of Medicine; Westbrook, E.M. [Argonne National Lab., IL (United States)]|[Northwestern Univ., Evanston, IL (United States); Scott, D.L.; Otwinowski, Z. [Yale Univ., New Haven, CT (United States)

1996-02-01

Cholera toxin, a heterohexameric AB{sub 5} enterotoxin released by Vibrio cholera, induces a profuse secretory diarrhea in susceptible hosts. Choleragenoid, the B subunit pentamer of cholera toxin, directs the enzymatic A subunit to its target by binding to GM{sub 1} gangliosides exposed on the luminal surface of intestinal epithelial cells. We have solved the crystal structure of choleragenoid at 2.3 {Angstrom} resolution by combining single isomorphous replacement with non-crystallographic symmetry averaging. The structure of the B subunits, and their pentameric arrangement, closely resembles that reported for the intact holotoxin (choleragen), the heat-labile enterotoxin from E. coli, and for a choleragenoid-GM{sub 1} pentasaccharide complex. In the absence of the A subunit the central cavity of the B pentamer is a highly solvated channel. The binding of the A subunit or the receptor pentasaccharide to choleragenoid has only a modest effect on the local stereochemistry and does not perceptibly alter the subunit interface.

An angstrom equation analysis of solar insolation data in Malaysia

International Nuclear Information System (INIS)

Lee Fai Tsen

2000-01-01

Solar energy systems rely extensively on the availability of global solar radiation for optimum performances. Standard method of measurements involves the use of sunshine recorders to record the sunshine hours, solarimeters and chart recorders to record the diffuse and direct solar radiation. The method tends to be expensive and time consuming. As a result, fewer stations may be set up to monitor the solar insulation data Linear regression method using Angstrom equation of the type G = G 0 (a +bn/N) has been used extensively to analyze global radiation at the site of the station. The equation gives the linear regression coefficients a and h which are characteristics of the station. The equation may therefore be used to predict global radiation at and around the station, if the area surrounding the station is geographically similar, or if it is not characteristically changed due to developments over the years. We present here an analysis of the solar insulation data of several meteorological stations in West Malaysia to obtain the linear regression coefficient a and b base on yearly analysis. It is interesting to find that the values of a and b have changed over the years. This may have been due to the global warming effect, or extensive land clearing for local developments which have resulted in haze and pollution that could affect the solar insulation data received at the station. (Author)

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

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

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

Linear versus non-linear structural information limit in high-resolution transmission electron microscopy

International Nuclear Information System (INIS)

Van Aert, S.; Chen, J.H.; Van Dyck, D.

2010-01-01

A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has

Nonlinear rock behavior and its implications on deeper-level platinum mining

CSIR Research Space (South Africa)

Watson, BP

2008-10-01

Full Text Available Uniaxial tests performed on core from instrumented sites at Amandelbult 1 shaft, Impala 10 shaft and Union Section Spud-shaft showed a nonlinear elastic relationship between applied load and induced deformation. This nonlinear behaviour does...

Inverse problem for a two-level medium with an inhomgeneously broadened transition in the field of a periodic wave

International Nuclear Information System (INIS)

Zabolotskii, A.A.

1995-01-01

The inverse problem is considered for a spectral problem, which is formally equivalent to a system of Bloch equations for an inhomogeneously broadened transition interacting with the electric field. Two cases are considered to demonstrate that, for any given frequency interval, one can determine the pulse of the shape which corresponds to the interaction with only this frequency interval. In the general case, the pulse shape is described by a nonlinear periodic wave. The first example is the resonance interaction of light with a gas of two-level atoms. The second example is interaction of a linearly polarized light with the molecular J-J transition, where J much-gt 1. In the latter case, the role of inhomogeneous broadening belongs to the frequency shift induced by the applied magnetic field. 10 refs

Nonlinear associations between plasma cholesterol levels and neuropsychological function.

Science.gov (United States)

Wendell, Carrington R; Zonderman, Alan B; Katzel, Leslie I; Rosenberger, William F; Plamadeala, Victoria V; Hosey, Megan M; Waldstein, Shari R

2016-11-01

Although both high and low levels of total and low-density lipoprotein (LDL) cholesterol have been associated with poor neuropsychological function, little research has examined nonlinear effects. We examined quadratic relations of cholesterol to performance on a comprehensive neuropsychological battery. Participants were 190 older adults (53% men, ages 54-83) free of major medical, neurologic, and psychiatric disease. Measures of fasting plasma total and high-density lipoprotein (HDL) cholesterol were assayed, and LDL cholesterol was calculated. Participants completed neuropsychological measures of attention, executive function, memory, visuospatial judgment, and manual speed and dexterity. Multiple regression analyses examined cholesterol levels as quadratic predictors of each measure of cognitive performance, with age (dichotomized as Reproduction II ( b = -.0020, p = .026) and log of the Trail Making Test, Part B (b = .0001, p = .044). Quadratic associations between HDL cholesterol and cognitive performance were nonsignificant. Results indicate differential associations between cholesterol and neuropsychological function across different ages and domains of function. High and low total and LDL cholesterol may confer both risk and benefit for suboptimal cognitive function at different ages. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

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

Sub-Angstrom oscillation amplitude non-contact atomic force microscopy for lateral force gradient measurement

International Nuclear Information System (INIS)

Atabak, Mehrdad; Unverdi, Ozhan; Ozer, H. Ozguer; Oral, Ahmet

2009-01-01

We report the first results from novel sub-Angstrom oscillation amplitude non-contact atomic force microscopy developed for lateral force gradient measurements. Quantitative lateral force gradients between a tungsten tip and Si(1 1 1)-(7 x 7) surface can be measured using this microscope. Simultaneous lateral force gradient and scanning tunnelling microscope images of single and multi atomic steps are obtained. In our measurement, tunnel current is used as feedback. The lateral stiffness contrast has been observed to be 2.5 N/m at single atomic step, in contrast to 13 N/m at multi atomic step on Si(1 1 1) surface. We also carried out a series of lateral stiffness-distance spectroscopy. We observed lateral stiffness-distance curves exhibit sharp increase in the stiffness as the sample is approached towards the surface. We usually observed positive stiffness and sometimes going into slightly negative region.

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.

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...

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

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...

Fast noise level estimation algorithm based on principal component analysis transform and nonlinear rectification

Science.gov (United States)

Xu, Shaoping; Zeng, Xiaoxia; Jiang, Yinnan; Tang, Yiling

2018-01-01

We proposed a noniterative principal component analysis (PCA)-based noise level estimation (NLE) algorithm that addresses the problem of estimating the noise level with a two-step scheme. First, we randomly extracted a number of raw patches from a given noisy image and took the smallest eigenvalue of the covariance matrix of the raw patches as the preliminary estimation of the noise level. Next, the final estimation was directly obtained with a nonlinear mapping (rectification) function that was trained on some representative noisy images corrupted with different known noise levels. Compared with the state-of-art NLE algorithms, the experiment results show that the proposed NLE algorithm can reliably infer the noise level and has robust performance over a wide range of image contents and noise levels, showing a good compromise between speed and accuracy in general.

Influence of unbalance levels on nonlinear dynamics of a rotor-backup rolling bearing system

DEFF Research Database (Denmark)

Fonseca, Cesar A.; Santos, Ilmar; Weber, Hans I.

2017-01-01

of nonlinear dynamics applied to the practical use. The theoretical and numerical analyses are shown through orbit plots, phase plans, Poincaré maps, force response in time and double sided spectrum. The latter is important to characterize the condition at different levels of unbalance between forward......Rotor drops in magnetic bearing and unbalance in rotors have been objective of study for many years. The combination of these two well-known phenomena led to an interesting chaotic response, when the rotor touches the inner race of the back-up bearing. The present work explores the nonlinear rotor...... backup bearing dynamics both theoretically and experimentally using a fully instrumented test rig, where the position of shaft, its angular velocity and the contact forces between the shaft and the backup bearing are sampled at 25 kHz. The test rig is built by a removable passive magnetic bearing, which...

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.)

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...

Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems

International Nuclear Information System (INIS)

Anistratov, Dmitriy Y.

2011-01-01

The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)

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...

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

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...

Non-Linear Relationships between Aflatoxin B1 Levels and the Biological Response of Monkey Kidney Vero Cells

Directory of Open Access Journals (Sweden)

Mendel Friedman

2013-08-01

Full Text Available Aflatoxin-producing fungi contaminate food and feed during pre-harvest, storage and processing periods. Once consumed, aflatoxins (AFs accumulate in tissues, causing illnesses in animals and humans. Most human exposure to AF seems to be a result of consumption of contaminated plant and animal products. The policy of blending and dilution of grain containing higher levels of aflatoxins with uncontaminated grains for use in animal feed implicitly assumes that the deleterious effects of low levels of the toxins are linearly correlated to concentration. This assumption may not be justified, since it involves extrapolation of these nontoxic levels in feed, which are not of further concern. To develop a better understanding of the significance of low dose effects, in the present study, we developed quantitative methods for the detection of biologically active aflatoxin B1 (AFB1 in Vero cells by two independent assays: the green fluorescent protein (GFP assay, as a measure of protein synthesis by the cells, and the microculture tetrazolium (MTT assay, as a measure of cell viability. The results demonstrate a non-linear dose-response relationship at the cellular level. AFB1 at low concentrations has an opposite biological effect to higher doses that inhibit protein synthesis. Additional studies showed that heat does not affect the stability of AFB1 in milk and that the Vero cell model can be used to determine the presence of bioactive AFB1 in spiked beef, lamb and turkey meat. The implication of the results for the cumulative effects of low amounts of AFB1 in numerous foods is discussed.

Nonstoichiometric complex of gramicidin D with KI at 0.80 (angstrom) resolution

International Nuclear Information System (INIS)

Olczak, A.; Glowka, M.L.; Szczesio, M.; Bojarsk, J.; Duax, W.L.; Burkhart, B.M.; Wawrzak, Z.

2007-01-01

The crystal structure of a nonstoichiometric complex of gramicidin D (gD) with KI has been determined at 100 K using synchrotron radiation. The final R factor was 0.106 for 83 988 observed reflections (Friedel pairs were not merged) collected to 0.80 (angstrom). The structure consists of four independent pentadecapeptides and numerous solvent molecules and salt ions. The general architecture of the antiparallel double-stranded gramicidin dimers in the crystal (a right-handed antiparallel DSβH R form) closely resembles that of previously published cation complexes of gD. However, a significantly different mixture of gramicidin isomers is found in the crystal of the KI complex, including partial occupancy of phenylalanine at position 11. Only three sites in each of the two crystallographically independent channels are partially occupied by potassium cations instead of the commonly observed seven sites. The sum of the partial occupancies of K + (1.10 per two dimers) is consistent with the sum of the iodide occupancies (1.095 over eight sites), which is also confirmed by the anomalous signal of the iodide. There was a significant asymmetry of the distribution and occupancies of cations in the crystallographically independent gramicidin channels, in contrast to the distribution found in the rubidium chloride complex with gD.

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Directory of Open Access Journals (Sweden)

Jong-Yun Yoon

2015-09-01

Full Text Available Dynamic behaviors in practical driveline systems for wind turbines or vehicles are inherently affected by multiple nonlinearities such as piecewise-type torsional springs. However, various excitation conditions with different levels of magnitudes also show strong relationships to the dynamic behaviors when system responses are examined in both frequency and time domains. This study investigated the nonlinear responses of torsional systems under various excitations by using the harmonic balance method and numerical analysis. In order to understand the effect of piecewise-type nonlinearities on vibrational energy with different excitations, the nonlinear responses were investigated with various comparisons. First, two different jumping phenomena with frequency up- and down-sweeping conditions were determined under severe excitation levels. Second, practical system analysis using the phase plane and Poincaré map was conducted in various ways. When the system responses were composed of quasi-periodic components, Poincaré map analysis clearly revealed the nonlinear dynamic characteristics and thus it is suggested to investigate complicated nonlinear dynamic responses in practical driveline systems.

Radiation damage characterization in reactor pressure vessel steels with nonlinear ultrasound

International Nuclear Information System (INIS)

Matlack, K. H.; Kim, J.-Y.; Wall, J. J.; Qu, J.; Jacobs, L. J.

2014-01-01

Nuclear generation currently accounts for roughly 20% of the US baseload power generation. Yet, many US nuclear plants are entering their first period of life extension and older plants are currently undergoing assessment of technical basis to operate beyond 60 years. This means that critical components, such as the reactor pressure vessel (RPV), will be exposed to higher levels of radiation than they were originally intended to withstand. Radiation damage in reactor pressure vessel steels causes microstructural changes such as vacancy clusters, precipitates, dislocations, and interstitial loops that leave the material in an embrittled state. The development of a nondestructive evaluation technique to characterize the effect of radiation exposure on the properties of the RPV would allow estimation of the remaining integrity of the RPV with time. Recent research has shown that nonlinear ultrasound is sensitive to radiation damage. The physical effect monitored by nonlinear ultrasonic techniques is the generation of higher harmonic frequencies in an initially monochromatic ultrasonic wave, arising from the interaction of the ultrasonic wave with microstructural features such as dislocations, precipitates, and their combinations. Current findings relating the measured acoustic nonlinearity parameter to increasing levels of neutron fluence for different representative RPV materials are presented

Radiation damage characterization in reactor pressure vessel steels with nonlinear ultrasound

Science.gov (United States)

Matlack, K. H.; Kim, J.-Y.; Wall, J. J.; Qu, J.; Jacobs, L. J.

2014-02-01

Nuclear generation currently accounts for roughly 20% of the US baseload power generation. Yet, many US nuclear plants are entering their first period of life extension and older plants are currently undergoing assessment of technical basis to operate beyond 60 years. This means that critical components, such as the reactor pressure vessel (RPV), will be exposed to higher levels of radiation than they were originally intended to withstand. Radiation damage in reactor pressure vessel steels causes microstructural changes such as vacancy clusters, precipitates, dislocations, and interstitial loops that leave the material in an embrittled state. The development of a nondestructive evaluation technique to characterize the effect of radiation exposure on the properties of the RPV would allow estimation of the remaining integrity of the RPV with time. Recent research has shown that nonlinear ultrasound is sensitive to radiation damage. The physical effect monitored by nonlinear ultrasonic techniques is the generation of higher harmonic frequencies in an initially monochromatic ultrasonic wave, arising from the interaction of the ultrasonic wave with microstructural features such as dislocations, precipitates, and their combinations. Current findings relating the measured acoustic nonlinearity parameter to increasing levels of neutron fluence for different representative RPV materials are presented.

Limitations of two-level emitters as nonlinearities in two-photon controlled-PHASE gates

DEFF Research Database (Denmark)

Nysteen, Anders; McCutcheon, Dara P. S.; Heuck, Mikkel

2017-01-01

We investigate the origin of imperfections in the fidelity of a two-photon controlled-PHASE gate based on two-level-emitter nonlinearities. We focus on a passive system that operates without external modulations to enhance its performance. We demonstrate that the fidelity of the gate is limited...... by opposing requirements on the input pulse width for one-and two-photon-scattering events. For one-photon scattering, the spectral pulse width must be narrow compared with the emitter linewidth, while two-photon-scattering processes require the pulse width and emitter linewidth to be comparable. We find...

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.

Effects of structural nonlinearity and foundation sliding on probabilistic response of a nuclear structure

International Nuclear Information System (INIS)

Hashemi, Alidad; Elkhoraibi, Tarek; Ostadan, Farhang

2015-01-01

Highlights: • Probabilistic SSI analysis including structural nonlinearity and sliding are shown. • Analysis is done for a soil and a rock site and probabilistic demands are obtained. • Structural drift ratios and In-structure response spectra are evaluated. • Structural nonlinearity significantly impacts local demands in the structure. • Sliding generally reduces seismic demands and can be accommodated in design. - Abstract: This paper examines the effects of structural nonlinearity and foundation sliding on the results of probabilistic structural analysis of a typical nuclear structure where structural nonlinearity, foundation sliding and soil-structure interaction (SSI) are explicitly included. The evaluation is carried out for a soil and a rock site at 10"4, 10"5, and 10"6 year return periods (1E − 4, 1E − 5, and 1E − 6 hazard levels, respectively). The input motions at each considered hazard level are deaggregated into low frequency (LF) and high frequency (HF) motions and a sample size of 30 is used for uncertainty propagation. The statistical distribution of structural responses including story drifts, and in-structure response spectra (ISRS) as well as foundation sliding displacements are examined. The probabilistic implementation of explicit structural nonlinearity and foundation sliding in combination with the SSI effects are demonstrated using nonlinear response history analysis (RHA) of the structure with the foundation motions obtained from elastic SSI analyses, which are applied as input to fixed-base inelastic analyses. This approach quantifies the expected structural nonlinearity and sliding for the particular structural configuration and provides a robust analytical basis for the estimation of the probabilistic distribution of selected demands parameters both at the design level and beyond design level seismic input. For the subject structure, the inclusion of foundation sliding in the analysis is found to have reduced both

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.

Tectonic imprints upon inferences of eustatic sea level history: the Pliocene warm period and the Orangeburg Scarp

Science.gov (United States)

Chandan, D.; Peltier, W. R.

2013-12-01

The issue of tectonic contamination of geological inferences of relative sea level history is an important one. The issue arises on timescales that range from the 21-26 kyrs that have passed since the Last Glacial Maximum, to the most recent time when periods as warm as the present are expected to have existed, such as the mid-Pliocene. The coral based record from Barbados, for example, is known to be contaminated by continuing tectonic uplift of the island at a rate of approximately 0.34 mm/yr. For the Pliocene warm period at ~3 Myr, records from geological sites, such as the Orangeburg Scarp in North Carolina, have played a prominent role in arguments underpinning the design of the ongoing international PlioMIP program. In connection with the latter site, Rowley et al (2013) have recently argued that this record is contaminated by a tectonic imprint sufficiently strong to suggest that the usual inferences of Pliocene eustatic sea level based upon it (eg. Miller et al, 2012) must be seen as highly suspect. Here we employ a tomographically constrained model of the mantle convection process to revisit the issue of the tectonic imprint on relative sea level at the Orangeburg site, as well as other similar locations. Our analysis is based upon the inferred time dependence of dynamic topography forced by the mantle's internal density heterogeneities delivered by the S20RTS seismic tomography model. We begin by comparing the static, present day dynamic topography predicted by the (linear) internal loading theory based on the formalism of Pari and Peltier (2000) with that predicted using using a full three dimensional version of the nonlinear time-dependent mantle convection model of Shahnas and Peltier (2010, 2011). We demonstrate first that these two methodologies produce extremely similar results for the static field. We then proceed to run the nonlinear convection model in data assimilation mode while continuously nudging the internal density field back towards the

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

Science.gov (United States)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

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.

A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps

International Nuclear Information System (INIS)

Behnia, S.; Akhshani, A.; Ahadpour, S.; Mahmodi, H.; Akhavan, A.

2007-01-01

In recent years, a growing number of discrete chaotic cryptographic algorithms have been proposed. However, most of them encounter some problems such as the lack of robustness and security. In this Letter, we introduce a new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps. The system is a measurable dynamical system with an interesting property of being either ergodic or having stable period-one fixed point. They bifurcate from a stable single periodic state to chaotic one and vice versa without having usual period-doubling or period-n-tippling scenario. Also, we present the KS-entropy of this maps with respect to control parameter. This algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security

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 ...

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...

Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow

Science.gov (United States)

Tsvelodub, O. Yu; Bocharov, A. A.

2017-09-01

The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. The paper studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small Reynolds numbers the problem is reduced to the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. The periodic and soliton steady-state traveling solutions of this equation have been numerically found. The analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that this model equation has solutions in the form of solitons-humps.

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 Optical Fiber Arrays for Limiting Application

National Research Council Canada - National Science Library

Khoo, Iam-Choon

2006-01-01

.... Measurements show that they possess desirable nonlinear optical such as low-freezing pint, non-volatile, transparent for low light level and possess large effective nonlinear absorption coefficients...

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

A Busy period analysis of the level dependent PH/PH/1/K queue

NARCIS (Netherlands)

Al Hanbali, Ahmad

2011-01-01

In this paper, we study the transient behavior of a level dependent single server queuing system with a waiting room of finite size during the busy period. The focus is on the level dependent PH/PH/1/K queue. We derive in closed form the joint transform of the length of the busy period, the number

Identification of X-ray spectra in the Na-like to O-like rubidium ions in the range of 3.8-7.3 Angstroms

International Nuclear Information System (INIS)

Denis-Petit, D.; Bonnet, T.; Hannachi, F.; Gobet, F.; Tarisien, M.; Versteegen, M.; Comet, M.; Gosselin, G.; Meot, V.; Morel, P.; Pain, J.Ch.; Gilleron, F.; Frank, A.; Bagnoud, V.; Blazevic, A.; Dorchies, F.; Peyrusse, O.; Cayzac, W.; Roth, M.

2014-01-01

The X-rays emitted by a rubidium plasma source created by the PHELIX laser at an intensity of about 6*10"1"4 W/cm"2 were studied. The lines have been measured using Bragg crystals in the wavelength range between 3.8 and 7.3 Angstroms and identified by means of a numerical method developed to describe highly charged rubidium ions in LTE plasma. The experimental plasma temperature, density and charge state distributions have been estimated using non-LTE codes such as CHIVAS and AVERROES. The LTE plasma temperature and density used in the calculations are those allowing to reproduce the calculated NLTE charge state distribution. In order to optimize the use of computational resources, a criterion is established to select the configurations contributing most to the spectra among all those obtained in detailed level accounting based on the MCDF code. Seventy Rb-X-rays have been identified among which forty-nine are reported for the first time. The capabilities of our method are demonstrated by the good agreement of our identifications with previously published data when available. (authors)

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 ...

Generalized solutions of nonlinear partial differential equations

CERN Document Server

Rosinger, EE

1987-01-01

During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin

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.

Periodic and chaotic psychological stress variations as predicted by a social support buffered response model

Science.gov (United States)

Field, Richard J.; Gallas, Jason A. C.; Schuldberg, David

2017-08-01

Recent work has introduced social dynamic models of people's stress-related processes, some including amelioration of stress symptoms by support from others. The effects of support may be ;direct;, depending only on the level of support, or ;buffering;, depending on the product of the level of support and level of stress. We focus here on the nonlinear buffering term and use a model involving three variables (and 12 control parameters), including stress as perceived by the individual, physical and psychological symptoms, and currently active social support. This model is quantified by a set of three nonlinear differential equations governing its stationary-state stability, temporal evolution (sometimes oscillatory), and how each variable affects the others. Chaos may appear with periodic forcing of an environmental stress parameter. Here we explore this model carefully as the strength and amplitude of this forcing, and an important psychological parameter relating to self-kindling in the stress response, are varied. Three significant observations are made: 1. There exist many complex but orderly regions of periodicity and chaos, 2. there are nested regions of increasing number of peaks per cycle that may cascade to chaos, and 3. there are areas where more than one state, e.g., a period-2 oscillation and chaos, coexist for the same parameters; which one is reached depends on initial conditions.

Physics constrained nonlinear regression models for time series

International Nuclear Information System (INIS)

Majda, Andrew J; Harlim, John

2013-01-01

A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)

Nonlinear vibration and radiation from a panel with transition to chaos induced by acoustic waves

Science.gov (United States)

Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.

1992-01-01

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling) and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance, bifurcation is diffused and difficult to maintain, thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on aluminum panel and using a graphite epoxy panel having the same size and weight. Good agreement is obtained between the experimental and numerical results.

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.

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.

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.

Novel approach of wavelet analysis for nonlinear ultrasonic measurements and fatigue assessment of jet engine components

Science.gov (United States)

Bunget, Gheorghe; Tilmon, Brevin; Yee, Andrew; Stewart, Dylan; Rogers, James; Webster, Matthew; Farinholt, Kevin; Friedersdorf, Fritz; Pepi, Marc; Ghoshal, Anindya

2018-04-01

Widespread damage in aging aircraft is becoming an increasing concern as both civil and military fleet operators are extending the service lifetime of their aircraft. Metallic components undergoing variable cyclic loadings eventually fatigue and form dislocations as precursors to ultimate failure. In order to characterize the progression of fatigue damage precursors (DP), the acoustic nonlinearity parameter is measured as the primary indicator. However, using proven standard ultrasonic technology for nonlinear measurements presents limitations for settings outside of the laboratory environment. This paper presents an approach for ultrasonic inspection through automated immersion scanning of hot section engine components where mature ultrasonic technology is used during periodic inspections. Nonlinear ultrasonic measurements were analyzed using wavelet analysis to extract multiple harmonics from the received signals. Measurements indicated strong correlations of nonlinearity coefficients and levels of fatigue in aluminum and Ni-based superalloys. This novel wavelet cross-correlation (WCC) algorithm is a potential technique to scan for fatigue damage precursors and identify critical locations for remaining life prediction.

Nonlinearities in reservoir engineering: Enhancing quantum correlations

Science.gov (United States)

Hu, Xiangming; Hu, Qingping; Li, Lingchao; Huang, Chen; Rao, Shi

2017-12-01

There are two decisive factors for quantum correlations in reservoir engineering, but they are strongly reversely dependent on the atom-field nonlinearities. One is the squeezing parameter for the Bogoliubov modes-mediated collective interactions, while the other is the dissipative rates for the engineered collective dissipations. Exemplifying two-level atomic ensembles, we show that the moderate nonlinearities can compromise these two factors and thus enhance remarkably two-mode squeezing and entanglement of different spin atomic ensembles or different optical fields. This suggests that the moderate nonlinearities of the two-level systems are more advantageous for applications in quantum networks associated with reservoir engineering.

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)

Design and implementation plan for indirect-drive highly nonlinear ablative Rayleigh-Taylor instability experiments on the National Ignition Facility

International Nuclear Information System (INIS)

Casner, A.; Masse, L.; Delorme, B.; Jacquet, L.; Liberatore, S.; Smalyuk, V.; Martinez, D.; Seugling, R.; Park, H.S.; Remington, B.A.; Moore, A.; Igumenshev, I.; Chicanne, C.

2013-01-01

In the context of National Ignition Facility Basic Science program we propose to study on the NIF ablative Rayleigh-Taylor (RT) instability in transition from weakly nonlinear to highly nonlinear regimes. Based on the analogy between flame front and ablation front, highly nonlinear RT instability measurements at the ablation front can provide important insights into the initial deflagration stage of thermonuclear supernovae of type Ia. NIF provides a unique platform to study the rich physics of nonlinear and turbulent mixing flows in High Energy Density plasmas because it can accelerate targets over much larger distances and longer time periods than previously achieved on the NOVA and OMEGA lasers. In one shot, growth of RT modulations can be measured from the weakly nonlinear stage near nonlinear saturation levels to the highly nonlinear bubble-competition, bubble-merger regimes and perhaps into a turbulent-like regime. The role of ablation on highly-nonlinear RT instability evolution will be comprehensively studied by varying ablation velocity using indirect and direct-drive platforms. We present a detailed hydro-code design of the indirect-drive platform and discuss the implementation plan for these experiments which only use NIF diagnostics already qualified. (authors)

Essentials of nonlinear optics

CERN Document Server

Murti, Y V G S

2014-01-01

Current literature on Nonlinear Optics varies widely in terms of content, style, and coverage of specific topics, relative emphasis of areas and the depth of treatment. While most of these books are excellent resources for the researchers, there is a strong need for books appropriate for presenting the subject at the undergraduate or postgraduate levels in Universities. The need for such a book to serve as a textbook at the level of the bachelors and masters courses was felt by the authors while teaching courses on nonlinear optics to students of both science and engineering during the past two decades. This book has emerged from an attempt to address the requirement of presenting the subject at college level. A one-semester course covering the essentials can effectively be designed based on this.

Consideration of tidal influences in determining measurement periods when monitoring built-environment radon levels

International Nuclear Information System (INIS)

Crockett, R.G.M.; Phillips, P.S.; Gillmore, G.K.; Denman, A.R.; Groves-Kirkby, C.J.

2006-01-01

Using three hourly-sampling continuous radon monitors, deployed at separate locations in and around the town of Northampton, UK, during the period May 2002 to September 2005, evidence has been identified of tidal influences on built environment radon levels. The data-sets from these deployments, together with additional data-sets collected from a house in Devon, UK, over the period May 1994 to October 1996, and made available by the UK Building Research Establishment, have been analysed using a number of analytical techniques, including a novel correlation technique developed during the investigation. Radon concentration levels in all of the investigated sites exhibit cyclic variation with a period of approximately 14-15 days, equivalent to the spring-tide interval, and lag the corresponding new and full moons by varying periods. The tide/radon lag interval for the two public-sector buildings changes abruptly in September/October, indicating that a significant characteristic of these buildings changes at this time. For domestic properties, the lag is relatively unchanged during the year, but is greater in Devon, in the South-West of England, than in Northampton, in the English East Midlands. These differences are attributed to location relative to coastlines (the South-West experiences greater tidal-loading than the Midlands), underlying geology and rock/soil hydration. Depending on its position within the local 14 to 15-day tidally-induced radon cycle, an individual 7-day radon measurement may yield an erroneous estimate of longer term average levels, up to 46% higher or lower than the average level for one of the reported data-sets. Thus a building with a mean radon concentration below the local Action Level could appear to be unsafe if measured around a tidal-cyclic radon maximum: conversely, a building with a mean radon concentration above the Action Level could appear to be safe when measured around a tidal-cyclic radon minimum. A minimum radon

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

LDV measurement of small nonlinearities in flat and curved membranes. A model for eardrum nonlinear acoustic behaviour

Science.gov (United States)

Kilian, Gladiné; Pieter, Muyshondt; Joris, Dirckx

2016-06-01

Laser Doppler Vibrometry is an intrinsic highly linear measurement technique which makes it a great tool to measure extremely small nonlinearities in the vibration response of a system. Although the measurement technique is highly linear, other components in the experimental setup may introduce nonlinearities. An important source of artificially introduced nonlinearities is the speaker, which generates the stimulus. In this work, two correction methods to remove the effects of stimulus nonlinearity are investigated. Both correction methods were found to give similar results but have different pros and cons. The aim of this work is to investigate the importance of the conical shape of the eardrum as a source of nonlinearity in hearing. We present measurements on flat and indented membranes. The data shows that the curved membrane exhibit slightly higher levels of nonlinearity compared to the flat membrane.

Nonlinear acoustic waves in micro-inhomogeneous solids

CERN Document Server

Nazarov, Veniamin

2014-01-01

Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives. The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book. The subsequent eight chapters covering: Physical m

Time Variance of the Suspension Nonlinearity

DEFF Research Database (Denmark)

Agerkvist, Finn T.; Pedersen, Bo Rohde

2008-01-01

but recovers quickly. The the high power and long term measurements affect the non-linearity of the speaker, by incresing the compliance value for all values of displacement. This level dependency is validated with distortion measurements and it is demonstrated how improved accuracy of the non-linear model can...

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...

Channeling and radiation in periodically bent crystals

CERN Document Server

Korol, Andrey V; Greiner, Walter

2014-01-01

The development of coherent radiation sources for sub-angstrom wavelengths - i.e. in the hard X-ray and gamma-ray range -  is a challenging goal of modern physics. The availability of such sources will have many applications in basic science, technology and medicine, and, in particular, they may have a revolutionary impact on nuclear and solid state physics, as well as on the life sciences. The present state-of-the-art lasers are capable of emitting electromagnetic radiation from the infrared to the ultraviolet, while free electron lasers (X-FELs) are now entering the soft X-ray region. Moving further, i.e. into the hard X and/or gamma ray band, however, is not possible without new approaches and technologies.   In this book we introduce and discuss one such novel approach -the radiation formed in a Crystalline Undulator - whereby electromagnetic radiation is generated by a bunch of ultra-relativistic particles channeling through a periodically bent crystalline structure. Under certain conditions, such a d...

Nonlinear Growth Curves in Developmental Research

Science.gov (United States)

Grimm, Kevin J.; Ram, Nilam; Hamagami, Fumiaki

2011-01-01

Developmentalists are often interested in understanding change processes and growth models are the most common analytic tool for examining such processes. Nonlinear growth curves are especially valuable to developmentalists because the defining characteristics of the growth process such as initial levels, rates of change during growth spurts, and asymptotic levels can be estimated. A variety of growth models are described beginning with the linear growth model and moving to nonlinear models of varying complexity. A detailed discussion of nonlinear models is provided, highlighting the added insights into complex developmental processes associated with their use. A collection of growth models are fit to repeated measures of height from participants of the Berkeley Growth and Guidance Studies from early childhood through adulthood. PMID:21824131

A nonlinear plate control without linearization

Directory of Open Access Journals (Sweden)

Yildirim Kenan

2017-03-01

Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

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.

Retrieval of high-order susceptibilities of nonlinear metamaterials

International Nuclear Information System (INIS)

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

2017-01-01

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

Nonlinear NDT: A Route to Conventional Ultrasonic Testing

OpenAIRE

Igor Solodov

2016-01-01

The bottleneck problem of nonlinear NDT is a low efficiency of conversion from fundamental frequency to nonlinear frequency components. In this paper, it is proposed to use a combination of nonlinearity with Local Defect Resonance (LDR) to enhance substantially the input-output conversion. Since LDR is an efficient resonance “amplifier” of the local vibrations, it manifests a profound nonlinearity even at moderate ultrasonic excitation level. As the driving frequency matches the LDR-frequency...

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

International Nuclear Information System (INIS)

Klein, A.; Krejs, F.

1976-01-01

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

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'.

Crossing rule for a PT-symmetric two-level time-periodic system

International Nuclear Information System (INIS)

Moiseyev, Nimrod

2011-01-01

For a two-level system in a time-periodic field we show that in the non-Hermitian PT case the level crossing is of two quasistationary states that have the same dynamical symmetry property. At the field's parameters where the two levels which have the same dynamical symmetry cross, the corresponding quasienergy states coalesce and a self-orthogonal state is obtained. This situation is very different from the Hermitian case where a crossing of two quasienergy levels happens only when the corresponding two quasistationary states have different dynamical symmetry properties and, unlike the situation in the non-Hermitian case, the spectrum remains complete also when the two levels cross.

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

Hydrazine levels in formulations of hydralazine, isoniazid, and phenelzine over a 2-year period.

Science.gov (United States)

Lovering, E G; Matsui, F; Curran, N M; Robertson, D L; Sears, R W

1983-08-01

Hydrazine levels in formulations of hydralazine, isoniazid, and phenelzine have been measured over a 2-year period under ambient conditions and under temperature and humidity stress. Hydralazine tablets are stable under ambient conditions, but the hydrazine level in an injectable formulation increased from 4.5 to 10 micrograms/ml over a 23-month period. Isoniazid tablets are also stable, but hydrazine levels in an elixir and a pyridoxine combination product doubled to 44 micrograms/ml and 19 micrograms/tablet, respectively. Levels in phenelzine tablets appeared to remain constant at approximately 60 micrograms/tablet, with considerable tablet-to-tablet variation.

Variability of aerosol optical depth and Angstrom wavelength exponent derived from AERONET observations in recent decades

International Nuclear Information System (INIS)

Xia Xiangao

2011-01-01

Using aerosol loading data from 79 Aerosol Robotic Network (AERONET) stations with observations from more than six years, changes in aerosol optical depth (AOD) and Angstrom wavelength exponent (AWE) were studied. A statistical method was developed to determine whether AOD changes were due to increased background AOD values and/or an increased number of high AOD events. AOD decreased significantly at AERONET sites in northeastern North American and in Western Europe, which was accompanied by decreased AWE. Reduction of AOD there was mainly due to a decreased frequency of high AOD events and an increased frequency of background AOD events. In addition, decreased AOD values for high AOD events also accounted for ∼ 16–32% of the AOD reduction. This is indicative of significant meteorological effects on AOD variability. AOD trends in other regions were marginal and most were not significant; however, AOD increased significantly at one site in the Sahel and another in Saudi Arabia, predominantly due to the increased frequency of high AOD events and their average AOD.

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.

Implementation of the - Constraint Method in Special Class of Multi-objective Fuzzy Bi-Level Nonlinear Problems

Directory of Open Access Journals (Sweden)

Azza Hassan Amer

2017-12-01

Full Text Available Geometric programming problem is a powerful tool for solving some special type nonlinear programming problems. In the last few years we have seen a very rapid development on solving multiobjective geometric programming problem. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper, -constraint method has been applied in bi-level multiobjective geometric programming problem to find the Pareto optimal solution at each level. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem at eash level. Here, we have developed a new algorithm for fuzzy programming technique to solve bi-level multiobjective geometric programming problems to find an optimal compromise solution. Finally the solution procedure of the fuzzy technique is illustrated by a numerical example

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.

Nonlinear theory of collisionless trapped ion modes

International Nuclear Information System (INIS)

Hahm, T.S.; Tang, W.M.

1996-01-01

A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level δn/n 0 is lower than the conventional mixing length estimate, Δr/L n (ii) the ion temperature fluctuation level δT i /T i significantly exceeds the density fluctuation level δn/n 0 ; and (iii) the parallel ion velocity fluctuation level δv iparallel /v Ti is expected to be negligible

Nonlinear soil-structure interaction due to base slab uplift on the seismic response of an HTGR plant

International Nuclear Information System (INIS)

Kennedy, R.P.; Short, S.A.; Wesley, D.A.; Lee, T.H.

1975-01-01

The importance of the nonlinear soil-structure interaction effects resulting from substantial base slab uplift occurring during a seismic excitation are evaluated. The structure considered consisted of the containment building and prestressed concrete reactor vessel for a typical HTGR plant. A simplified dynamic mathematical model was utilized consisting of a conventional lumped mass structure with soil-structure interaction accounted for by translational and rotational springs whose properties are determined by elastic half space theory. Three different site soil conditions (a rock site, a moderately stiff soil and a soft soil site) and two levels of horizontal ground motion (0.3g and 0.5g earthquakes) were considered. It may be concluded that linear analysis can be used to conservatively estimate the important behavior of the base slab, even under conditions of substantial base slab uplift. For all cases investigated, linear analysis resulted in higher base overturning moments, greater toe pressures, and greater heel uplift distances than nonlinear analyses. It may also be concluded that the nonlinear effect of uplift does not result in any significant lengthening of the fundamental period of the structure. Also, except in the short period region only negligible differences exist between instructure response spectra based on linear analysis and those based on nonlinear analysis. Finally, for sites in which soil-structure interaction is not significant, as for the rock site, the peak structural response at all locations above the base mat are not significantly influenced by the nonlinear effects of base slab uplift. However, for the two soil sites, the peak shears and moments are, in a few instances, significantly different between linear and nonlinear analyses

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

Backward Response-Level Crosstalk in the Psychological Refractory Period Paradigm

Science.gov (United States)

Miller, Jeff; Alderton, Mark

2006-01-01

Bottleneck models of psychological refractory period (PRP) tasks suggest that a Task 1 response should be unaffected by the Task 2 response in the same trial, because selection of the former finishes before selection of the latter begins. Contrary to this conception, the authors found backward response-level crosstalk effects in which Task 2…

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)

Non-linear Loudspeaker Unit Modelling

DEFF Research Database (Denmark)

Pedersen, Bo Rohde; Agerkvist, Finn T.

2008-01-01

Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of thr...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....

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...

Broadband Nonlinear Signal Processing in Silicon Nanowires

DEFF Research Database (Denmark)

Yvind, Kresten; Pu, Minhao; Hvam, Jørn Märcher

The fast non-linearity of silicon allows Tbit/s optical signal processing. By choosing suitable dimensions of silicon nanowires their dispersion can be tailored to ensure a high nonlinearity at power levels low enough to avoid significant two-photon abso We have fabricated low insertion...

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

Nonlinear structural mechanics theory, dynamical phenomena and modeling

CERN Document Server

Lacarbonara, Walter

2013-01-01

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

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.

Coherent Femtosecond Spectroscopy and Nonlinear Optical Imaging on the Nanoscale

Science.gov (United States)

Kravtsov, Vasily

Optical properties of many materials and macroscopic systems are defined by ultrafast dynamics of electronic, vibrational, and spin excitations localized on the nanoscale. Harnessing these excitations for material engineering, optical computing, and control of chemical reactions has been a long-standing goal in science and technology. However, it is challenging due to the lack of spectroscopic techniques that can resolve processes simultaneously on the nanometer spatial and femtosecond temporal scales. This thesis describes the fundamental principles, implementation, and experimental demonstration of a novel type of ultrafast microscopy based on the concept of adiabatic plasmonic nanofocusing. Simultaneous spatio-temporal resolution on a nanometer-femtosecond scale is achieved by using a near-field nonlinear optical response induced by ultrafast surface plasmon polaritons nanofocused on a metal tip. First, we study the surface plasmon response in metallic structures and evaluate its prospects and limitations for ultrafast near-field microscopy. Through plasmon emission-based spectroscopy, we investigate dephasing times and interplay between radiative and non-radiative decay rates of localized plasmons and their modification due to coupling. We identify a new regime of quantum plasmonic coupling, which limits the achievable spatial resolution to several angstroms but at the same time provides a potential channel for generating ultrafast electron currents at optical frequencies. Next, we study propagation of femtosecond wavepackets of surface plasmon polaritons on a metal tip. In time-domain interferometric measurements we detect group delays that correspond to slowing of the plasmon polaritons down to 20% of the speed of light at the tip apex. This provides direct experimental verification of the plasmonic nanofocusing mechanism and suggests enhanced nonlinear optical interactions at the tip apex. We then measure a plasmon-generated third-order nonlinear optical

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...

The Non-Linear Effect of Corporate Taxes on Economic Growth

Directory of Open Access Journals (Sweden)

Huňady Ján

2015-03-01

Full Text Available The paper deals with the problem of taxation and its potential impact on economic growth and presents some new empirical insights into this topic. The main aim of the paper is to verify an assumed nonlinear impact of corporate tax rates on economic growth. Based on the theory of public finance and taxation, we hypothesize that at relatively low tax rates it is possible that the impact of taxation on economic growth become slightly positive. On the other hand when the tax rates are higher a negative impact of taxation on economic growth could be expected. Despite the fact that the most of the existing studies find a negative linear relationship between these variables, we can also find strong support for a non-linear relationship from several theoretical models as well as some empirical studies. Based on panel data fixed-effects econometric models, we, as well, find empirical evidence for a non-linear relationship between nominal and effective corporate tax rates and economic growth. Our data consists of annual observations for the period 1999 to 2011 for EU Member States. Based on the results, we also estimated the optimal level of the corporate tax rate in terms of maximizing economic growth in the average of the EU countries.

Hydrophone area-averaging correction factors in nonlinearly generated ultrasonic beams

International Nuclear Information System (INIS)

Cooling, M P; Humphrey, V F; Wilkens, V

2011-01-01

The nonlinear propagation of an ultrasonic wave can be used to produce a wavefield rich in higher frequency components that is ideally suited to the calibration, or inter-calibration, of hydrophones. These techniques usually use a tone-burst signal, limiting the measurements to harmonics of the fundamental calibration frequency. Alternatively, using a short pulse enables calibration at a continuous spectrum of frequencies. Such a technique is used at PTB in conjunction with an optical measurement technique to calibrate devices. Experimental findings indicate that the area-averaging correction factor for a hydrophone in such a field demonstrates a complex behaviour, most notably varying periodically between frequencies that are harmonics of the centre frequency of the original pulse and frequencies that lie midway between these harmonics. The beam characteristics of such nonlinearly generated fields have been investigated using a finite difference solution to the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a focused field. The simulation results are used to calculate the hydrophone area-averaging correction factors for 0.2 mm and 0.5 mm devices. The results clearly demonstrate a number of significant features observed in the experimental investigations, including the variation with frequency, drive level and hydrophone element size. An explanation for these effects is also proposed.

Hydrophone area-averaging correction factors in nonlinearly generated ultrasonic beams

Science.gov (United States)

Cooling, M. P.; Humphrey, V. F.; Wilkens, V.

2011-02-01

The nonlinear propagation of an ultrasonic wave can be used to produce a wavefield rich in higher frequency components that is ideally suited to the calibration, or inter-calibration, of hydrophones. These techniques usually use a tone-burst signal, limiting the measurements to harmonics of the fundamental calibration frequency. Alternatively, using a short pulse enables calibration at a continuous spectrum of frequencies. Such a technique is used at PTB in conjunction with an optical measurement technique to calibrate devices. Experimental findings indicate that the area-averaging correction factor for a hydrophone in such a field demonstrates a complex behaviour, most notably varying periodically between frequencies that are harmonics of the centre frequency of the original pulse and frequencies that lie midway between these harmonics. The beam characteristics of such nonlinearly generated fields have been investigated using a finite difference solution to the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a focused field. The simulation results are used to calculate the hydrophone area-averaging correction factors for 0.2 mm and 0.5 mm devices. The results clearly demonstrate a number of significant features observed in the experimental investigations, including the variation with frequency, drive level and hydrophone element size. An explanation for these effects is also proposed.

Level of males participation during perinatal period in rural areas of district layyah

International Nuclear Information System (INIS)

Ishtiaq, M.; Khalid, R.

2016-01-01

Background: Although pregnancy is not a disease but life partner and other family members must realize distress and fatigue caused by the pregnancy to pregnant women. Husbands play a very important role in ensuring healthy pregnancy outcomes. Males are mainly responsible in taking decision regarding health seeking of pregnant women in rural areas of Pakistan. This study aimed to explore the level of males participation during perinatal period and to assess their knowledge about danger signs of perinatal period in rural areas of District Layyah, South Punjab. Methods: A community based cross sectional study on pregnant women and their husbands was undertaken in one union council (UC) of district Layyah. 369 couples were selected using proportionate simple random sampling technique. Three hundred and thirty-five agreed and filled the complete questionnaire. Couples having pregnancy or delivery during last one year were included in the study. Women who were divorced, separated or living away from their spouses were excluded. Structured interviewer administered questionnaire adopted from a Nigerian study was translated into Urdu and used to collect data via home visiting. Ethical approval was taken from IRB and written informed consent from the participants. Data was entered and analysed in SPSS V.16. Results: Males level of participation in domestic chores was 326 out of 335 (97.31) and their overall level of knowledge regarding danger signs of pregnancy was 135 out of 335 (40.30 percentage).Economic status (Chi square 6.23, p-value 0.045) and husband educated more than wife (Chi square 10.20, p-value 0.006) were significantly associated with level of knowledge regarding danger signs of pregnancy. Whereas, parity was (Fisher exact test 8.07, p-value 0.017) significantly associated with level of males participation in domestic chores. Conclusion: Husbands have high level of participation in domestic chores but moderate level of knowledge regarding danger signs of

Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks

Science.gov (United States)

Sebastian, Resmi; Sitharam, T. G.

2018-01-01

Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.

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.

Nonlinear optics principles and applications

CERN Document Server

Li, Chunfei

2017-01-01

This book reflects the latest advances in nonlinear optics. Besides the simple, strict mathematical deduction, it also discusses the experimental verification and possible future applications, such as the all-optical switches. It consistently uses the practical unit system throughout. It employs simple physical images, such as "light waves" and "photons" to systematically explain the main principles of nonlinear optical effects. It uses the first-order nonlinear wave equation in frequency domain under the condition of “slowly varying amplitude approximation" and the classical model of the interaction between the light and electric dipole. At the same time, it also uses the rate equations based on the energy-level transition of particle systems excited by photons and the energy and momentum conservation principles to explain the nonlinear optical phenomenon. The book is intended for researchers, engineers and graduate students in the field of the optics, optoelectronics, fiber communication, information tech...

Nonlinear optics an analytical approach

CERN Document Server

Mandel, Paul

2010-01-01

Based on the author's extensive teaching experience and lecture notes, this textbook provides a substantially analytical rather than descriptive presentation of nonlinear optics. Divided into five parts, with most chapters corresponding to a two-hour lecture, the book begins with a unique account of the historical development from Kirchhoff's law for the black-body radiation to Planck's quantum hypothesis and Einstein's discovery of spontaneous emission - providing all the explicit proofs. The subsequent sections deal with matter quantization, ultrashort pulse propagation in 2-level media, cavity nonlinear optics, chi(2) and chi(3) media. For graduate and PhD students in nonlinear optics or photonics, while also representing a valuable reference for researchers in these fields.

Transition to instability in a periodically kicked Bose-Einstein condensate on a ring

International Nuclear Information System (INIS)

Liu Jie; Zhang Chuanwei; Raizen, Mark G.; Niu Qian

2006-01-01

A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor, where the nonlinearity stems from the mean-field interactions between the condensed atoms. For weak interactions, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. In the stable regime, the system remains predominantly in the two lowest energy states and may be mapped onto a spin model, from which we obtain an analytic expression for the beat frequency and discuss the route to instability. We numerically explore a parameter regime for the occurrence of instability and reveal the characteristic density profile for both condensed and noncondensed atoms. The Arnold diffusion to higher energy levels is found to be responsible for the transition to instability. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions

Theory of coherent Stark nonlinear spectroscopy in a three-level system

International Nuclear Information System (INIS)

Loiko, Yurii; Serrat, Carles

2007-01-01

Coherent Stark nonlinear spectroscopy (CSNS) is a spectroscopic tool based on the cancellation of the phase sensitivity at frequency 5ω in the ultrafast four-wave mixing (FWM) of two-color pulses with frequencies ω and 3ω. We develop a theory for CSNS in three-level V-type systems, and reveal that the mechanism for the phase sensitivity at 5ω is the quantum interference between the two primary paths in the FWM of the ω and 3ω fields. We find that the cancellation phenomenon occurs when the probability amplitude of one of these two primary pathways becomes equal to zero due to the competition effect between the two allowed transitions in the V-type system. The analytical expressions that describe the phase-sensitivity phenomenon and the conditions for its cancellation have been derived on the basis of perturbation theory, and are confirmed by numerical integration of the density matrix and Maxwell equations. We argue that CSNS can be utilized, in particular, for the investigation of optically dense media

Flexibility of the myosin heavy chain: direct evidence that the region containing SH/sub 1/ and SH/sub 2/ can move 10 /Angstrom/ under the influence of nucleotide binding

Energy Technology Data Exchange (ETDEWEB)

Huston, E.E.; Grammer, J.C.; Yount, R.G.

1988-12-13

Previous experiments demonstrated that two thiols of skeletal myosin subfragment 1 (SF/sub 1/) could be oxidized to a disulfide bond by treatment with a 2-fold excess of 5,5'-dithiobis (2-nitrobenzoic acid) (DTNB) in the presence of MgADP. The resulting characteristic changes in the ATPase activities of SF/sub 1/ and the fact that MgADP was stably trapped at the active site, suggested that the two thiols cross-linked were SH/sub 1/ (Cys-707) and SH/sub 2/ (Cys-697) from the myosin heavy chain. To verify this suggestion, SF/sub 1/, after DTNB treatment as above, was treated with an excess of N-ethylmaleimide to block all accessible thiols. The single protein disulfide produced by DTNB oxidation was reduced with dithioerythritol and the modified SF/sub 1/ internally cross-linked with equimolar (/sup 14/C)p-phenylenedimaleimide (pPDM) in the presence of MgADP. After extensive trypsinization, the major /sup 14/C-labeled peptide was isolated, characterized, and shown to be Cys-Asn-Gly-Val-Leu-Gly-Ile-Arg-Ile-Cys-Arg, in which the two cysteines were cross-linked by pPDM. This peptide is known to contain SH/sub 2/ and SH/sub 1/ in this order and to come from residues 697-708 in the rabbit skeletal myosin heavy chain. Parallel experiments with (/sup 14/C)pPDM and unmodified SF/sub 1/ similar to those above gave an identical SH/sub 1/, SH/sub 2/ tryptic peptide, verifying earlier labeling results. These combined results demonstrate that SH/sub 1/ and SH/sub 2/ cross-linked by pPDM (12-13 /Angstrom/, S to S) or by oxidation with DTNB (2 /Angstrom/, S to S) can move a minimum of 10 /Angstrom/ under the influence of nucleotide binding. Because these residues are separated by only nine amino acids in the primary sequence, this small section of the heavy chain must possess extraordinary flexibility.

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.

A Mesoscale Analysis of Column-Integrated Aerosol Properties in Northern India During the TIGERZ 2008 Pre-Monsoon Period and a Comparison to MODIS Retrievals

Science.gov (United States)

Giles, D. M.; Holben, B. N.; Tripathi, S. N.; Eck, T. F.; Newcomb, W. W.; Slutsker, I.; Dickerson, R. R.; Thompson, A. M.; Wang, S.-H.; Singh, R. P.;

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.

Age, period and cohort effects on adult physical activity levels from 1991 to 2011 in China.

Science.gov (United States)

Zang, Jiajie; Ng, Shu Wen

2016-04-20

To date no work has differentiated the effects of age, period, and cohort on physical activity (PA) among Chinese adults, while also considering biological, behavioral, economic, and environmental factors over time. We used data from the China Health and Nutrition Survey (CHNS) between 1991 and 2011 (20 years). The outcomes of interest are metabolic equivalent of task (MET) hours per week from work and domestic activities. Age, individual characteristics, household size, asset ownership, urbanization were included as covariates. Analyses for adult (≥20y) males (n = 29,343) and females (n = 31,094) was conducted to explicitly assess differences in PA due to age vs period effects, and implicitly assess differences by cohorts due to the period-specific experiences across individuals of varying ages. The mean age of the sample rose from 41.31 to 50.8 years and PA decreased from 427.75 ± 264.35 MET hours per week (MET-hr/wk) in 1991 to 245.99 ± 206.65 MET-hr/wk in 2011, with much steeper declines for women compared to men. For both genders, we found non-linear decreases in PA with age over time. Controlling for age effects, negative period effects on PA were observed in each survey year, and were substantial from 1993 to 2000 for males and from 1993 to 2011 for females. The interaction between survey year and age (P < 0.05) were observed from 2004 to 2011. Higher community urbanicity, vehicle ownership, TV and computer ownership, overweight and obese, higher education served as negative predictors. Bicycle ownership, bigger household size, non-professional jobs, being married and having more children (for women) were positive predictors of PA (P < 0.05). Furthermore, at any given age, individuals who were younger at baseline had higher mean PA compared with individuals older at baseline. This study followed a large cohort of adults over a significant portion of their lives. Strong age and secular trends were observed, resulting in an

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.

Nonlinear and quantum optics near nanoparticles

Science.gov (United States)

Dhayal, Suman

We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. We have also studied the modifications of the electromagnetic fields in a collection of nanoparticles due to strong near field nonlinear interactions using the generalized Mie theory for the case of many particles applicable in photovoltaics (PV). We also consider quantum coherence phenomena such as modification of dark states, stimulated Raman adiabatic passage (STIRAP), optical pumping in 4-level atoms near nanoparticles by using rotating wave approximation to describe the Hamiltonian of the atomic system. We also considered the behavior of atomic and the averaged atomic polarization in 7-level atoms near nanoparticles. This could be used as a prototype to study

Multi-level approach for parametric roll analysis

Science.gov (United States)

Kim, Taeyoung; Kim, Yonghwan

2011-03-01

The present study considers multi-level approach for the analysis of parametric roll phenomena. Three kinds of computation method, GM variation, impulse response function (IRF), and Rankine panel method, are applied for the multi-level approach. IRF and Rankine panel method are based on the weakly nonlinear formulation which includes nonlinear Froude- Krylov and restoring forces. In the computation result of parametric roll occurrence test in regular waves, IRF and Rankine panel method show similar tendency. Although the GM variation approach predicts the occurrence of parametric roll at twice roll natural frequency, its frequency criteria shows a little difference. Nonlinear roll motion in bichromatic wave is also considered in this study. To prove the unstable roll motion in bichromatic waves, theoretical and numerical approaches are applied. The occurrence of parametric roll is theoretically examined by introducing the quasi-periodic Mathieu equation. Instability criteria are well predicted from stability analysis in theoretical approach. From the Fourier analysis, it has been verified that difference-frequency effects create the unstable roll motion. The occurrence of unstable roll motion in bichromatic wave is also observed in the experiment.

Atomic energy-level and Grotrian diagrams. Vol. 4

International Nuclear Information System (INIS)

Bashkin, S.; Stoner, J.O. Jr.

1982-01-01

This is the fifth in a series of volumes that present diagrammatically the spectra of atoms and monatomic ions. All observed transitions and all known levels of manganese are included. All wavelengths are given in angstroms in vacuum below 2000 A, in air above 2000 A. Energies of levels are specified in wavenumbers (cm -1 ), kcm -1 (1 X 10 3 cm -1 ), or Mcm -1 (1 X 10 6 cm -1 ). For energies, all experimentally significant figures are included; for wavelengths, we usually include two decimal places (three for the shortest wavelengths). Descriptions of levels are based in most cases upon the largest percentage contributions of elementary coupling arrangements to the levels. In a few instances several different descriptions of the same levels are presented. (Auth.)

Tide-surge historical assessment of extreme water levels for the St. Johns River: 1928-2017

Science.gov (United States)

Bacopoulos, Peter

2017-10-01

An historical storm population is developed for the St. Johns River, located in northeast Florida-US east coast, via extreme value assessment of an 89-year-long record of hourly water-level data. Storm surge extrema and the corresponding (independent) storm systems are extracted from the historical record as well as the linear and nonlinear trends of mean sea level. Peaks-over-threshold analysis reveals the top 16 most-impactful (storm surge) systems in the general return-period range of 1-100 years. Hurricane Matthew (2016) broke the record with a new absolute maximum water level of 1.56 m, although the peak surge occurred during slack tide level (0.00 m). Hurricanes and tropical systems contribute to return periods of 10-100 years with water levels in the approximate range of 1.3-1.55 m. Extratropical systems and nor'easters contribute to the historical storm population (in the general return-period range of 1-10 years) and are capable of producing extreme storm surges (in the approximate range of 1.15-1.3 m) on par with those generated by hurricanes and tropical systems. The highest astronomical tide is 1.02 m, which by evaluation of the historical record can contribute as much as 94% to the total storm-tide water level. Statically, a hypothetical scenario of Hurricane Matthew's peak surge coinciding with the highest astronomical tide would yield an overall storm-tide water level of 2.58 m, corresponding to an approximate 1000-year return period by historical comparison. Sea-level trends (linear and nonlinear) impact water-level return periods and constitute additional risk hazard for coastal engineering designs.

Does more energy consumption bolster economic growth? An application of the nonlinear threshold regression model

International Nuclear Information System (INIS)

Huang, B.-N.; Hwang, M.J.; Yang, C.W.

2008-01-01

This paper separates data extending from 1971 to 2002 into the energy crisis period (1971-1980) and the post-energy crisis period (1981-2000) for 82 countries. The cross-sectional data (yearly averages) in these two periods are used to investigate the nonlinear relationships between energy consumption growth and economic growth when threshold variables are used. If threshold variables are higher than certain optimal threshold levels, there is either no significant relationship or else a significant negative relationship between energy consumption and economic growth. However, when these threshold variables are lower than certain optimal levels, there is a significant positive relationship between the two. In 48 out of the 82 countries studied, none of the four threshold variables is found to be higher than the optimal levels. It is inferred that these 48 countries should adopt a more aggressive energy policy. As for the other 34 countries, at least one threshold variable is higher than the optimal threshold level and thus these countries should adopt energy policies with varying degrees of conservation based on the number of threshold variables that are higher than the optimal threshold levels

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

Extreme Nonlinear Optics An Introduction

CERN Document Server

Wegener, Martin

2005-01-01

Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged. Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself. This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The followi...

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.

Site-level progression of periodontal disease during a follow-up period

Science.gov (United States)

Morozumi, Toshiya; Nakagawa, Taneaki; Sugaya, Tsutomu; Kawanami, Masamitsu; Suzuki, Fumihiko; Takahashi, Keiso; Abe, Yuzo; Sato, Soh; Makino-Oi, Asako; Saito, Atsushi; Takano, Satomi; Minabe, Masato; Nakayama, Yohei; Ogata, Yorimasa; Kobayashi, Hiroaki; Izumi, Yuichi; Sugano, Naoyuki; Ito, Koichi; Sekino, Satoshi; Numabe, Yukihiro; Fukaya, Chie; Yoshinari, Nobuo; Fukuda, Mitsuo; Noguchi, Toshihide; Kono, Tomoo; Umeda, Makoto; Fujise, Osamu; Nishimura, Fusanori; Yoshimura, Atsutoshi; Hara, Yoshitaka; Nakamura, Toshiaki; Noguchi, Kazuyuki; Kakuta, Erika; Hanada, Nobuhiro; Takashiba, Shogo; Amitani, Yasuharu; Yoshie, Hiromasa

2017-01-01

Periodontal disease is assessed and its progression is determined via observations on a site-by-site basis. Periodontal data are complex and structured in multiple levels; thus, applying a summary statistical approach (i.e., the mean) for site-level evaluations results in loss of information. Previous studies have shown the availability of mixed effects modeling. However, clinically beneficial information on the progression of periodontal disease during the follow-up period is not available. We conducted a multicenter prospective cohort study. Using mixed effects modeling, we analyzed 18,834 sites distributed on 3,139 teeth in 124 patients, and data were collected 5 times over a 24-month follow-up period. The change in the clinical attachment level (CAL) was used as the outcome variable. The CAL at baseline was an important determinant of the CAL changes, which varied widely according to the tooth surface. The salivary levels of periodontal pathogens, such as Porphyromonas gingivalis and Aggregatibacter actinomycetemcomitans, were affected by CAL progression. “Linear”- and “burst”-type patterns of CAL progression occurred simultaneously within the same patient. More than half of the teeth that presented burst-type progression sites also presented linear-type progression sites, and most of the progressions were of the linear type. Maxillary premolars and anterior teeth tended to show burst-type progression. The parameters identified in this study may guide practitioners in determining the type and extent of treatment needed at the site and patient levels. In addition, these results show that prior hypotheses concerning "burst" and "linear" theories are not valid. PMID:29206238

Nonlinear Pricing in Energy and Environmental Markets

Science.gov (United States)

Ito, Koichiro

This dissertation consists of three empirical studies on nonlinear pricing in energy and environmental markets. The first investigates how consumers respond to multi-tier nonlinear price schedules for residential electricity. Chapter 2 asks a similar research question for residential water pricing. Finally, I examine the effect of nonlinear financial rewards for energy conservation by applying a regression discontinuity design to a large-scale electricity rebate program that was implemented in California. Economic theory generally assumes that consumers respond to marginal prices when making economic decisions, but this assumption may not hold for complex price schedules. The chapter "Do Consumers Respond to Marginal or Average Price? Evidence from Nonlinear Electricity Pricing" provides empirical evidence that consumers respond to average price rather than marginal price when faced with nonlinear electricity price schedules. Nonlinear price schedules, such as progressive income tax rates and multi-tier electricity prices, complicate economic decisions by creating multiple marginal prices for the same good. Evidence from laboratory experiments suggests that consumers facing such price schedules may respond to average price as a heuristic. I empirically test this prediction using field data by exploiting price variation across a spatial discontinuity in electric utility service areas. The territory border of two electric utilities lies within several city boundaries in southern California. As a result, nearly identical households experience substantially different nonlinear electricity price schedules. Using monthly household-level panel data from 1999 to 2008, I find strong evidence that consumers respond to average price rather than marginal or expected marginal price. I show that even though this sub-optimizing behavior has a minimal impact on individual welfare, it can critically alter the policy implications of nonlinear pricing. The second chapter " How Do

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

Analytical approximations for the amplitude and period of a relaxation oscillator

Directory of Open Access Journals (Sweden)

Golkhou Vahid

2009-01-01

Full Text Available Abstract Background Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters. Results We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10× less sensitive to protein decay rates, efficiency (2× more efficient, and dynamic range (30 to 60 decibel increase. The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level. Conclusion Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits.

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...

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.

Non-reciprocity in nonlinear elastodynamics

Science.gov (United States)

Blanchard, Antoine; Sapsis, Themistoklis P.; Vakakis, Alexander F.

2018-01-01

Reciprocity is a fundamental property of linear time-invariant (LTI) acoustic waveguides governed by self-adjoint operators with symmetric Green's functions. The break of reciprocity in LTI elastodynamics is only possible through the break of time reversal symmetry on the micro-level, and this can be achieved by imposing external biases, adding nonlinearities or allowing for time-varying system properties. We present a Volterra-series based asymptotic analysis for studying spatial non-reciprocity in a class of one-dimensional (1D), time-invariant elastic systems with weak stiffness nonlinearities. We show that nonlinearity is neither necessary nor sufficient for breaking reciprocity in this class of systems; rather, it depends on the boundary conditions, the symmetries of the governing linear and nonlinear operators, and the choice of the spatial points where the non-reciprocity criterion is tested. Extension of the analysis to higher dimensions and time-varying systems is straightforward from a mathematical point of view (but not in terms of new non-reciprocal physical phenomena), whereas the connection of non-reciprocity and time irreversibility can be studied as well. Finally, we show that suitably defined non-reciprocity measures enable optimization, and can provide physical understanding of the nonlinear effects in the dynamics, enabling one to establish regimes of "maximum nonlinearity." We highlight the theoretical developments by means of a numerical example.

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)

A structural investigation of complex I and I+III2 supercomplex from Zea mays at 11-13 angstrom resolution : Assignment of the carbonic anhydrase domain and evidence for structural heterogeneity within complex I

NARCIS (Netherlands)

Peters, Katrin; Dudkina, Natalya V.; Jaensch, Lothar; Braun, Hans-Peter; Boekema, Egbert J.; Jänsch, Lothar

The projection structures of complex I and the I+III2 supercomplex from the C-4 plant Zea mays were determined by electron microscopy and single particle image analysis to a resolution of up to 11 angstrom. Maize complex I has a typical L-shape. Additionally, it has a large hydrophilic, extra-domain

Teaching nonlinear dynamics through elastic cords

International Nuclear Information System (INIS)

Chacon, R; Galan, C A; Sanchez-Bajo, F

2011-01-01

We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.

Origin of the low-level EMG during the silent period following transcranial magnetic stimulation

DEFF Research Database (Denmark)

Butler, Jane E; Petersen, Nicolas C; Herbert, Robert D

2012-01-01

OBJECTIVE: The cortical silent period refers to a period of near silence in the electromyogram (EMG) after transcranial magnetic stimulation (TMS) of the motor cortex during contraction. However, low-level EMG of unknown origin is often present. We hypothesised that it arises through spinal...

Describing pediatric dysphonia with nonlinear dynamic parameters

Science.gov (United States)

Meredith, Morgan L.; Theis, Shannon M.; McMurray, J. Scott; Zhang, Yu; Jiang, Jack J.

2008-01-01

Objective Nonlinear dynamic analysis has emerged as a reliable and objective tool for assessing voice disorders. However, it has only been tested on adult populations. In the present study, nonlinear dynamic analysis was applied to normal and dysphonic pediatric populations with the goal of collecting normative data. Jitter analysis was also applied in order to compare nonlinear dynamic and perturbation measures. This study’s findings will be useful in creating standards for the use of nonlinear dynamic analysis as a tool to describe dysphonia in the pediatric population. Methods The study included 38 pediatric subjects (23 children with dysphonia and 15 without). Recordings of sustained vowels were obtained from each subject and underwent nonlinear dynamic analysis and percent jitter analysis. The resulting correlation dimension (D2) and percent jitter values were compared across the two groups using t-tests set at a significance level of p = 0.05. Results It was shown that D2 values covary with the presence of pathology in children. D2 values were significantly higher in dysphonic children than in normal children (p = 0.002). Standard deviations indicated a higher level of variation in normal children’s D2 values than in dysphonic children’s D2 values. Jitter analysis showed markedly higher percent jitter in dysphonic children than in normal children (p = 0.025) and large standard deviations for both groups. Conclusion This study indicates that nonlinear dynamic analysis could be a viable tool for the detection and assessment of dysphonia in children. Further investigations and more normative data are needed to create standards for using nonlinear dynamic parameters for the clinical evaluation of pediatric dysphonia. PMID:18947887

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.

The constructive approach to nonlinear quantum field theory

International Nuclear Information System (INIS)

Segal, I.

1976-01-01

The general situation in nonlinear quantum field theory is outlined. The author discusses a reversion to the canonical quantization formalism and develops it to the maximal level attainable on the basis of advances in the past decade in nonlinear scattering and functional integration. (B.R.H.)

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...

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 Analysis of Renal Autoregulation Under Broadband Forcing Conditions

DEFF Research Database (Denmark)

Marmarelis, V Z; Chon, K H; Chen, Y M

1994-01-01

Linear analysis of renal blood flow fluctuations, induced experimentally in rats by broad-band (pseudorandom) arterial blood pressure forcing at various power levels, has been unable to explain fully the dynamics of renal autoregulation at low frequencies. This observation has suggested...... the possibility of nonlinear mechanisms subserving renal autoregulation at frequencies below 0.2 Hz. This paper presents results of 3rd-order Volterra-Wiener analysis that appear to explain adequately the nonlinearities in the pressure-flow relation below 0.2 Hz in rats. The contribution of the 3rd-order kernel...... in describing the dynamic pressure-flow relation is found to be important. Furthermore, the dependence of 1st-order kernel waveforms on the power level of broadband pressure forcing indicates the presence of nonlinear feedback (of sigmoid type) based on previously reported analysis of a class of nonlinear...

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 response of the quantum Hall system to a strong electromagnetic radiation

International Nuclear Information System (INIS)

Avetissian, H.K.; Mkrtchian, G.F.

2016-01-01

We study nonlinear response of a quantum Hall system in semiconductor-hetero-structures via third harmonic generation process and nonlinear Faraday effect. We demonstrate that Faraday rotation angle and third harmonic radiation intensity have a characteristic Hall plateaus feature. These nonlinear effects remain robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and Faraday rotation angle, which are within the experimental feasibility. - Highlights: • Nonlinear optical response of a quantum Hall system has specific plateaus feature. • This effect remains robust against the significant broadening of Landau levels. • It can be observed via the third harmonic signal and the nonlinear Faraday effect.

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

SEA-LEVEL RISE. Sea-level rise due to polar ice-sheet mass loss during past warm periods.

Science.gov (United States)

Dutton, A; Carlson, A E; Long, A J; Milne, G A; Clark, P U; DeConto, R; Horton, B P; Rahmstorf, S; Raymo, M E

2015-07-10

Interdisciplinary studies of geologic archives have ushered in a new era of deciphering magnitudes, rates, and sources of sea-level rise from polar ice-sheet loss during past warm periods. Accounting for glacial isostatic processes helps to reconcile spatial variability in peak sea level during marine isotope stages 5e and 11, when the global mean reached 6 to 9 meters and 6 to 13 meters higher than present, respectively. Dynamic topography introduces large uncertainties on longer time scales, precluding robust sea-level estimates for intervals such as the Pliocene. Present climate is warming to a level associated with significant polar ice-sheet loss in the past. Here, we outline advances and challenges involved in constraining ice-sheet sensitivity to climate change with use of paleo-sea level records. Copyright © 2015, American Association for the Advancement of Science.

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.

E11 and the non-linear dual graviton

Science.gov (United States)

Tumanov, Alexander G.; West, Peter

2018-04-01

The non-linear dual graviton equation of motion as well as the duality relation between the gravity and dual gravity fields are found in E theory by carrying out E11 variations of previously found equations of motion. As a result the equations of motion in E theory have now been found at the full non-linear level up to, and including, level three, which contains the dual graviton field. When truncated to contain fields at levels three and less, and the spacetime is restricted to be the familiar eleven dimensional space time, the equations are equivalent to those of eleven dimensional supergravity.

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.

Advances in nonlinear vibration analysis of structures. Part-I. Beams

Indian Academy of Sciences (India)

Unknown

element analysis of nonlinear beams under static and dynamic loads. ... linearization, substitution of inplane boundary conditions at element level rather .... Modelling the nonlinear vibration problems using finite elements, albeit with a couple.

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)

Dynamics and vibrations progress in nonlinear analysis

CERN Document Server

Kachapi, Seyed Habibollah Hashemi

2014-01-01

Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...

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

Nonlinear effects in varactor-tuned resonators.

Science.gov (United States)

Everard, Jeremy; Zhou, Liang

2006-05-01

This paper describes the effects of RF power level on the performance of varactor-tuned resonator circuits. A variety of topologies are considered, including series and parallel resonators operating in both unbalanced and balanced modes. As these resonators were designed to produce oscillators with minimum phase noise, the initial small signal insertion loss was set to 6 dB and, hence, QL/Q0 = 1/2. To enable accurate analysis and simulation, S parameter and PSPICE models for the varactors were optimized and developed. It is shown that these resonators start to demonstrate nonlinear operation at very low power levels demonstrating saturation and lowering of the resonant frequency. On occasion squegging is observed for modified bias conditions. The nonlinear effects are dependent on the unloaded Q (Q0), the ratio of loaded to unloaded Q (QL/Q0), the bias voltage, and circuit configurations with typical nonlinear effects occurring at -8 dBm in a circuit with a loaded Q of 63 and a varactor bias voltage of 3 V. Analysis, simulation, and measurements that show close correlation are presented.

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

Elevated Serum Hepcidin Levels during an Intensified Training Period in Well-Trained Female Long-Distance Runners

Directory of Open Access Journals (Sweden)

Aya Ishibashi

2017-03-01

Full Text Available Iron is essential for providing oxygen to working muscles during exercise, and iron deficiency leads to decreased exercise capacity during endurance events. However, the mechanism of iron deficiency among endurance athletes remains unclear. In this study, we compared iron status between two periods involving different training regimens. Sixteen female long-distance runners participated. Over a seven-month period, fasting blood samples were collected during their regular training period (LOW; middle of February and during an intensified training period (INT; late of August to determine blood hematological, iron, and inflammatory parameters. Three-day food diaries were also assessed. Body weight and lean body mass did not differ significantly between LOW and INT, while body fat and body fat percentage were significantly lower in INT (p < 0.05. Blood hemoglobin, serum ferritin, total protein, and iron levels, total iron-binding capacity, and transferrin saturation did not differ significantly between the two periods. Serum hepcidin levels were significantly higher during INT than LOW (p < 0.05. Carbohydrate and iron intakes from the daily diet were significantly higher during INT than LOW (p < 0.05. In conclusion, an elevated hepcidin level was observed during an intensified training period in long-distance runners, despite an apparently adequate daily intake of iron.

Probabilistic and Scenario Seismic and Liquefaction Hazard Analysis of the Mississippi Embayment Incorporating Nonlinear Site Effects

Science.gov (United States)

Cramer, C. H.; Dhar, M. S.

2017-12-01

The influence of deep sediment deposits of the Mississippi Embayment (ME) on the propagation of seismic waves is poorly understood and remains a major source of uncertainty for site response analysis. Many researchers have studied the effects of these deposits on seismic hazard of the area using available information at the time. In this study, we have used updated and newly available resources for seismic and liquefaction hazard analyses of the ME. We have developed an improved 3D geological model. Additionally, we used surface geological maps from Cupples and Van Arsdale (2013) to prepare liquefaction hazard maps. Both equivalent linear and nonlinear site response codes were used to develop site amplification distributions for use in generating hazard maps. The site amplification distributions are created using the Monte Carlo approach of Cramer et al. (2004, 2006) on a 0.1-degree grid. The 2014 National Seismic Hazard model and attenuation relations (Petersen et al., 2014) are used to prepare seismic hazard maps. Then liquefaction hazard maps are generated using liquefaction probability curves from Holzer (2011) and Cramer et al. (2015). Equivalent linear response (w/ increased precision, restricted nonlinear behavior with depth) shows similar hazard for the ME compared to nonlinear analysis (w/o pore pressure) results. At short periods nonlinear deamplification dominates the hazard, but at long periods resonance amplification dominates. The liquefaction hazard tends to be high in Holocene and late Pleistocene lowland sediments, even with lowered ground water levels, and low in Pleistocene loess of the uplands. Considering pore pressure effects in nonlinear site response analysis at a test site on the lowlands shows amplification of ground motion at short periods. PGA estimates from ME liquefaction and MMI observations are in the 0.25 to 0.4 g range. Our estimated M7.5 PGA hazard within 10 km of the fault can exceed this. Ground motion observations from

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.

Design of HIFU Transducers for Generating Specified Nonlinear Ultrasound Fields.

Science.gov (United States)

Rosnitskiy, Pavel B; Yuldashev, Petr V; Sapozhnikov, Oleg A; Maxwell, Adam D; Kreider, Wayne; Bailey, Michael R; Khokhlova, Vera A

2017-02-01

Various clinical applications of high-intensity focused ultrasound have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this paper is to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasi-linear conditions at the focus. Multiparametric nonlinear modeling based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. The results are presented in terms of the parameters of an equivalent single-element spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields.

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.

On applying safety archetypes to the Fukushima accident to identify nonlinear influencing factors

Energy Technology Data Exchange (ETDEWEB)

Sousa, A.L., E-mail: alsousa@cnen.gov.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil); Ribeiro, A.C.O., E-mail: antonio.ribeiro@bayer.com [Bayer Crop Science Brasil S.A., Belford Roxo, RJ (Brazil); Duarte, J.P., E-mail: julianapduarte@poli.ufrj.br [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Escola Politecnica. Departamento de Engenharia Nuclear; Frutuoso e Melo, P.F., E-mail: frutuoso@nuclear.ufrj.br [Coordenacao dos Programas de Pos-Graduacao em Engenharia (COOPE/UFRJ), RJ (Brazil). Programa de Engenharia Nuclear

2013-07-01

Nuclear power plants are typically characterized as high reliable organizations. In other words, they are organizations defined as relatively error free over a long period of time. Another relevant characteristic of the nuclear industry is that safety efforts are credited to design. However, major accidents, like the Fukushima accident, have shown that new tools are needed to identify latent deficiencies and help improve their safety level. Safety archetypes proposed elsewhere (e. g., safety issues stalled in the face of technological advances and eroding safety) consonant with International Atomic Energy Agency (IAEA) efforts are used to examine different aspects of accidents in a systemic perspective of the interaction between individuals, technology and organizational factors. Safety archetypes can help consider nonlinear interactions. Effects are rarely proportional to causes and what happens locally in a system (near the current operating point) often does not apply to distant regions (other system states), so that one has to consider the so-called nonlinear interactions. This is the case, for instance, with human probability failure estimates and safety level identification. In this paper, we discuss the Fukushima accident in order to show how archetypes can highlight nonlinear interactions of factors that influenced it and how to maintain safety levels in order to prevent other accidents. The initial evaluation of the set of archetypes suggested in the literature showed that at least four of them are applicable to the Fukushima accident, as is inferred from official reports on the accident. These are: complacency (that is, the effects of complacency on safety), decreased safety awareness, fixing on symptoms and not the real causes and eroding safety. (author)

On applying safety archetypes to the Fukushima accident to identify nonlinear influencing factors

International Nuclear Information System (INIS)

Sousa, A.L.; Ribeiro, A.C.O.; Duarte, J.P.; Frutuoso e Melo, P.F.

2013-01-01

Nuclear power plants are typically characterized as high reliable organizations. In other words, they are organizations defined as relatively error free over a long period of time. Another relevant characteristic of the nuclear industry is that safety efforts are credited to design. However, major accidents, like the Fukushima accident, have shown that new tools are needed to identify latent deficiencies and help improve their safety level. Safety archetypes proposed elsewhere (e. g., safety issues stalled in the face of technological advances and eroding safety) consonant with International Atomic Energy Agency (IAEA) efforts are used to examine different aspects of accidents in a systemic perspective of the interaction between individuals, technology and organizational factors. Safety archetypes can help consider nonlinear interactions. Effects are rarely proportional to causes and what happens locally in a system (near the current operating point) often does not apply to distant regions (other system states), so that one has to consider the so-called nonlinear interactions. This is the case, for instance, with human probability failure estimates and safety level identification. In this paper, we discuss the Fukushima accident in order to show how archetypes can highlight nonlinear interactions of factors that influenced it and how to maintain safety levels in order to prevent other accidents. The initial evaluation of the set of archetypes suggested in the literature showed that at least four of them are applicable to the Fukushima accident, as is inferred from official reports on the accident. These are: complacency (that is, the effects of complacency on safety), decreased safety awareness, fixing on symptoms and not the real causes and eroding safety. (author)

Changes in adiposity levels in schoolchildren according to nutritional status: analysis over a 30-year period

Directory of Open Access Journals (Sweden)

Gerson Luis de Moraes Ferrari

2013-05-01

Full Text Available The aim of this study was to analyze changes in adiposity levels over a 30-year period in schoolchildren according to nutritional status. This study is part of Projeto Misto Longitudinal de Crescimento, Desenvolvimento e Aptidão Física de Ilhabela. 1.144 schoolchildren of both sexes, aged between 10 and 11 years, met the following inclusion criteria: (a have at least one complete evaluation in one of the analyzed periods; (b be in the prepubertal stage of sexual maturation;and (c be apparently healthy. Analyzed periods were 1978/1980 (Baseline,1988/1990 (10 years, 1998/2000 (20 years, 2008/2010 (30 years. Analyzed variables were: body mass (kg, height (cm and adiposity levels (mm. Children were classified into three categories: eutrophic, overweight and obese, according to nutritional status, using World Health Organization (WHO body mass index (BMI curves for age and sex. For a comparison between periods, Two-Factor Analysis of Variance and Bonferroni’s test were used. In both sexes, the most significant increase in adiposity levels occurred among the eutrophic group, followed by the overweight group and obese group. Results showed an increase in adiposity levels over a 30-year period, even with nutritional status control. It shows that individuals with a similar BMI may vary in proportion and distribution of subcutaneous adipose tissue.

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.

The numerical dynamic for highly nonlinear partial differential equations

Science.gov (United States)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

Energy nonlinearity in radiation detection materials: Causes and consequences

International Nuclear Information System (INIS)

Jaffe, J.E.; Jordan, D.V.; Peurrung, A.J.

2007-01-01

The phenomenology and present theoretical understanding of energy nonlinearity (nonproportionality) in radiation detection materials is reviewed, with emphasis on gamma-ray spectroscopy. Scintillators display varying degrees and patterns of nonlinearity, while semiconductor detectors are extremely linear, and gas detectors show a characteristic form of nonproportionality associated with core levels. The relation between nonlinear response (to both primary particles and secondary electrons) and spectrometer resolution is also discussed. We review the qualitative ideas about the origin of nonlinearity in scintillators that have been proposed to date, with emphasis on transport and recombination of electronic excitations. Recent computational and experimental work on the basic physics of scintillators is leading towards a better understanding of energy nonlinearity and should result in new, more linear scintillator materials in the near future

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)

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

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

International Nuclear Information System (INIS)

Dubrovsky, V. G.; Topovsky, A. V.

2013-01-01

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u (n) , n= 1, …, N are constructed via Zakharov and Manakov ∂-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u (n) and calculated by ∂-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u (n) . It is shown that the sums u=u (k 1 ) +...+u (k m ) , 1 ⩽k 1 2 m ⩽N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

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.

Electrically-controlled nonlinear switching and multi-level storage characteristics in WOx film-based memory cells

Science.gov (United States)

Duan, W. J.; Wang, J. B.; Zhong, X. L.

2018-05-01

Resistive switching random access memory (RRAM) is considered as a promising candidate for the next generation memory due to its scalability, high integration density and non-volatile storage characteristics. Here, the multiple electrical characteristics in Pt/WOx/Pt cells are investigated. Both of the nonlinear switching and multi-level storage can be achieved by setting different compliance current in the same cell. The correlations among the current, time and temperature are analyzed by using contours and 3D surfaces. The switching mechanism is explained in terms of the formation and rupture of conductive filament which is related to oxygen vacancies. The experimental results show that the non-stoichiometric WOx film-based device offers a feasible way for the applications of oxide-based RRAMs.

Nonlinear principal component analysis and its applications

CERN Document Server

Mori, Yuichi; Makino, Naomichi

2016-01-01

This book expounds the principle and related applications of nonlinear principal component analysis (PCA), which is useful method to analyze mixed measurement levels data. In the part dealing with the principle, after a brief introduction of ordinary PCA, a PCA for categorical data (nominal and ordinal) is introduced as nonlinear PCA, in which an optimal scaling technique is used to quantify the categorical variables. The alternating least squares (ALS) is the main algorithm in the method. Multiple correspondence analysis (MCA), a special case of nonlinear PCA, is also introduced. All formulations in these methods are integrated in the same manner as matrix operations. Because any measurement levels data can be treated consistently as numerical data and ALS is a very powerful tool for estimations, the methods can be utilized in a variety of fields such as biometrics, econometrics, psychometrics, and sociology. In the applications part of the book, four applications are introduced: variable selection for mixed...

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

Nonlinear dynamics in biological systems

CERN Document Server

Carballido-Landeira, Jorge

2016-01-01

This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...

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.

Matrix Metalloproteinase Activities And Some Hormones Levels During Gestation Period In Cows

International Nuclear Information System (INIS)

TEAMA, F.E.

2010-01-01

Many factors including proteases, growth factors and hormones play important role in implantation and tissue remodelling of endometrium during different stages of gestation.Matrix metalloproteinases (MMP) such as gelatinases mainly MMP-2 and MMP-9 are implicated in the degradation of extracellular matrix for tissue remodelling.The aim of the present study is to evaluate the role of matrix metalloproteinases (MMP-2 and MMP-9) and hormones including progesterone (P4) and estradiol (E2) in the gestation process. The enzyme activities of MMP-2 and MMP-9 in serum collected from 8 Brown Swiss cows during different periods of gestation using zymography technique were examined. Hormonal levels for both P4 and E2 were determined using radioimmunoassay and also total proteins were estimated. A significant increase in MMP-2 activity by about 98%, 115% and 110% in the 1 st , 2 nd and 3 rd trimester of gestation were recorded, respectively, whereas it increased to be 185% in the pre-partum period as compared to non-pregnant cows (P nd trimester was recorded where the activity elevated by about 85% of non-pregnant controls (P st and 3 rd trimesters, the enzyme activity was not detectable. P4 level was increased gradually until its maximum at the 2 nd trimester then decreased until pre-partum.E2 level recorded too little increase at the beginning of the 1 st and 2 nd trimesters then sharply increased at the 3 rd one reached its maximum at pre-partum. There were significant decreases in total protein concentrations in the 2 nd and 3 rd trimesters then reached the lowest level before parturition .It could be concluded that the high activity of MMP-2 but not MMP-9 enzyme has important role throughout the gestation period in cows and P4 has important role in the fetal growth and E2 in the placental loss.

Optoelectronic and nonlinear optical processes in low dimensional ...

Indian Academy of Sciences (India)

Optoelectronic process; nonlinear optical process; semiconductor. Quest for ever faster and intelligent information processing technologies has sparked ..... Schematic energy level diagram for the proposed 4-level model. States other than the.

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 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...

Changes in adiposity levels in schoolchildren according to nutritional status: analysis over a 30-year period

Directory of Open Access Journals (Sweden)

Gerson Luis de Moraes Ferrari

2013-04-01

Full Text Available DOI: http://dx.doi.org/10.5007/1980-0037.2013v15n4p405 The aim of this study was to analyze changes in adiposity levels over a 30-year period in schoolchildren according to nutritional status. This study is part of Projeto Misto Longitudinal de Crescimento, Desenvolvimento e Aptidão Física de Ilhabela. 1.144 schoolchildren of both sexes, aged between 10 and 11 years, met the following inclusion criteria: (a have at least one complete evaluation in one of the analyzed periods; (b be in the prepubertal stage of sexual maturation;and (c be apparently healthy. Analyzed periods were 1978/1980 (Baseline,1988/1990 (10 years, 1998/2000 (20 years, 2008/2010 (30 years. Analyzed variables were: body mass (kg, height (cm and adiposity levels (mm. Children were classified into three categories: eutrophic, overweight and obese, according to nutritional status, using World Health Organization (WHO body mass index (BMI curves for age and sex. For a comparison between periods, Two-Factor Analysis of Variance and Bonferroni’s test were used. In both sexes, the most significant increase in adiposity levels occurred among the eutrophic group, followed by the overweight group and obese group. Results showed an increase in adiposity levels over a 30-year period, even with nutritional status control. It shows that individuals with a similar BMI may vary in proportion and distribution of subcutaneous adipose tissue.

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....

Turning the tide: comparison of tidal flow by periodic sea level fluctuation and by periodic bed tilting in scaled landscape experiments of estuaries

Science.gov (United States)

Kleinhans, Maarten G.; van der Vegt, Maarten; Leuven, Jasper; Braat, Lisanne; Markies, Henk; Simmelink, Arjan; Roosendaal, Chris; van Eijk, Arjan; Vrijbergen, Paul; van Maarseveen, Marcel

2017-11-01

Analogue models or scale experiments of estuaries and short tidal basins are notoriously difficult to create in the laboratory because of the difficulty to obtain currents strong enough to transport sand. Our recently discovered method to drive tidal currents by periodically tilting the entire flume leads to intense sediment transport in both the ebb and flood phase, causing dynamic channel and shoal patterns. However, it remains unclear whether tilting produces periodic flows with characteristic tidal properties that are sufficiently similar to those in nature for the purpose of landscape experiments. Moreover, it is not well understood why the flows driven by periodic sea level fluctuation, as in nature, are not sufficient for morphodynamic experiments. Here we compare for the first time the tidal currents driven by sea level fluctuations and by tilting. Experiments were run in a 20 × 3 m straight flume, the Metronome, for a range of tilting periods and with one or two boundaries open at constant head with free inflow and outflow. Also, experiments were run with flow driven by periodic sea level fluctuations. We recorded surface flow velocity along the flume with particle imaging velocimetry and measured water levels along the flume. We compared the results to a one-dimensional model with shallow flow equations for a rough bed, which was tested on the experiments and applied to a range of length scales bridging small experiments and large estuaries. We found that the Reynolds method results in negligible flows along the flume except for the first few metres, whereas flume tilting results in nearly uniform reversing flow velocities along the entire flume that are strong enough to move sand. Furthermore, tidal excursion length relative to basin length and the dominance of friction over inertia is similar in tidal experiments and reality. The sediment mobility converges between the Reynolds method and tilting for flumes hundreds of metres long, which is impractical

Turning the tide: comparison of tidal flow by periodic sea level fluctuation and by periodic bed tilting in scaled landscape experiments of estuaries

Directory of Open Access Journals (Sweden)

M. G. Kleinhans

2017-11-01

Full Text Available Analogue models or scale experiments of estuaries and short tidal basins are notoriously difficult to create in the laboratory because of the difficulty to obtain currents strong enough to transport sand. Our recently discovered method to drive tidal currents by periodically tilting the entire flume leads to intense sediment transport in both the ebb and flood phase, causing dynamic channel and shoal patterns. However, it remains unclear whether tilting produces periodic flows with characteristic tidal properties that are sufficiently similar to those in nature for the purpose of landscape experiments. Moreover, it is not well understood why the flows driven by periodic sea level fluctuation, as in nature, are not sufficient for morphodynamic experiments. Here we compare for the first time the tidal currents driven by sea level fluctuations and by tilting. Experiments were run in a 20  ×  3 m straight flume, the Metronome, for a range of tilting periods and with one or two boundaries open at constant head with free inflow and outflow. Also, experiments were run with flow driven by periodic sea level fluctuations. We recorded surface flow velocity along the flume with particle imaging velocimetry and measured water levels along the flume. We compared the results to a one-dimensional model with shallow flow equations for a rough bed, which was tested on the experiments and applied to a range of length scales bridging small experiments and large estuaries. We found that the Reynolds method results in negligible flows along the flume except for the first few metres, whereas flume tilting results in nearly uniform reversing flow velocities along the entire flume that are strong enough to move sand. Furthermore, tidal excursion length relative to basin length and the dominance of friction over inertia is similar in tidal experiments and reality. The sediment mobility converges between the Reynolds method and tilting for flumes hundreds of

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